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As the polar blast bites, a kind-hearted Kiwi farmer has insulated his dogs' kennels with wool, because "no one wants to go home to a cold house." Your playlist will load after this ad Raymond Rolston is the kind of landlord many humans would hope to have, pulling out all the stops for his four-legged friends on the farm north of Taihape where he works. "What we're doing here is making it comfortable for the dogs to live in, because no one wants to go home to a cold house. "We're just trying to do the best we can for them to make sure they're comfortable, we really need them, without dogs you can't farm," Raymond told 1 NEWS. The dogs' upgraded digs now come with woolen underlays, hidden under a layer of carpet. However, Raymond credits the idea for the insulation to his boss Sarah. The kennels now also have flaps covering the doors to "keep out the wind."
Capitalism in America: Is Capitalism the root of all evil in America?Is it the cause of drug abuse?Is it the cause of poverty?Is it the cause of class distinction?Is it the cause of racism?Will it be the cause of the end of the world?...wondering. It's not about abilities, societies progress only if each put the society's interest above ones self interest. In capitalism competition is the higher priority not cooperation and hence promote self interest above societal interest.Abilities differ but opportunities too. Opportunity is not under the individuals control. "Abilities differ but opportunities too. Opportunity is not under the individuals control." - we do not have equal opportunity… how could that be possible? It is the nature of reality. We can make our own opportunities in a free society, however. Many people are inventing entrepreneurial businesses and are working from home via computer these days. - "societal interest" is another impossible ideal. Yes, we care about those we are familiar and naturally unified with: our families and loved ones… home towns…maybe our cities…our country on a patriotic level, outside of that...???? why would we care? How can we care? We have enough to do in looking out for our own! The bible says to earn enough money "to help the poor."- not "in order to help the poor!" Common sense, please! I don't think it's the root of anything but to turn a profit in a free open way. Where it goes wrong is when it infects the governing of the people with those who would buy favor to counter any competition. ....Is it the cause of drug abuse? I don't think it is the cause as people make their own choices according to their proclivities. Is the war against drugs working should be a bigger question. Economic conditions create an atmosphere for some that can't cope and abuse drugs, alcohol and just about anything else. ....Is it the cause of poverty? Unchecked capitalism in this country has created a growing middle class and poor downturn. The money at the top is becoming more belligerent about how they got there and what should be done. Many there feel that harder work and frugal lifestyles are what gets them ahead. How little they know. Is it the cause of class distinction? I don't think so as the lower class people are hesitant to have rules that penalize the rich because in the back of their mind they hope to be rich and do not wish those same rules to apply to them. The rich just want to get richer whether it be on a poor persons back or a rich persons blunder. ....Is it the cause of racism? I don't know if it is the cause of racism but it certainly helps it along. Much of the poor are in the minorities so there is some correlation of exploitation but not so much cause. At the basis of the Reagan New Capitalism is the belief that greed is good. When people believe it's okay to get money by any means whatsoever that makes capitalism falter. Hence, billionaires now rig the system to scam everyone and think it's OK. This is supported in large by many folks believing that poor people are lazy. This idea of saying there's two classes, the rich and the lazy, is behind much of America's problems. That's because people stop believing in American values. And slowly the system is starting to collapse from within for that reason. So the belief in the New Capitalistic system of honoring those who are greedy is indeed one of the root problems of the U.S.'s slide from grace. One word comes to mind in reading your question, 'absurd', but I will not use it. I would be interested in your reasoning, as to how you use capitalism, as the cause of all these ills?To prove your assertions, you will have to show that these social problems do not exist in countries where capitalism does not exist. Can you do that?If Man is to cause the end of the world and we do not have the power to do that at this juncture, it will be do to the arrogance of a god belief or the idiocy of a totalitarian mindset.Drug abuse is the result of weak minds, the exploitation of those minds in the pursuit of wealth. This is not conducive with the definition of capitalism.Poverty is the result of a promoted sense of entitlement, the lack of capitalism in the creation of jobs, a weak or failed educational system and the quest of a government to control people.Class distinction is inherent in all societies and has been around since the dawn of Man.Racism, too, has existed since one race discovered the other. If you are looking for a document that promotes the sovereignty of the individual, that holds the individual up above all these things, a document that allows the individual, regardless of race, birth or status the freedom to achieve based on his own merits, I suggest you look at the Bill of Rights. Is Individual Freedom your desired goal or are you seeking the creation of a society that bans the individual and individual achievement for a drone mentality? If it is the drone society that excites you, then Marxism, a theocracy or some other form of totalitarianism are your options. cjhunsinger: If you look more closely at my responses, you will see that I lean to the conservative, logical and educated point of view. But no one said one must look closely. I was asking due to another thread where the OP was alluding to capitalism as being the culprit in civilization for the all its ills and the eventual cause of the end of the world. I thought it would be an interesting discussion… because some people really do think this way! Not me… but then, I am a civilized European-decent, anglo-saxon type…And I would believe this way, as I have been indoctrinated and lied to by my kind, (according to him.) Happy to read it. Now there are two of us. I, don't think the decent has much to do with the appreciation of Individual Freedom and Capitalism, as I know many who are not European who enjoy and respect these concepts. Capitalism is not an economic system of least traditionally. Capitalism is a component of economic systems and is a process. Emphasis on systems being more than one. It is social, legal, individual, and market. Bare bones basics capitalism means I have a store of corn. That is my capital. When I invest that corn in another person's hog as an agreement of worth for a value I have capitalized on that corn in a marketplace. It's worth to me has increased at the exchange of an agreed value. It occurred socially, in a market no matter how wide or narrow, and it was a legal agreement between two entities (persons). Is Capitalism the root of all evil in America?Nope!!! IMHO Evil is either a concept or could be thought of as a force. Evil is not power. Power directs force. Therefore, some power directs evil. Capitalism too is a force as shared above. If the entity of power or with possession of power directs that force - capitalism, with evil (force) intentions, then it is the onus of responsibility of that entity. That is the agency. Is it the cause of drug abuse?No! Capitalism is a component of the drug trade. Emphasis on economic trade. Again, capitalism is a force directed by a power. Look to the power and whom or of what possesses that power for the directing evil (a force). Is it the cause of poverty?It may contribute to the proliferation of poverty. If I only have two bushels of corn to trade and the hog costs three bushels then I am in poverty regarding gaining the worth of the hog. Simply the land I have produce five bushels of corn, three I need to get through the winter, and two were extra. I still have capital. It is worth a hog to me, but it is not worth a hog to another who possess the hog. There is opportunity of negotiation at an established value. I may have to give up some more capital from the three needed bushels to gain the luxury of the hog. Is it the cause of class distinction?Capitalism is not a cause for class distinction as it is a process. As a process it operates or functions within classes as well as across classes. Capital in abundance as wealth could be considered a cause for class distinction. Is it the cause of racism?I would have to ponder a bit. However, I have difficulty as how it could. Again, capitalism occurs as a process. Capitalism exists without prejudice. Even the exchange of thought is a process of capitalism. I share the sky is blue. That is worth expressed as a value. Another says the sky is light blue. That is worth expressed as a value. Next, if agreed upon an exchange occurs. I say thank you for sharing that knowledge. An agreed value was met, agreed upon, and exchanged. Both have a changed sense of worth. One receives new knowledge and the other possibly respect and heightened self-esteem. Will it be the cause of the end of the world?I have and IMHO an odd view of the adage the end of the word. I tend to think that occurs everyday and every moment. With each death the world ends. And, also, with each birth there is a new world. A matter of perspective. So, the world has already ended countless times leaving whats left - Life. ...wondering. Interesting questions and answers, Katheryn. My answer is no for all but one, "Class Distinctions". Some dictionary that first popped up has this as a definition; "an economic and political system in which a country's trade and industry are controlled by private owners for profit, rather than by the state." ... and that about sums it up. There are extremely few things about capitalism which, when left on its own, are neither good nor bad; it is just a system. As many before me in this forum have pointed out, all of those bad outcomes you mention are the result of people acting badly; capitalism is just one of the platforms for which they can accomplish their dirty work. Consequently, since those have been addressed, I don't really have anything to add other than Capitalism didn't didn't pull the trigger, People did. One of the few outcomes of a capitalist system that does have a bad outcome, even when it is working perfectly as it should and with everybody pulling together with no bad actors, is wage and capital inequality. I won't bore you with the details (I am actually working on a dynamic model so I can illustrate this clearly in some future hubs) know that left on its own, wages will become distributed unequally; and the longer time goes on, the greater the divergence between wage incomes become. The same is true of capital accumulation, although one facet of this is easy to explain. Once there is a divergence in wealth, say one person has a million dollars and the next person dollars has a billion dollars, then, because the billion dollar guy can command a higher interest rate on their money, their pot will grow faster. Capitalism is an invention of man. Its rules can be changed. A change in rule will entail a change in its internal logic. For example, the means of creating money. Before money can be created when there is gold to back it up. Today, that is no longer necessary. Money is created by means of an entry in the book of accounts of the one or entity with authority. So it is linked to power. Power can manipulate the rules.Capitalism can be used for bad or for good. I believe the human propensity for unchecked greed is the cause of all our woes. Not capitalism. The fact that capitalism can aid the greedy is not the fault of Capitalism! Only UNCHECKED GREED can possibly cause the destruction of the world and cause its demise in many ways. The only check on human nature is the individual himself through conscience or the school of hard knocks. An old movie called "Ace in the Hole" aired last night here in LA. With Kirk Douglas. He was excellent in this tale about a greedy newspaper man who kept a guy trapped in a mine alive for five days He to wanted string out the story and make his name, fame and fortune through the misfortune of this man. (He really thought the man would make it and had no sympathy for the man's condition… legs crushed under rubble,etc.) Of course, in the end, the man died… and Kirk admitted to murder...feeling really CRUMMY about what he had done. Tough and not so simple.Greed; love of money.Drug abuse is wrong choice of evil…Poverty- due too many non-productive elements accepting other people hard earned money / laziness preference of lifestyle …Class-distiction promoted by politicians also racism-- because evil is having much power over righteous citizens- bringing this social system to the end... An individual starts an institution. The institution affects the individual. The corporation promotes greed when the power, political, economic, and persuasive, it possesses is unlimited. The anti trust laws put a break on the corporation. But corporations have found a way to get back power. Corporation is an invention that has been given a legal personality. It can commit crime but the board members are immune from punishment. Power has made that so. The Federal Reserve Bank is a private corporation that controls the economy of the United States, in effect the capitalist world. US Congress was made to give that power to the Fed in the 1930s. The hope is deem that this power can be taken back. Pres. JF Kennedy tried to that triggered his assassination. "The hope is dim that this power can be taken back." It took a lot of dishonest people to let it go.… we cannot maintain a democratic republic unless the people in it follow morals. - what does the future look like to you? An excellent book to read on the Fed is "Secrets of the Federal Reserve" by Eustace Mullins. It outlines it's inception with Woodrow Wilson and how Presidents have supported the favoritism of installing their own people to perpetuate the group of banks that profit from our debt. The Fed created the recessions and bankrupted the banks in 1929 by exporting billions in gold to Europe necessitating the Great Depression. If you want to see incredible greed at the expense of the countries well being this is a must read. It is on Kindle. I beg to differ slightly. While the Federal Reserve Act was signed about 8 months after Wilson took office, it hardly started with him. It began as the result of the private TARP created to save the banking system in New York which was collapsing because of the Panic of 1907. J.P. Morgan used his wealth and position to essentially force his peers to create a fund to bail out banks that were failing; they were successful. Instead of treating Morgan like a hero from preventing yet another depression, Congress and the public had the bejezzus scared out of them when they realized one man (really a small group of men) had that kind of power, power that was bigger than the United States government. Seeing the writing on the wall, it was Morgan, through intermediaries, who pressured President Theodore Roosevelt to work on the creation of a Federal Reserve System. Over time, this led to the infamous Jekyll Island meeting where the initial framework of the Federal Reserve was worked out between gov't and the banking industry. It was Morgan's hope that it would turn out as many, including some in this forum, think it did; that the private banks (meaning him) would control the system; and Morgan got his wish, which is why so many Jekyll Island myths abound. This was in 1910. As Congress is wont to do, they then sat on it. It took two more recessions, 1911 and 1913, to finally motivate Congress to get off of their collective butts. In Dec 1913, they passed the Federal Reserve Act. BUT, it wasn't the Federal Reserve Morgan had flitting around in his mind. Congress, in its rare wisdom, kept the controls of the Federal Reserve firmly in government hands run at the top by government employed people. While there is a large private component to the system, there has to be to make it work, they are secondary to the federal governments role in setting policy and direction; the private sector only has an advisory role. What does the future look like to me? That is a lot to ask of me, or to look into. But the Trilateralist seem to have ensconced themselves to the seat of pretenders. One of their designs was to weaken Europe, particularly the pound and replace it with the dollar. It was done with the use of WWII. It was not yet over but already Bretton Woods was convened and the dollar was made currency of the world. Gold was the standard but then it limited expansion of the economy because there is not enough gold, or gold is not the monopoly of the West. So the gold standard was replaced with the floating rate controlled by the IMF and World Bank. But woes in the capitalist world have not gone away. Hegemony in world economy does not seem to work. There has to be another economic power. It is like in boxing where there are several world boxing powers, the side of Mayweather and the side of Pacquiao. However, the power of the Fed looks to stay indefinitely like the power of the Catholic church or the Vatican that centuries are counted according to the Gregorian calendar. Unless America implodes like USSR and a new democracy ushers in. Look now, but the Chinese calendar may come around. And a new economic power may emerge, the likes managed by China, Brazil, India, etcetera. A competitor to IMF and World Bank may improve their philosophy and performance.Greed may eventually decimate human beings from the surface of the earth by the simple consumption of energy and increase of temperature by carbon dioxide. Was it temperature that caused the extinction of the dinosaur? Sudden death may have been mitigated with entente like the SALT I and SALT II. But slow disappearance of humans will come with climate change if there were no drastic change in the source of energy, no emission of carbon dioxide and avoidance of poisoning from radioactive materials. 1.An economic system in which the means of production and distribution are privately or corporately owned and development occurs through the accumulation and reinvestment of profits gained in a free market. The definition of capitalism seems innocuous enough when put into a simple setting. I think problems arise when those who would profit from it more want to tip the scales to their advantage. I think it spills over into greed and that Is where it all goes horribly wrong. When greed drives the purpose and methods for profits rather than competing with sound business practices and sensible returns on investments short term thinking takes over. Global warming is happening. The cause's are theories that either you believe them or you don't. Those who are greedy wish it to be understood that the condition is not man made while the rest believe that it is. It is advantageous to the greedy in this scenario so we may never know until the next phase or the one after that. The greedy have a lot of money to perpetuate their beliefs. I'm not saying global warming is not scientifically true, but to assume that only greedy, wealthy people believe that global warming is false is absurd. Sorry. Plenty of the middle class and poor believe that global warming is not a reality. To assume otherwise is to. . .assume. Further, there are plenty of rich people, some greedy, who believe in global warming. You almost sound like you exclusively blame wealthy people for pollution. I stand corrected. After reading my response I can understand how you got that impression. What I meant in my comment is that while we are all responsible to some degree there is little progress in accepting it and curbing our behavior as to its implied causes. For instance we still heat with oil while there are alternatives and the oil companies are more than willing to supply as much as we want. The greediness on the oil companies side is predicated by profits while the consumer side is responsible for its demand. Both are guilty but one is profiting immensely from it. Coal and gas consumption follows in the same strain. Next time I will try to slow myself down a little and read what I wrote with a more discerning eye. Thank you It is more convenient to stratify cause and effect this way:Physical as in: lightning causes thunder. This can also be called immediate cause and effect because thunder immediately follows lightning. Another stratification is motive-tool-effect (MTE). This is derived from the the case of murder. A person has a motive: to acquire profits; a tool: capitalism; effects: profits, social injustice in case acquisition of profits takes advantage of factors like inside trading, monopoly, power, ignorance, naivete, weakness, blind faith. Power is further classified into naked power (point of the gun, dictatorship); executive power (as exercised by those in authority like president, congressman, mayor); persuasive power (by speech, writing); economic power (bribery, access, abundance); priestly power (blind faith, exercised by the religious).MTE has another application, like: motive: to acquire wealth in excess (greed) - tool: capitalism - effect: excessive wealth. Here, capitalism is not an immediate cause. Capitalism is being used in a bad way.One way to acquire excessive wealth is production of fuel (by the application of capitalism) that has carbon dioxide as byproduct that results in global warming. Medicine has another concept: compounding factors (of a disease). For example, heart disease or narrowing of heart artery. Stress produces free radicals. Metabolism produces free radicals. Pollution produces free radicals. Free radicals injure the inside wall of an artery. The body patches it up with collagen, elastin, fibrin, cholesterol and calcium. Their combination results in a mound that grows with more deposition of cholesterol, calcium, and other debris. This mound results in a plaque that partially or completely blocks a coronary artery whose one symptom is angina. Both. Capitalism has tremendously helped the movie, entertainment, and music industry. Without capital, there would be no financing of movies and music. Making movies and music costs monies. Besides the labor costs in making the movies, there also promotional and advertising costs. The same with music. It is promotion and advertising via television, radio, magazines, and now the internet which conveys the movie and music to the public who pay their money to see the movie and hear the music. While capitalism has tremendously helped the entertainment business to flourish. It has also hindered it. There are independent movies and music that does not come to the forefront of fame because they are not considered to be box office hits. Many high calibre movies, television shows, documentaries, and music fall by the wayside because it is not greenlighted by the POWERS THAT BE as it is believed that the public will not like them hence they won't make money. So as a result, many movies and music have to succumb to the lowest common denominator in order to make the most money. That is why there are so many cheap movie remakes of the same genre because that genre generates the most income and business for the movie studio and the music business. As for the arts, our technical/scientific/business oriented society does not value the arts. The arts is seen as something impractical, even frivilious. That is why so many creative types have it so difficult in this society. This society is not geared nor supportive of the creative type because creativity is not rewarded but hard, cold scientific analysis IS. That explains why so many parents, unless they are enlightened, dissaude their children from going into the entertainment business and instead exhort them to get a "real" job because in the parents' purview, the arts are unsteady, impractical, and the chances of monetary success is one in a million. That is why those in the technical fields, engineering, and other hard sciences earn excellent salaries because our society supports such fields while decrying the more creative fields. Good question, Kathryn, methinks that YOU should create a new forum thread, asking this question. There will be MANY wonderful answers! There's no one to step on/take advantage of anymore?Capitalism is defined as:- free-market system: an economic system based on the private ownership of the means of production and distribution of goods, characterized by... It just occurred to me, and I wanted to record it before it slipped away again, that there are two types of Capitalism; Theoretical and Practical (Duh!) What I also noticed is that the endless debates about... Most of us battled at some point (and others still do) with understanding what an economic system is. At its bare bones, an economic system is simply a method of production and distribution. One can have an economic... I recently was watching a show I often watch that do documentaries about the suffering and hellish situations people live in around the world, usually third world countries (tho not always). From children mining in...
Determination of the viability of Toxoplasma gondii in cured ham using bioassay: influence of technological processing and food safety implications. Toxoplasmosis is a zoonotic disease caused by the protozoan Toxoplasma gondii and distributed worldwide. Ingestion of viable cysts from infected raw or undercooked meat is an important route of horizontal transmission of the parasite to humans. Little information is available concerning the effect of commercial curing on cysts of T. gondii. This study is the first in which the influence of processing of cured ham on the viability of T. gondii has been evaluated, using bioassay to assess the risk of infection from eating this meat product. Naturally infected pigs were selected for the study, and a mouse concentration bioassay technique was used to demonstrate viable bradyzoites of T. gondii in porcine tissues and hams. No viable parasites were found in the final product (14 months of curing) based on results of the indirect immunofluorescence assay and histological and PCR analyses. Our results indicate that the consumption of hams cured as described here poses an insignificant risk of acquiring toxoplasmosis. However, additional studies are required to evaluate the safety of ham products cured under different conditions of curing time, salt, and nitrite concentration.
1. Field of the Invention This invention relates to a semiconductor device wherein a high speed vertical type bipolar transistor and high voltage vertical type bipolar transistor are formed on the same substrate and a method of making the same. 2. Description of the Related Art A vertical type NPN bipolar transistor of the related art constructed as a high speed bipolar transistor and a vertical type NPN bipolar transistor of the related art constructed as a high voltage bipolar transistor will be described with reference to FIG. 1 and FIG. 2. FIG. 1 is a schematic sectional view of the construction of a high speed bipolar transistor. As shown in FIG. 1, an N-type epitaxial layer 12 is formed on a P-type silicon substrate 11. An N+-type embedded diffusion layer 31 is formed in an upper part of the P-type silicon substrate 11, and this N+-type embedded diffusion layer 31 is also diffused into a lower part of the epitaxial layer 12. Also, on the epitaxial layer 12 is formed a device separating oxide film 13 for isolating a region where a high speed bipolar transistor 1 is formed. Below this device separating oxide film 13 a P+-type device separating diffusion layer 14 reaching the silicon substrate 11 is formed. A P-type base layer 32 and a P+-type graft base layer 33 connecting with this base layer 32 are formed in an upper part of the epitaxial layer 12 in the region where the high speed bipolar transistor 1 is formed. An N+-type emitter layer 34 is formed in an upper part of this base layer 32. Also, an N+-type collector leading layer 35 connecting with the embedded diffusion layer 31 is formed in a position away from the graft base layer 33 in the epitaxial layer 12 in the region where the high speed bipolar transistor 1 is formed. A first oxide film 15 is formed on the epitaxial layer 12, and a first opening 16 is formed in the first oxide film 15 above the graft base layer 33. A base leading electrode 36 connecting with the graft base layer 33 through the first opening 16 is formed on the first oxide film 15. Also, a second oxide film 17 is formed on the first oxide film 15 in such a state that it covers the base leading electrode 36. A second opening 18 is formed in the second oxide film 17 above the base layer 32, and on the side wall thereof a side wall insulating film 19 is formed. The inner side of this side wall insulating film 19 forms an emitter opening, and the above-mentioned emitter layer 34 is at the bottom of this emitter opening. An emitter leading electrode 37 connecting with the emitter layer 34 through the emitter opening is formed on the second oxide film 17. Also formed are a base electrode 38 connecting with the base leading electrode 36 through the second oxide film 17, an emitter electrode 39 connecting with the emitter leading electrode 37, and a collector electrode 40 connecting with the collector leading layer 35 through the second oxide film 17 and the first oxide film 15. Thus is constructed the high speed bipolar transistor 1. FIG. 2 is a schematic sectional view of the construction of a high voltage bipolar transistor. As shown in FIG. 2, an N-type epitaxial layer 50 thicker than the epitaxial layer (12) of the high speed bipolar transistor (1) described above is formed on a P-type silicon substrate 11. An N+-type embedded diffusion layer 51 deeper than the embedded diffusion layer (31) of the high speed bipolar transistor (1) described above is formed in an upper part of the silicon substrate 11, and this embedded diffusion layer 51 is also diffused into a lower part of the epitaxial layer 50. Also, on the epitaxial layer 50 is formed a device separating oxide film 13 for isolating a region where a high voltage bipolar transistor 2 is formed. Below this device separating oxide film 13 a P+-type device separating diffusion layer 14 reaching the silicon substrate 11 is formed. A P-type base layer 52 and a P+-type graft base layer 53 connecting with this base layer 52 are formed in an upper part of the epitaxial layer 50 in the region where the high voltage bipolar transistor 2 is formed. An N+-type emitter layer 54 is formed in an upper part of this base layer 52. Also, an N+-type collector leading layer 55 connecting with the embedded diffusion layer 51 is formed in the epitaxial layer 50 in a position away from the graft base layer 53 in the region where the high voltage bipolar transistor 2 is formed. A first oxide film 15 is formed on the epitaxial layer 50, and a first opening 16 is formed in the first oxide film 15 above the graft base layer 53. A base leading electrode 56 connecting with the graft base layer 53 through the first opening 16 is formed on the first oxide film 15. Also, a second oxide film 17 is formed on the first oxide film 15 in such a state that it covers the base leading electrode 56. A second opening 18 is formed in the second oxide film 17 above the base layer 52, and on the side wall thereof a side wall insulating film 19 is formed. The inner side of this side wall insulating film 19 forms an emitter opening, and the above-mentioned emitter layer 54 is at the bottom of this emitter opening. An emitter leading electrode 57 connecting with the emitter layer 54 through the emitter opening is formed on the second oxide film 17. Also formed are a base electrode 58 connecting with the base leading electrode 56 through the second oxide film 17, an emitter electrode 59 connecting with the emitter leading electrode 57, and a collector electrode 60 connecting with the collector leading layer 55 through the second oxide film 17 and the first oxide film 15. Thus is constructed the high voltage bipolar transistor 2. The impurity distributions of the high speed bipolar transistor 1 and the high voltage bipolar transistor 2 described above will now be explained with reference to FIG. 3 and FIG. 4. FIG. 3 shows the impurity distribution in the depth direction of the high speed bipolar transistor 1. In FIG. 3, the vertical axis shows impurity concentration on a log scale and the horizontal axis shows depth from the surface of the silicon substrate. As shown in FIG. 3, the impurity distribution in the depth direction of the high speed bipolar transistor 1 has the characteristic that the N-type epitaxial layer 12 is thin and its impurity concentration is high. FIG. 4 shows the impurity distribution of the high voltage bipolar transistor 2. In FIG. 4 also, the vertical axis shows impurity concentration on a log scale and the horizontal axis shows depth from the surface of the silicon substrate. As shown in FIG. 4, in the impurity distribution of the high voltage bipolar transistor 2, the impurity concentrations of the N+-type emitter layer 54 and the P-type silicon substrate 11 are the same as the impurity concentrations of their counterparts in the high speed bipolar transistor 1. On the other hand, there is the characteristic that the N-type epitaxial layer 50, compared to the N-type epitaxial layer 12 of the high speed bipolar transistor 1, is thick and its impurity concentration is low. Also, the P-type base layer 52 generally is thicker than the base layer of a high speed bipolar transistor. Generally, to make the breakdown voltage of the kind of bipolar transistor described above high, it is necessary to make the concentration of the N-type epitaxial layer low and make the layer thick. The lower the impurity density of the epitaxial layer is, and the thicker the epitaxial layer is, the greater the voltage (breakdown voltage) of the bipolar transistor is. Also, even if the density of the epitaxial layer is kept fixed and only the thickness of the epitaxial layer is increased, the voltage (breakdown voltage) of the bipolar transistor rises. The relationship between the base impurity density and the base width is such that to increase the breakdown voltage of a bipolar transistor it is necessary to moderately increase the base concentration and to some extent make the base width thick. For this reason also, it is necessary to make the N-type epitaxial layer thick. When the concentration of the N-type epitaxial layer is made low and the layer is made thick, it is necessary to make the N+-type embedded layer region for suppressing parasitic bipolar transistor operation wide and make the P+ separating region deep in order to certainly effect device separation. That is, it is necessary to make the cell dimensions large. However, in a high speed bipolar transistor, to suppress the collector Kirk effect, it is necessary to make the concentration of the N-type epitaxial layer high and make the layer thin. On the other hand, as explained above, in a high voltage bipolar transistor, to obtain voltage, it is necessary to make the concentration of the N-type epitaxial layer low and make the layer thick. Thus, the epitaxial layer requirements of a high speed bipolar transistor and a high voltage bipolar transistor have been conflicting ones. Consequently, it has been difficult to form a high speed bipolar transistor and a high voltage bipolar transistor on the same substrate.
Accuracy of universal formulas for percolation thresholds based on dimension and coordination number. Recent mathematical results regarding percolation thresholds are relevant to efforts to find universal formulas for the percolation threshold. This Brief Report uses exact solutions and recent rigorous bounds for site and bond percolation thresholds to demonstrate that any universal formula based on only the dimension and the coordination number must provide estimates differing substantially from the true threshold value for some lattices.
Comedian Sarah Silverman’s liberal leanings are almost as well-known as her raunchy style. Her 2008 pro-Barack Obama video " The Great Schlep " attracted 2.2 million views on YouTube; a follow-up from 2012 attracted another 1.1 million views. Recently, a reader forwarded us this shareable meme from Silverman’s feed at WhoSay , a social media site, that’s critical of presidential candidate and Sen. Rand Paul, R-Ky. The meme -- which Silverman had passed along from the Twitter account of actor Michael Sheen -- shows Paul seated at a congressional hearing. The meme purports to quote Paul equating the right to health care with slavery. What do the facts say? We were able to track down the source of the comments. They stem from a Senate Health, Education, Labor and Pensions subcommittee hearing on May 11, 2011. Paul’s unusual comparison attracted a flurry of media attention at the time, as well as sniping by Paul’s critics. The meme shortened Paul’s comments to fit the available space, but the abridgement doesn’t strike us as twisting the gist of his comments. Here’s the full excerpt: "With regard to the idea of whether you have a right to health care, you have to realize what that implies. It’s not an abstraction. I’m a physician. That means you have a right to come to my house and conscript me. It means you believe in slavery. It means that you’re going to enslave not only me, but the janitor at my hospital, the person who cleans my office, the assistants who work in my office, the nurses. "Basically, once you imply a belief in a right to someone’s services, do you have a right to plumbing? Do you have a right to water? Do you have right to food? You’re basically saying you believe in slavery. You’re saying you believe in taking and extracting from another person. Our founding documents were very clear about this. You have a right to pursue happiness but there’s no guarantee of physical comfort. There’s no guarantee of concrete items. In order to give something concrete, you have to take it from someone. So there’s an implied threat of force. "If I’m a physician in your community and you say you have a right to health care, do you have a right to beat down my door with the police, escort me away and force me to take care of you? That’s ultimately what the right to free health care would be. If you believe in a right to health care, you’re believing in basically the use of force to conscript someone to do your bidding." A few days after the speech, the Association of American Physicians and Surgeons, a free-market group, posted a longer version of Paul’s speech on YouTube , suggesting that the next 30 seconds or so provided more nuance to Paul’s comments and had been overlooked by commentators. Here is the additional comment: "Now just because it's a noble thing to believe that we are obligated as Christians, we are obligated to the Hippocratic Oath, we have always done this. Since the beginning of modern medicine we have always provided 100 percent access. I do it in exchange for privileges. I do it because I believe in the Hippocratic Oath. But my hospital also says to me you can only operate in this hospital if you agree to see everyone coming through the emergency room. I always have. People have always had 100 percent access to our emergency room. Those are for emergencies -- those are not the best place for primary care." We don’t think Paul’s subsequent comments greatly change what he said earlier, since he’s saying he’s consenting to the servitude of treating non-paying patients as a condition of being allowed to practice at certain hospitals. In this comment, he still sees it as a burden to be borne. In addition, Paul says he’s referring to emergency-room care, not to primary care. Primary care was the point of getting uninsured Americans covered under the Affordable Care Act, so they wouldn’t have to resort to going to emergency rooms for basic services. Sen. Bernie Sanders, I-Vt. -- who, as it happens, is also running for president in 2016 -- used his perch as the chairman of the subcommittee to ask a witness, physician Dana Kraus, whether she felt like a "slave" working at her federally qualified health center. "I love my job," she responded . "I do not feel like a slave." Even Matt Welch, the editor of the libertarian magazine Reason, had harsh words for Paul, who has long been identified with the libertarian movement. "Could slaves free themselves by changing professions?" Welch wrote. "Do doctors in Switzerland get taken away at gunpoint? To treat the analogy with technical seriousness, even setting aside (as if you could) the colossal weight of America's most lasting shame, is to render it ridiculous, in my opinion." We could not find an instance of Paul addressing these comments further, and Paul’s staff didn’t respond to a pair of inquiries. Our ruling Silverman forwarded a social media meme that said Paul has stated that supporting the "right to health care … means you believe in slavery." The meme has been abridged from the full quote, but we see no significant change in his meaning. We also found no evidence that Paul had backtracked on the views he expressed. We rate the meme’s claim True.
Ruminations on Spirituality, Recovery and Creativity Facing Late Autumn The leaves lay like a wound, red and deep across the lawn, while what remains is frightened away by bursts of November wind. I look at concrete-gray clouds and sigh, knowing it is time to cover flower beds, yank out roots of annuals, their petals shriveled and frail, as fine as dust released to the air. Soon I will cut back roots of perennials, until everything in the yard is brown, until birds no longer chirp, but vacate their nests, more visible now as branches of trees shake against the wind and scrape against windows like angry fingers, while the house creaks at its joints.
1. Discrepancy in the Role of HLA-G in Solid and Liquid Tumors {#sec1} ============================================================== Although various immune effector cells are recruited to the tumor site, their antitumor functions are downregulated, largely in response to tumor-derived signals \[[@B1]\]. In this context, expression of the tolerogenic HLA-G molecule represents a mechanism that may favor tumor survival through interaction with inhibitory receptors. We will here focus on the ILT2 and ILT4 inhibitory receptors that are present on NK, T, B, dendritic cells, and neutrophils in which they mediate negative signaling that counteracts immune activation ([Figure 1](#fig1){ref-type="fig"}). The result is tumor escape from the host immune system \[[@B2]\]. Thus, understanding such mechanism is an important challenge in order to develop optimal immunotherapeutic strategies. HLA-G has been shown to be expressed in many types of primary solid tumors and metastases and in malignant effusions \[[@B3]\]. HLA-G can be found on tumor cells as well as on tumor-infiltrating cells \[[@B4]\]. The clinical relevance of HLA-G in cancer is supported by the following observations: (i) HLA-G expression is associated with malignant transformation and is never observed in healthy surrounding tissues \[[@B5]\]; (ii) HLA-G is found to be expressed in solid tumors of high histological grades and advanced clinical stages \[[@B6], [@B7]\]; and (iii) the use of HLA-G as a prognostic marker has been proposed since HLA-G expression in biopsies and/or high levels of soluble HLA-G (sHLA-G) in plasma from patients have been significantly correlated with poor prognosis \[[@B6]--[@B11]\]. All these data highlight a role for HLA-G in the immune surveillance of solid tumors and the progression of the disease. Regarding the relationships between tumor and immune system, the concept of cancer immunoediting has been described as an important host protection process that includes three essential phases: elimination, equilibrium, and escape \[[@B12]\]. HLA-G can interfere with each of these phases. Indeed, (i) HLA-G can downregulate the elimination phase by inhibiting the proliferation of T and B cells, the cytotoxic activity of NK cells and CTL, the phagocytic activity of neutrophils, and the function of DC, via ILT2 and ILT4 signaling \[[@B3], [@B102]--[@B110]\] ([Figure 1](#fig1){ref-type="fig"}). In this phase, HLA-G expression would enable a proportion of tumor cells to evade the host immune response. (ii) Proinflammatory cytokines such as IFNγ which are secreted in high amounts may upregulate HLA-G expression \[[@B13]\]. HLA-G could also affect the equilibrium phase by controlling the expression of HLA class II molecules by DC \[[@B14]\]. (iii) In the evasion phase, tumor cells have lost molecules important for the immune recognition and tend to express only HLA-G on the cell surface, rendering them less susceptible to effector cells. The resulting rapidly growing tumors create a hypoxic microenvironment which promotes angiogenesis, invasion and metastases, but also induces HLA-G expression on tumor cells. Additionally, the immunosuppressive cytokine IL-10 which is produced in high quantities during this phase upregulates HLA-G expression \[[@B15]\]. Both IL-10 and HLA-G may be produced by tumor cells but also by tumor-infiltrating leucocytes \[[@B16]\]. Finally, HLA-G has been shown to induce regulatory T cells reinforcing tolerogenic environment \[[@B17]--[@B20]\]. All these mechanisms may profoundly alter antitumoral immune responses leading to tumor expansion and spread through blockage of both innate and adaptive immunity and by inducing tolerance to the tumor. Recently, the development of animal models established the proof of concept that an HLA-G^+^ tumor cell can develop and tolerize the host antitumor immune responsein vivo\[[@B21], [@B22]\]. Although there is no murine homologue of HLA-G,in vivo studies were made possible by the fact that human HLA-G can bind and mediate a signal via the murine receptor Paired immunoglobulin-like receptor (PIR)-B, the homologue of human ILTs \[[@B14], [@B23]\]. Results showed that human or murine tumor cells expressing HLA-G can grow in an immunocompetent host and that blocking HLA-G function by a specific antibody inhibits the development of the tumor. Characterization of the mechanisms by which HLA-G operatesin vivo shows that both innate and adaptive immunity are affected \[[@B21], [@B22]\]. Hence, tumor proliferation is accompanied by an expansion of CD11b+ Gr1+ myeloid-derived suppressor cells, loss of peripheral T cells, and a cytokine balance in favor of a Th2 profile versus Th1/Th17. Therefore, blocking HLA-G may constitute a novel innovative antitumoral approach \[[@B2], [@B24]\]. Whereas HLA-G expression and its clinical significance in solid tumors have been extensively investigated showing that HLA-G expression in such tumor cells has unfavorable outcome or prognosis \[[@B25]\]; only a few data are available for the HLA-G expression and its clinical significance in liquid malignancies. In this regard, enhanced sHLA-G (i.e., HLA-G5 and shed HLA-G1) plasma levels have been described in B cell malignancies, such as multiple myeloma, non-Hodgkin B-lymphoma, and B-CLL \[[@B26], [@B27]\]. However, no clear correlation was established between HLA-G and unfavorable clinical outcome in hematological malignancies. Several factors may account for these controversial results such as clinical status, chemotherapy, and methodological differences between the studies. Of note, discrepancy between solid and liquid tumors may be due to the nature of malignant cells: in hematological malignancies, tumor cells are immune cells able to express HLA-G receptors and HLA-G may have an unexpected role through inhibition of neoplastic cell proliferation. In this regard, we recently demonstrated that proliferation of hematological tumors expressing HLA-G receptor (ILT2) may be inhibited by HLA-G \[[@B28]\]. Indeed, HLA-G inhibits the proliferation of human B cell lymphomas, myelomas, and B cell leukemia expressing at their surface the receptor ILT2. Blocking HLA-G or its receptor ILT2 by specific antibody or siRNA could restore B cell proliferation demonstrating the role played by the interaction between ILT2 and HLA-G in the antiproliferative activity observed. HLA-G was found to reduce B cell proliferation by inducing a G0/G1 cell cycle arrest. Signaling events leading to HLA-G inhibitory effects on malignant B cells were mediated through increased PKCα/βII, PKCδ, and PKCμ phosphorylation and decreased phosphorylation of AKT, mTOR, GSK-3β, c-Raf, and Foxo proteins. All these effects converge to activate inhibitors or to inhibit activators of cell survival, growth, and proliferation. Indeed, PKCδ and PKCμ phosphorylated active forms have been described to negatively regulate B cells \[[@B29]\]. In addition, the mTOR pathway is a critical part of the cellular circuitry which is often constitutively activated in tumor cells. Our data provide evidence that HLA-G may inhibit tumor cell proliferation through mTOR signaling blockade. These results were consolidated by studies using bone marrow specimens from myeloma patients in whom HLA-G limits CD138^−^ stem cell differentiation into CD138^+^ myelomatous tumor cells. Of note, we previously described the production of soluble HLA-G proteins by bone marrow-derived mesenchymal stem cells \[[@B20]\] as well as by osteoblasts \[[@B30]\]. Analysis of cross-talk between tumor B cells, HLA-G^+^ mesenchymal stem cells, and osteoblasts in bone marrow may provide insights in understanding the mechanisms of tumor suppressionin vivo in this biological compartment \[[@B31]\]. These data indicate a particularly innovative use of HLA-G in cancer since we propose a radically opposite action of HLA-G if the tumor cell is an immune system cell, the function of which could be affected by HLA-G due to the presence of surface inhibitory receptors for HLA-G. This does not involve blocking HLA-G to favor antitumoral response against solid tumor but, conversely, using the antiproliferative properties of HLA-G to limit tumor progression for hematological malignancies. Although, we are describing the role of HLA-G on B-cell malignancies, we can expect a similar effect on malignant blood diseases involving T cells, NK cells, and monocytes since these fulfil the same criteria as B cells (i.e., cell-surface expression of HLA-G receptors with inhibitory functions). In agreement with this HLA-G antitumor activity in B cell malignancies, we previously showed that soluble HLA-G inhibits the growth of erythropoietin (EPO)-independent colonies in patients suffering frompolycythaemia vera\[[@B32], [@B33]\]. This myeloproliferative syndrome is characterized by erythroid cells displaying deregulated proliferation due to a mutation (V617F) in the signaling protein JAK2, inducing autoactivation of this kinase by autophosphorylation \[[@B34]\]. As JAK2 is directly related to the EPO receptor, this increase in activity leads to constitutive signaling of the EPO receptor and leads to the formation of EPO-independent erythroid colonies, one of the biological criteria of this disease. The patient presents proliferation of erythroid cells in the bone marrow which gives rise to hyperproduction of red blood cells, leading to polycythaemia in the peripheral blood. This disease has serious consequences since it may progress towards myelofibrosis with splenomegaly, or indeed leukaemia. Hence, the ability to thwart the effects of JAK2 V617F mutation could represent a major therapeutic benefit. Our research shows that the soluble HLA-G protein acts on protein kinase JAK2 by inducing its dephosphorylation. Notably, none of the known HLA-G receptors was found on erythroid cells leading to the hypothesis that HLA-G may act on this lineage through an unidentified receptor. Hence, soluble HLA-G may be perceived as a new negative regulator for the EPO receptor signaling and may therefore represent a potential therapeutic agent for the treatment of patients carrying the mutation JAK2 V617F found not only inpolycythaemia vera but also in the other two main myeloproliferative syndromes, essential thrombocythemia and idiopathic myelofibrosis. The HLA-G primary transcript is alternatively spliced leading to seven splice variants encoding 4 membrane-bound (HLA-G1 to -G4) and 3 soluble (HLA-G5 to -G7) protein isoforms. Although both membrane-bound and soluble HLA-G forms exert similar immunosuppressive functions through binding to ILT receptors, the soluble forms constitute the most relevant and adapted tools for therapeutic use. Nevertheless, the main obstacle to the implementation of soluble HLA-G as therapeutic is the absence of a form that is simpler than the complex trimolecular heavy chain/B2M/peptide with which the majority of data on HLA-G were obtained. Current knowledge on the multiple HLA-G active structures and their potential use in therapy is described in the following section. 2. The Multiple HLA-G Active Structures and Their Corresponding Receptors {#sec2} ========================================================================= What is the actual structure of tolerogenic HLA-G is an important question. With very few exceptions, the only HLA-G structures that are currently investigated,in vitro andin vivo, are B2M-associated isoforms. Consequently, only the HLA-G/ILT2 interaction is taken into consideration since ILT4 binds mostly B2M-free isoforms. Because it was clearly demonstrated that HLA-G dimers carry most if not all of HLA-G immune-inhibitory functions \[[@B35]--[@B37]\], it is fair to state that currently, "tolerogenic HLA-G" is "dimeric B2M-associated HLA-G that acts through ILT2." This conception, which originates from the translation ofin vitro experiments to thein vivo setting, is accentuated by the lack of analytic tools (especially antibodies) capable of specifically detecting anything more precise than "B2M-associated HLA-G," "unfolded HLA-G," or "secreted HLA-G," and might be incomplete at best. First of all, B2M-associated HLA-G and its interaction with ILT2 might not be the most important, or the most functional HLA-G structurein vivo. Indeed, cytotrophoblast cells express HLA-G heavy chains that are not associated with B2M for the lack of expression of this protein \[[@B38], [@B39]\]. Therefore, if the assumption holds true that HLA-G exerts its primary function at the fetal-maternal interface and that HLA-G functions in an identical fashion in other contexts in the adult, B2M-free HLA-G should bear high significance in the periphery as well. In this regards,in vitro studies demonstrated that B2M-associated HLA-G and B2M-free HLA-G molecules were identically capable of inhibiting the alloproliferation of T cells in mixed lymphocyte reactions \[[@B18]\]. Knowing that B2M-free HLA-G binds ILT4 but not ILT2 \[[@B36], [@B40]\], it may be that ILT4 and not ILT2 is the receptor most relevant to HLA-Gin vivo function. This notion is strengthened by recent data showing that ILT4 is the receptor for dimers of the alpha1-alpha3 structure of HLA-G (HLA-G2 and HLA-G6 isoforms) that is tolerogenicin vivo in murine skin transplantation models \[[@B41]\]. Atop of variations in its basic backbone and association with B2M, HLA-G can undergo posttranslational modifications. (i) It is long known that HLA-G can be glycosylated, especially when produced by trophoblast cells \[[@B42]\]. More recently, (ii) it was demonstrated that HLA-G can also be nitrated \[[@B43]\]. As nitration is produced at the site of nitric oxide production where the immune system is activated, HLA-G produced at sites of inflammation could be distinguished from HLA-G produced elsewhere. (iii) Due to ubiquitination, HLA-G can form high molecular weight complexes through disulfide bridges. These high molecular weight complexes are present in exudates from patients with inflammatory diseases or cancer and may also bear pathology-specific significance \[[@B44]\]. The notion that the function of HLA-G may depend on additional molecules is barely considered. Yet, given the diversity of HLA-G functions, it is very likely that all of them are not solely due to the interaction of HLA-G with its inhibitory receptors. It is entirely possible that the function of HLA-G is boosted by a synergy with other molecules, or reduced by others. In this regard, molecules that are functionally linked to HLA-G are already known. For instance, IL-10 is an inducer of HLA-G expression and is induced by HLA-G \[[@B15], [@B20], [@B45]\]. Similarly, indoleamine 2,3 dioxygenase (IDO) expression and/or function was shown to modulate and to be modulated by HLA-G \[[@B46], [@B47]\]. Amongst molecules that may deeply affect the function of soluble HLA-G are soluble HLA-G inhibitory receptors. Indeed, binding of soluble ILT2 or ILT4 to HLA-G is likely to block HLA-G function. Thus, parameters of the microenvironment might be crucial to HLA-G function. In addition, recent data confirm the original observation \[[@B48]\] that HLA-G is present in exosomes, in the culture supernatants of bladder cancer cells, and within exudates \[[@B44]\] and plasma (see Rebmann in \[[@B49]\]) of cancer patients. Exosomes are immune-active microparticlesper se, either because of the external proteins they display or because of their internal immunomodulatory content or both. The actual function of HLA-G-loaded exosomes is yet to be elucidated, but it is likely that,depending on the exosome composition, HLA-G function might vary in terms of efficiency, and/or nature. Thus, exosome-bound and not-exosome-bound HLA-G may bear different pathological significance. For lack of tools to specifically detect any of the HLA-G structures mentioned above, all get pooled into the "B2M-associated," "unfolded," or "secreted" categories, and, thus, their specific characteristics are not considered. Analysis of the receptors that are responsible for HLA-G function in vivo represents also a critical point. This question may seem trivial since it is commonly admitted that HLA-G has two main inhibitory receptors: ILT2 and ILT4, that these are differentially expressed by all immune cells, and that they recognize different structural features of HLA-G (for review, see \[[@B50]\]). Yet, the situation might not be so simple as shown by a very simple fact: only 0--5% of CD4^+^ T cells, 10--15% of CD8^+^ T cells, and 20--25% of NK cells from PBMC express ILT2. How then, in mixed lymphocyte reactions and allocytotoxicity experiments, can HLA-G reliably inhibit PBMC T cells and NK cells directly through ILT2, ILT2^+^ cells and ILT2^−^ cells alike? One possibility is that HLA-G does not act directly on the T cell or NK populations but on APCs (B cells of myeloid) which all express HLA-G receptors. Another possibility is that HLA-G does act directly on the T and NK cell effectors, but not through the ILT2 receptors that they express. We investigated this latter hypothesis. In a first set of studies, we evaluated the capability of HLA-G to act through the mechanism of trogocytosis, that is, the transfer of membrane fragments and the proteins they contain from one cell to another. This work revealed that HLA-G can be transferred from cells that express it to cells that do not and still exert its function \[[@B51], [@B52]\]. We also demonstrated that not only HLA-G but also ILT2 could function through trogocytosis: ILT2-negative T cells acquired ILT2 from monocytes, transiently becoming ILT2^+^ T cells that could use this borrowed receptor to respond to HLA-G direct stimulation \[[@B53]\]. Thus, trogocytosis of HLA-G receptors can explain the general inhibitory effect of HLA-G through known receptors on a cell population that in majority does not produce them endogenously, as long as some HLA-G receptor-expressing cells are present. In a second set of studies, we investigated whether HLA-G could act through yet unknown receptors and we demonstrated, in systems where trogocytosis of HLA-G receptors was not possible, that cells which did not express HLA-G receptors could still respond to HLA-G stimulation. For instance, we demonstrated that HLA-G induced the upregulation of inhibitory receptor transcription in several immune cell lines including the KG1a promyeloblast line, which did not transcribe the known HLA-G receptors \[[@B54]\]. In another study, we investigated the capability of synthetic HLA-G proteins to inhibit the cellular multiplication of hematological tumor cell lines. This had previously been reported for membrane-bound HLA-G1 and soluble HLA-G5 and was shown to occur through HLA-G/ILT2 engagement \[[@B28], [@B52]\]. We found that HLA-G synthetic proteins which were not capable of binding ILT2 could nevertheless inhibit the cellular multiplication of hematological cell lines. Furthermore, HLA-G synthetic proteins were shown to inhibit cell lines that did not even express known HLA-G receptors \[[@B33], [@B55]\]. The identification of such a novel HLA-G receptor and of its associated functions, the possible functional associations, or overlaps with the already known ones is crucial to HLA-G biology and to the clinical applications of this molecule, as well as to the determination of its cellular expression pattern. In addition to the need of better definingin vivo active HLA-G structures and their interactions with other molecules from the microenvironment, the last part of this review is dedicated to the regulation ofHLA-G expression, an additional critical point to elucidate in the context of tumors. 3. The Control of HLA-G Expression {#sec3} ================================== In healthy tissues, HLA-G molecules are absent with the exception of placenta \[[@B56], [@B57]\], thymus \[[@B58]\], pancreas \[[@B59]\], cornea \[[@B60]\], proximal nail matrix \[[@B61]\], and organs sustaining erythropoiesis \[[@B32]\]. Nevertheless, ectopic expression of HLA-G is commonly observed in pathological situations such as cancer, not rejected allografts, virus infections, autoimmune diseases, and inflammation \[[@B3]\]. In both normal and pathological contexts, the presence or absence of HLA-G is generally independent of classical HLA class I molecules and involves transcriptional, posttranscriptional, and posttranslational mechanisms. Among key regulatory processes involved in HLA-G expression, DNA methylation (CpG) and hypoacetylation of H3 and H4 histones at the HLA-G locus have been associated with the absence of HLA-G expression commonly observed in cultured tumor cells expressing or not classical HLA molecules. The HLA-G gene repression can be reversed by demethylating agents used in some cancer therapies such as 5-aza-2′-deoxycytidine \[[@B62], [@B63]\] and inhibitors of histone deacetylases \[[@B63]\] and may directly induce HLA-G cell surface expression. HLA-G transcriptional activity is also controlled by a unique machinery since almost all known regulatory sequences for classical HLA class I gene are disrupted for HLA-G gene, including some that are shared with HLA class II genes \[[@B64]\]. Alternative regulatory elements have been identified such as a putative locus control region (LCR) contained in a 250 bp fragment at 1.2 kb from the ATG translation initiation site \[[@B65]\]. The LCR was shown to be critical for spatiotemporal HLA-G transcription in transgenic mouse placenta \[[@B66]\]. Among factors demonstrated to target this region, CREB1 factor was described by the group of Peter van den Elsen to bind two cAMP response elements (CRE) at positions −1381 and −1371 (3′ ends) from the ATG \[[@B67]\]. CREB-1 was also demonstrated to bind two additional CREs scattered through the distal promoter region at positions −935 and −771 \[[@B67]\]. In addition, we reported the location of a functional binding site for IRF-1 (−744) in response to IFN-beta \[[@B13]\] and binding sites for heat shock factor 1 (HSF1) (−459/−453) in response to heat-shock or arsenate treatments \[[@B68]\]. Besides these regulatory elements, a binding site for the progesterone receptor (PR) was located at position −38 \[[@B69]\]. Recently, HLA-G repressors have been identified by our group and others, including Ras responsive element binding protein 1 (RREB-1) which binds three Ras response elements (RRE) dispersed along the HLA-G proximal and distal gene promoter (−1357, −143, and −54) \[[@B70]\], GLI-3 factor (−1108) \[[@B30]\], and a LINE-1 element in which 3′ end is located at −4 kb \[[@B71]\]. Interestingly, a hairpin loop can form in the LINE-1 element leading to HLA-G silencing \[[@B71]\]. HLA-G expression is also controlled at the posttranscriptional levels by mechanisms targeting the 3′ untranslated region (3′ UTR) that affect mRNA stability \[[@B69], [@B72]\] and by specific microRNAs (miR-133a, miR-148a, miR-148b, and miR-152) \[[@B73], [@B74]\]. At the posttranslational level, HLA-G expression is regulated by the antigen presenting machinery (APM) \[[@B75], [@B76]\] and a specific quality-control process mediated by the truncated HLA-G tail that control high affinity peptide loading and increases HLA-G cell-surface expression \[[@B77]\]. Environmental factors commonly found in placenta or tumors are certainly crucial in the induction, upregulation, and maintaining of HLA-G expression since HLA-G^+^ cells may lose HLA-G expression during long term cultures in standard conditions \[[@B78]\]. These factors include cytokines (IL-10 \[[@B15]\], IFN-γ \[[@B79]\], IFN-γ+GM-CSF, IFN-γ+IL-12 \[[@B80], [@B81]\], IFN-β \[[@B81]\], and LIF \[[@B82]\]), hormones (dexamethasone, hydrocortisone \[[@B83]\], and progesterone \[[@B83]\]), galectin-1 \[[@B84]\], IDO \[[@B47]\], and stress conditions (heat shock \[[@B81]\] and hypoxia \[[@B85], [@B86]\]). These regulatory molecules exert a control on the amounts of HLA-G transcripts and/or HLA-G protein and for some may have the opposite effect (downregulation) on classical HLA-class I expression (IL-10 \[[@B15]\], glucocorticoid hormones \[[@B83]\]).In vitro experiments reveal that most of them requireHLA-G basal transcriptional activity to have an effect. Among environmental factors able to reverseHLA-G repression, hypoxia, which is a common stress condition (cancer, transplantation, and pregnancy), is considered as a critical candidate \[[@B85], [@B86]\]. Otherwise, several lines of evidence are reported for balancing selection acting on the 5′ and 3′ untranslated regions of the HLA-G gene (5′ UTR and 3′ UTR) \[[@B87], [@B88]\]. Considering 46 HLA-G alleles (50 alleles have been recognized to date), six different HLA-G lineages are identified showing variations mainly in the regulatory regions \[[@B88]\]. This indicates that these lineages are probably related to different expression profiles depending on microenvironmental factors and on physiological or pathological conditions. Interestingly, at least 33 single nucleotide polymorphisms (SNP) are described in the 5′ UTR, defining at least 11 haplotypes \[[@B87]--[@B91]\]. They can modify potentially methylated CpG sites and are within or close to known or putative regulatory elements and thus might influence transcriptional activity \[[@B64], [@B91]--[@B93]\]. For instance, it should be noted that (i) a CpG site at positions −965/−964 may be affected by the presence of an Adenine at position −964 (0.5 frequency); (ii) the −56 C-T polymorphism coincides with the RREB-1 binding site located in the proximal HLA-G promoter region and is close to the PR element located at position −38 (iii) −762 C-T and −725 C-T-G polymorphisms surround the ISRE at position −744. Nonetheless, very few studies have investigated the impact of HLA-G promoter polymorphisms on the level of HLA-G expression. In particular, using luciferase reporter assays performed in JEG-3 choriocarcinoma cell line showed that a Guanine instead of a Cytosine or Thymine at nucleotide position --725 in the promoter region of HLA-G results in increased transcription rates \[[@B92]\]. Several polymorphic sites are also identified in the 3′ UTR, a 14 bp insertion/deletion (Indel) \[[@B94]\] and 7 SNPS (+3003T-C, +3010C-G, +3027A-C, +3035C-T, +3142G-C, +3187A-G, and +3196 C-G), defining at least 7 haplotypes with frequency \>0.05 \[[@B95]\]. The presence/absence of the 14 bp sequence has been associated with the magnitude of HLA-G production in normal and pathological situations \[[@B91]\]. In particular, alleles presenting the 14 bp sequence are associated with reduced HLA-G mRNA and lower levels of sHLA-G in the plasma from healthy subjects \[[@B96]--[@B99]\]. Moreover, a minor fraction of HLA-G transcripts generated by the 14 bp alleles can be further processed by the removal of a 92 b fragment containing the 14 b sequence. These transcripts are more stable than the complete form and might be the consequence of the presence of an AU-rich element (ARE) within the 14 b fragment \[[@B72]\]. Another variation site at position +3187 may also influence HLA-G mRNA stability, with the presence of an Adenine associated with decreased mRNA stabilityin vitro and decreased HLA-G expression \[[@B69]\]. Interestingly, the SNP is found 4 bp upstream of an ARE. Furthermore, the nucleotide variation at the +3142 position was demonstrated to influence the binding of miR-148a, miR-148b, and miR-152 to the HLA-G messenger with an increased affinity in the presence of a Guanine instead of a Cytosine \[[@B74]\]. Despite a controversial data published by Manaster and colleagues \[[@B100]\], these results are consistent with thein silicoanalysis of microRNAs targeting the 3′ UTR \[[@B101]\]. Indeed, in addition to miR-148a, miR-148b, and miR-152, the binding ability of several miRNAs may potentially be influenced by the 3′UTR variations, emphasizing the role of the 14 bp indel, and SNPs at the +3003, +3010, +3027, and +3035 positions. Interestingly, we recently showed that most of 3′UTR SNPs are associated with differential amounts of sHLA-G in the plasma from healthy Brazilian and French populations \[[@B99]\]. In agreement with the known or putative specific impact of each variants, UTR-1 haplotype (14 bp Del, +3003T, +3010G, +3027C, +3035C, +3142C, +3187G, and +3196C) was classified as a high producer of sHLA-G while UTR-5 (14 bp In, +3003T, +3010C, +3027C, +3035T, +3142G, +3187A, and +3196C) and UTR-7 (14 bp In, +3003T, +3010C, +3027A, +3035T, +3142G, +3187A, and +3196C) were classified as low producers of sHLA-G \[[@B99]\]. Therefore in addition to microenvironment factors, HLA-G gene polymorphism is likely a relevant parameter to consider in tumoral HLA-G expression. 4. Concluding Remarks {#sec4} ===================== Based on the tolerogenic properties of HLA-G in the solid tumor context, blocking its expression and function may be considered as potential targets for antitumor therapy. One might either stopHLA-G transcription or interfere with its surface expression or secretion or block direct interaction between HLA-G expressed by tumor cells and inhibitory ILT receptors present on immune cells. Strategies aimed at blocking HLA-G expression by using RNA interference or HLA-G function by using specific antibodies may enhance the immune clearance of HLA-G^+^ tumor cells since all cell subsets involved in tumor rejection can express at least one receptor for HLA-G. In hematological malignancies, such as B cell malignancies, the role of HLA-G seems more complex and may depend on a balance between the HLA-G-driven inhibitory mechanism of antitumor responses and the antiproliferative effects on malignant B cells which will be under the control of ILT2 expression or of another as yet unknown receptor ([Figure 2](#fig2){ref-type="fig"}). Accordingly, considering ILT receptor expression and function in malignant hematopoietic cells will be of particular importance in understanding the mechanisms of tumor progressionin vivo. In this regard, more clinical and basic studies are now required to establish a clear significance of HLA-G expression in hematological malignancies. Finally, precise determination of the nature of the HLA-G molecular structures/superstructures that are pathologically relevantin vivoas well asthe identification of individuals genetically prone to differentially express HLA-G in a specific environment will contribute to develop optimal HLA-G-based clinical strategies for diagnostic and therapy in cancer. This work was supported by the CEA. Conflict of Interests ===================== The authors declare that there is no conflict of interests regarding the publication of this paper. ![Tolerogenic functions of HLA-G.](JIR2014-359748.001){#fig1} ![Dual role of HLA-G in hematological malignancies.](JIR2014-359748.002){#fig2} [^1]: Academic Editor: Fabio Morandi
Bacterial resistance to silver-based antibiotics. Alan Lansdown and Angela Williams discuss the potential problem of silver resistance in wound care and suggest that on the basis of present knowledge, true bacterial resistance to silver is rare.
MEMBERSHIP TERMS AND CONDITIONS Definitions. In this Agreement, “Club Owner” or “we” means the Club Owner identified on the Agreement, a franchisee of Lift Brands UK Limited. “Club” means the Club identified on the Agreement. “Snap Fitness” means Lift Brands UK Limited. “You” and “member” means the person(s) whose name(s) and signature(s) and initials appear on the Agreement. You are responsible for updating address and contact information. 1. MEMBERS INDUCTION. To mitigate risk and ensure that you correctly operate or use any of our facilities, services, products or equipment, including the adjustments of levels or settings on any equipment, you are required to undertake an instructional consultation with a member of our staff before use. I understand that an introduction to the club facilities are a requirement prior to using the Club’s facilities. 2. MEMBERSHIP TYPE. The type of membership that applies to you is set out on the first page of this agreement. If your membership is month to month, you will pay the monthly fee set out on the first page of this agreement by direct debit each month. If your membership is pre-paid, you acknowledge that the fee paid by you is on or before the date of this agreement is not refundable in any circumstances (save in accordance with clause 5(2) below). If your membership is a 12-month membership, you will pay the monthly fee set out on the first page of this agreement by direct debit each month. 3. MEMBER’S RIGHT TO CANCEL. Regardless of your membership type,you may cancel your membership by giving us one month’s notice and filling out a cancellation form at your home club. The notice will be effective on the last day of the month which is at least 30 days from the date of your notice and, if your membership is month to month or 12-month membership, you will be required to pay all fees on a pro rata basis up to that date and any outstanding fees for other services already supplied to you, regardless of whether or not you use the club after the date of your notice. If collection or legal services are needed to collect any unpaid amount, you are responsible for all costs of collection, including solicitor’s fees of Club Owner and/or Lift Brands UK Limited. 4. OTHER WAYS THAT YOU CAN END YOUR MEMBERSHIP. You can also cancel your membership for the following reasons: IF WE DON’T KEEP OUR END OF THE DEAL: You can cancel your membership by written notice to us if we breach any of our obligations under this agreement and we have not remedied that breach within a reasonable time after you have given us a written request that we do so. In the case of cancellation for this reason, you will be responsible for the membership fees calculated on a pro-rata basis and any outstanding fees for other services already supplied to you. If your membership is pre-paid, you will be entitled to a refund on a pro-rata basis. YOU CAN CANCEL FOR MEDICAL REASONS: If your membership is a 12-month membership, you can end your membership by telling us in writing if you cannot exercise for the remainder of term due to an illness or a physical incapacity and you produce supporting documentation to our reasonable satisfaction. In that event, you will be responsible for the membership fees for the time you have been a member calculated on a pro rata basis and any outstanding fees for other services already supplied to you. ON OR AFTER EXPIRY OF THE MINIMUM TERM: If your membership is a 12-month membership, you do not need to do anything, as it will automatically end when the term expires. We will seek to remind you before the end of your membership in these circumstances in order that we can discuss renewal of your membership. 5. OUR RIGHT TO CANCEL. In addition to our other rights under this agreement, we can terminate your membership by written notice to you if you fail to act in accordance with any obligation under this agreement and if capable of remedy you do not remedy the failure within a reasonable time of us giving you written notice requiring you do so. However, we will not seek to end your membership in this way if you have failed to make a payment and we are also in breach of a material condition of this agreement. If we cancel this agreement under this paragraph you will be liable for the joining fee, membership fees for the time you were a member and any other fees payable for further ﬁtness services already supplied. On rare occasions we may cancel a membership by written notice to the member without the need to give a reason. If we cancel your membership in this way you will be liable for the membership fees for the time you were a member and any other fees for other ﬁtness services already provided. Club Owner may, at its option, terminate my membership if (1) I fail to make payments or any payments or fees are late, (2) the monthly EFT payments or membership fees are interrupted or discontinued for any reason and I or my co-signer do not provide an acceptable alternative, (3) I fail to follow any membership policies or club rules or violate any part of this agreement, or (4) my conduct is improper and harmful to the best interest of the Club or its members or (5) I fail to provide doctor’s approval for exercising if so requested. Termination is effective on the date a written notice to my last known address. I am liable for all ﬁnancial obligations until that date. Club Owner also reserves the right to terminate my membership for any reason not stated above and if not prohibited by law. 6. MEMBERSHIP FREEZE. If your membership is month to month or a 12-month membership,you have the right to freeze your membership for up to three months annually. You must provide written notice by the 28th of the month before the month for which the freeze is to take effect. You will incur a £3 processing charge for each frozen month. I understand that if I elect to freeze my membership I cannot cancel my membership during the “freeze” period. If the membership is a pre-paid or 12 month membership, that is extended by the number of “freeze” months. 7. PHYSICAL CONDITION AND NO MEDICAL ADVICE. I represent that I am in good physical condition and have no medical reason or impairment that might prevent me from my intended use of the Club facilities. I acknowledge that I have been informed that the Club offers a consultation which includes a brief interview regarding my medical history. However, I understand and acknowledge that Club Owner and Snap Fitness will not and cannot provide me any medical advice. If I have any health or medical concerns now or after I join the Club, I will discuss them with my doctor before using the Club facilities. 8. DAMAGED, LOST OR STOLEN PROPERTY. I understand that I am solely responsible for any damage which I may cause to the Club, its facilities, services, products or equipment, if such damage is caused by my wilful act and/or negligence. I understand that neither personnel at the Club nor Snap Fitness are responsible for any of my personal property that is damaged, lost or stolen while in or around the club or any other Snap Fitness location. 9. GUESTS. I may bring a guest with me during staffed hours for the first time free workout. I understand that all guests must sign the Guest Waiver before using the Club. I understand the club reserves the right to charge a £20 per visit fee for any unauthorised guests I allow into the Club. The Club also reserves the right to charge a fee to guests who are not local residents or who visit repeatedly without joining. I will not allow any non-member to use my membership access card, and I understand that if I do, the card may be deactivated and a fee will be charged to activate the card. I am liable for all damage, I, my family members or guests cause to the equipment or physical infrastructure of the Club and will reimburse the Club via the payment method used to pay my membership fees. 10. USE OF OTHER Snap Fitness CLUBS. I understand that my membership to the Club allows me to access all other Snap Fitness locations free of charge. My use of all Snap Fitness locations is subject to the terms of this Agreement and I have the same obligations to any Snap Fitness location as I have to the Club and all club personnel. I understand that if I use another Snap Fitness location more than my home club, my membership may be transferred to that location according to the then-current membership transfer policy. If my membership is transferred, I will be charged the current membership price of the Snap Fitness location I use most often and I may be required to enter into a new membership agreement. 11. LIMIT ON OUR LIABILITY TO YOU. Except for any legal responsibility that we cannot exclude in law (such as for death or personal injury), we are not legally responsible for any: (i) losses that :(a) were not foreseeable to you and us when the contract was formed; (b) that were not caused by any breach on our part; (ii) business losses; or (iii) losses to non-consumers. 12. DISCLOSURE OF YOUR PHYSICAL CONDITION. Provision of a safe and effective exercise program is dependent upon accurate health and ﬁtness proﬁling. You agree to disclose to us all relevant personal health and ﬁtness information both prior to and during engagement in any exercise program, service or facility we provide to you, as a part of your membership. This is inclusive of any health risk assessment, initial and periodic ﬁtness assessment and relevant information or recommendations provided by your medical or allied health practitioner/s. You further warrant and represent that you will not use the Club or any of our facilities, services or products whilst you are suffering from any infections or contagious illness, disease or other ailment or whilst you are suffering from any physical ailment such as open cuts or sores or minor infections where there is a risk, however small, to other members and guests. 13. JOINT AND FAMILY MEMBERSHIP INDEMNIFICATION. If “Joint” or “Family” is the membership plan checked on the ﬁrst page of this agreement, I agree that if the other joint or family members cancel their membership, I am liable to have an increase in membership dues to the then current price for an individual member. 14. MINIMUM AGE: All membership holders of Snap Fitness must be a minimum of 14 years of age. All minors under the age of 18 are restricted to access during staffed hours only, and must co-sign the membership agreement and acknowledgment of indemnity waiver. Minors between 14-18 years of age must comply with the follow restrictions: Access during staffed hours only. All paperwork must be completed, including the membership agreement. 15. COOLING OFF PERIOD: The cooling off period starts if the member enters into the agreement before the centre opens (1) if the ﬁtness centre opens on the proposed opening day, on that day (2) if the ﬁtness centre opens on a new opening day and the ﬁtness centre has not opened when the centre notiﬁes the member of the new opening day, on that day or (3) if the ﬁtness centre opens on a new opening day and the ﬁtness centre has opened while the supplier notiﬁes the member of the new opening day-when the member receives notice that the ﬁtness centre has opened. The cooling off period ends 48 hours after the cooling off period starts. If you change your mind shortly after committing to a Snap Fitness membership, you may have an opportunity to cancel. You will need to let us know in writing within 30 days for it be effective. We will charge an administration fee of £50 or 10% (whichever is lesser) of fees paid. All refunds will be by credit or direct deposit into a nominated account – there are no cash refunds. 16. PERSONAL E-MAIL ADDRESS. I understand that by providing my e-mail address, I will receive occasional e-mails from Snap Fitness updating me on my membership beneﬁts. However, I will always have the option to opt-out from receiving these updates by replying and requesting to be unsubscribed. 17. PRIVACY STATEMENT. OUR PRIVACY POLICY: From when you apply for membership we will have access to personal information about you, such as information relating to your health and ﬁnances. We will protect this information and only use, disclose or deal with this information in accordance with our Privacy Policy. The latest version of the Privacy Policy is available on our website. If you provide your email address you consent to occasional emails from Snap Fitness and Club Owner updating you on your membership benefits. You agree that Snap Fitness and Club Owner may use your e-mail address and other personal information as stated in the Privacy Policy, which includes that we may transfer your personal information to our service providers located in the United States or another country to provide the information, products and services you request, assist us to carry-out our obligations under this agreement and any other purpose identified in the privacy policy or other agreement between you and us. You may opt-out from receiving these updates by checking the box above. At any time you may also update your privacy preferences by following the instructions provided in the Privacy Policy. By signing this membership agreement, you confirm that the above has been explained to you and you consent to your personal information being transferred for the purposes as specified herein. VIDEO MONITORING: We may use video monitoring in our facilities for health, safety and security reasons. If you have any queries in relation to the use of monitors operating in and around our facilities, please contact us. PLEASE KEEP YOUR CONTACT DETAILS UP TO DATE: You promise to tell us promptly if you change your address, phone number, email, bank account, credit card information for payment or if there is a change to any other personal information relevant to your membership with us. This includes any matters that affect the health or safety of you or others.
Netflix's new docuseries, The Innocent Man, examines two true crime cases in Ada, Oklahoma, during the early '80s. One of them involves the murder of Denice Haraway, for which Karl Fontenot and Tommy Ward were convicted. However, Tommy Ward updates from 2018 show that, in the three decades since, he's been pushing to appeal his case. The release of The Innocent Man docuseries seems to be the biggest update about Ward within the last few years. Prior to its premiere, perhaps the biggest news to come out regarding Ward's incarceration was an Oklahoman article about Fontenot in 2015, in which Ward's attorney, Mark Barrett, told the outlet he was planning to appeal Ward's conviction and seek exoneration. In the same article, the Oklahoman reported that Fontenot's own appeal was denied because Pontotoc County District Judge Tom Landrith ruled that too much time had passed since his original conviction. But while Fontenot's appeal was unsuccessful, Barrett said that he would file for appeal on behalf of Ward on different grounds. However, there doesn't appear to have been any news about an attempted appeal since that article was published, so it's unclear if Barrett followed through, and if so, where Ward's case stands now. In the trailer for The Innocent Man, multiple subjects allege Ward's confession in Haraway's case was coerced. (Bustle reached out to the Ada Police Department for comment on these claims, but did not receive a response by the time of publication). John Grisham, who wrote the book The Innocent Man is based on, has also spoken out about his belief in Ward's innocence. "Tommy Ward broke down after a long night of abusive interrogation. When he cracked, he decided to give the police the sensational story they wanted, knowing full well that a complete investigation would clear him," he told The Marshall Project in 2017. "It doesn't work that way. He's been in prison for 31 years." Ward and Fontenot have long claimed their confessions were coerced. In a 1986 report from the Oklahoman, Ward's lawyer, Don Wyatt, alleged that details of their confessions were "fed to them by the police," and that interrogators "kept going over and over on [Ward and Fontenot] until they gave those stories to get them off their backs." Further, some of the information Ward and Fontenot gave police did not match details of the case, such as what Haraway was wearing when she was killed and the fact that she was shot, not stabbed, as Ward and Fontenot claimed. Records from the Oklahoman Department of Corrections confirm Ward is still in prison, where he is serving a life sentence. His most recent photograph in the department's database is dated July 12, 2018. Despite the great deal of time that Ward has spent in prison, subjects featured in The Innocent Man are pushing for him to be exonerated. Whether or not he will ever be released remains to be seen. The Innocent Man's six-episode first season premieres on Netflix on Dec. 14.
President Judge Bowman and Judges Crumlish, Jr., Wilkinson, Jr., Rogers, Blatt, DiSalle and Craig. Judges Mencer and MacPhail did not participate. Opinion by President Judge Bowman. Author: Bowman [ 41 Pa. Commw. Page 372] By complaint in equity, which we shall consider as a petition for review in the nature of a complaint in equity, Pa. R.A.P. 1503, Mechanicsburg Area School District seeks injunctive and other relief against the Secretary of Education, the Secretary of Revenue, the State Treasurer and the Auditor General. The gravamen of the School District's petition is alleged error on the part of the Secretary of Revenue, and reliance thereon by the Secretary of Education, in determining the "market value/income aid" ratio -- one of three basic elements of the state subsidy formula -- as mandated by the Act of August 24, 1977 (Act No. 59), P.L. 199, 24 P.S. §§ 25-2501 to 2502.3, which amended the Public School Code of 1949, Act of March 10, 1949, P.L. 30, as amended, 24 P.S. § 1-101 et seq. Act No. 59 requires the Secretary of Revenue to determine and certify to the Secretary of Education the "personal income valuation" of each school district for purposes of reimbursement which shall be "the valuation of the total taxable income determined under Article III of the Act of March 4, 1971 (P.L. 6, No. 2), known as the 'Tax Reform Code of 1971'. . . ." By separate counts against each respondent, the School District alleges its personal income valuation was incorrectly computed by the Secretary of Revenue, and relied upon by the Secretary of Education in determining its state subsidy. It seeks a recalculation [ 41 Pa. Commw. Page 373] of its personal income valuation, recomputation of its subsidy payable (now paid) for the school year 1977-78 and injunctive relief against each of the respondents in their respective administrative and fiscal capacities with respect to the subsidy year in question. Before us at this juncture are preliminary objections by the respondents asserting (1) want of jurisdiction of this Court to entertain and act upon the petition for review for failure of the School District to join all other school districts of the Commonwealth as indispensable parties, and (2) laches. "In Pennsylvania, an indispensable party is one whose rights are so directly connected with and affected by litigation that he must be a party of record to protect such rights, and his absence renders any order or decree of court null and void for want of jurisdiction." Columbia Gas Transmission Corp. v. Diamond Fuel Co., 464 Pa. 377, 379, 346 A.2d 788, ... Our website includes the first part of the main text of the court's opinion. To read the entire case, you must purchase the decision for download. With purchase, you also receive any available docket numbers, case citations or footnotes, dissents and concurrences that accompany the decision. Docket numbers and/or citations allow you to research a case further or to use a case in a legal proceeding. Footnotes (if any) include details of the court's decision. If the document contains a simple affirmation or denial without discussion, there may not be additional text. Buy This Entire Record For $7.95 Download the entire decision to receive the complete text, official citation, docket number, dissents and concurrences, and footnotes for this case.
This invention generally relates to jack-up offshore platforms of the type that include a platform structure, a plurality of support legs extending into the water down to the ocean floor, and jacking units on the platform structure for engaging such support leg to raise and lower the platform structure relative to the surface of the water. More particularly, the present invention relates to a truss leg structure for use in jack-up offshore platforms which have a plurality of mutually parallel and laterally spaced apart column members rigidly interconnected and adapted for use with a rack and pinion jacking system. The need for additional oil, gas and other mineral resources has in recent years brought about increased activity in the exploration for and recovery of such resources from offshore locations. In order to perform the necessary exploration drilling, production drilling, and in some instances petrochemical-processing, it is necessary to provide a platform structure from which such activities can be conducted. At locations having substantial oil and gas reserves, the approach taken in recovering the minerals has been to erect a permanent platform at the proposed well site and lay pipelines between the platform and the shore to transport the oil and gas to onshore storage or processing facilities. The fixed platform is, however, for the most part limited to situations where the reservoir is large enough to amortize the investment. As the erection of a fixed platform requires a large capital investment, and consequently the offshore hydrocarbon reservoir must be sufficiently large to justify the investment, there are a large number of smaller wells with respectable quantities of oil and gas which cannot be produced profitably. In order to improve the profitability of the small or marginal offshore reservoirs, mobile offshore platforms have been designed to permit a single platform structure to be utilized at several successive reservoirs. There are many different jack-up platforms in use today. However, a typical jack-up platform has a buoyant hull that permits transporting of the platforms to well site and has separate support legs that project upwardly from the hull during transport. Once the platform has reached the desired location, the support legs are lowered into contact with the ocean floor and the platform is jacked up to a level above the surface of the water. When operations are finished at a particular location, the structure can be jacked down and moved to another site. Prior art jack-up-type offshore platforms have typically utilized a trussed leg structure of triangular or other polygonal cross-sectional configurations. The leg structure comprises a plurality of cylindrical column members that are mutually parallel and spaced apart laterally to define the corners of the geometrical shape in which the leg structure is configured. The column members are interconnected by crossbracing that extends between adjacent column members, making the leg a unitary structure. Each column member has a dual rack member in the form of a heavy flat metal bar of elongated rectangular transverse cross-section mounted to it and extending parallel through the longitudinal axis of the column member. Two sets of rack teeth are provided, each extending along a different one of the two edges of the rack member. In jack-up platforms in the prior art having this type of leg structure, it has been taught to provide for each rack member a jacking unit having a rigid frame carrying the motor and gear reduction equipment arranged to drive pinions arranged in pairs. The axes of rotation for each pair of pinions are usually mutually parallel, horizontal and spaced apart, with the pairs being lined vertically one above the other. Each pair of pinions are spaced apart by a distance that permits each pinion to be meshed with a different one of the sets of rack teeth on a rack carried by a column member. Typical leg supported offshore platform structures with jacking apparatus of this type are disclosed in U.S. Pat. No. 3,743,247 and U.S. Pat. No. 3,606,251, both to Willke, et al. Offshore platforms utilizing jacking systems of the rack-and-pinion type typically have three or four separate support legs of equal length. In the case of a triangular or rectangular leg configuration, the number of separate sets of jacking systems can be from a minimum of nine or as many as sixteen. It is not only quite expensive to provide such a large number of jacking systems, but it is also necessary to synchronize the operation of each jacking unit on a particular leg structure to prevent unequal vertical displacement of one portion of the leg structure relative to the remainder. Other jack-up platform leg structures now in the prior art include those disclosed in U.S. Pat. No. 2,924,077 to LeTourneau; U.S. Pat. No. 3,183,676 to Heitkamp; U.S. Pat. No. 3,851,482 to LeTourneau et al; and U.S. Pat. No. 3,367,119 to Rybicki. The leg structure used in all of the aforementioned patents utilizes one outwardly facing rack surface on each column of the truss leg. Although single faced rack surfaces reduce the amount of material needed to construct the support leg structure, the construction cost remains great. The Rybicki patent also discloses a triangular truss-type leg provided with racks on two columns of the leg.
package xorm import ( "database/sql" "strings" ) type SqlTemplatesExecutor struct { session Session sqlkeys interface{} parmas interface{} err error } func (sqlTemplatesExecutor SqlTemplatesExecutor) Execute() ([][]map[string]interface{}, map[string][]map[string]interface{}, error) { defer sqlTemplatesExecutor.session.resetStatement() defer sqlTemplatesExecutor.session.Close() if sqlTemplatesExecutor.err != nil { return nil, nil, sqlTemplatesExecutor.err } var model_1_results *ResultMap var model_2_results sql.Result var err error var sqlStr string sqlModel := 1 if sqlTemplatesExecutor.session.isSqlFunc == true { err := sqlTemplatesExecutor.session.Begin() if err != nil { return nil, nil, err } } switch sqlTemplatesExecutor.sqlkeys.(type) { case string: sqlkey := strings.TrimSpace(sqlTemplatesExecutor.sqlkeys.(string)) if sqlTemplatesExecutor.parmas == nil { sqlStr, err = sqlTemplatesExecutor.session.engine.SqlTemplate.Execute(sqlkey) if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } sqlStr = strings.TrimSpace(sqlStr) sqlCmd := strings.ToLower(strings.Split(sqlStr, " ")[0]) switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkey).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkey).Execute() sqlModel = 2 default: sqlModel = 3 } } else { switch sqlTemplatesExecutor.parmas.(type) { case []map[string]interface{}: parmaMap, _ := sqlTemplatesExecutor.parmas.([]map[string]interface{}) sqlStr, err = sqlTemplatesExecutor.session.engine.SqlTemplate.Execute(sqlkey, parmaMap[0]) if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } sqlStr = strings.TrimSpace(sqlStr) sqlCmd := strings.ToLower(strings.Split(sqlStr, " ")[0]) switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkey, &parmaMap[0]).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkey, &parmaMap[0]).Execute() sqlModel = 2 default: sqlModel = 3 } case map[string]interface{}: parmaMap, _ := sqlTemplatesExecutor.parmas.(map[string]interface{}) sqlStr, err = sqlTemplatesExecutor.session.engine.SqlTemplate.Execute(sqlkey, parmaMap) if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } sqlStr = strings.TrimSpace(sqlStr) sqlCmd := strings.ToLower(strings.Split(sqlStr, " ")[0]) switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkey, &parmaMap).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkey, &parmaMap).Execute() sqlModel = 2 default: sqlModel = 3 } default: return nil, nil, ErrParamsType } } resultSlice := make([][]map[string]interface{}, 1) if sqlModel == 1 { if model_1_results.Error != nil { return nil, nil, model_1_results.Error } resultSlice[0] = model_1_results.Result if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Commit() if err1 != nil { return nil, nil, err1 } } return resultSlice, nil, nil } else if sqlModel == 2 { if err != nil { return nil, nil, err } resultMap := make([]map[string]interface{}, 1) resultMap[0] = make(map[string]interface{}) //todo all database support LastInsertId LastInsertId, _ := model_2_results.LastInsertId() resultMap[0]["LastInsertId"] = LastInsertId RowsAffected, err := model_2_results.RowsAffected() if err != nil { return nil, nil, err } resultMap[0]["RowsAffected"] = RowsAffected resultSlice[0] = resultMap if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Commit() if err1 != nil { return nil, nil, err1 } } return resultSlice, nil, nil } else { resultSlice[0] = nil } case []string: sqlkeysSlice := sqlTemplatesExecutor.sqlkeys.([]string) n := len(sqlkeysSlice) resultSlice := make([][]map[string]interface{}, n) parmaSlice := make([]map[string]interface{}, n) if sqlTemplatesExecutor.parmas == nil { for i, _ := range sqlkeysSlice { sqlTemplatesExecutor.session.isSqlFunc = true sqlStr, err := sqlTemplatesExecutor.session.engine.SqlTemplate.Execute(sqlkeysSlice[i]) if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } sqlStr = strings.TrimSpace(sqlStr) sqlCmd := strings.ToLower(strings.Split(sqlStr, " ")[0]) switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysSlice[i]).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysSlice[i]).Execute() sqlModel = 2 default: sqlModel = 3 } sqlTemplatesExecutor.session.isSqlFunc = true if sqlModel == 1 { if model_1_results.Error != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, model_1_results.Error } resultSlice[i] = model_1_results.Result } else if sqlModel == 2 { if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } resultMap := make([]map[string]interface{}, 1) resultMap[0] = make(map[string]interface{}) //todo all database support LastInsertId LastInsertId, _ := model_2_results.LastInsertId() resultMap[0]["LastInsertId"] = LastInsertId RowsAffected, err := model_2_results.RowsAffected() if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } resultMap[0]["RowsAffected"] = RowsAffected resultSlice[i] = make([]map[string]interface{}, 1) resultSlice[i] = resultMap } else { resultSlice[i] = nil } } } else { switch sqlTemplatesExecutor.parmas.(type) { case []map[string]interface{}: parmaSlice = sqlTemplatesExecutor.parmas.([]map[string]interface{}) default: if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, ErrParamsType } for i, _ := range sqlkeysSlice { sqlTemplatesExecutor.session.isSqlFunc = true sqlStr, err := sqlTemplatesExecutor.session.engine.SqlTemplate.Execute(sqlkeysSlice[i], parmaSlice[i]) if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } sqlStr = strings.TrimSpace(sqlStr) sqlCmd := strings.ToLower(strings.Split(sqlStr, " ")[0]) if parmaSlice[i] == nil { switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysSlice[i]).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysSlice[i]).Execute() sqlModel = 2 default: sqlModel = 3 } } else { switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysSlice[i], &parmaSlice[i]).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysSlice[i], &parmaSlice[i]).Execute() sqlModel = 2 default: sqlModel = 3 } } sqlTemplatesExecutor.session.isSqlFunc = true if sqlModel == 1 { if model_1_results.Error != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, model_1_results.Error } resultSlice[i] = model_1_results.Result } else if sqlModel == 2 { if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } resultMap := make([]map[string]interface{}, 1) resultMap[0] = make(map[string]interface{}) //todo all database support LastInsertId LastInsertId, _ := model_2_results.LastInsertId() resultMap[0]["LastInsertId"] = LastInsertId RowsAffected, err := model_2_results.RowsAffected() if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } resultMap[0]["RowsAffected"] = RowsAffected resultSlice[i] = make([]map[string]interface{}, 1) resultSlice[i] = resultMap } else { resultSlice[i] = nil } } } if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Commit() if err1 != nil { return nil, nil, err1 } } return resultSlice, nil, nil case map[string]string: sqlkeysMap := sqlTemplatesExecutor.sqlkeys.(map[string]string) n := len(sqlkeysMap) resultsMap := make(map[string][]map[string]interface{}, n) parmasMap := make(map[string]map[string]interface{}, n) if sqlTemplatesExecutor.parmas == nil { for k, _ := range sqlkeysMap { sqlTemplatesExecutor.session.isSqlFunc = true sqlStr, err := sqlTemplatesExecutor.session.engine.SqlTemplate.Execute(sqlkeysMap[k]) if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } sqlStr = strings.TrimSpace(sqlStr) sqlCmd := strings.ToLower(strings.Split(sqlStr, " ")[0]) switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysMap[k]).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysMap[k]).Execute() sqlModel = 2 default: sqlModel = 3 } sqlTemplatesExecutor.session.isSqlFunc = true if sqlModel == 1 { if model_1_results.Error != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, model_1_results.Error } resultsMap[k] = model_1_results.Result } else if sqlModel == 2 { if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } resultMap := make([]map[string]interface{}, 1) resultMap[0] = make(map[string]interface{}) //todo all database support LastInsertId LastInsertId, _ := model_2_results.LastInsertId() resultMap[0]["LastInsertId"] = LastInsertId RowsAffected, err := model_2_results.RowsAffected() if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } resultMap[0]["RowsAffected"] = RowsAffected resultsMap[k] = make([]map[string]interface{}, 1) resultsMap[k] = resultMap } else { resultsMap[k] = nil } } } else { switch sqlTemplatesExecutor.parmas.(type) { case map[string]map[string]interface{}: parmasMap = sqlTemplatesExecutor.parmas.(map[string]map[string]interface{}) default: if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, ErrParamsType } for k, _ := range sqlkeysMap { sqlTemplatesExecutor.session.isSqlFunc = true sqlStr, err := sqlTemplatesExecutor.session.engine.SqlTemplate.Execute(sqlkeysMap[k], parmasMap[k]) if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } sqlStr = strings.TrimSpace(sqlStr) sqlCmd := strings.ToLower(strings.Split(sqlStr, " ")[0]) if parmasMap[k] == nil { switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysMap[k]).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysMap[k]).Execute() sqlModel = 2 default: sqlModel = 3 } } else { parmaMap := parmasMap[k] switch sqlCmd { case "select": model_1_results = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysMap[k], &parmaMap).Query() sqlModel = 1 case "insert", "delete", "update", "create", "drop": model_2_results, err = sqlTemplatesExecutor.session.SqlTemplateClient(sqlkeysMap[k], &parmaMap).Execute() sqlModel = 2 default: sqlModel = 3 } } sqlTemplatesExecutor.session.isSqlFunc = true if sqlModel == 1 { if model_1_results.Error != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, model_1_results.Error } resultsMap[k] = model_1_results.Result } else if sqlModel == 2 { if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } resultMap := make([]map[string]interface{}, 1) resultMap[0] = make(map[string]interface{}) //todo all database support LastInsertId LastInsertId, _ := model_2_results.LastInsertId() resultMap[0]["LastInsertId"] = LastInsertId RowsAffected, err := model_2_results.RowsAffected() if err != nil { if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Rollback() if err1 != nil { return nil, nil, err1 } } return nil, nil, err } resultMap[0]["RowsAffected"] = RowsAffected resultsMap[k] = make([]map[string]interface{}, 1) resultsMap[k] = resultMap } else { resultsMap[k] = nil } } } if sqlTemplatesExecutor.session.isSqlFunc == true { err1 := sqlTemplatesExecutor.session.Commit() if err1 != nil { return nil, nil, err1 } } return nil, resultsMap, nil } return nil, nil, nil }
Q: Adding multiple executables in CMake My code in a C++ project is organised as follows I have several .cpp and .h files which contains my classes I have several .cxx files which have to be compiled against the .cpp files and some external libraries. Now, each of the .cxx files have a main() method, so I need to add a different executable for each of these files having the same name as the file. Also, these .cxx files might not get linked to the same external libraries. I want to write this build in CMake, in which I am kind of a newbie, how do I go about this? A: My suggestion is to tackle this in two phases: Build a library from the .cpp and .h files, using add_library Iterate through all your .cxx files and create an executable from each, using add_executable and foreach Build the library This could be something as simple as file( GLOB LIB_SOURCES lib/.cpp ) file( GLOB LIB_HEADERS lib/.h ) add_library( YourLib ${LIB_SOURCES} ${LIB_HEADERS} ) Build all the executables Simply loop over all the .cpp files and create separate executables. # If necessary, use the RELATIVE flag, otherwise each source file may be listed # with full pathname. RELATIVE may makes it easier to extract an executable name # automatically. # file( GLOB APP_SOURCES RELATIVE app/.cxx ) file( GLOB APP_SOURCES app/.cxx ) foreach( testsourcefile ${APP_SOURCES} ) # I used a simple string replace, to cut off .cpp. string( REPLACE ".cpp" "" testname ${testsourcefile} ) add_executable( ${testname} ${testsourcefile} ) # Make sure YourLib is linked to each app target_link_libraries( ${testname} YourLib ) endforeach( testsourcefile ${APP_SOURCES} ) Some warnings: file( GLOB ) is usually not recommended, because CMake will not automatically rebuild if a new file is added. I used it here, because I do not know your sourcefiles. In some situations, source-files may be found with a full pathname. If necessary, use the RELATIVE flag for find( GLOB ... ). Manually setting the source-files requires a change to CMakeLists.txt, which triggers a rebuild. See this question for the (dis-)advantages of globbing. I generated the testname using a string( REPLACE ... ). I could have used get_filename_component with the NAME_WE flag. Concerning "general" CMake info, I advise you to read some of the broad "CMake Overview" questions already asked here on stackoverflow. E.g.: CMake tutorial What are the dusty corners a newcomer to CMake will want to know?
Q: Authentication failed in curl request to list plans I am trying to list the billing plans in my PayPal https://developer.paypal.com/docs/api/subscriptions/v1/#plans_list this is the example in the developer.paypal.com about the request to list all the plans in my sandbox curl -v -X GET https://api.sandbox.paypal.com/v1/billing/plans?page_size=2&page=1&total_required=true \ -H "Content-Type: application/json" \ -H "Authorization: Bearer Access-Token" The document says that I can use Authorization: Basic <client_id>:<secret> so what I did is this: curl -v -X GET https://api.sandbox.paypal.com/v1/billing/plans?page_size=2&page=1&total_required=true \ -H "Content-Type: application/json" \ -H "Authorization: Basic qwerty:zxcvbn" I just replaced my client id and secret id in the example, and I got those from my account's sandbox here: If I use that curl in my git bash I get this error: { [244 bytes data] 100 244 100 244 0 0 177 0 0:00:01 0:00:01 --:--:-- 177{"name":"AUTHENTICATION_FAILURE","message":"Authentication failed due to invalid authentication credentials or a missing Authorization header.","links":[{"href":"https://developer.paypal.com/docs/api/overview/#error","rel":"information_link"}]} How come I still get an "Authentication failed due to invalid authentication credentials" even as I added my correct sandbox ids? A: The oAuth URI is https://api.sandbox.paypal.com/v1/oauth2/token So your call should be something like curl -v https://api.sandbox.paypal.com/v1/oauth2/token \ -H "Accept: application/json" \ -H "Accept-Language: en_US" \ -u "client_id:secret" \ -d "grant_type=client_credentials" More info on https://developer.paypal.com/docs/api/get-an-access-token-curl/
Jyanen Or Jian Nen? The asian astrological sign for the year 2013 is the snake (black snake or water snake). It is called Jyanen (snake year) in Japanese and the new year just began a few days ago. A few weeks before that sensei uncovered the theme for the year which is the Chinese sword, 劍. The Chinese sword (“jian” in Chinese, 劍) is called Ken (剣) in Japan. Having followed sensei’s teachings for many years I am used to his interesting way of interchanging kanji and his ability to create deep meanings in an apparent shallow sentence or aphorism. The beauty of Japanese language is that one (often him) can play endlessly with the sounds and say different things while using the same sounds. As you know, Hatsumi Sensei is very fond of puns and interchanging kanji. If we follow his reasoning or at least his “wicked mind” (another邪念 janen)- we can say that as Ken is called Jian in China, maybe we should understand the year of the snake 蛇年 (jyanen) as being also the year of the Chinese sword 劒年 (Jian nen). Until last summer sensei used to say that in 2013 we would be studying yari but then we are studying Chinese sword! So what happened? Here we can only guess. During the dkms sensei purchased a rare painting of Amateratsu in her cave (see post concerning that on this blog) that he exposed during training. Maybe this is what triggered him for changing the yearly theme and move to the study of the Chinese Ken. Jyanen (year of the snake) sounds like jiannen (year of the Jian). But do you know that there is a connection between the Jian/Ken and Amateratsu no Kami the sun goddess of the Kojiki (Japanese mythology)? Kojiki reminder: Because of Amateratsu’s brother, Susanô, the sun goddess decided not to get out anymore of her cave. Consequence: there was no more sun on earth. All the gods gathered and decided to organise dances and music to please the goddess. They finally succed and Amateratsu came out again, this is why every morning the sun rises and gives light to mankind. So, shortly after the cave incident Susanô went to fight a hydra with eight heads. Like our Hercules of the Greek Mythology he had a hard time but he finally killed the monster. After his victory Susanô found a sword (the famous “Kusanagi no Tsurugi”) inside the tail of the hydra. Susanô decided to give it to Amateratsu to settle their dispute over the cave incident. This is why these two events are linked historically or at least in Japanese mythology. But this is not all. Amateratsu was the grandmother of Ninigi no Mikoto, the first emperor of Japan and gave him this Ken, the mirror and the jewel (the three regalia of the Japanese Emperor) to show everyone that he was supported by the gods. This is the origin of the imperial power, and the proof of the link of the Emperor to the gods. As a side note, Wikipedia explains that “the Imperial Regalia of Japan (三種の神器 Sanshu no Jingi / Mikusa no Kandakara), also known as the Three Sacred Treasures of Japan, consist of the sword Kusanagi (草薙劍 Kusanagi no Tsurugi), the mirror Yata no Kagami (八咫鏡), and the jewel Yasakani no Magatama (八尺瓊曲玉). The regalia represent the three primary virtues: valor (the sword), wisdom (the mirror), and benevolence (the jewel).” When Amateratsu gave the sword Kusanagi to the Emperor she said it was to chase the demons, establish peace and restore unity. This transmission of power from the sun goddess to the first emperor is quite similar to the transmission given to Hatsumi sensei by the late Takamatsu sensei. On the makimono this year at the side of the Shinden is written a sentence of Takamatsu sensei: “Kami Ori Tatara no Hôken Tamarite Tôyô Ashi ara Rokuni Arabaru no Takamatsu Sensei Tamawari”. Or “The divine protecting sword, is transmitted from Takamatsu to Hatsumi sensei to destroy evil and create peace and unity”. Myths always carry symbols and we can easily understand here that, symbolically, the gods, by giving Kusanagi to the first emperor were in fact “transmitting their power” to mankind. From this day on, humans were to take responsibility for their own destiny. That was the beginning of our civilization. When Takamatsu sensei gave the nine schools to Hatsumi sensei he did the same: he transmitted this power to Hatsumi sensei. And we can imagine that this is what sensei is doing now, he is giving us back our freedom of action. And the reason why he is doing that is, once again, hidden inside the kanji. The year of the Ken which is 劒年 (jiannen) can also be written as 自案年 (ji-an-nen – self thought year) or the year where we have to think on our own, i.e. to be the master of our destiny, to decide for ourselves and be responsible for our actions. All over these years, Hatsumi sensei has created a dôjô to bring us to this level: this is the Bujinden, the place (palace?) for the transmission. Thank you sensei for your trust. I sincerely hope that many of us will seize this chance to become a Bujin, a true being. Arnaud… Awesome read filled with many great insights both to this years training and to the wisdom that Soke truly offers. About 10 years ago Soke told me that the year that he taught this method of the sword would perhaps be his most revealing and most important. So let’s all pay attention to what Arnaud writes and what Soke transmits. Very well done Richard Van Donk
#!/bin/bash echo "kubectl grouplogs cr composition" echo "kubectl grouplogs cr connections" echo "kubectl grouplogs service" echo "kubectl grouplogs helmrelease"
Q: Bayes-Nash equilibrium and correctness of beliefs Define a Bayesian game as follows: $$G = \left\langle I, \left(A_i,T_i,(p_{t_i})_{t_i \in T_i}, u_i \right)_{i \in I} \right\rangle$$ $I$ is the set of players $A_i$ is the action set for player $i$, $T_i$ is the set of possible types for player $i$, $p_{t_i} \in \Delta(T_{-i})$ is player $i$'s beliefs regarding the types of the other players. $(T_{-i}=\times_{j \ne i}T_j)$ $u_i : A \times T \rightarrow \mathbb{R}$ is player $i$'s utility function Then a Bayes-Nash equilibrium is defined as follows: A (pure) Bayes-Nash equilibrium is a profile of choice functions (or strategies) $(\sigma_i:T_i \rightarrow A_i)_{i \in I}$ such that, $\forall i \in I, \forall t_i \in T_i, \forall a_i \in A_i$, $$\sum_{t_-{i}}p_{t_i}(t_{-i}) \cdot u_i(\sigma_i(t_i), \sigma_{-i}(t_{-i}); t_i, t_{-i}) \geq \sum_{t_-{i}}p_{t_i}(t_{-i}) \cdot u_i(a_i, \sigma_{-i}(t_{-i}); t_i, t_{-i}) $$ where, for every $t_{-i}, \sigma_{-i}(t_{-i}) = (\sigma_j(t_j))_{j\ne i}$. And now my question: Am I correct that this implies that, in a BNE, every player (or rather, every type of every player) best responds given their beliefs about the types of other players, but that there is nothing in a BNE that pins down the beliefs a player (or type of player) has on the types of other players? That is to say, in a BNE, a player (or type of player) could have a degenerate belief (putting full probability on some $t_j^$ for player $j$) in an equilibrium in which $t_j \ne t_j^$? Put more simply, can a type of player's beliefs about the type of another player be wrong in a BNE? A: I think your definition is incorrect, or at least incomplete. Usually, in a Bayesian game, there is assumed to be a prior distribution on $T$ (where $T = \times_i T_i$). This distribution is called the "common prior" and it is assumed to be common knowledge that types are drawn according to this distribution. In this case, each player $i$'s belief $p_i$ is given by Bayesian updating on $T_i$ and this prior; and in BNE player $i$ must be best-responding to this belief. The assumption of a common prior and Bayesian update rule (which is what gives this solution concept its name, after all) mean that players cannot be wrong, merely underinformed. In other words, a player with posterior belief $p_i$ is correct about the distribution of types of other players conditioned on her own, even though she does not know which realizations they have. Edit. Osborne and Rubenstein's text mentions that it is possible to define a more general game in which each player has a different prior distribution (there is no common prior). So your definition does match their most general definition. I suppose that in such a case two players may hold incompatible views, hence you could say that someone must be incorrect. That all being said, the vast majority of Bayesian games assume a common prior.
Short Movie Reviews Dean (2016) Kevin Kline – Most experienced actor and a Oscar winner. It is one of his casual and cool performance.Demetri Martin – A young man with different faces in this movie performed as a actor, director and writer. Great jobOthers – GoodStory – A true bonding and caring between father and son after their loss of wife and mother. Cinematography – AwesomeScreenplay – BalancedDirection – CreativeDean (2016) – The core of the story is when you miss someone in life and you will find them in some-other way but still the true love always sticks in us. Love is unlimited and it can be shown in different ways from different person which makes this movie special. Excellent artistic work, Humorous movie and Cool background music.
Thoughts on Life and Christ from a Stay at Home Mom Christianity Post navigation So I’m on day seven of Jillian Michael’s 30 Day Shred, the workouts are finally getting easier although I’m still doing modified push-ups. I think I can handle moving up to level two. I stepped on the scale before my shower hoping….hoping…and nothing. I still haven’t lost any weight. I’ve been doing okay eating, well maybe I had an egg biscuit sandwich yesterday, that probably wasn’t good, and maybe I did have some chocolate chips before bed last night. Okay, I need to start tracking my food, really start tracking it, and planning what I’m going to eat BEFORE I eat it. God, you are a God who can do ALL things, You can do anything! Please help me to get rid of this ugly stomach, that’s all I’m asking, just this one thing….and you know what pops into my head? Coffee. Really God, coffee? This doesn’t sound like it’s from the bible, I’m not sure that’s You speaking, maybe it’s just my subconscious putting weird things into my head. Coffee isn’t supposed to be that bad for you. I’m Swedish, coffee and cinnamon rolls are what I’ve been consuming since I was 4 yrs old. Home isn’t home without the smell of coffee brewing. I do put about an eighth cup of cream and a spoonful of sugar in it, and I do drink it all day long when it’s cold out. Water is gross. I don’t want to give up my coffee!!!!! But I do want to get rid of this ugly ugly stomach. But this weekend we’ll be travelling. Okay, giving it up on Monday. God, I’m going to need your help, and I’m going to need a new smell in my house to replace coffee smell. Please make my house smell like home if I have to give up coffee. Small steps forward against the wind Forces trying to pull me back into the abyss A dark place of fear and demons It would be so easy to turn around Keeping my eyes upwards steady on the light Falling forwards to hope Believing His promises and not the buttery smooth lies -Sis We made paper mermaid tales and got stressed out by the timers on free online typing games for kids today. My husband put “The Chronicles of Narnia” on the girls’ ipod for them to listen to at night and they love it. We made a pumpkin cake with cream cheese frosting and I bought a new pencil box for Cara. Hers has been broken and had a huge hole in it for over a month and she never complains, she just turns it upside down so the crayons don’t fall out, I love that about her; it is a strength and a weakness. I gave lots of hugs and cuddles and throwings into the air today, we had a relaxed morning cleaning and playing and an intense afternoon doing workbooks, flashcards, and reading books. My husband and I are sharing the frosting container from the cake, I’d thought of a new diet rule that I can’t have anything sweet unless I lick it off of him, but I haven’t told him about it yet, he might reinforce it :). My supper turned out amazing tonight, the chicken was juicy and cooked just right and the homemade French fries were delish too. That doesn’t happen too much, so I’m reveling in it. I don’t understand when to love the world despite their sin and when to withdraw from them because of the awfulness of their sin. I wish it were easier, we are told to love them, but sometimes what they do and say are so painful to watch that it is hard to be around them. I am thankful for good friends who I can go to when I have questions, I’m thankful for my family, and for our ten butterflies flying in a netted cage in our living room, I’m thankful for hamsters that keep two year olds excited about life, I’m thankful for busy days at home with my family. Thoughts The kids are really starting to look forward to summer, we will be starting homeschooling and I’m a little nervous about getting started correctly. I’m thinking of changing their tv schedule so that they watch less. It was really nice to sit and cuddle with my husband on the couch last night, I’ve been missing him lately. Prov has started waking Cara up in the mornings after we let her get up, they both like it. The girls are really going to have fun playing in the puddles later this morning, I think the kiddie pool filled up with water from the rain also, as soon as the sun comes out, I think I’ll send them outside with their rain boots on! Exercise and Diet It thundered and rained heavily this morning so I didn’t go for my long run, instead I told my husband he could sleep in while I watched the kids and I think I’ll go run after he wakes up. I’ll probably try to just get 5 miles in instead of 8. Yesterday was another good eating day! Today is going to be one of my two “cheat” days for the week. I have cinnamon rolls rising for breakfast and we will be having dessert after supper tonight (but those are the only two times I get to cheat today, not all day long!) Goals Sew up tear in the couch (for real this time) Do some planning for homeschool and activities this summer Family Fun Night Relax and play run play piano read books to kids laundry/dishes/pick-up toys Family Fun Night We are going to start doing family fun nights on Saturdays at our home. This just means a bible memory verse, a game, and a dessert. Tonight we will be memorizing Proverbs 30:5 (make memory cards), playing bingo and making ice cream sundaes. Reflection It was good to spend time as a family today, I think it was all of our favorite part of the day. Prov made bingo a little difficult, she kept knocking people’s cards around which would mess up their markers. I took Cara and Hope out to pick wildflowers and we made bouquets, they picked so many we gave bouquets to our neighbors too. We also picked some blackberries and ate them on our ice cream tonight, yum! I tried to take the girls down to the river to play, but we saw a snake and left right away, I just don’t know this town we are in well enough to know if their snakes are poisonous or not, but I do know that water snakes usually are bad ones. Kept to the eating plan well and I ran about 4.5 miles this morning. Read stories, played with girls lots, I think they appreciated all the extra attention. They are sharing a bed tonight just because they want to, very sweet. Yesterday was a good eating day and my run this morning went well. My friend wants me to go on a long run with her this weekend, 8 miles, I’m a little scared, my husband said he doesn’t mind watching the kids while I go. Some cute things the girls did yesterday -Prov spent quite a long time playing and laughing with a fly in the window. -Cara covered herself in hair-tyes and accessories and rode her scooter through the house all morning. (Yesterday she told me she wants to be a stunt skateboarder and I told her to start out on her scooter.) -We had to come home twice because we couldn’t get Cara’s shoes right before preschool. The first ones were too small, the next ones were two right feet (one her sister’s). The third pair she didn’t like, but she wore them anyway. -After naptime, Prov insisted that I carry four stuffed animals to the couch along with her to cuddle. -Hope has told me that she plans to marry Nicholas when she gets older, he has told her he is a farmer boy and he loves God (she really wants horses), so her criteria for a husband has been met by him. Goals for Today eat strictly low carb spend time playing with girls go to playgroup make supper sew up tear in couch plan an at-home date night for my husband and myself don’t play on the computer during my evening hours “To fully experience our fulfillment in Christ and fulfill His will for our lives, we must come to the point where we give our whole selves to Him –our freedom, our time, our bodies, all of our possessions and gifts–trusting Him to show us how to use all that we are for His glory. To sacrifice means to give up or surrender something of value. We are living sacrifices, which means that moment by moment, out of our worship of Him, we are to surrender our own needs and expectations for the greater value of pleasing our Lord…..He clearly states, again and again, that if we lose our lives for Him, we will find our lives–the joy and fulfillment we long for.”The Mission of Motherhood by Sally Clarkson I’ve kind of been feeling the tug of my heart to go more this direction, but I’ve been ignoring it in favor of my own desires. To be honest, I know exactly what things I do in my life that are frivolous and don’t bring me satisfaction..only temporary amusement, but I keep doing them anyway just because I want to. Today I want to give my time to my daughters, I want to put puzzles together with them, spend an hour reading every book in the house, bake something delicious, teach them some bible stories and love on them all throughout the day without them having to beg for my attention. God, help me to put my wants aside and go get what I really need. Help me to find my life. Show me what it really means to sacrifice my desires. Amen Following God’s will has always been confusing for me, but I’m starting to figure out how to do it slowly and here are some tips that I have learned along the way that might help you. I think there are several different ways to follow God’s will depending on our situation and circumstances. 1. There are some general commands in the bible that are God’s will for everyone as a life purpose and we must use these to direct our lives. We are all called to evangelize through loving other people, this is to be one of our main goals in this life. Also we are all called to glorify God and to love Him forever.“Come, follow me,” Jesus said, “and I will make you fishers of men.” Mark 1:17 2. First and foremost, we must go to the bible. If the bible says something, then it is God’s will. For instance, the bible tells us not to murder. So no matter what we think, we should not murder someone. That is God’s will. We must weigh whatever we “think” God is telling us to do with the scripture and make sure they match. If they don’t match, it is a good sign that it is NOT God’s will. 3. If you are unsure about a decision, ask trusted Christian friends or elders for advice. It is very easy to get confused or emotionally wrapped up in something and a wise outside source is often a good idea. 4. The third way to follow God’s will is more vague and requires some faith. One of my friends described it to me by saying, “you have to hold your hand out and tell God that whatever He decides to place into your hand, you will obey, but be careful, if you say yes, He might give you something bigger to do next time and if you say no, He might not ask you again”. I thought it was crazy when she told me that, it was just too naive and trusting and I didn’t think God would speak to me that way, but I had to give it a try; I didn’t want to miss out on anything. So that evening I went for a walk and I actually held my hand out and asked God if He wanted to place anything in it. It didn’t happen immediately After waiting awhile, I passes a church and I felt strongly that God wanted me to go inside and pray. He didn’t tell me what to pray for, just to go inside and pray. I did not want to do it. I’d never been in that church before, I didn’t know anything about it, I didn’t even know anyone who went there. So I walked right by the church and told myself the door was probably locked and why would God ask me to do something so stupid anyway. Then I worried, “what if He doesn’t ask me to do anything again?” Can I take that risk? What if it REALLY is God talking to me and telling me this? So I turned around and went into the church (the door wasn’t locked), I went into the sanctuary, sat in one of the pews and just bowed my head and prayed about whatever came into my head. It wasn’t special or anything. That’s how it started with me, and now I try to keep my hands open to God and if I “feel” a sense that He is telling me to do something, I try to obey. I don’t always obey, sometimes I intentionally ignore Him and this is wrong. Even if I don’t understand the reasoning behind it, as long as it’s not against the bible, I obey. Usually it is something small, and often it is Him telling me to stay away from something that is harmful to me.And your ears will hear a word behind you, “This is the way, walk in it,” whenever you turn to the right or to the left. Isaiah 30:21 5. I think the 5th way that we need to consider God’s will is through signs and dreams. I do believe that God speaks to us this way, but I also think we need to be highly skeptical of this form of communication and test, test, test it because I think that Satan uses this against us too. Sometimes Satan gives us a dream or idea and makes us think it is from God when it is really from Satan. Or Satan will try to make us dependent on signs and not on trusting God alone to communicate with God. 6. Sometimes God doesn’t tell us what to do, we just have to decide for ourselves what we want to do (refer back to #1). Like for instance our career. We can pray to Him and ask Him what He wants us to do, and not get an answer, so we might have to wait or we might just have to choose something and trust that He will guide us gently where to go with it. Following God’s will is not something to stress over too much, He is sovereign and will get you where you need to go, but make sure that your faith in Him is strong. Spend time with Him daily in His word and worshipping Him, the better you know Him, the easier it will be to listen to Him. God bless you on your journey..
PhoneGap Build - Build native, cross-platform mobile apps in the cloud - jasongullickson http://build.phonegap.com/ ====== zoowar Interesting, but if you have to write html/js/css, why not just use html5 and get cross-platform apps without the extra step. ~~~ jasongullickson The first reason is that in the app stores, you can get paid :) Second would be that PhoneGap exposes some functionality you can't get at with a standard web app (some hardware sensors, contact data, etc.). Third would be exposure. Most folks are now familiar with shopping for apps in the app store. While you can accomplish the same thing by visiting a website and "adding to home screen" or whatever, the "workflow" isn't as well known.
# 2010 June 15 # # The author disclaims copyright to this source code. In place of # a legal notice, here is a blessing: # # May you do good and not evil. # May you find forgiveness for yourself and forgive others. # May you share freely, never taking more than you give. # #*********************************************************************** # set testdir [file dirname $argv0] source $testdir/tester.tcl source $testdir/lock_common.tcl source $testdir/malloc_common.tcl set otn 0 testvfs tv -default 1 foreach code [list { set s 512 } { set s 1024 set sql { PRAGMA journal_mode = memory } } { set s 1024 set sql { PRAGMA journal_mode = memory; PRAGMA locking_mode = exclusive; } } { set s 2048 tv devchar safe_append } { set s 4096 } { set s 4096 set sql { PRAGMA journal_mode = WAL } } { set s 4096 set sql { PRAGMA auto_vacuum = 1 } } { set s 8192 set sql { PRAGMA synchronous = off } }] { incr otn set sql "" tv devchar {} eval $code tv sectorsize $s do_test pager2-1.$otn.0 { faultsim_delete_and_reopen execsql $sql execsql { PRAGMA cache_size = 10; CREATE TABLE t1(i INTEGER PRIMARY KEY, j blob); } } {} set tn 0 set lowpoint 0 foreach x { 100 x 0 100 x 70 22 96 59 96 50 22 56 21 16 37 64 43 40 0 38 22 38 55 0 6 43 62 32 93 54 18 13 29 45 66 29 25 61 31 53 82 75 25 96 86 10 69 2 29 6 60 80 95 42 82 85 50 68 96 90 39 78 69 87 97 48 74 65 43 x 86 34 26 50 41 85 58 44 89 22 6 51 45 46 58 32 97 6 1 12 32 2 69 39 48 71 33 31 5 58 90 43 24 54 12 9 18 57 4 38 91 42 27 45 50 38 56 29 10 0 26 37 83 1 78 15 47 30 75 62 46 29 68 5 30 4 27 96 33 95 79 75 56 10 29 70 32 75 52 88 5 36 50 57 46 63 88 65 x 44 95 64 20 24 35 69 61 61 2 35 92 42 46 23 98 78 1 38 72 79 35 94 37 13 59 5 93 27 58 80 75 58 7 67 13 10 76 84 4 8 70 81 45 8 41 98 5 60 26 92 29 91 90 2 62 40 4 5 22 80 15 83 76 52 88 29 5 68 73 72 7 54 17 89 32 81 94 51 28 53 71 8 42 54 59 70 79 x } { incr tn set now [db one {SELECT count(i) FROM t1}] if {$x == "x"} { execsql { COMMIT ; BEGIN } set lowpoint $now do_test pager2.1.$otn.$tn { sqlite3 db2 test.db execsql { SELECT COALESCE(max(i), 0) FROM t1; PRAGMA integrity_check; } } [list $lowpoint ok] db2 close } else { if {$now > $x } { if { $x>=$lowpoint } { execsql "ROLLBACK TO sp_$x" } else { execsql "DELETE FROM t1 WHERE i>$x" set lowpoint $x } } elseif {$now < $x} { for {set k $now} {$k < $x} {incr k} { execsql "SAVEPOINT sp_$k" execsql { INSERT INTO t1(j) VALUES(randomblob(1500)) } } } do_execsql_test pager2.1.$otn.$tn { SELECT COALESCE(max(i), 0) FROM t1; PRAGMA integrity_check; } [list $x ok] } } } db close tv delete #------------------------------------------------------------------------- # pager2-2.1: Test a ROLLBACK with journal_mode=off. # pager2-2.2: Test shrinking the database (auto-vacuum) with # journal_mode=off # do_test pager2-2.1 { faultsim_delete_and_reopen execsql { CREATE TABLE t1(a, b); PRAGMA journal_mode = off; BEGIN; INSERT INTO t1 VALUES(1, 2); ROLLBACK; SELECT * FROM t1; } } {off} do_test pager2-2.2 { faultsim_delete_and_reopen execsql { PRAGMA auto_vacuum = incremental; PRAGMA page_size = 1024; PRAGMA journal_mode = off; CREATE TABLE t1(a, b); INSERT INTO t1 VALUES(zeroblob(5000), zeroblob(5000)); DELETE FROM t1; PRAGMA incremental_vacuum; } file size test.db } {3072} #------------------------------------------------------------------------- # Test that shared in-memory databases seem to work. # db close do_test pager2-3.1 { forcedelete test.db sqlite3_shutdown sqlite3_config_uri 1 sqlite3 db1 {file:test.db?mode=memory&cache=shared} sqlite3 db2 {file:test.db?mode=memory&cache=shared} sqlite3 db3 test.db db1 eval { CREATE TABLE t1(a, b) } db2 eval { INSERT INTO t1 VALUES(1, 2) } list [catch { db3 eval { INSERT INTO t1 VALUES(3, 4) } } msg] $msg } {1 {no such table: t1}} finish_test
Morning!! I show you a lookbook with the outfit I am wearing. As I think this is a great idea to show you my outfits, I will try to make some videos from now on :). I have to say this is the comfiest combination ever, Zara kids’ t-shirt (that will be my new favorite shop soon) and ankle length pants. I hope you like it!! Thanks for your comments and thank you so much for stay there, day by day!!
Uninsured? Here's how you still can get health care If you don't have insurance, getting health care is more difficult these days — but not impossible. Patients typically line up hours before the doors open at any of the free medical clinics run by Shepherd's Hope. Last year, more than 3,300 people were turned away because the group's volunteer doctors and nurses can treat only a limited number of patients on any given day. "The system is burdened," said Cindi Kopelman, president of the Orlando nonprofit. "It's not easy to get in right away; some locations are busier than others. Some people will try to come back; some people will end up in the [emergency room], and some will just do nothing. A lot of people go without medical care for a long, long time." A variety of state and private groups offer low-cost or no-cost health services in Orange and neighboring counties. Most clinics focus on primary care, or the type of complaints seen by a family doctor: earaches and urinary-tract infections. Sore throats and stomach viruses. Even diabetes and kidney stones. Each organization is different. Many groups charge patients low fees based on their incomes. Others have no restrictions and charge nothing. Florida Hospital runs a thrice-weekly Community After-Hours Clinic inside a small building near its main hospital in Orlando. There is no charge, but care is limited to the first 25 to 30 people each day. Louis Federick, 52, was making his second visit to the clinic on a recent evening. He learned about it after seeking help at the hospital's emergency room. The Pine Hills man doesn't have health insurance — or any interest in going back to the ER. "I'd rather come here," said Federick, who recently lost his job in a catering business. "You don't have the wait, and the doctors are nicer." He got treatment for shingles, a painful rash triggered by the same virus that causes chickenpox, and then a flulike illness he probably picked up from his grandchildren. Federick is lucky. His diagnosis and treatment were straightforward. Difficulties arise for similar patients with chronic or life-threatening conditions. Josephine Mercado, who runs the nonprofit Hispanic Health Initiatives, remembers a recent breast-cancer patient granted emergency Medicaid coverage through the state. It lasts 45 days. When her Medicaid ran out, so did her chemotherapy. "She had to scramble around for weeks and weeks before she could find anyone who would take her," Mercado said. "That's terrible, and it's happening all the time." Dental services, mental-health treatment, even eye exams and routine screenings such as colonoscopies are scarce for the poor or uninsured. County health departments, a longtime source of care for the vulnerable, are straining under greater demand. The Orange County Health Department saw a 15 percent increase in its uninsured clients, who rose from 5,524 in 2007 to about 6,500 in 2008. The lack of insurance will cause many to postpone treatment and create more problems down the road, said Dr. Kevin Sherin, department director. "People who don't have insurance are always going to think, 'What am I going to have to pay to see a doctor?'" he said. "By the time they are seen, they're going to end up sicker, with more-intensive costs."
Each time you start BITBOX it creates a fresh Bitcoin Cash blockchain just for you. This blockchain doesn’t connect to the actual $BCH network and only consists of blocks and transactions which you create locally so it’s quick and responsive. You can mine new blocks with the click of a button and the coinbase reward will go to the first account in your BITBOX wallet. Click on any block to learn more. Blocks Each block consists of an index, timestamp, array of transactions and the previous block’s header. All of these are hashed and stored as the block’s header. Click on any transaction to learn more. Transactions Transactions consist of the value, transaction encoded as hex, timestamp, hash, inputs and outputs. Inputs Inputs consist of hex, inputPubKey and script. Outputs Outputs consist of hex, outputPubKey and script. Search BITBOX now has a search field at the top right into which you can input a block height/hash or a transaction hash/rawHex and you’ll be redirected to that page. Summary BITBOX is a full local $BCH blockchain. It’s quick and responsive. You can now easily explore your BITBOX via search or clicking from block to transaction. More info
Win $5,000 on O-Cedar Sweepstakes O-Cedar is organizing a contest and is giving you the chance ton win $5,000 in form of check! So, if you want to win cash online then why not entering this amazing contest that will make you richer by $5,000.
“Pretty Little Liars” recap (2.14): One Dragon at a Time When I was writing our AfterEllen.com 2011 TV review, I had to go digging through a whole year’s worth reader comments on recaps, lots of which were all, “I can’t believe you said that one thing about Rachel Berry! I disagree with my whole soul! I hope a meteor explodes down from heaven and hits you in the face!” After reading about one gajillon of those furious quips, I was feeling kind of discouraged and kind of disheartened and so my attitude wasn’t very sparkly when I started watching my Pretty Little Liars winter premiere screener. I was just sort of like, Siiiiigh. Here we go again. Near the end of the episode, though, I was legitimately sitting six inches away from the TV shouting like a lunatic, and my phone rang and I answered it all, “WHAT!” And it was Shay Mitchell calling for an interview I’d scheduled with her. She said, “Hey Heather, it’s Shay!” And I was like, “Oh my God, why are you phoning me at a time like this? You’re about to get stabbed to death by A! Run! RUUUUUUN!” ‘Cause that’s what this show does to me. It makes me forget I’m supposed to be taking notes or thinking of clever things to write. It makes me forget people want to set me on fire if I don’t say nice things about their favorite character or ship. Heck, most of the time it makes me forget I’m watching a fictional story inside a magic box. It’s like I’m eleven years old, just gasping and wringing my hands and hollering at Emily about, “Stop getting murdered, you gorgeous fool!” And Aria and Spencer about, “What the actual hell are you wearing?!” Or gently caressing Hanna’s face on the screen, because what kind of soulless hell-demon would shout at Hanna? Luckily, Shay Mitchell is forever warm and gracious, so she laughed at me and told me it was (mostly) going to be OK and she didn’t even hang up the phone. Also, though, Pretty Little Liars isn’t just enormously (addictively!) entertaining; it’s really smart television. But subversively smart. Quietly smart. By this time in Glee‘s second season, the show was already so off the rails that practically everyone on earth was just hanging around hoping for morsels of Naya Rivera to fall like manna from heaven. And even though Veronica Mars turned in one of the best inaugural seasons of murder-mystery television in the history of the world, it also lost its damn mind in season two. It’s not an easy thing to frame a TV show with a narrative device and then move that frame along while moving each of the characters’ personal lives along inside it. But Pretty Little Liars is doing it brilliantly. In fact, its trajectory is the exact opposite of Glee. I think Marlene King has made the correct decision to offer up the identity of “A” at the end of this season. It takes the stakes to eleven, makes every moment more delicious and sinister. It’s like one of those word problems in physics class. Like we’re the train leaving the station heading to Rosewood and there’s also a train leaving Rosewood station heading toward us. We’re both going fifty-eleven gazillion miles per hour. When will we meet? The finale. What will happen? A colossal explosion. Guaranteed. Previously on Pretty Little Liars, “A” buried Annabeth Gish alive in her brown Tory Burch boots and then offered a shovel for the Liars to dig her out of her death pit, except for psyche! — Annabeth Gish was really enjoying a delicious cup of coffee with the Risen Mitten and that shovel was the one hundred percent guaranteed no questions asked absolutely irrefutable unequivocal murder weapon that did the murdering of the murdered Alison DiLaurentis. Definitely. Probably. Most likely. Twenty percent sure. The penalty for being found with a murder weapon in Rosewood — even if the murder investigation is closed due to Ian’s ghost confessing to the killing like ten months ago — is community service. The Liars are sad-sacking around the highway in orange jumpsuits scowling at each other and stabbing empty soda cans with those trash stick things. Spencer is picking up garbage twice as fast as everybody else, of course, because Spencer doesn’t half-ass anything. Probably she’s going to add it to her college applications: Valedictorian of Litter. Emily tries to talk to her about some techniques for bartering with A the Rattlesnake, which causes Hanna to throw up her hands and run around in circles screaming about “Snaaaaakes!” Spencer tells Emily to stop saying dumb ideas out loud and Emily says she’ll say all the dumb ideas out loud she wants to, thank you very much, and next thing you know they are pelting garbage at each other and rolling around on the ground like a pair of common hoodlums. Aria stomps her foot all, “You guys!” And Hanna’s over there all, “Snaaaaaakes!” And Aria stomps her foot again: “Stop it!” And Hanna’s still: “Snaaaaakes!” Officer Garrett watches from his squad car with an evil grin and like a giant tub of movie theater popcorn in his lap.
Day Treatment Info.! I stayed up late last night (couldn't sleep anyway) and searched on line, read through school regulations, etc. First thing this morning I called to get info. on the day treatment program that is at the place where I had difficult child's MDE done last year. Here is the way they work... The average stay is 4-6 months. Some kids are pretty much just severe behavior problems; not all, and they do have several that are bipolar. They have a psychiatrist on board to work on medications and have a lot of therapy- individual, group, art, music, etc. They run all year but the minimal school component is not there at all in July. They said if he came in the summer, we would need to address his IEP not having extended school year requirement. Basicly no insurance, including medicaid (which I need to get difficult child on), will cover the cost. It has to be initiated by the sd - they refer it to CSA (whatever that is) of the locality, and they determine if they will pay for it. It takes about a month or so, usually, to get them in once the sd makes a referral. I asked about difficult child's probable need to go to summer school and if he went to this program in the summer, would this keep him on track to progress to next grade next school year. He said they turn the grades over to the school and the regular school determines grade placement. He, also, said the sd that difficult child is in has referred many students to their program because they just aren't equipped to deal with BiPolar (BP) issues. Oh, boy, did that make my blood boil. Last year they were trying to send my son to a school that was all "bad behavior" issues- kids throwing chairs acroos the room- no substantial diagnosis's like we see on this board- and the best one out of three that they had me look at had about a 20% success rate of the kid ever going back to a regular school (even if in Special Education classes). I went to the school in Aug. last summer and showed, in writing, difficult child's new diagnosis of BiPolar (BP), then the MDE evaluation that said they don't think it is true BiPolar (BP), but difficult child has mood cycling and needs to be on mood stabilizer until he learns skills and strategies for stressors, etc. Wouldn't you think the people at school- or at least ONE PERSON could have mentioned to me in all their conversations about how they can't/wont deal with these issues at their school, even if it is written in his IEP, that they can refer him to a treatment facility that will? That's ok, I think it will help my case. Anyway, I called the ed. spec. from this place, who was on the MDE team and who also had accompanied me to one of difficult child's iep meetings in Jan to see what he thinks. He was in a hurry and told me to call him again Mon. morning when he can pull the file and we can discuss it. I want to ask him if he thinks this would be the right place for difficult child. My main concerns are 1) since difficult child's number of violations has so drasticly reduced this school year, he doesn't meet their definition of "behavior problem" anymore. Great! However, when he "shuts down" at school or home, or becomes so overwhelmed with work sometimes to the point of crying and raging - he rips his work up and it never gets completed. Then, there are the few times that has has DONE the projects or homework and refuses to turn it in because, in his words, "it just isn't good enough" (sometimes- many times- he does the work and turns everything in normally). I thought this meant that according to IDEA, this fell into the category of a disorder that effects behavior that effects ability to learn. Well, the teachers give him zeros for all this lack of completed work. This is why he is failing so much this year- along with memory and processing issues that might be a part of medications but I'm not sure- he showed deficiencies in these areas on his testing before. The school says they don't help with this because he doesn't have a Learning Disability (LD). Anyway- I need to know how this place defines "behavior" and if they can help difficult child learn strategies and coping skills to deal with these emotions and cycles, rather than giving him a behavioral contract that just rewards and punishes what he is capable of doing now, without helping him learn how to be capable of more. Does that make sense? And my second worry- if the sd is involved in getting this paid for, my gut tells me there is a catch. Like, how much control does this give the sd over difficult child and my lives for the rest of the time he is in this sd? Does this mean more pressure to sign any iep they stick in front of me in the future? I think I will take a little time this weekend to see if I can find another local day treatment program that insurance will cover. In the meantime, any thoughts, suggestions, advice, pointers will be appreciated!! by the way- Smallworld, you have kept me going this week! Thanks so much!! I'll be checking back in but haven't been on much this evening- difficult child and I are spending some quality time together- (at least that is the plan LOL) KLMNO, I don't know that the sd would have much say once they recommended him but maybe they would. Our sd will not recommend anything like that due to costs. They set up their own alternative schools. I spoke with the ed spec from MDE team today- this is also the place of the day treatment. He says he isn't sure difficult child needs this yet- that it sounds more like the sd isn't in compliance with the law. He offered to attend another iep meeting and help with fba and bip and help make sure it is written to help difficult child learn skills, not just reward and punish. He said this would be a necessary procedure to ensure best chances for sd to refer difficult child to day treatment and to help a due process case. He also, said if he was the parent going thru this, he would be extremely angry at this sd. I assured him that I am. So, I emailed case amanger at school to ask for iep meeting and told him this ed spec would be there and that GAL and PO might also be there. I am thinking I should also contact Special Education attny and update him and see if he wants to be there, or at least find out what steps I should make sure are followed to help our case in due process, or to get them to refer difficult child to day treatment if he needs it. K, I haven't been around all weekend so I am just reading this thread for the first time tonight. Glad to hear of all the progress you're making. The day treatment program my daughter attended was based at the children's hospital in our area. The day treatment program my son attended was based at a psychiatric hospital in Northern Virginia (I think it's too far from where you live). Have you checked into children's hospitals or psychiatric hospitals in your area? I'm trying to check on that type of day treatment, Smallworld. I have to cahnge our medication insurance due to my employer not paying it anymore (I had too much time off work because of all this). Anyway, the MDE was done at and the day treatment is at a university hospital that has a specialty area for kids with mood disorders. The head of it all is supposed to be an authority on this, although they have a different psychiatrist who deals with the students at the day treatment. So, on the one hand, it would be better to find a place that insurance paid for instead of sd. On the other hand, this place offers the most expertise and the ed spec seems to be willing to become an advocate for us. This place is listed in the well-known books for mood disorders/bipolar and they have not billed my insurance company or me one penny- I could be wrong, but that leaves me with the impression that they are giving us their best professional shot at helping. First, I would definitely call the sped lawyer. Your SD is not in compliance! Your difficult child should qualify for the day treatment program under an ED diagnosis, so make sure that the IEP states that instead of OHI (which is where they place most of our difficult children). Your school district has to put your child into a learning situation in which he is actually learning. As a teacher I can understand the teachers giving your difficult child a zero on assignments that are not turned in. However, if he's considered SE, then it is there responsibility to find out why the assignments are not turned in and to make sure that he has the help he needs to complete the assignments in a timely manner. It sounds like this isn't being done. It took me almost two years, but I did get my difficult child into a school that has a day treatment program attached to it. The SD pays for the tuition (it's a nonpublic school) and provides door to door transportation as well. This is the law per IDEA. We had to go through several schools and an expulsion before he got sent here, and the school district has agreed that in retrospect, the expulsion should never have occurred. But at least he's found a soft place to land, and is doing well. You should also be aware that the school district will keep trying the least cost solution until it is clear that it isn't working, and that the Warrior Parents are pushing back. This particular school takes kids from two counties and several school districts, which is often the case in these types of schools. Keep pushing and you'll get there. NEVER leave the Special Education attorney out of the loop. The only exception would be if you have proof the attorney is being rewarded by the school district for not pushing your difficult child's best interests. I think you are doing a great job! I hope this IS a good program. The school can be reported to the state dept of ed and other places for being out of compliance. I would also do that. You might even take your story to the media, this school situation seems very abusive, just based on what you have experienced.
[bitcoin-dev] Proof-of-Stake Bitcoin Sidechains Hi ZmnSCPxj, Just to clarify, my design does not specify the source of voting power, so it is agnostic to whatever system you want to derive stake or valdiator set membership from. Your idea of timelocking Bitcoin is interesting, I am eager to find a solution where holding Bitcoin is enough to get voting power. It's possible there may be an issue with the fact that the Bitcoin is not slashable (although their voting power is), meaning a validator who double-signs cannot have their Bitcoin removed from them. However their UTXO can be blacklisted which does make their attack costly since they lose out on the time-value of their stake. Our current thinking for the source of stake is to pay out stake to Bitcoin merged-miners although I'll definitely do some more thinking about timelocked Bitcoin as stake. On Fri, Jan 18, 2019, 5:42 PM ZmnSCPxj <ZmnSCPxj at protonmail.com wrote: > Good morning Matt, > > It seems to me much more interesting if the stakes used to weigh voting > power are UTXOs on the Bitcoin blockchain. > This idea is what I call "mainstake"; rather than a blockchain having its > own token that is self-attesting (which is insecure). > It seems to me, naively, that the same script you propose here can be used > for mainstake. > > For instance, the sidechain network might accept potential stakers on the > mainchain, if the staker proves the existence of a mainchain transaction > whose output is for example: > > <sidechain identifier> OP_DROP > "1 year" OP_CHECKSEQUENCEVERIFY OP_DROP > <pubkey> OP_CHECKSIG > > The sidechain network could accept this and use the value of the output as > the weight of the vote of that stake. > > Regards, > ZmnSCPxj > > Sent with ProtonMail Secure Email. > > ‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐ > On Saturday, January 19, 2019 6:59 AM, Matt Bell via bitcoin-dev < > bitcoin-dev at lists.linuxfoundation.org> wrote: > > > I have been working on a design for Bitcoin sidechains using the > Tendermint BFT consensus protocol, which is commonly used to build > proof-of-stake networks (Cosmos is the notable one). > > > > The design ends up being very similar to Blockstream's Liquid sidechain, > since Tendermint consensus is not far off from Liquid's "strong federation" > consensus. > > > > Any feedback about improvements or critical flaws would be greatly > appreciated. The design document is here: > https://github.com/mappum/bitcoin-peg/blob/master/bitcoinPeg.md (that > repo also contains a simplified implementation of this sidechain design). > > > > Thanks for your feedback, > > Matt Bell > -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.linuxfoundation.org/pipermail/bitcoin-dev/attachments/20190118/de50b59d/attachment.html>
Seattle mayor signs KeyArena deal to lure NBA, NHL teams SEATTLE (AP) — Seattle Mayor Jenny Durkan has signed an agreement with a developer to renovate KeyArena so the venue could be ready for an NBA or NHL team. Durkan told reporters Wednesday the deal with Los Angeles-based Oak View Group is the best path for Seattle to get an NHL team and bring back the NBA. OVG CEO Tim Leiweke says his group will work to get a team to join the WNBA's Seattle Storm at KeyArena. OVG would privately finance a $600 million remodel of the aging arena. The deal includes $20 million in cash and in-kind contributions to nonprofit organizations and $40 million for traffic improvements. Durkan says the deal protects taxpayers and is good for the city. She says it does not block other possible arena projects.
Q: Error with MongoDB, Can't locate object method I want to access at my database in this way: my $db = MongoDB::Connection->new or die( "erreur de connection" ); db = $db->chasseur_de_tete; and I get this error: Can't locate object method "chasseur_de_tete" via package "MongoDB::Connection" at ../AbstractExtract.pm line 25. I don't understand why, after search for similar cases, I saw that problemme could be caused by not updating modules (like DateTime). but even after update, I get the same error. Have you some idea please ? Thanks A: The preferred method is to use the MongoClient class and accessors to databases and collections are not built in, they require separate methods to retrieve. use MongoDB; my $client = MongoDB::MongoClient->new(host => 'localhost', port => 27017); my $database = $client->get_database( 'chasseur_de_tete' ); my $collection = $database->get_collection( 'mycollection' ); Also the same code is equivalent for the $client connection: my $client = MongoDB::MongoClient->new(); Which assumes the default values for the connection.
1. Field of the Invention The present invention concerns a lock adapted to be accommodated within the thickness of an opening panel, to be actuated from either side of said opening panel by an operating member and/or a key, and to allow retraction of the latch bolt from the outside only by means of the key, this lock having two nuts rotatable about a common axis and attached to respective corresponding operating members. The present invention is generally concerned with a lock, an espagnolette bolt lock or the like, of the aforementioned type, for doors, French windows or the like. 2. Description of the Prior Art Many different locks of this type are known in themselves and are generally in the form of espagnolette bolt locks adapted to operate simultaneously a latch bolt, a lock bolt and at least one operating link. In locks of this known type the mechanical members or the functions of the lock are controlled differently according to whether the user is on the inside or on the outside of the opening panel fitted with the lock. The objective is to lock the opening panel as soon as the user leaves the room to which it gives access. It is a question of making the lock inviolable by a third party on the outside of the opening panel who does not have the key. The opening panel can be unlocked only with the key. It is the latch bolt that locks the opening panel. Locks of this kind are usually fitted to apartment front doors. One such lock is described in FR-A-2 657 385, for example. This lock includes a conventional nut attached to the inside operating member and which assures all the functions of a conventional espagnolette bolt lock. It also has a second nut attached to the exterior operating member which is adapted to engage with the square shaft operating the first nut through coupling means such that the nut attached to the outside operating member has a lost motion in one direction or the other before it is able to entrain the main nut. This lost motion prevents operation of the latch bolt by the outside operating member. This lock requires the use of a support plate that has to be applied to the exterior face of the opening panel. Also, it is not reversible, i.e. when the lock is fitted to the opening panel it is not possible to choose, from the point of view of an observer regarding the lock accommodated within the thickness of the opening panel, whether the righthand side or the lefthand side should correspond to the exterior of the room to which the opening panel provides access. Other locks of the aforementioned type known in themselves include two conventional nuts. These locks are thicker than conventional locks with the result that they cannot be accommodated in the slot usually made within the thickness of an opening panel. This makes it necessary either to increase the width of the slot, which weakens the opening panel, or to transfer to the exterior of the lock, for example inside cover plates, functions for which the mechanical parts cannot be housed within a standard size lock casing. An aim of the present invention is to eliminate the drawbacks of the systems known in themselves and to propose a lock of the aforementioned type that is very easily and very simply reversible and which enables all of the mechanisms of a lock of this kind to be housed within a standard thickness casing.
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Introduction {#Sec1} ============ It has been about 100 years since the mouse became a premier model organism. This status has been reinforced by the arrival of high-throughput RNA sequencing technologies, making it possible to investigate the regulatory circuits underlying development in detail. However, it is uncertain how closely RNA changes correlate with the operational level of the proteins. In fact, work in plants, yeast, lower vertebrates^[@CR1]^ and mammalian cell lines^[@CR2]^ has revealed a modest correlation. Mouse oocytes and early embryos feature an atypical translational machinery regarded to be poorly competent for mRNA translation ('cytoplasmic lattices' in place of free ribosomes^[@CR3]^). Thus, the impact of transcriptional changes on the embryo proteome is expected to be limited. Indeed, in some cases the mRNA is detected throughout preimplantation development, but the protein is only observed from a certain preimplantation stage onward^[@CR4]^; or the mRNA is degraded soon after fertilization, while the protein persists through the blastocyst stage^[@CR5]--[@CR7]^. Unfortunately, conventional tools for protein analysis such as antibodies (immunofluorescence, immunocytochemistry, western blotting) do not scale well to genome-wide investigations. Large-scale qualitative and quantitative proteomic technologies have matured over the past two decades. In particular, direct measurement of proteins using mass spectrometry (MS) holds great promise as a complement to transcriptomics. Still, current high-throughput protein quantification methods are less sensitive than those for mRNA. Because mammalian oocytes and embryos are small and the size of the detected proteome is directly related to the amount of input material, the analysis of the mammalian oocyte and embryo proteomes with MS was effectively prohibitive until a few years ago. This is in contrast to Xenopus or Drosophila, in which a single or a few oocytes are sufficient to detect \~5,000 proteins^[@CR1],[@CR8]--[@CR10]^. Even in the case of relatively large mammalian oocytes and embryos, such as those of bovines, 100 of them^[@CR11],[@CR12]^ only enabled the detection of \~1,000 and 1,500 proteins. Mouse oocytes and embryos are smaller and, thus, 7,000 oocytes/zygotes were required to identify \~3,000 proteins up to the 1-cell stage in 2010^[@CR13]^, while 3,000 blastocysts were necessary to determine \~2,500 proteins in 2014^[@CR14]^. Very recently, Gao et al. collected samples consisting of 4,000 to 8,000 embryos to distinguish \~5,000 proteins across six developmental stages, from the 1-cell stage to the blastocyst^[@CR15]^. Hence, refraining from mass-killing oocyte donors or producing oocytes from stem cells in vitro^[@CR16]^, mouse embryologists are forced to achieve more with less. Gradual and continuous improvement of our protocols^[@CR17]--[@CR20]^ over several years, including the optimization of buffers and sample collection conditions, have substantially improved our yields. We combined high-throughput liquid chromatography-tandem mass spectrometry (LC-MS/MS) with mRNA sequencing to generate datasets encompassing seven stages of mouse development spanning from the oocyte to the blastocyst. We anticipate that this resource will be key to gaining a greater understanding of the oocyte to embryo transition, and provide two examples of its varied applications: (1) how to query the 'rule' of weak transcript/protein correlation in order to expose exceptions to the rule; and (2) how to expand the list of markers in order to follow the oocyte-to-embryo transition. Our dataset enriches the status of the mouse as a model system in developmental biology with the protein dimension, enabling a better understanding of the gene expression cascade that leads to the phenotype. Results {#Sec2} ======= Ultrastructural data underscore the relevance of a direct examination of the embryonic proteome {#Sec3} ----------------------------------------------------------------------------------------------- To systematically investigate the relationship between the proteome and the transcriptome in the developing mouse, we chose the paradigm of recovering fertilized oocytes in vivo after ovarian stimulation and culturing them in vitro in KSOM(aa) medium under 5% CO~2~ in air (see Methods). This made it possible to continuously monitor the progression of the embryos, to identify and collect stages more precisely, and to allay concerns over the quality of embryos developing inside a hormonally stimulated genital tract^[@CR21],[@CR22]^. In a separate group of embryos used to test for developmental quality, 89.5% (N = 258) of the fertilized oocytes developed to blastocyst and, of these, 42.3% (N = 104) progressed to term (embryo transfer). Typical features of early mouse development, including changes in endoplasmic reticulum (ER) architecture^[@CR23]^ and in ribosome morphology^[@CR24]--[@CR26]^ were recapitulated, supporting the use of our in vitro system to yield embryos that are representative of normal development. In particular, we noted that hexagonal-shaped free ribosomes enabling efficient protein synthesis^[@CR24]--[@CR26]^ are rare prior to the morula stage (see Fig. [1A](#Fig1){ref-type="fig"}). Nevertheless, developmental progression was impeded when cycloheximide (CHX) -- an inhibitor of protein synthesis -- was added to the culture medium (see Fig. [1B](#Fig1){ref-type="fig"}). Briefly, the number of embryos that were able to develop to the next stage was always smaller in the presence of cycloheximide, independently of the developmental stage. Although the numbers have been reported to be sensitive to the exact time when CHX is added to the culture medium and to its concentration, our results are in agreement with previous studies^[@CR27],[@CR28]^ and indicate that protein synthesis is essential for further development of the early embryo.Figure 1In vivo-fertilized, in vitro-cultured mouse oocytes as a source of embryonic material for proteomic analysis. (A) Oocytes and developmental stages were examined in ultrastructure. The density of hexagonal-shaped free ribosomes increases over time during preimplantation development (estimates are based on three sections from three different embryos of each stage). hCG was injected at 5 pm. Indicated under each stage is the number of hours post hCG (hphCG). Micrographs of cytoplasmic lattices (black arrow, "CPL") and free ribosomes (black arrow, "Rb") are shown. (B) The treatment of embryos with cycloheximide (CHX) documents that protein synthesis is necessary for developmental progression to the next stage. For each stage transition, the height of the bars denotes the percentage of embryos developing to the next stage without adding CHX; orange bars denote the same percentage (if any) after treatment with CHX. The numbers under the bars indicate the total number of embryos examined. Together, these data suggest that the impact of transcriptional changes on the proteome may be small, calling for a direct examination of the embryonic proteome. A high-quality proteome of mouse oocytes and preimplantation embryos to a depth of 6,550 proteins {#Sec4} ------------------------------------------------------------------------------------------------- For the proteome analysis we collected and processed a total of \~12,600 oocytes or embryos, in three biological replicates of \~600 oocytes/embryos per developmental stage: unfertilized oocytes, fertilized oocytes with pronuclei, and preimplantation embryos at the 2-, 4-, 8-cell, advanced morula and blastocyst stages (see Methods). The detected proteome comprised 6,550 proteins. Among these, 5,217 proteins were detected in at least two replicates of one or more developmental stages, and 1,709 proteins were detected in all replicates of all developmental stages. Protein abundance measurements (L/H ratios, see Methods) were highly reproducible, with minimum Spearman's rank correlation coefficients between replicates in the range of 0.67 to 0.76 (for the oocyte and 2-cell stage, respectively, see Supplemental Fig. [S1](#MOESM2){ref-type="media"}). Compared to the theoretical proteome (see Supplemental Methods), the 6,550 detected proteins are mainly involved in RNA processing, organelle organization, intracellular transport and cellular metabolism. Although these processes are not exclusive to preimplantation development, they are consistent with the nature of embryonic cleavage as a phase of development during which biomass is not produced de novo but rather reorganized. The complete proteome of the mouse preimplantation embryo is unknown. In order to estimate the completeness of our dataset, we computed the fraction of members of 233 known mammalian protein complexes that are present in our dataset (based on^[@CR29]^, see Supplemental Methods). Since all protein members are required for the function of a complex, undetected members hint at a technical limitation rather than genuine biological absence. The overall median for the fractions of complex members detected in at least one replicate was 0.80, and ranged from 0.75 to 0.80, depending on the developmental stage (see Supplemental Fig. [S2](#MOESM2){ref-type="media"}). In addition, we directly compared our dataset to a very recently published dataset^[@CR15]^ in which 4,830 different proteins were identified in at least one of two replicates from six developmental stages (1-cell to blastocyst). We found that 4,028 (83%) of these proteins are contained in a reduced version of our dataset comprising the same six developmental stages (see Supplemental Fig. [S3](#MOESM2){ref-type="media"}), and that our reduced dataset contains an additional 2,369 proteins (not present in the alternative dataset^[@CR15]^). These findings suggest that we have achieved a high coverage -- of up to 80% -- of the mouse preimplantation proteome. The dynamics of protein expression orchestrating preimplantation development is complex {#Sec5} --------------------------------------------------------------------------------------- As described numerous times on the mRNA level, fertilization is followed by extensive gene expression reprogramming. Nevertheless, the impact of transcriptional changes on the proteome is uncertain. Thus, it has been hypothesized that once activated, a gene continues to be transcribed during later developmental stages, resulting in product accumulation^[@CR30]^ that extends into the proteins. On the other hand, early protein studies of the mouse embryo based on radioactive gel electrophoresis support the hypothesis that protein expression occurs in phases^[@CR31]^. To identify proteins whose expression significantly fluctuates as a function of the developmental stage, we subjected the 5,217 proteins detected in at least two replicates of at least one developmental stage to an analysis of variance (ANOVA, see Methods). This revealed a total of 1,290 (25%) differentially expressed proteins (P-value ≤ 0.05). Among these, 905 proteins exhibited fold changes ≥2 or ≤0.5 between any two developmental stages and 488 proteins did between consecutive developmental stages (see Fig. [2A](#Fig2){ref-type="fig"}). A relatively large amount of the latter -- 253 proteins -- only featured such fold changes during the transition from the morula to the blastocyst (see Supplemental Fig. [S4](#MOESM2){ref-type="media"}). Compared to the detected proteome, the 488 proteins were associated with small molecule and carboxylic acid/carbohydrate metabolism, enzymatic activity; and (extracellular) exosome production (FDR ≤ 0.05, see Supplemental Methods and Table [S1](#MOESM3){ref-type="media"}). These terms are consistent with a sequence of landmark events in mouse preimplantation development, such as the enzymatic transition from metabolic usage of pyruvate to usage of glucose^[@CR32]^, and the paracrine communication between embryos^[@CR33]^ as well as between the embryos and the maternal genital tract^[@CR34]^.Figure 2Differentially expressed proteins across preimplantation development and their functional enrichment. (A) Number of differentially expressed proteins between pairs of consecutive developmental stages (fold-change ≥2 or ≤0.5 between any two developmental stages, P-value ≤ 0.05 from ANOVA). (B) Expression profile of protein clusters. The heatmaps show fold-changes relative to the oocyte scaled using the z-score transformation. The height of the heatmaps is proportional to the number of proteins in each cluster, which is also indicated. The median fold-change across all cluster members for each developmental stage is represented below the heatmaps. (C) Annotation of protein clusters. Gene Ontology (GO) terms associated (FDR ≤ 0.05) with each cluster were summarized with REVIGO^[@CR89]^. REVIGO "representatives" for the individual GO terms are listed on the right of the heatmap. Statistical significance (sum of the -log~10~ FDR of the individual GO terms) for the annotation of each of the clusters is represented using a color gradient. Non-significant associations are represented in gray. Details are presented in Supplemental Table [S2](#MOESM4){ref-type="media"}. Fuzzy clustering of the 772 proteins detected in at least two replicates of each developmental stage that were differentially expressed (P-value ≤ 0.05) and showed a fold change ≥2 or ≤0.5 between any two developmental stages revealed six clusters (see Supplemental Methods and Fig. [2B,C](#Fig2){ref-type="fig"}). The two largest clusters (P5 and P4) comprise proteins whose expression decreases sharply between the morula and blastocyst stages and, compared to the detected proteome, are primarily enriched in monocarboxylic acid metabolism (P5), and nucleobase-containing small molecule metabolism (P4, see Fig. [2C](#Fig2){ref-type="fig"} and Supplemental Table [S2](#MOESM4){ref-type="media"}). Clusters P5 and P4 are approximately mirror images of clusters P6 and P3, respectively. Nevertheless, the proteins in clusters P6 and P3 have their own functional profiles; thus, both clusters are connected to small molecule catabolism and cellular response to indole-3-methanol. The two remaining clusters (P1 and P2) are mirror images of each other and comprise proteins that steadily decrease or increase towards the blastocyst. Proteins in cluster P1 are mainly associated with response to endoplasmic reticulum stress and protein folding, whereas those in cluster P2 are related to GMP biosynthesis, nitrogen compound metabolism and response to starvation. We independently validated our proteomics measurements using immunofluorescence assays. Among the proteins that are present throughout development (albeit more abundant at the beginning) we selected Ddx6, which is associated with processing bodies (P-bodies) involved in the storage and degradation of mRNAs^[@CR35]^. Among the proteins that are detected in oocytes and early stages but become undetected later on, we selected Rc3h1 (roquin), which is an element of a post-transcriptional repression pathway and whose mutation leads to the sanroque phenotype^[@CR36]^. Among the proteins that are not detected in oocytes and early stages but become detected later on, we selected Alppl2, known for its role in the placenta and expressed in the trophectoderm of the preimplantation embryo^[@CR37]--[@CR39]^. The immunofluorescence profiles of Ddx6, Rc3h1 and Alppl2 matched the corresponding proteomics profiles (see Supplemental Fig. [S5](#MOESM2){ref-type="media"}). We further validated our proteomics measurements with enzymatic/immunofluorescence data collected from the literature and/or obtained in the past by our own laboratory on 33 proteins (37 sets of measurements across multiple developmental stages, see Supplemental Table [S3](#MOESM5){ref-type="media"}). Specifically, we quantified the similarity between the expression profiles as determined by enzymatic/immunofluorescence assays and our proteomics pipeline by computing the Spearman's rank correlation. We observed strong correlations (Spearman's rank correlation coefficients between 0.6 and 0.79) for seven proteins (and seven sets of measurements) and very strong correlations (Spearman's rank correlation coefficients between 0.8 and 1.00) for five proteins (seven sets of measurements). The results are significant compared to the random expectation (empirical P-value \< 0.006, see Methods). Taken together, these results reveal systematic changes of the proteome of the embryo as it develops. Furthermore, these changes are complex and unlikely to reflect a mere alternative between monotonic accumulation and stage-specific expression^[@CR30],[@CR31]^. Changes in protein abundances become more prominent as development progresses, and so does the concordance with changes in transcript expression values {#Sec6} ------------------------------------------------------------------------------------------------------------------------------------------------------- Previous transcriptome-based studies of mouse embryonic development have shown that the transcriptomes of oocytes and early embryos can be clearly divided into two groups: prior and after the 2-cell stage^[@CR40]--[@CR42]^. However, the most conspicuous morphological changes during preimplantation development -- compaction and cavitation -- occur well after the 2-cell stage, in the morula^[@CR41]^. To directly compare the oocyte-to-embryo transition on the protein and mRNA levels, we generated our own transcriptome using RNA-seq. For this purpose, we collected and processed a total of 3,424 oocytes or embryos in two biological replicates of 214 oocytes/embryos per developmental stage (see Methods). Anticipating major differences between the early and late 2-cell stage, we considered these separately. We identified a total of 20,535 protein-coding transcripts with at least one read count in any of the samples. As expected, principal component analysis (PCA) of the expression values of the transcripts showed that developmental stages can be distinguished based on their transcriptomes and that most of the variance in the data is contributed by changes at early developmental stages, (see Fig. [3A](#Fig3){ref-type="fig"}). PCA performed on the abundances of the cognate proteins clearly distinguished the developmental stages based on their proteomes, albeit with most of the variance in the data being contributed by changes between the morula and the blastocyst. Indeed, the progression from the 4-cell to the blastocyst embryo aligned almost perfectly with the increase of the first principal component (PC) and explained 31.1% of the variance, while the progression from the oocyte to the 4-cell stage aligned with the decrease of the second PC and explained only 11.8% of the variance (see Fig. [3B](#Fig3){ref-type="fig"}). These findings indicate that in contrast to the transcriptome, in the proteome the oocyte-to-embryo transition is less connected to the 2-cell stage, with the protein expression signature of the blastocyst being particularly further apart from those of the other developmental stages considered. This is in agreement with the establishment of two blastocyst cell populations that differ radically in their metabolic and cell cycle parameters: polarized external cells (the future trophectoderm) and apolar internal cells (the future inner cell mass)^[@CR43],[@CR44]^.Figure 3The proteome and the transcriptome develop differently in time. (A) Principal component analysis (PCA) of the expression values of the detected transcripts that are the cognates of the proteins detected in all replicates at all developmental stages (see B). The first two PCs are shown, with sample points colored by developmental stage. (B) Principal-component analysis of the (log~2~) L/H ratios of the 1,709 proteins detected in all replicates of all developmental stages. Consistent with the PCA, we found a strikingly weak correlation between the changes in protein abundances and the changes in transcript expression values relative to the oocyte, with Spearman's rank correlation coefficients in the range of −0.06 (2-cell early versus 1-cell and 2-cell early versus 2-cell) to 0.41 (morula versus blastocyst, see Supplemental Fig. [S6](#MOESM2){ref-type="media"}). Thus, to explore the relationship between the transcriptome and the proteome in the course of preimplanatation development, we divided the proteins into two disjoint groups according to the direction of change in expression of their cognate transcripts relative to the oocyte (see Fig. [4A](#Fig4){ref-type="fig"}). More precisely, given developmental stages S~i~ and S~j~, we separated the proteins into two groups: (i) those with transcripts up-regulated at S~i~; and (ii) those with transcript down-regulated at S~i~. Then, for each of the two groups of proteins, we estimated the probability of observing a certain protein (log~2~) fold-change at S~j~ relative to the oocyte (see Fig. [4B,C](#Fig4){ref-type="fig"} and Supplementary Methods). For any (log~2~) fold-change x, if the protein expression changes at S~j~ reflect the transcript expression changes at S~i~, the probability of observing a protein with a (log~2~) fold-change of x or less at S~j~ is expected to be greater for those proteins whose transcripts are down-regulated than for those whose transcripts are up-regulated at S~i~. Hence, we quantified the concordance between protein and transcript expression changes by measuring the difference between the areas bounded by the two implicit cumulative distribution functions (CDFs, see Supplementary Methods). This analysis revealed little or no concordance between protein and transcript expression changes at early developmental stages (see Fig. [4D](#Fig4){ref-type="fig"} and Supplemental Fig. [S7](#MOESM2){ref-type="media"}). The concordance, however, increased towards later developmental stages, with expression changes at the morula and blastocyst stages exhibiting the overall highest concordances. Moreover, the concordance for the transcript expression changes at the 4-cell, 8-cell and morula stages was highest for the protein changes at the blastocyst stage, and higher than that between transcript expression changes at the blastocyst stage and protein changes at the blastocyst stage (see Fig. [4D](#Fig4){ref-type="fig"}).Figure 4Changes in the transcriptome are reflected at the proteome level from the morula stage onwards. (A) Number of differentially expressed transcripts at each developmental stage relative to the oocyte (FDR ≤ 1 × 10^−5^ and fold-change ≥2 or ≤0.5 between any two developmental stages). (B) Violin plot showing the distribution of protein (log~2~) fold-changes at the blastocyst stage relative to the oocyte for proteins whose cognate transcripts are down- (blue) or up- (yellow) regulated at the morula stage relative to the oocyte. (C) Cumulative distribution functions (CDFs) of protein (log~2~) fold-changes at the blastocyst stage relative to the oocyte for proteins whose cognate transcripts are down- (blue) or up- (yellow) regulated at the morula stage relative to the oocyte. 1,617 proteins and their cognate transcripts were used to estimate the CDF: 5,565 transcripts were found differentially expressed between the morula and the oocyte; 1,617 of the cognate proteins were detected in both the blastocyst and the oocyte. The CDF for the proteins whose transcripts are up-regulated is shifted to the right compared to the CDF for the proteins whose transcripts are down-regulated. We used the difference between the two areas bounded by the CDFs (shaded) to quantify the shift and, thereby, the impact of the transcript expression changes at the morula stage on the protein expression changes at the blastocyst stage. (D) Heatmap representing the difference in the area of the two CDFs for all pairs of stages. The x-axis of the grid corresponds to transcripts; the y-axis corresponds to proteins. The colors indicate the differences between the two areas bounded by the corresponding CDFs normalized using the entire protein fold-change range. Red indicates a large area, and hence a considerable shift between the distributions, while blue indicates the opposite. Gray indicates the pairs of stages for which we did not estimate the CDFs because less than 25 proteins/transcripts were detected and/or found differentially expressed, respectively. Altogether, these results are in agreement with the increase in the density of free ribosomes that enable efficient protein synthesis only starting at the morula stage (see Fig. [1A](#Fig1){ref-type="fig"}). Despite some de novo transcript synthesis beginning at the 1-cell stage, the paucity of a conventional translation machinery (i.e., the paucity of free ribosomes) prevents transcripts from being robustly translated until the morula stage. Furthermore, despite the steep increase of the free ribosomes, a delay between transcription and translation is still evident at the blastocyst stage. Overall, the majority of the proteins do not match the previously described^[@CR45]^ stage-specific groups of transcripts that support a 'hit and run cascade' model for early embryonic development. Instead, our results document only a moderate amount of change in the proteome, suggesting a steady basal translation of transcripts into proteins, and a role for subcellular compartmentalization and storage in order to make the proteins available when and where required. Exceptions to the rule of weak transcript-protein correlation define a special class of genes with distinct developmental functions {#Sec7} ----------------------------------------------------------------------------------------------------------------------------------- To exemplify how our dataset can be analyzed to better understand the relationship between the transcriptome and the proteome during preimplantation development, we applied fuzzy clustering to the transcripts of the 772 proteins that we had clustered before, and compared the transcript and protein clusters. Specifically, we clustered the (log~2~) fold-changes of the transcripts relative to the oocyte, and found seven clusters (see Supplemental Methods, Fig. [S8](#MOESM2){ref-type="media"} and Table [S4](#MOESM6){ref-type="media"}), which, in contrast to the protein clusters, are often characterized by expression profiles with evident inflection points either at the early or late 2-cell-embryo stage. Next, to quantify the similarity between the protein and transcript clusters, we computed the Pearson's correlation coefficient (r) between their expression profiles in a pairwise manner (see Methods). Out of a total of 42, 14 pairs had a Pearson's correlation coefficient greater than or equal to 0.5, indicating high similarity (see Fig. [5A](#Fig5){ref-type="fig"}). In addition, we assessed the overlap between the members of all pairs of protein and transcript clusters and found that only ten shared more proteins/transcripts than expected by chance (P-value ≤ 0.05, one-sided Fisher's exact test, see Fig. [5B](#Fig5){ref-type="fig"}). The overlap was particularly high among pairs of protein and transcript clusters with similar expression profiles (r ≥ 0.5), with an odds-ratio of 7.8 (P-value = 0.008, one-sided Fisher's exact test), highlighting the fact that, despite the little overall concordance between protein and transcript expression changes, the expression of some proteins indeed mirrors that of their cognate transcripts. Compared to the 772 differentially expressed proteins and their cognate transcripts considered for clustering, the 146 genes that overlap among the pairs of clusters with similar expression profiles were enriched in positive regulation of secretion, reflecting the increasing role of the embryo-derived 'secretome' as development progresses in preparing the ground for the molecular dialogue between the embryo and the maternal endometrium^[@CR34]^.Figure 5Comparison between protein and transcript clusters. (A) Pearson correlation coefficients (in black) computed between the medians of the expression profiles of pairs of protein and transcript clusters. The correlation matrix based on the Pearson correlation coefficients between the median (log2) fold changes across the members of protein and transcript clusters was visualized using the R corrplot package^[@CR90]^. The size and color of the circles are both indicators of the magnitude and sign of the correlation. The matrix was reordered based on hierarchical clustering using the complete linkage method. (B) Significance of the overlap (−log10 P-value calculated using Fisher's Exact test) between the members of protein (rows) and transcript (columns) clusters. Significant enrichments are depicted in red and depletions in blue. The numbers indicate the size of the overlap; overlaps of size zero are not indicated. For the purpose of identifying and characterizing the genes with either strongly correlated or anticorrelated protein and transcript expression profiles, we perused the correlation between the expression profiles across the developmental series of the aforementioned 772 differentially expressed proteins and their cognate transcripts. Despite the expected weak overall correlation (with a median Spearman's rank correlation coefficient across all genes of 0.18), we observed that the distribution of Spearman's rank correlation coefficients was relatively broad (see Supplemental Fig. [S9](#MOESM2){ref-type="media"}). To enhance confidence in the observed profiles, we independently validated our proteomics and transcriptomics data using immunofluorescence and TaqMan (qPCR) respectively (see Methods). We selected three genes among those exhibiting strong negative correlations during preimplantation development and particularly from the 1- to the 4-cell stage: Pdia3, Top1, and DNAjb11. These genes are particularly appropriate in the context of our study, because mutations of Pdia3, Top1 and Dnajb11 interfere with development and prove lethal in homozygosis^[@CR46]--[@CR49]^. The results of the TaqMan assay for Pdia3, Top1 and Dnajb11 correlated positively with those of RNA-seq, as did the results of the immunofluorescence with those of LC-MS/MS (see Supplemental Fig. [S10](#MOESM2){ref-type="media"}), confirming the existence of genes with strongly anticorrelated protein and transcript expression profiles. Finally, with the comfort of the validation data, we moved on to analyze the features of the genes at the extremes of the distribution of Spearman's rank correlation coefficients. Indeed, 7% of the proteins and transcripts exhibited very strong positive correlations (≥0.8) and 3% showed very strong negative correlations (≤−0.8). Among the former are genes involved in ubiquitin metabolism and ubiquitination (Dcun1d5, Uspx9, Dcaf8, Gabarapl2, Rnf114, Stt3b, Ube2g1), signal transduction (Arhgap12, Gna13, Pdpk1), synthesis and modification of DNA (Ctc1, Rrm2, Hmces), splicing and storage of mRNA, including translational initiation (Paip1, Rbm8a, C1qbp, Igf2bp3, Igf2bp2, Xab2, Nhp2). Among the latter are genes involved in membrane vesicle trafficking (Dynlrb1, Epn2, Vta1, Napa, Eea1), chaperoning (Hypk, Fkbp2), and protein glycosylation in association with ribosome binding (Rpn1, Rpn2). Known genes with established roles in development are found in both groups (e.g., Rrm2^[@CR50]^; Igf2bp2^[@CR51]^; Igf2bp3^[@CR52]^; Epn2^[@CR53]^). Overall, the proteins with very strong positive correlations are implicated in dynamic processes, while those with very strong negative correlations represent maintenance systems, with a convergence on signaling. Thus, the release and uptake of vesicles supported by the anticorrelated genes is one way to modulate the concentration of signaling molecules supported by the highly correlated genes, as exemplified by the case of Epn2^[@CR53]^. Proteomic profiles suggest new markers to better follow the oocyte-to-embryo transition {#Sec8} --------------------------------------------------------------------------------------- To show how our dataset can be applied to the identification of new candidate developmental markers, thereby broadening the options offered by morphology/morphokinetics or metabolic markers secreted into the culture medium, we examined the molecular basis of morphological staging. As an illustration, we uncovered new candidate markers to follow the oocyte-to-embryo transition, and thus compared the proteomes of early (oocyte, 1- and 2-cell embryos) and late (4-cell to blastocyst embryos) developmental stages. In particular, we trained and tested linear discriminant analysis (LDA) classifiers. Our results show that protein expression can be used to perfectly separate between early and late developmental stages, with an area under the Receiver Operator Characteristic (ROC) curve of 1.00 (see Supplemental Methods and Fig. [S11](#MOESM2){ref-type="media"}). Samples from the 4-cell stage embryos were close to the decision boundary of the classifier, indicating at this stage the coexistence of features from both previous and later stages, and characterizing the 4-cell stage as a transitional stage. Further, we inferred twenty candidate markers for early and late developmental stages by ranking the proteins according to their relevance for the classification (see Supplemental Methods and Fig. [6A](#Fig6){ref-type="fig"}). These proteins include enzyme modulators, hydrolases and ligases (see Fig. [6B](#Fig6){ref-type="fig"} and Supplemental Fig. [S12](#MOESM2){ref-type="media"}). In particular, Ddx6 is an RNA helicase that has been found in P-bodies^[@CR54]^ and is involved in translation repression and in 2-cell stage embryonic arrest^[@CR35]^. Moreover, some of these proteins (e.g., Ppm1a and Wtap) are mediators of TGF-β and Wnt signaling^[@CR55],[@CR56]^. This finding is compatible with the aforementioned overrepresentation of 'exosome production' among differentially expressed proteins, since signaling pathways rely in part on exosome-mediated mobilization. Interestingly, five of the twenty candidate markers (Calr, Hyou1, Pdia3, Pdia4 and Txndc5) are involved in the protein processing in endoplasmic reticulum (ER) pathway (KEGG identifier mmu04141^[@CR57]--[@CR59]^, odds-ratio = 6.7, P-value = 0.002, Fisher's Exact test, see Fig. [6C](#Fig6){ref-type="fig"}), enlightening the molecular basis of the changes in ER architecture that take place during the transition from oocyte to embryo^[@CR60]^ and that are concomitant to the increase in protein synthesis and folding after EGA^[@CR61]^. We independently validated the expression profiles of the candidate makers using a recently published dataset study^[@CR15]^ as well as additional SILAC data (see Supplemental Methods, Table [S5](#MOESM1){ref-type="media"} and Fig. [S13](#MOESM2){ref-type="media"}). These twenty marker proteins constitute good candidates for further molecular studies of mammalian preimplantation development.Figure 6Classification of early and late preimplantation developmental stages based on protein abundances using Linear Discriminant Analysis (LDA). (A) Heatmap of (log~2~) L/H ratios for 20 candidate protein markers for distinguishing between early and late preimplantation developmental stages. The 20 samples are sorted chronologically according to developmental stage and replicate number. Row clustering was performed with a Pearson correlation-based distance using the complete linkage method. The package pheatmap in R was used for visualization^[@CR91]^. (B) PANTHER14.1^[@CR92],[@CR93]^ protein classification available for seven of the twenty candidate proteins markers (see A). (C) Pathway analysis of genes differentially expressed in the murine "protein processing in endoplasmic reticulum" KEGG^[@CR57]--[@CR59]^ pathway (mmu04141). The boxes representing the proteins/genes are uniformly divided by the number of developmental stages. Replicate averages are laid out chronologically from left to right across all developmental stages considered. The (log~2~) of the fold-change relative to the oocyte is indicated in yellow (up-regulated) or blue (down-regulated). Only proteins/genes among the 764 that were found differentially expressed across the developmental series are colored. The graphical representation of the KEGG^[@CR57]--[@CR59]^ pathway was visualized using the "Pathview" R/Bioconductor package^[@CR94]^. Discussion {#Sec9} ========== In this study, we used MS-based proteomics to generate a proteome dataset with three biological replicates for the preimplantation stages of mouse development, from the oocyte to the blastocyst. This proteome was compared to the cognate transcriptome generated by RNA-seq. With 6,550 detected proteins, ours is the largest developmental proteome of a mammalian species characterized to date, and yet substantially smaller than the number of 20,535 protein-coding transcripts found in the same samples. A similarly conceived, recently published study conducted with a different workflow (TMT instead of SILAC) revealed nearly 5,000 proteins despite the much higher amount of input material used^[@CR15]^. While neither of these datasets is complete, we found that our proteome coverage is in the order of magnitude of up to 80%. Clearly, most mRNAs are stored and only translated when needed, and MS-based proteomics of developmental stages is not solely a matter of input amount: it is largely a matter of sample preparation and preprocessing (e.g., prefractionating) and of the experimental procedures and equipment used. Our main finding when taking the sole proteome into consideration is that the majority of detected proteins change only moderately in abundance during the development from oocyte to morula. Accordingly, we hypothesize that the oocyte-to-embryo transition may last until the morula stage, in contrast to the swifter transition at the transcriptome level, largely accomplished between 2-cell and 4-cell stage. The blastocyst's proteome stands out as markedly different from the proteomes of the preblastocyst stages. This distinction is consistent with the formation of the first epithelium, the trophectoderm. Translation in the preimplantation embryo is limited by the availability of free ribosomes, which are the most active players of a cell's translational machinery, but poorly represented in pre-morula-stage mouse embryos. This explains why an impaired translational machinery does not affect blastocyst formation, but causes blastocyst implantation failure in mice^[@CR62]^. Our main finding when comparing the protein abundance profiles with their cognate transcript profiles is that the projection of the proteome onto the developmental time axis differs from the prediction based on the transcriptome, with the correlation improving as development progresses. While most changes at the protein level explain the transition between the morula and the blastocyst, most changes at the mRNA level explain the transition between the oocyte and the 2- to 4-cell stage. Although the overall protein-mRNA correlation is weak, for a small subset (7%) of the detected proteome, the proteins and their cognate mRNAs have very similar profiles. Moreover, for another small subset (3%) of the detected proteome, the correlation is even negative, with protein levels increasing as transcript levels decrease. These cases may be explained, for example, by the packaging of RNA in granules, such as P-bodies^[@CR63],[@CR64]^, whereby the mRNA broken free from these granules becomes available for both translation and degradation. Notably, we observed a decrease of the P-body protein Ddx6 from oocyte to blastocyst, which together with the increase in free ribosomes would explain the improving protein-mRNA correlation as development progresses. These covariates make the anti-correlated proteins virtually impossible to predict from their transcripts. From our data it is now clear that these anti-correlations are no exceptions, but manifestations of a non-negligible phenomenon in mouse development. Two limitations of our study, apart from artifacts that may occur in our in vitro setting as well as in the in vivo situation (caused by the hormonal status of the genital tract^[@CR15]^), are the following. First, it is difficult to determine whether we failed to detect important proteins. However, our coverage estimates are in the order of magnitude of up to 80%, suggesting that the number of false negatives is bounded. Second, it is not known how the genotype of the gametes influences the composition of the developmental proteome. However, as reported by us^[@CR19]^, the proteomes of the oocytes of different inbred strains (129/Sv, C57Bl/6J, C3H/HeN, DBA/2J), while not identical, only differ in a minor proportion of detected proteins. A third limitation is that our ability to detect proteins in oocytes and embryos depends on the reference we used for SILAC. For example, trophectodermal markers seemed to be underrepresented in our dataset, although several of these proteins were also underrepresented in a study that did not use SILAC^[@CR15]^. In summary, while there is still a long journey ahead until the proteome of mouse preimplantation development is exhaustively enumerated, our dataset constitutes a substantial contribution to closing the gap between 'predicted' phenotype (based on mRNA) and 'actual' phenotype (based on protein) of the mouse embryo. Except for a small subset of genes, proteins and mRNAs have discordant profiles, and this is in agreement with the paucity of free ribosomes observed at early stages of development. Hence, our proteome dataset enables a more direct investigation of mammalian developmental processes. The range of applications of our resource is broad. For instance, it facilitates the molecular definition of embryo quality, which has a major impact on the course of gestation and yet is insufficiently accounted for on the molecular level. While morphological/morphokinetic markers commonly used to predict an embryo's chances to develop can be subjective, our proteomic resource offers specific and measurable molecular candidates to complement the non-molecular markers. Thus, our LDA classifier was able to attain perfect separation between early and late developmental stages based solely on protein abundances. Also, since mammalian oocytes and embryos are produced in the gonads in comparatively small numbers (compared to e.g. Xenopus) and their availability can be subject to ethical and legal restrictions (e.g. in humans), knowing which gene products can be reliably predicted from mRNA has diagnostic value: these mRNA markers allow to make predictions that are backed by the proteins, and they do not require to consume the whole oocyte or embryo since cytoplasmic biopsies can be amplified for mRNA. For example, the cases of anti-correlation in which the mRNA is rapidly degraded after fertilization whereas the protein persist throughout the blastocyst stage, may be cases of candidate maternal genes. In any event, the biological implications of our findings are enormous: although virtually all studies of mammalian preimplantation development rely on transcriptomic data, we show that the predictive value of mRNAs for protein abundances -- which are closer to the phenotype -- is, at most, modest. Methods {#Sec10} ======= Ethics statement {#Sec11} ---------------- This mouse study was performed in accordance with the recommendations of the Federation of Laboratory Animal Science Associations (FELASA) and with the ethical permit issued by the Landesamt fuer Natur, Umwelt und Verbraucherschutz (LANUV) of the state of North Rhine Westphalia, Germany (permit number: LANUV 81-02.04.2017.A432). Metaphase II oocyte collection {#Sec12} ------------------------------ Metaphase II (MII) oocytes of B6C3F1 mice aged 8--10 weeks were collected from the oviductal ampullae after gonadotropin priming with 10 IU of each PMSG and hCG, injected 48 hours apart, at 5 pm, as described^[@CR20],[@CR65]^. In vivo oocyte fertilization and in vitro embryo production {#Sec13} --------------------------------------------------------------- Gonadotropin-primed B6C3F1 females were mated to CD1 males (see Supplemental Fig. [S14](#MOESM2){ref-type="media"}). Pronuclear oocytes were collected from oviductal ampullae at 10am on the day of the copulation plug. By 11am they had been freed of expanded cumulus cells in 50 U/mL hyaluronidase in HZCB medium, and placed in culture in 500 microliters KSOM(aa) medium^[@CR66]^ in 4-well plates (Nunc) under an atmosphere of 5% CO~2~ in air at 37 degrees Celsius. All embryos were staged carefully based on morphology and time spent in culture (beginning at 11am on the day of isolation from the oviduct). Transmission electron microscopy (TEM) {#Sec14} -------------------------------------- Mouse embryos were fixed 2 h at room temperature in 2,5% glutaraldehyde (Merck, Darmstadt, Germany) in 0.1 M cacodylate buffer, pH 7,4 subsequently post-fixed for 2 h in 1% aqueous osmium tetroxide (Plano, Germany), dehydrated stepwise in a graded ethanol series and afterwards embedded in Epon 812 (Fluka, Buchs, Switzerland). Ultrathin (70-nm) sections were prepared with an ultramicrotome (EM UC6, Leica, Wetzlar, Germany), stained for 30 min with 1% uranyl acetate and 20 min in 3% lead citrate. Sections were examined at 50 kV in a Zeiss 109 transmission electron microscope (Zeiss, Oberkochen, Germany). Sample preparation for LC-MS/MS {#Sec15} ------------------------------- For the proteome analysis we collected and processed a total of \~12,600 oocytes or embryos from May 2014 to October 2016. During this time, mouse housing conditions, including diet (Teklad 2020SX), did not change. Specifically, we lysed, in triplicate, an average of \~600 oocytes/embryos per developmental stage: unfertilized oocytes, fertilized oocytes with pronuclei, and preimplantation embryos at the 2-, 4-, 8-cell, advanced morula and blastocyst stages. The samples were true biological replicates that were handled independently from start to end. Protein quantification was performed with our established spike-in SILAC-based labeling pipeline^[@CR17],[@CR19],[@CR20]^. Briefly, oocytes and embryos were deprived of the zona pellucida by pipetting in warm acidic Tyrode solution for 30--60 seconds and then rinsing in protein-free HCZB medium (BSA replaced through polyvinylpyrrolidone 40 kDa). Each sample lysate was then mixed with an equal amount of isotopically labeled (heavy) lysate from F9 embryonic carcinoma (EC) cells^[@CR67]^, digested with trypsin, and subjected to MS analysis. F9 EC cells were grown for several passages in RPMI 1640 medium (PAA, Cölbe, Germany), supplemented with 10% dialyzed fetal calf serum (Sigma, Deisenhofen, Germany), heavy amino acids ^13^C~6~^15^N~2~-L-Lysine (K8) and ^13^C~6~^15^N~4~-L-Arginine (R10; Silantes, Martinsried, Germany) as well as Glutamine and the antibiotics penicillin and streptomycin (Gibco, Darmstadt, Germany). The extent of labeling was 97.8%. The F9 EC cell line was originally isolated by Berstine et al.^[@CR67]^ as a subline of the teratocarcinoma OTT6050 established by implanting a 6 day-old embryo in the testis of a 129/J mouse. F9 EC cells, have many characteristics of early mouse embryonal cells and can differentiate into almost all cell types^[@CR68]--[@CR70]^, are grown without feeders^[@CR71]^, and are expected to provide a labeled counterpart for a large share of the proteins present in early embryos, making them a very appropriate SILAC reference for our purposes. LC-MS/MS analysis of SILAC mixtures {#Sec16} ----------------------------------- Subsequent to the tryptic digest, the peptide mixtures were offline fractionated by high pH reversed phase chromatography with fraction concatenation. The resulting peptide pools were analyzed by MS on a Q-Exactive mass spectrometer. The MS proteomics data have been deposited to the ProteomeXchange Consortium (<http://proteomecentral.proteomexchange.org>) via the PRIDE partner repository^[@CR72]^ with the accession number PXD007082 and are summarized in Supplemental Table [S6](#MOESM8){ref-type="media"}. Basic processing of raw LC-MS/MS data (MaxQuant, Perseus) {#Sec17} --------------------------------------------------------- Raw data were processed by MaxQuant Software (v1.5.3.8, Martinsried, Bavaria, Germany) involving the built-in Andromeda search engine^[@CR73],[@CR74]^. MS/MS spectra were searched against the mouse UniprotKB database (version from Dec. 2015) concatenated with reversed sequence versions of all entries and supplemented with common contaminants (see Supplemental Methods). Primary quantification was performed using the heavy F9 lysate mix as an internal standard, and ratios between corresponding light (L) and heavy (H) peptide versions were normalized to correct for unequal protein amounts and expressed as L/H (i.e., light/heavy: sample/SILAC internal standard). All these protein ratios are the means of at least two (light and heavy) peptide ratios from the raw spectra. Quality control determined that the sample corresponding to the blastocyst stage for replicate 3 was of low quality; this sample was therefore omitted from all analyses. The ID mapping procedure in some cases returned more than one gene name for a given peptide group; those may or may not correspond to distinct genes. To avoid ambiguities, we excluded such entries from the dataset. Protein data normalization and batch correction {#Sec18} ----------------------------------------------- We log~2~-transformed and quantile-normalized the L/H ratios of all proteins detected at least in two developmental stages in at least two replicates. To correct for the batch effect (see Supplemental Fig. [S15](#MOESM2){ref-type="media"}), we performed an ANOVA for each protein, using the log~2~-transformed L/H ratios as response variable and the replicate identifier as categorical explanatory variable X~i~:$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\log }_{2}\frac{L}{H}=\mu +{X}_{i}+{\epsilon }$$\end{document}$$where μ is the global mean for the protein and ∈ denotes the error. The residuals of the model were used as the corrected L/H ratios for each protein, after adding to each value the global mean µ for the given protein as a constant. Batch-corrected, normalized L/H ratios were used to express protein abundance throughout this study. RNA isolation and RNA sequencing {#Sec19} -------------------------------- For the transcriptome analysis we collected and lysed, in duplicate, an average of 214 oocytes/embryos per developmental stage: unfertilized oocytes, fertilized oocytes with pronuclei and preimplantation embryos at the (early and late) 2-, 4-, 8-cell, advanced morula and blastocyst stages, on which we then performed RNA sequencing (RNA-seq). Total RNA was converted to cDNA using the Smarter system (Takara) and sequencing libraries were prepared using the Nextera kit (Illumina). Libraries were sequenced on Illumina HiSeq3000 platform to obtain \~43 million 36-base-single-end reads per library. The raw data are available at the DNA Databank of Japan (DDBJ) Sequence Read Archive (DRA005956 and DRA006335). RNA-seq trimming and mapping {#Sec20} ---------------------------- Low quality reads were filtered using Trimmomatic (version 0.36^[@CR75]^) with the following parameters: HEADCROP:15 LEADING:3 TRAILING:3 SLIDINGWINDOW:4:15 MINLEN:20. The remaining reads were mapped to the Mus musculus Ensembl GRCm38 assembly using TopHat (version 2.1.1^[@CR76]^) and Bowtie (version 2.2.9^[@CR77]^). As the only non-default parameter for TopHat, we provided the GRCm38 Ensembl 87 (version 1) GTF annotation with the "-G" option. The number of reads mapped to each gene was quantified with with HTSeqCount (version 0.6.1^[@CR78]^) using standard parameters. RNA differential expression analysis {#Sec21} ------------------------------------ A matrix containing the number of reads mapped to each protein-coding gene for each sample was used as input for differential expression analysis with the DESeq2 R/Bioconductor package^[@CR79],[@CR80]^. The P-values obtained from DESeq2 were adjusted with Benjamini-Hochberg's method to control the false discovery rate (FDR)^[@CR81]^. Genes were considered significantly differentially expressed on the basis of (log~2~) fold-change ((log~2~) fold-change ≥1 or ≤−1 between the two developmental stages considered) and FDR ≤ 1 × 10^−5^. Expression values of protein-coding transcripts were calculated using DESeq2 using the regularized log-transformation^[@CR79],[@CR80]^. Protein differential expression analysis {#Sec22} ---------------------------------------- For each protein detected at least in two developmental stages in at least two replicates we computed a linear model:$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\log }_{2}\frac{L}{H}=\mu +{T}_{i}+{\epsilon }$$\end{document}$$where μ is the global mean for the gene, T~i~ is a categorical explanatory variable representing the developmental stage, and ∈ denotes the error. For 1,290 proteins, the ANOVA P-value corresponding to T~i~ was ≤ 0.05. Validation of proteins by enzymatic assays and immunofluorescence {#Sec23} ----------------------------------------------------------------- Results of enzymatic assays for G6PD (EC 1.1.1.49) and HPRT (EC 2.4.2.7) were retrieved from the literature^[@CR82]--[@CR86]^. Additional proteins including proteins without enzymatic activity were verified by immunofluorescence, using commercial antibodies. For each target gene, at least 5 MII oocytes or embryos per stage were examined using the following antibodies, all rabbit polyclonal: anti-DNAJB11 (Sigma-Aldrich cat.no. HPA010814), anti-PDIA3 (Abcam cat.no. ab228789), anti-TOP1 (Sigma-Aldrich cat.no. HPA019039), anti-Rc3h1 (Thermo Scientific catalog no. PA5-34519), anti-Alppl2 (Thermo Scientific catalog no. PA5-22336), anti-DDX6 (Thermo scientific catalog no. PA5-55012). Secondary antibodies were Alexa-Fluor conjugates reactive against the species of the primary antibody. Following our standard fixation, permeabilization, incubation and washing protocol^[@CR87]^, samples were imaged using a 20X objective on an inverted motorized Nikon TiE2000 microscope fitted with an Andor Dragonfly spinning disc confocal unit Scanning System. Immunofluorescent signals were quantified using Image-J^[@CR88]^. For each protein, we calculated the Spearman's rank correlation coefficient between the immunofluorescent signals or enzymatic measurements and the average L/H ratios in our dataset for all available developmental stages. For proteins for which multiple sets of measurements were available we computed and considered as many correlation coefficients. An empirical P-value was computed by randomly associating each of the protein measurements from the literature with one of the corresponding sets of measurements in our dataset (see Supplemental Table [S3](#MOESM5){ref-type="media"}) and repeating this 10,000 times. The reported empirical P-value is the number of times in which we obtained the same number of correlation coefficients greater or equal than 0.6 as with the original data out of the 10,000 attempts, expressed as a relative frequency. TaqMan validation of RNAseq {#Sec24} --------------------------- For each target gene, the cDNA equivalent of 10 MII oocytes or embryos per stage was used. Total RNA was isolated from large pools (\>100 oocytes or embryos) using Quick-RNA™ MicroPrep (Zymo Research) following the manufacturer's instructions and was reverse-transcribed on a GeneAmp® PCR System 9700 (Applied Biosystems). Real-time quantitative PCR reactions were performed on cDNA on a 7900 HT FAST Realtime PCR System (Applied Biosystems). PrimeTime®Predesigned qPCR Assay (6-FAM/ZEN/IBFQ) from Integrated DNA Technologies were used. Assay IDs: Dnajb11_Mm.PT.58.9272431, Pdia3_Mm.PT.8194853; Top1_Mm.PT.58.6752545. All samples were processed as technical duplicates/replicates. Data were analyzed using the Applied Biosystems RQ Manager (Version 1.2.2) and Microsoft Excel. Data access {#Sec25} ----------- The proteomic data from this study have been submitted to the ProteomeXchange Consortium (<http://proteomecentral.proteomexchange.org>) via the PRIDE partner repository^[@CR72]^ under accession number PXD007082. The sequence data generated for this study have been submitted to DNA Databank of Japan (DDBJ, <http://www.ddbj.nig.ac.jp/>) under the accession numbers DRA005956 and DRA006335. Supplementary information ========================= {#Sec26} Supplementary Methods Supplementary Figures and Table Legends Supplementary Table S1 Supplementary Table S2 Supplementary Table S3 Supplementary Table S4 Supplementary Table S5 Supplementary Table S6 Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Steffen Israel and Mathias Ernst contributed equally. Supplementary information ========================= Supplementary information accompanies this paper at 10.1038/s41598-019-49817-3. We thank the Max-Planck-Institute for Molecular Biomedicine and its Director, Prof. Hans R. Schöler, for infrastructural support. We thank the personnel of the MPI mouse housing facility for making it possible to collect as many oocytes and embryos as needed for the proteomics and RNA sequencing. We are indebted to Annalen Nolte for processing the probes for mass spectrometry, and Terumi Horiuchi for processing the probes for RNA sequencing. Jeroen Krijgsveld commented on an earlier version of the manuscript. This study was supported by the Deutsche Forschungsgemeinschaft (grant DFG BO 2540/4-3 to M.B., grant TA 1076/1-1 to L.T., and grant FU-583/5-1 to G.F.; O.E.P. acknowledges support for the transmission electron microscopy from the SFB 944). L.T., G.F. and M.B. planned the study. H.C.D. performed the proteomics experiments. Y.S. performed the RNA-seq experiments. S.I., M.E., L.T., G.F. and M.B. designed the analytical pipeline, analyzed and interpreted the data. L.T., G.F. and M.B. wrote the manuscript with help from S.I. and M.E. O.E.P. performed the transmission electron microscopy. S.I. and E.C. performed the confocal immunofluorescence imaging. W.M. provided intellectual guidance with RNA-seq analysis and feedback on the experimental design. All authors discussed the results and commented on the manuscript. The authors declare no competing interests.
Sous Chef Secrets from The Baraza at Southern Sun Someone very wise once observed that any eatery is only as good as those who work there. Baraza Grill at Southern Sun is no exception. One talented team member is Sous Chef Saleh Ali Amed, third in command of Baraza’s kitchen. In 1992, the young Saleh found himself working as a gardener for expatriate tour operators in Stone Town. They saw potential in the hard-working house boy and encouraged him to consider a career in hospitality. “I was enrolled at the Zanzibar Institute of Tourism before joining the kitchen staff of a mobile camp working across Tanzania,” explains Saleh, “plus I underwent training at the famous Utalii College during occasional visits to Kenya.” His talents eventually landed him a job at one of Dar’s most respected hotels where the Zanzibari chef is known for his flair with seafood which features prominently on Baraza’s menu. Saleh always recommends sourcing seafood at Ferry’s auction instead of stalls to secure the freshest catches for the best price. He also suggests always buying ice at Ferry to keep seafood purchases in peak condition in the heat of Dar and avoiding filling your vehicle with a fishy aroma no matter how short your journey home. Saleh explains that King prawns are more readily available than larger Jumbo or Giant prawns in Dar. His preference, however, are the Tiger prawns which are slightly smaller than King-size. “If you leave the head on a prawn always remove the vein,” advises Saleh who adds, “and use running water to thoroughly wash the head as they often contain a lot of sand.” One of his favourite ways to serve Tiger prawns is to use a Swahili-style marinade of curry powder, turmeric, cumin, lemon juice, garlic, onion, oil, salt, pepper and freshly-chopped coriander. Equally delicious for Saleh is Swahili Prawn Curry. This is not just a family favourite but can be ordered from Baraza’s a la carte menu. The spicy, fresh and creamy dish is given its special Coastal flavour from the use of local seafood and coconut milk. Another regional favourite of the Zanzibar chef is Swahili-style chicken soup. Saleh warns that some less honest poultry sellers these days will try to sell a layer as a broiler. “The broiler is far softer with smoother skin.” says Saleh who notes that the meat of layers will be more ‘yellowish’ in appearance. Once you have secured good chicken meat the next step in creating such a Swahili dish is to combine spices to create the perfect flavour. Saleh loves to use the abundant selection of spices found on the Swahili Coast but prefers not to use pre-packaged, supermarket options. “They often lose their aroma if they stay on shelves for a long time,” says the sous chef, “so I prefer to grind spices myself to get more flavour.” Creativity shines in his food presentation. One simple tip from Saleh is to use fresh herbs that are actually used in the dish itself. Naturally, the Baraza team have a professional kitchen set-up but Saleh believes every home cook can follow simple steps to create an organised, hygienic workspace. “Any kitchen can be organised into specific areas, for example pots or pans in one place,” suggests Saleh, “so utensils or ingredients are easily located.” Finally, Saleh is keen for everyone to remember proper food storage practice. He notes it is often forgotten that cooked food suitable for refrigeration must be allowed to cool properly. Failure to do so can raise the fridge temperature thereby encouraging bacterial growth while the steam produced may also affect the taste of the actual dish. Saleh’s final foodie tip is to encourage everyone to discover the diverse taste experiences of regional food across Tanzania. He is passionate to have both visitors and citizens have more opportunity to enjoy Tanzanian dishes prepared by professional chefs. Swahili Coast Foodie certainly agrees! Visit Baraza Grill to speak to the staff about their a la carte menu, weekly specials and private dining options.
Influence of emotion on memory for temporal information. Contextual information, such as color and spatial location, has been found to be better remembered for emotional than for neutral items. The current study examined whether the influence of emotion extends to memory for another fundamental feature of episodic memory: temporal information. Results from a list-discrimination paradigm showed that (a) item memory was enhanced for both negative and positive pictures compared with neutral ones and was better for negative than for positive pictures and (b) temporal information was better remembered for negative than for positive and neutral pictures, whereas positive and neutral pictures did not differ from each other. These findings are discussed in relation to the processes involved in memory for temporal information.
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# Read about factories at https://github.com/thoughtbot/factory_girl FactoryGirl.define do factory :message do conversation person content { Faker::Lorem.paragraph(3) } end end
Tuesday, 2 April 2013 REVIEW: OUTSIDERS BY BAILEY VAUGHN "Outsiders" is a young adult story about a small town that invites a group of foreigners, to the town, to teach them about their way of life in America. However, the newcomers aren’t all they appear. The main character, Hannah, falls in love with one of the "outsiders", and finds herself in compromising circumstances due to this forbidden love. Once the horrible intentions of the outsiders are revealed, Hannah must find the courage and strength to save her town MY REVIEW! Looking at the given summary doesn’t always speak what resides inside the book. When i read the synopsis, i expected a lot, a very lot out of it, but sadly i was disappointed. The story was simple, fast, short, and non clarifying. It actually didn’t clarify what was happening. To me it felt like it was a small part of a huge book about what wrong was happening in Patterson falls. There were no details, nothing that would actually made one wonder that ah yes, this is possble, or yeah, this could’ve happened. The story was revolving hopelessly without knowing the actual path. I expected a clarification, and i expected to actually believe that yes this is real, this might have happened somewhere. I am a believer, but i couldn’t believe in anything. I just felt this is not how the world works. The details were missing, and by details i don’t only mean about where they came from, why they did what they did, and how it happened but i mean that everything was sudden and clear. I really love when things are coiled, and while mentioning a love story, i starve for beautiful moments. The proposal, the cuddles, the beautiful time they would spend together, and the very sweet little romantic moments. To be honest i missed it, the very feel that they were in love didn’t touch my heart. I was not convinced that maybe what they had was true love, and most of all “ it didn’t make me think”. Unfortunately, it didn’t reach to my expectations. The whole atmosphere was very light, and the book demanded intensity which was not provided. The theme when looked at was very good, but somehow it wasn’t at that level as i expected it would be. May be i expect too much, may be yes, but hey, what is the joy in reading if you don’t have expectations already. But i would say good try though. I RATED IT:2/5 POINTS AND SO 2 FLOWERS! DISCLAIMER: author gave me a free copy of this book in exchange on an honest review. My review is in no way influenced by anyone/ anything
Q: WPF RDLC Report and pass parameters I have some problems when I run my app to display a ReportViewer. This is my C# code: private void Report_Load(object sender, EventArgs e) { ShowReport(); } private DataTable GetData() { DateTime dtStart = DateTime.Parse(txtDataS.Text); DateTime dtEnd = DateTime.Parse(txtDataE.Text); DataTable _dt = new DataTable(); using (_con = new SqlConnection(_strConexao)) { _cmd = new SqlCommand("SELECT_CADS", _con); _cmd.CommandType = CommandType.StoredProcedure; _cmd.Parameters.Add("@SDATE", SqlDbType.DateTime).Value = dtStart; _cmd.Parameters.Add("@EDATE", SqlDbType.DateTime).Value = dtEnd; _adp = new SqlDataAdapter(_cmd); _adp.Fill(_dt); } return _dt; } private void ShowReport() { _reportViewer.Reset(); DataTable _dt = GetData(); ReportDataSource rds = new ReportDataSource("DataSetRel",_dt); _reportViewer.LocalReport.DataSources.Add(rds); _reportViewer.LocalReport.ReportEmbeddedResource = "Project.Rel.rdlc"; _reportViewer.ProcessingMode = ProcessingMode.Local; ReportParameter dt1 = new ReportParameter("dtStart", txtDataS.Text); ReportParameter dt2 = new ReportParameter("dtEnd", txtDataE.Text); _reportViewer.LocalReport.SetParameters(new ReportParameter[] {dt1,dt2}); _reportViewer.LocalReport.Refresh(); } When I run this app and I input Initial Date and final date and click in show button nothing happened Note in my rdlc report i have two parameters dtStart and dtEnd and i use it as a expression in textbox. Whats is the problem? Why I can't pass this parameters to rdlc report? A: Create a form and put a ReportViewr on it, then in form load event write such code: var reportBindingSource = new System.Windows.Forms.BindingSource(); var reportDataSource = new Microsoft.Reporting.WinForms.ReportDataSource(); //Name of dataset in your rdlc report reportDataSource.Name = "DataSet1"; reportDataSource.Value = reportBindingSource; this.reportViewer1.LocalReport.DataSources.Add(reportDataSource); this.reportViewer1.LocalReport.ReportEmbeddedResource = "StackSamplesCS.Data.Report1.rdlc"; //Set parameters //These are repot parameters, so use the names that you gave them in report. this.reportViewer1.LocalReport.SetParameters(new Microsoft.Reporting.WinForms.ReportParameter("StartDate", this.DatePicker1.SelectedDate.ToString())); this.reportViewer1.LocalReport.SetParameters(new Microsoft.Reporting.WinForms.ReportParameter("EndDate", this.DatePicker1.SelectedDate.ToString())); //put your connection string //example: @"data source=(localdb)\v11.0;initial catalog=YourDatabase;integrated security=True;" //example @".\sqlexpress;;initial catalog=YourDatabase;integrated security=True;" var connection = W"Your Connection String" ; //your command //example: "SELECT * FROM YourTable WHERE StartDate>@StartDate AND EndDate<@EndDate" var command = "Your Command"; var tableAdapter = new System.Data.SqlClient.SqlDataAdapter(command, connection); //Set Sql Parameters tableAdapter.SelectCommand.Parameters.Add(new System.Data.SqlClient.SqlParameter("@StartDate", this.DatePicker1.SelectedDate)); tableAdapter.SelectCommand.Parameters.Add(new System.Data.SqlClient.SqlParameter("@EndDate", DatePicker2.SelectedDate)); var dataTable= new DataTable(); //Get data tableAdapter.Fill(dataTable); reportBindingSource.DataSource = dataTable; this.reportViewer1.RefreshReport(); Please Carefully read comments Look in your Report and see what is the name of DataSet that it use Look in Your Report and see what is the name of parameters in report and use them when passing report parameters. Use parameters in your code not in Report
Exchange-mediated anisotropy of (ga,mn)as valence-band probed by resonant tunneling spectroscopy. We report on experiments and theory of resonant tunneling anisotropic magnetoresistance (TAMR) in AlAs/GaAs/AlAs quantum wells (QW) contacted by a (Ga,Mn)As ferromagnetic electrode. Such resonance effects manifest themselves by bias-dependent oscillations of the TAMR signal correlated to the successive positions of heavy (HH) and light (LH) quantized hole energy levels in GaAs QW. We have modeled the experimental data by calculating the spin-dependent resonant tunneling transmission in the frame of the 6 x 6 valence-band k.p theory. The calculations emphasize the opposite contributions of the (Ga,Mn)As HH and LH subbands near the Gamma point, unraveling the anatomy of the diluted magnetic semiconductor valence band.
NATO Archives presents ''NATO’s First Enlargement'' On 18 June 2012, the NATO Archives celebrated the 60th anniversary of the accession of Greece and Turkey to the North Atlantic Treaty with a commemorative exhibition titled ‘NATO’s First Enlargement: Greece and Turkey 1952’. The exhibition focused on the accession ceremony and its surrounding events, using publicly disclosed NATO documents to present the historical moment in its formal, political, strategic and public diplomacy contexts. NATO Deputy Secretary General Ambassador Alexander Vershbow inaugurated the exhibition with Mme. Ekaterini Nassika, the Deputy Permanent Representative for Greece, and H.E. Mr. Haydar Berk, the Permanent Representative for the Republic of Turkey at his side. In his opening speech, Ambassador Vershbow congratulated Greece and Turkey for this historic milestone and spoke to the key role that both countries have played over the years in NATO’s policy of partnership and cooperation in advancing Euro-Atlantic integration. As the first two nations to be part of NATO’s first enlargement, Greece and Turkey have served as role models by ‘keeping NATO’s door open for countries that aspire to join our Alliance’. Ambassador Vershbow concluded with a statement about the important role that Greece and Turkey must play in the 21st century. ‘Thanks to NATO’, Vershbow said, ‘you have lived through an unprecedented period of peace and stability. By reaching out to your southern neighbours and showing the way for your NATO Allies, you can help to extend that peace and stability well into this century.’ To celebrate this occasion, the NATO Archives collaborated with other memory institutions to present an authentic representation of this historical event. The United States National Archives and Records Administration provided access to the original signed instruments of protocol and accession for Greece and Turkey deposited at the Departement of State in Washington. The Imperial War Museum in London provided the rarely seen film footage of the Lisbon Ministerial where Greece and Turkey formally acceded to the Treaty, as well as film footage of Supreme Allied Commander Europe General Dwight D. Eisenhower’s subsequent visits to Greece and Turkey in early March 1952. Facsimiles of these archival documents, along with a selection of publicly disclosed NATO documents, were reprinted in a special commemorative booklet that served as a companion to the exhibition. For online access to the documents related to the accession of Greece and Turkey, please click here (PDF/6MB). For complete access to the thousands of other declassified documents that have been publicly disclosed, researchers and others interested in the history of the Organization are welcome to visit the NATO Archives Reading Room at NATO HQ in Brussels.
Q: Jquery check if control is empty and display != "none", Why does not work? The following if statement. emptyFields = false; $(".ClassNanme").each(function() { if(($.trim($(this).val()) == "") && ($(this).css('display') != 'none' ) { emptyFields = true; return false; // break out of the each-loop } }); But does not work, I don't know how to check if the css property display is set to none with jquery. This if statement should pick when one of the objects are either empty or its css property display its not set to none. Checking if the value is empty works, what I am stuck with is with checking if the object its hidden (or display:none). Thanks. Cesar. A: emptyFields = false; $(".ClassName").each(function() { if($.trim($(this).val()) === "" && $(this).is(":hidden")) { emptyFields = true; return false; // break out of the each-loop } }); Using is(":hidden") is, in my opinion, syntactically cleaner and easier to read than checking the actual CSS value. Give that a try. Also, use === (type equality) when comparing with an empty string. Edit: Gah, changing "visible" to "hidden" - my mistake.
The emotional wounds from Pulse were fresh as Orlando woke up to news of a sniper-style ambush that killed five police officers in Texas, putting the Central Florida law enforcement community on the defensive for potential danger. At least three law enforcement agencies in Central Florida received threats against their departments. Orange County Sheriff Jerry Demings said their office and the Winter Park Police Department received bomb threats. A person called into the agencies and threatened a bomb would explode at a specific time. Demings said the threats were found to have been unsubstantiated and officials are investigating. Orlando Police are also investigating a "vague threat" made Friday morning against its department, said Chief John Mina, who would not elaborate. Reports from Dallas stirred more feelings in a city that has barely begun to heal after the deadliest mass shooting in U.S. history left 49 dead at a gay nightclub. Across downtown Orlando Friday, people spoke about race, guns and the importance of unity following another national tragedy. "The only thing that can kill the human race is the human race," said Robbie Clark, a 27-year-old financial adviser from Winter Haven who was standing outside of Pulse, where a memorial to the victims remains. "We're in an election year ... and it's important who we put in office, but people are losing their lives: Black lives, Spanish lives, lives of those who choose to love other people." Clark, who is white, said he has fears about the world his 4-year-old daughter will inherit if people remain divided. In the "coordinated" attack in Dallas, a sniper opened fire from elevated rooftops during a protest over fatal police shootings of black men in Louisiana and Minnesota, according to The Dallas Morning News. Other attacks on law enforcement officers were reported in three states after the news in Dallas. At a press conference Friday alongside black members of clergy and police chiefs from agencies across Central Florida, Demings said the region is united and will not allow the violence that has occurred in communities across the nation. "[We want] to make sure none of that comes to this community," he said. "I am confident the people who live here who believe and trust in this community will come together and won't allow that lawlessness that is happening in other places to happen here." For residents, some complained of gun laws being a factor that's led to the uptick in violence. "Something needs to be done related to the guns--it's getting worse," said Chester Davis, a 59-year-old black man from Cocoa Beach visiting the Pulse memorial Friday. He said he doesn't think everyone should be stripped of their weapons, but advocated for steeper penalties for those convicted of crimes with firearms. For Ricardo Catabay, a dark-skinned Filipino man who served in the U.S. Navy until 2013, issues of guns and race cannot be separated. The 28-year-old Winter Springs man said he carries a gun with a concealed weapons permit and fears that one day he'll be pulled over by a police officer and get shot because of the weapon and his skin color. It's not fair that police officers who shoot black men "get placed on administrative leave and nothing will happen to them," he said Friday while getting a haircut at Urban Stylez in downtown Orlando. Even before the shootings in Dallas, Mina sent out a message to his officers, urging them to be careful in an atmosphere of anti-police sentiments stoked by the deaths of Alton Sterling in Baton Rouge and Philando Castile in suburban St. Paul, both of which were captured on video. OPD SWAT snipers were deployed on the roofs of buildings near Lake Eola on the Fourth of July "to observe the crowd from an elevated position," said Sgt. David Baker. He would not elaborate or say if the measure was taken before the Pulse attack. echerney@orlandosentinel.com; dharris@orlandosentinel.com; rstutzman@orlandosentinel.com; chayes@orlandosentinel.com
Roaming the library, outside of academia Tag Archives: student number controls I have been interested to read recently about the move to provide additional funding for postgraduate students at the cost of scrapping an undergraduate scholarship programme, in an attempt to allow a wider range of people to engage with postgraduate learning. However, the more interesting story that I haven’t been hearing people talking about quite so much is the recent Higher Education Funding Council for England (HEFCE) consultation on “student number controls”. Measures to control student numbers started around 2008, but have been implemented on an increasingly stringent level ever since. The controls have escalated mostly in response to the rise in fees, the spike of which was 2010/11 academic year. The current system of student number controls has some troubling implications, in particular for those students from underprivileged backgrounds, and I am of the firm belief that it is potentially far more damaging than the low take-up of postgraduate courses. In the current system, Universities are able to accept applicants from as many entrants as they wish with UCAS entry grades of AAB or more. However, the number of students a University can admit with lower entry grades than this is restricted. These restrictions vary by institution, but exist mostly to encourage a constant number of students within an institution. If a University has yearly fees of less than £7,500 per year are able to compete to bid for an additional allocation from a pool of 20,000 reserve places that they can offer to students. The important thing to note at this stage is that these restrictions apply to any undergraduate-level programme being offered by a provider, which means that the restrictions are not only applicable to bachelor’s degrees, but also to Foundation Degrees and Higher National Diplomas. These foundation programmes are usually provided in partnership with local colleges and admit students with far lower entry credits than traditional degree routes. Students who enter on these programmes are often from low participation backgrounds and are far more likely to come from deprived areas than students who enter directly on to bachelor’s degrees. Foundation Degrees in particular are a core and important route for mature students seeking an opportunity to study for a bachelor’s degree who are not able to commit to full-time study, as they often offer flexible learning arrangements. Once they have completed their Foundation Degree or Higher National Diploma, students are usually able to sit a “top-up” year at the provider college on an affiliated course and can then receive a full bachelor’s degree. In some cases, programmes like this would be the only possible entry route for young people and mature learners to higher education. Student numbers are “allocated” to the provider – in this case, the University – who will then distribute the places across their provision strategically, and this includes the allocation of places to partner colleges who may be delivering their foundation courses. What we will no doubt see evidence in the near future that Universities who rely on students with lower entry tariffs and may only exceptionally have applicant students with AAB+ are withdrawing their number allocations from foundation programmes delivered by local partner colleges and redistributing them among their core provision. This will be partly because the funding is more efficient for the University when it doesn’t have to share with a college, and because restrictions on its own growth will hinder development of new mainstream bachelor’s undergraduate programmes which are simply of a higher priority. A situation like this is absolutely fine for a Russell Group institution, or a University who would generally be expecting an entry tariff of AAB+ from their prospective students, and will probably not struggle to allocate additional places to their partner colleges. The knock-on effect is that there will be fewer and fewer places available on Higher National Diplomas or Foundation Degrees, and that fewer young people who would have been able to progress to a top-up bachelor’s degree are being denied the opportunity to do so. We are also seeing in the news countless examples of Universities engaging in risky overseas delivery. With the current system of student number controls in place, ambitious Universities who wish to expand their provision and generate more income are drawn to what may be seen as an easy solution to a difficult problem in tapping lucrative overseas markets. The reality is that these strategies are often not sustainable and without extreme care can very easily lose their rigour. With this in mind, are postgraduate bursaries the best way to increase participation? Although the root cause for the drop in postgraduate numbers is the same as the root cause for undergraduate number controls – the change to the fee structures – more Universities are wanting to tap postgraduate student markets. Postgraduate students don’t carry with them the same load in terms of funding complications and don’t have restrictions on number. Although I certainly welcome additional support for aspiring postgraduates, I am uncomfortable with it being at the cost of undergraduate students, particularly in the current landscape where number restrictions are potentially affecting deprived students from participating fully in higher education. I will be interested to see in the coming years whether we do see a decline in the HND and Foundation Degree, and more interested to note what kind of attention this attracts. My cynical gut feeling is that few commentators will be interested in this particular HE issue – one which will be affecting some of our most deprived and underprivileged students.
Covid-19 and Ultralight Outdoor Gear We are still open for on-line customers We are maintaining our warehouse and customer service teams with minimum numbers so that we can continue to send out ultra-lightweight gear across the world. With countries at various stages of Covid-19 infection, including some that have relaxed restrictions, we want to continue to offer our products and advice to our customers, so long as we can do this without risking our colleagues, customers or community. In order to continue in this way we are carefully following UK Government guidelines, and those things that can be done remotely, by people working from home (such as Newsletters, purchasing functions and website maintenance), are being done in that way. The UK Government documents, released following the Prime Ministers televised address of the evening of the 23rd March 2020 included the statement that “Online retail is still open and encouraged and postal and delivery service will run as normal.” We have implemented UK Government advice We have implemented all the recommendations of the UK Government in order to protect our colleagues at work, our customers and our community, here's what we've done so far: The majority of the workforce are able to work from home and are now doing so Anyone still working at our premises who has felt unwell has been sent home in order to self-isolate for at least 7 days to see if the virus develops Our warehouse staff are working to new practices designed to minimise proximity to each other Everyone in the building is wearing gloves and facemasks, surfaces and workstations are wiped down regularly and social distancing is being practiced We have closed our showroom until the emergency is over We will be keeping everything under review The situation in the UK has been changing rapidly and restrictions have been tightened on a virtual daily basis, we follow any announcement very closely to see if the advice affecting our business has changed. At the present time we are OK to operate, in fact online retailers are being encouraged to continue operating subject to the well-documented guidelines. If this changes we will scrupulously comply with any new instructions. Thank you and stay safe We'd just like to say thank you to our customers, many longstanding, for your continued support. If we can point to any good news in the current emergency lets highlight the reduced pollution around the world that's literally giving our planet a 'breather'. Our open and wild places are waiting for us when this is over. Best wishes, look after each other and stay safe.
--- author: - \| David Bekker$^{1}$, Robert de Mello Koch$^{1,2}$ and Michael Stephanou$^{1}$\ \ $^{1}$ National Institute for Theoretical Physics,\ Department of Physics and Centre for Theoretical Physics,\ University of the Witwatersrand,\ Wits, 2050,\ South Africa\ \ $^{2}$Stellenbosch Institute for Advanced Studies,\ Stellenbosch,\ South Africa\ \ E-mail: title: 'Giant Gravitons - with Strings Attached (III)' --- Introduction and Summary ======================== The gauge theory/gravity correspondence[@Maldacena:1997re],[@Gubser:1998bc],[@Witten:1998qj] has provided powerful clues into quantum gravity. For example, the correspondence claims the exact identity of maximally supersymmetric ${\cal N}=4$ Yang-Mills quantum field theory with gauge group $SU(N)$ and type IIB string theory on the negatively curved AdS$_5\times$S$^5$ space with $N$ units of five form flux. Thus, we should be able to use the ${\cal N}=4$ super Yang-Mills theory as a definition of quantum gravity on AdS$_5\times$S$^5$. For interesting recent progress in this direction, see [@friends],[@Berenstein:2007wz]. The correspondence is however, not yet understood well enough, for this to be possible. A detailed understanding of the gauge theory/gravity correspondence is frustrated by the fact that it is a weak/strong coupling duality in the ’t Hooft coupling. At weak ’t Hooft coupling the field theory may be treated perturbatively, but the spacetime of the dual quantum gravity is highly curved. In the opposite limit of strong ’t Hooft coupling we have to face the difficult problem of strongly coupled quantum field theory. The dual quantum gravity however, simplifies, because in this limit the curvature of the spacetime is small. For this reason, most computations which can be carried out on both sides of the correspondence (and hence clearly shed light on the correspondence) compute quantities that are protected by symmetry - typically supersymmetry (see [@Aharony:1999ti] and references therein). The number of these tests and the agreement found is impressive. However, computing and comparing protected quantities is not satisfying - to probe dynamical features of the correspondence it would be nice to be able to compare quantities that are not protected by any symmetries. This is in general, a formidable problem. In [@DBer], the notion of an [almost BPS state]{} was introduced. These states are systematically small deformations of states that are protected. For this reason, for almost BPS states, it is possible to reliably extrapolate from weak to strong coupling. A good example of almost BPS states are the BMN loops[@Berenstein:2002jq]. By studying BMN loops it has been possible to probe truly stringy aspects of the gauge theory/gravity correspondence (see [@Russo:2004kr] and references therein). Giant gravitons, which are half-BPS states, have proved to be the source of many valuable quantities that are accessible on both sides of the correspondence. Further, they are very interesting from a string theory point of view, since they are good examples of protected non perturbative objects. Giant gravitons are spherical D3 branes extended in the sphere[@McGreevy:2000cw] or in the AdS space [@Grisaru:2000zn],[@Hashimoto:2000zp],[@Das:2000fu] of the AdS$\times$S background. They are (classically) stable due to the presence of the five form flux which produces a force that exactly balances their tension. The dual description of giant gravitons is in terms of Schur polynomials in the Higgs fields[@Corley:2001zk],[@Balasubramanian:2001nh]. Our interest in giant gravitons is related to the fact that excited giant gravitons provide a rich source of nearly BPS states. Excitations of giant gravitons are obtained by attaching open strings to the giant. The gauge theory operator dual to an excited sphere giant is known and the anomalous dimension of this operator reproduces the expected open string spectrum[@Balasubramanian:2002sa][^1]. This has been extended and the operators dual to an arbitrary system of excited giant gravitons is now known[@Balasubramanian:2004nb]. The dual operators, restricted Schur polynomials[^2], beautifully reproduce the restrictions imposed on excitations of the brane system by the Gauss law. Further, these excited giant gravitons have recently been identified as the microstates of near-extremal black holes in AdS$_5\times$S$^5$[@Balasubramanian:2007bs]. Although the evidence for identifying the restricted Schur polynomials as the operators dual to excited giant gravitons is convincing, much remains to be done. For example, we do not yet understand the detailed mechanism allowing Chan-Paton factors, expected for strings attached to a bound state of giant gravitons, to emerge from the super Yang-Mills theory. In this article, our goal is to explore this issue, by providing techniques which allow the computation of the anomalous dimensions of excited giant gravitons, to one loop. We will argue that the Chan-Paton factors emerge from the symmetric group labels of the restricted Schur polynomials. The computation of anomalous dimensions of operators in ${\cal N}=4$ super Yang-Mills theory has progressed considerably. Much of the recent progress was sparked by a remarkable paper of Minahan and Zarembo[@Minahan:2002ve] which shows that the spectrum of one loop anomalous dimensions of operators dual to closed string states, in a sub sector of the theory, gives rise to an integrable $SO(6)$ spin chain. This result can be generalized to include the full set of local operators of the theory[@Beisert:2003yb]. The integrable spin chain model describing the full planar one loop spectrum of anomalous dimensions can be solved by Bethe-Ansatz techniques[@Beisert:2003yb]. Clearly, it is desirable to find a similar approach for operators dual to open strings. A naive generalization is frustrated by the fact that, since the open string and giant can exchange momentum, the number of sites of the open string lattice becomes a dynamical variable[^3]. This was circumvented in [@CuntzChain] by introducing a Cuntz oscillator chain. Restricting to the $SU(2)$ sector, the spin chain is obtained by mapping one of the matrices, say $Z$, into a spin up and the other, say $Y$, into a spin down. In contrast to this, the Cuntz chain uses the $Y$s to set up a lattice which is populated by the $Z$s. Thus the number of sites in the Cuntz chain is fixed. The power of the spin chain goes beyond the computation of anomalous dimensions. Indeed, the low energy description of the spin chain relevant for closed string states appearing on the field theory side matches perfectly with the low energy limit of the string action in AdS$_5\times$S$^5$[@Kr]. This is an important result because it shows how a string action can emerge from large $N$ gauge theory. For the open string, the coherent state expectation value of the Cuntz chain Hamiltonian reproduces the open string action for an open string attached to a sphere giant in AdS$_5\times$S$^5$[@CuntzChain],[@Berenstein:2006qk], for an open string attached to an AdS giant in AdS$_5\times$S$^5$[@adsgiant] and for an open string attached to a sphere giant in a deformed AdS$_5\times$S$^5$ background[@deMelloKoch:2005jg]. Recently[@Hofman:2007xp], the worldsheet theory of an open string attached to a maximal giant has been studied. Evidence that the system is integrable at two loops has been obtained. The fact that the open string can exchange momentum with the giant is reflected in the fact that there are sources and sinks (at the endpoints of the string) for the particles on the chain. The structure of these boundary interactions is complicated: since the brane can exchange momentum with the string, the brane will in general be deformed by these boundary interactions. The goal of this article is to determine this Cuntz chain Hamiltonian for multiple strings attached to an arbitrary system of giant gravitons. In particular, this entails accounting for back reaction on the giant graviton. To compute the Cuntz chain Hamiltonian, we need the two point functions of restricted Schur polynomials. It is an involved combinatoric task to compute the two point functions of restricted Schur polynomials. The required technology to compute these correlators, in the free field limit, has recently been developed in [@de; @Mello; @Koch:2007uu][^4]. This was then extended to one loop, for operators dual to giants with a single string attached[@de; @Mello; @Koch:2007uv]. In this article, we extend the existing technology, allowing the one loop computation of correlators dual to giant graviton systems with an arbitrary number of strings attached. In the remainder of this introduction, we will establish notation and give a sketch of the technology we develop. To make our discussion concrete, we mostly consider the specific example of two strings attached to a bound state of two sphere giants[^5]. Note however, that most of the formulas we derive (and certainly the techniques we develop) are applicable to the general problem. Both the strings and the branes that we consider are distinguishable. In this case there are a total of six possible states. For a bound state of two sphere giant gravitons, we need to consider restricted Schur polynomials labeled by Young diagrams with two columns each with $O(N)$ boxes. Denote the number of boxes in the first column by $b_0+b_1$ and the number of boxes in the second column by $b_0$. It is natural to interpret the number of boxes in each column as the momentum of each giant. We can use the state operator correspondence (see Appendices C.5 and D for further discussion) to associate a Cuntz chain state with each restricted Schur polynomial. The Cuntz chain states have six labels in total: the first two labels are $b_0$ and $b_1$ which determine the momenta of the two giants; the next two labels are the branes on which the endpoints of string one are attached and the final two labels are the branes on which the endpoints of string two are attached. We label the strings by ‘1’ and ‘2’. The brane corresponding to column 1 of the Young diagram is labeled ‘b’ (for big brane) and the brane corresponding to column 2 of the Young diagram is labeled ‘l’ (for little brane). Since the second column of a Young diagram can never contain more boxes that the first column, and since the radius of the giant graviton is determined by the square root of its angular momentum, these are accurate labels. Consider a state with string 1 on big brane and string 2 on little brane. The restricted Schur polynomial (written using the graphical notation of [@de; @Mello; @Koch:2007uu],[@de; @Mello; @Koch:2007uv]) together with the corresponding Cuntz chain state are (in this case, $b_0=3$ and $b_1=4$) $$\young({\,}{\,},{\,}{\,},{\,}{\,},{\,}{2},{\,},{\,},{\,},{1})\longleftrightarrow \|3,4,bb,ll\rangle .$$ We will call states with strings stretching between branes “stretched string states”. When labeling the Cuntz chain state corresponding to a stretched string state, we will write the end point label corresponding to the upper index first. Thus, $$\young({\,}{\,},{\,}{\,},{\,}{\,},{\,}{\onetwo},{\,},{\,},{\,},{\twoone})\longleftrightarrow \|3,4,lb,bl\rangle .$$ The remaing four states are $$\young({\,}{\,},{\,}{\,},{\,}{\,},{\,}{1},{\,},{\,},{\,},{2})\longleftrightarrow \|3,4,ll,bb\rangle \qquad \young({\,}{\,},{\,}{\,},{\,}{\,},{\,}{\twoone},{\,},{\,},{\,},{\onetwo})\longleftrightarrow \|3,4,bl,lb\rangle ,$$ $$\young({\,}{\,},{\,}{\,},{\,}{2},{\,}{1},{\,},{\,},{\,},{\,})\longleftrightarrow \|2,6,ll,ll\rangle \qquad \young({\,}{\,},{\,}{\,},{\,}{\,},{\,}{\,},{\,},{\,},{2},{1})\longleftrightarrow \|4,2,bb,bb\rangle .$$ The construction of the operators dual to excitations described by strings stretching between the branes requires the construction of an “intertwiner”[@de; @Mello; @Koch:2007uu]. One of the results of the present article, is to provide a general construction of the intertwiner. This construction is given in Appendix A. In the notation of [@de; @Mello; @Koch:2007uu], we assume that when the restricted Schur polynomial is to be reduced, string 1 is removed first and string 2 second. This implies that, when using the graphical notation, removing the box occupied by string 1 first will always leave a valid Young diagram. This choice is arbitrary, but useful for explicit computation. Once we have the form of the Hamiltonian, we can always change to a “physical basis”. To obtain operators dual to giant gravitons, we take $b_0$ to be $O(N)$ and $b_1$ to be $O(1)$. We want to compute the matrix of anomalous dimensions to one loop and at large $N$. To compute this matrix, we need to compute the two point functions of restricted Schur polynomials. This is a hard problem: since the number of fields in the giant graviton is $O(N)$, huge combinatoric factors pile up as the coefficient of non-planar diagrams and the usual the planar approximation fails. We need to contract all of the fields in the giant gravitons exactly. The two open strings are described by the words $W^{(1)}$ and $W^{(2)}$. The six Higgs fields $\phi^i$ $i=1,...,6$, of the ${\cal N}=4$ super Yang-Mills theory can be grouped into the following complex combinations $$Z=\phi^1+i\phi^2,\qquad Y=\phi^3+i\phi^4,\qquad X=\phi^5+i\phi^6 .$$ The giant gravitons are built out of the $Z$ field; the open string words out of the $Z$ and $Y$ fields. Thus, the open strings carry a component of angular momentum on the $S^3$ that the giant wraps, as well a component parallel to the giant’s angular momentum. We will normalize things so that the action of ${\cal N}=4$ super Yang-Mills theory on $R\times S^3$ is (we consider the Lorentzian theory and have set the radius of the $S^3$ to 1) $$S={N\over 4\pi \lambda}\int dt \int_{S^3} {d\Omega_3\over 2\pi^2} \left( {1\over 2}(D\phi^i)(D\phi^i)+{1\over 4}\big(\big[\phi^i,\phi^j\big]\big)^2 -{1\over 2}\phi^i\phi^i +\dots \right),$$ With these conventions, $$\langle Z^\dagger_{ij}(t)Z_{kl}(t)\rangle = {4\pi\lambda\over N}\delta_{il}\delta_{jk} = \langle Y^\dagger_{ij}(t)Y_{kl}(t)\rangle ,$$ The open string words can be labelled as $$(W(\{n_1,n_2,\cdots , n_{L-1}\}))^i_j= (YZ^{n_1}YZ^{n_2} Y\cdots YZ^{n_{L-1}}Y)^i_j,$$ where $\{n_1,n_2,\cdots , n_{L-1}\}$ are the Cuntz lattice occupation numbers. The giant is built out of $Z$s; the first and last letters of the open string word $W$ are not $Z$s. We will always use $L$ to denote the number of $Y$ fields in the open string word and $J=n_1+n_2+\cdots +n_{L-1}$ to denote the number of $Z$ fields in the open string word. The number of fields in each word is $J+L\approx L$ in the case that $J\ll L$ which we will assume in this article. For the words $W^{(1)},W^{(2)}$ to be dual to open strings, we need to take $L\sim O(\sqrt{N})$. We do not know how to contract the open strings words exactly; when contracting the open string words, only the planar diagrams are summed. To suppress the non-planar contributions we take ${L^2\over N}\ll 1$. To do this we consider a double scaling limit in which the first limit takes $N\to\infty$ holding ${L^2\over N}$ fixed and the second limit takes the effective genus counting parameter ${L^2\over N}$ to zero. Taking the limits in this way corresponds, in the dual string theory, to taking the string coupling to zero, in the string theory constructed in a fixed giant graviton background. Since the two strings are distinguishable they are represented by distinct words and hence, in the large $N$ limit, we have $$\langle W^{(i)}(W^{(j)})^\dagger\rangle\propto\delta^{ij}.$$ When computing a correlator of two restricted Schur polynomials, the fields belonging to the giants in the two systems of excited giant gravitons are contracted amongst each other, the fields in the first open string of each are contracted amongst each other and the fields in the second open string are contracted amongst each other. We drop the contributions coming from contractions between $Z$s in the open strings and $Z$s associated to the brane system, as well as contractions between $Z$s in different open string words. When computing two point functions in free field theory, if the number of boxes in the representation $R$ is less than[^6] $O(N^2)$ and the numbers of $Z$’s in the open string is $O(1)$, the contractions between any $Z$s in the open string and the rest of the operator are suppressed in the large $N$ limit[@recent]. Contractions between $Z$s in different open string words are non planar and are hence subleading (clearly there are no large combinatoric factors that modify this). An important parameter of our excited giant graviton system is $N-b_0$. This parameter can scale as $O(N)$, $O(\sqrt{N})$ or $O(1)$. In section 2, we will see that when $N-b_0$ is $O(1)$ the sphere giant boundary interaction is $O({1\over N})$, when $N-b_0$ is $O(\sqrt{N})$ the boundary interaction is $O({1\over\sqrt{N}})$ and when $N-b_0$ is $O(N)$, the boundary interaction is $O(1)$. Since we want to explore the dynamics arising from the boundary interaction, we will assume that $N-b_0$ is $O(N)$. The subspace of states reached by attaching two open strings to a giant graviton boundstate system is dynamically decoupled (from subspaces obtained by attaching a different number of open strings) at large $N$. It is possible to move out of this subspace by the process in which the word $W$ “fragments” thereby allowing $Y$s to populate more than a single box in $R$. In the dual string theory this corresponds to a splitting of the original string into smaller strings, which are still attached to the giant. This process was considered in [@de; @Mello; @Koch:2007uu] and from that result we know that it does not contribute in the large $N$ limit. One could also consider the process in which the open string detaches from the brane boundstate and is emitted as a closed string state, so that it no longer occupies any box in $R$. This process (decay of the excited giant boundstate by gravitational radiation) also does not contribute in the large $N$ limit[@Balasubramanian:2002sa],[@de; @Mello; @Koch:2007uu]. Since the giant boundstate and the open string can exchange momentum, the value of $J$ is not a parameter that we can choose, but rather, it is determined by the dynamics of the problem. Cases in which $J$ becomes large correspond to the situation in which a lot of momentum is transferred from the giant to the open string, presumably signaling an instability. See [@Berenstein:2006qk] for a good physical discussion of this instability. In cases where $J$ is large, back reaction is important and the approximations we are employing are no longer valid. This will happen when $J$ becomes $O(\sqrt{N})$ since the assumption that we can drop non-planar contributions when contracting the open string words breaks down. Essentially this is because as more and more $Z$s hop onto the open string, it is starting to grow into a state which is eventually best described as a giant graviton itself. One can also no longer neglect the contractions between any $Z$s in the open string and the rest of the operator, presumably because the composite system no longer looks like a string plus giant (which can be separated nicely) but rather, it starts to look like one large deformed threebrane. Thus, the fact that our approximation breaks down has a straight forward interpretation: We have set up our description by assuming that the operator we study is dual to a threebrane with an open string attached. This implies that our operator can be decomposed into a “threebrane piece” and a “string piece”. These two pieces are treated very differently: when contracting the threebrane piece, all contractions are summed; when contracting the string piece, only planar contractions are summed. Contractions between the two pieces are dropped. When a large number of $Z$s hop onto the open string our operator is simply not dual to a state that looks like a threebrane with an open string attached and our approximations are not valid. We are not claiming that this operator can not be studied using large $N$ techniques - it may still be possible to set up a systematic $1/N$ expansion. We are claiming that the diagrams we have summed do not give this approximation. It is useful to decompose the potential for the scalars into D terms and F terms. The advantage of this decomposition is that it is known that at one loop, the D term contributions cancel with the gauge boson exchange and the scalar self energies[@Constable:2002hw]. Consequently we will only consider the planar interactions arising from the F term. The F term interaction preserves the number of $Y$’s (the lattice is not dynamical) and allows impurities (the $Z$s) to hop between neighboring sites. The bulk interactions are described by the Hamiltonian $$H_{bulk} = 2\lambda\sum_{l=1}^L \hat{a}_l^\dagger \hat{a}_l -\lambda\sum_{l=1}^{L-1}(\hat{a}_l^\dagger \hat{a}_{l+1} +\hat{a}_l \hat{a}^\dagger_{l+1}), \label{bulk}$$ where $$\hat{a}_i \hat{a}_i^\dagger = I,\qquad \hat{a}^\dagger_i \hat{a}_i = I-\|0\rangle\langle 0\|.$$ The interested reader is referred to [@Berenstein:2006qk] for the derivation of this result. To obtain the full Hamiltonian, we need to include the boundary interactions arising from the string/brane system interaction. This interaction introduces sources and sinks for the impurities at the boundaries of the lattice. The boundary interaction allows $Z$s to hop from the string onto the giant, or from the giant onto the string. Since the number of $Z$s gives the angular momentum of the system in the plane that the giant is orbiting in, the boundary interaction allows the string and the brane to exchange angular momentum. We can classify the different types of boundary interaction depending on whether momentum flows from the string to the brane or from the brane to the string. Consider the interaction that allows a $Z$ to hop from the first or last site of either string onto the giant. In this process the string loses momentum to the giant graviton. We call this a “hop off” process because a $Z$ has hopped off the string. The opposite process in which a $Z$ hops off the brane and onto the string is called a “hop on” process. In the “hop on” process the giant loses momentum to the string. In addition to these momentum exchanging processes, there is also a boundary interaction in which a $Z$ belonging to the giant “kisses" the first (or last) $Y$ in the open string word so that no momentum is exchanged. We call this the kissing interaction. In Appendix C we will derive a set of identities that allow us to compute the term in the Hamiltonian describing the “hop off" process. These identities make extensive use of the technology for computing restricted characters which is developed in Appendix B. We will now explain what we mean by a restricted character. Let $R$ be an irrep of $S_n$ and let $R_1$ be an irrep of $S_{n-m}$ with $0<m<n$. If we restrict ourselves to elements $\sigma\in S_{n-m}$, then $\Gamma_R(\sigma)$ will, in general, subduce a number of irreps of $S_{n-m}$. One of these irreps is $R_1$. A restricted character $\chi_{R,R_1}(\sigma)$ is obtained by tracing the matrix representing $\sigma$ in irrep $R$, $\Gamma_R(\sigma)$, over the $R_1$ subspace. If $\sigma\in S_{n-m}$ this simply gives the character of $\sigma$ in irrep $R_1$. Our technology allows the computation of $\chi_{R,R_1}(\sigma)$ even when $\sigma\notin S_{n-m}$, in which case $\chi_{R,R_1}(\sigma)$ does not have an obvious group theory interpretation. The basic idea we exploit in constructing the “hop off” process is simple to state: In a string-giant system, whenever a $Z$ field hops past the borders of the open string word $W$, the resulting restricted Schur polynomial decomposes into a sum of two types of systems, one is a giant with a closed string and another is a string-giant system where the giant is now bigger. In the large $N$ limit only this second type needs to be considered. Our identities express this decomposition. Since the Hamiltonian must be Hermitian, we can obtain the “hop on" term by daggering the “hop off" term. Finally, we obtain the momentum conserving boundary interaction by expressing the kiss as a hop on followed by a hop off. This determines the complete Cuntz oscillator chain Hamiltonian needed for a one loop computation of the anomalous dimensions of operators dual to excited giant graviton bound states. This derivation of the Cuntz chain Hamiltonian, which is the main technical result of this article, is given in section 2. The resulting Hamiltonian clearly reflects the worldsheet structure of the open strings that are interacting. This explains how the Chan-Paton factors associated with strings in a multi-brane system dynamically emerge from Yang-Mills theory: they emerge from the symmetric group labels of the restricted Schur polynomials. Our Hamiltonian treats string 1 and string 2 differently. This is not at all surprising, since when we built our operator we treated the two strings differently. In section 3 we describe a new “physical basis” singled out by the requirement that the two strings enter on an equal footing. In section 4 we present our conclusions. Strings stretching between giants in AdS can be realized as solutions to the Born-Infeld action describing the world volume dynamics of these branes[@Shahin]. In this work the Gauss law is enforced by the construction of consistent solutions to the equations of motion on a compact space. In the work [@Balasubramanian:2004nb] the one loop anomalous dimension of operators representing a string attached to a two brane bound state was considered. One of the branes was taken to be a maximal giant to simplify the computation. For two coincident branes, the one-loop anomalous dimension for an open string is twice the answer for a single brane. This is the first, to the best of our knowledge, hint of the dynamical emergence of Chan-Paton factors for open strings on coincident branes. The demonstration of [@Balasubramanian:2004nb] identifies the extra factor of 2 with the trace over the indices of the enhanced gauge group associated to coincident branes. Our demonstration proves this identification: we can follow the Chan-Paton indices in the tree level transitions of two open strings. Further, using the technology we develop, it is straight forward (but technically involved) to generalize this result to a bound state of $m$ branes, where we expect a $U(m)$ gauge theory to emerge. As an example, in Appendix F we consider a boundstate of three sphere giants. In this case, a $U(3)$ gauge theory emerges. Cuntz Chain Hamiltonian ======================= In this section we will derive the form of the terms in the Hamiltonian describing the string boundary interactions. This will allow us to compute the complete Cuntz chain Hamiltonian, since the bulk Hamiltonian has already been given in (\[bulk\]). Hop Off Interaction ------------------- We start by deriving the hop off interaction. The F term vertex allows a $Z$ and a $Y$ to change position within a word. The hopping interaction corresponds to the situation in which a $Z$ hops past the $Y$ marking the end point of the string, i.e. a $Z$ hops off the string and onto the giant. Concretely, when acting on either open string, this hop takes $$W(\{n_1,n_2,\cdots,n_{L-1}\})\to ZW(\{n_1-1,n_2,\cdots,n_{L-1}\})\quad {\rm or}$$ $$W(\{n_1,n_2,\cdots,n_{L-1}\})\to W(\{n_1,n_2,\cdots,n_{L-1}-1\})Z .$$ To determine the corresponding term in the interaction Hamiltonian, we need to be able to express objects like $\chi_{R,R''}^{(2)}(Z,ZW^{(1)},W^{(2)})$ in terms of $\chi_{S,S''}^{(2)}(Z,W^{(1)},W^{(2)})$ where $S$ is a Young diagram with one more box than $R$[^7]. This is easily achieved by inverting the identities derived in Appendix C. To get the hop off interaction in the Hamiltonian, we rewrite the identities in terms of normalized Cuntz chain states. [1.0cm]{} [$+1\to 1$ Hop off Interaction:]{} This term in the Hamiltonian describes the hop off process in which a $Z$ hops out of the first site of string 1. We write $+1\to 1$ to indicate that the string before the hop has one extra $Z$ in its first site. $$H_{+1\to 1} \left[\matrix{\|b_0-1,b_1,bb,ll\rangle\cr \|b_0-1,b_1,ll,bb\rangle\cr \|b_0-1,b_1,bl,lb\rangle\cr \|b_0-1,b_1,lb,bl\rangle\cr \|b_0-2,b_1+2,ll,ll\rangle\cr \|b_0,b_1-2,bb,bb\rangle}\right] =-\lambda\sqrt{1-{b_0\over N}}M_1 \left[\matrix{\|b_0-1,b_1+1,bb,ll\rangle\cr \|b_0,b_1-1,ll,bb\rangle\cr \|b_0-1,b_1+1,bl,lb\rangle\cr \|b_0,b_1-1,lb,bl\rangle\cr \|b_0-1,b_1+1,ll,ll\rangle\cr \|b_0,b_1-1,bb,bb\rangle}\right],$$ where $$M_1=\left[\matrix{ -(b_1)_1^2 &{1\over b_1(b_1+1)^2} &0 &{(b_1)_0\over b_1+1} &{(b_1)_1\over b_1+1} &-{(b_1)_1\over b_1 (b_1+1)}\cr -{1\over (b_1+2)(b_1+1)^2} &-(b_1)_1^2 &-{(b_1)_2\over b_1+1} &0 &-{(b_1)_1\over (b_1+1)(b_1+2)} &-{(b_1)_1\over b_1+1}\cr -{(b_1)_1\over (b_1+1)(b_1+2)} &{(b_1)_1\over b_1+1} &-(b_1)_1(b_1)_2 &0 &-{b_1\over (b_1+1)^2} &{1\over (b_1+1)^2}\cr -{(b_1)_1\over b_1+1} &-{(b_1)_1\over b_1(b_1+1)} &0 &-(b_1)_0(b_1)_1 &{1\over (b_1+1)^2} &{b_1+2\over (b_1+1)^2}\cr -{(b_1)_2\over b_1+1} &0 &{1\over b_1+2} &0 &-(b_1)_1(b_1)_2 &0\cr 0 &{(b_1)_0\over b_1+1} &0 &-{1\over b_1} &0 &-(b_1)_0(b_1)_1 }\right],$$ and $$(b_1)_n={\sqrt{b_1+n-1}\sqrt{b_1+n+1}\over b_1+n}.$$ The term in the Hamiltonian describing the process in which the $Z$ hops out of the last site of string 1 is described by swapping the labels of the endpoints of the open strings. Concretely, it is given by $$H_{1+\to 1} \left[\matrix{\|b_0-1,b_1,bb,ll\rangle\cr \|b_0-1,b_1,ll,bb\rangle\cr \|b_0-1,b_1,lb,bl\rangle\cr \|b_0-1,b_1,bl,lb\rangle\cr \|b_0-2,b_1+2,ll,ll\rangle\cr \|b_0,b_1-2,bb,bb\rangle}\right] =-\lambda\sqrt{1-{b_0\over N}}M_1 \left[\matrix{\|b_0-1,b_1+1,bb,ll\rangle\cr \|b_0,b_1-1,ll,bb\rangle\cr \|b_0-1,b_1+1,lb,bl\rangle\cr \|b_0,b_1-1,bl,lb\rangle\cr \|b_0-1,b_1+1,ll,ll\rangle\cr \|b_0,b_1-1,bb,bb\rangle}\right],$$ where $M_1$ is the matrix given above. We write $1+\to 1$ to indicate that the string before the hop has one extra $Z$ in its last site. [1.0cm]{} [$+2\to 2$ Hop off Interaction:]{} This term in the Hamiltonian describes the hop off process in which a $Z$ hops out of the first site of string 2. $$H_{+2\to 2} \left[\matrix{\|b_0-2,b_1+1,bb,ll\rangle\cr \|b_0-1,b_1-1,ll,bb\rangle\cr \|b_0-2,b_1+1,bl,lb\rangle\cr \|b_0-1,b_1-1,lb,bl\rangle\cr \|b_0-2,b_1+1,ll,ll\rangle\cr \|b_0-1,b_1-1,bb,bb\rangle}\right] =-\lambda\sqrt{1-{b_0\over N}}M_2 \left[\matrix{\|b_0-1,b_1,bb,ll\rangle\cr \|b_0-1,b_1,ll,bb\rangle\cr \|b_0-1,b_1,bl,lb\rangle\cr \|b_0-1,b_1,lb,bl\rangle\cr \|b_0-1,b_1,ll,ll\rangle\cr \|b_0-1,b_1,bb,bb\rangle}\right],$$ where $$M_2=\left[\matrix{ -(b_1)_1^2 &-{1\over (b_1+2)(b_1+1)^2} &-{(b_1)_1\over (b_1+1)(b_1+2)} &-{(b_1)_1\over b_1+1} &0 &-{(b_1)_2\over b_1+1}\cr {1\over b_1(b_1+1)^2} &-(b_1)_1^2 &{(b_1)_1\over b_1+1} &-{(b_1)_1\over (b_1+1)b_1} &{(b_1)_0\over b_1+1} &0\cr 0 &-{(b_1)_2\over b_1+1} &-(b_1)_1(b_1)_2 &0 &0 &{1\over b_1+2}\cr {(b_1)_0\over b_1+1} &0 &0 &-(b_1)_0(b_1)_1 &-{1\over b_1} &0\cr -{(b_1)_1\over b_1(b_1+1)} &-{(b_1)_1\over b_1+1} &{1\over (b_1+1)^2} &{b_1+2\over (b_1+1)^2} &-(b_1)_1(b_1)_0 &0\cr {(b_1)_1\over b_1+1} &-{(b_1)_1\over (b_1+1)(b_1+2)} &-{b_1\over (b_1+1)^2} &{1\over (b_1+1)^2} &0 &-(b_1)_2(b_1)_1 }\right].$$ Notice that these interactions (as is the case for all of the boundary interactions) are highly suppressed for a maximal giant[@Maxg]. The term in the Hamiltonian describing the process in which the $Z$ hops out of the last site of string 2 is described by swapping the labels of the endpoints of the open strings. The function $(b_1)_n$ also appears in the Hamiltonian relevant for a single string attached to a giant[@de; @Mello; @Koch:2007uv]. Notice that $(b_1)_n$ vanishes when $b_1=1-n$, but tends to 1 very rapidly as $b_1$ is increased from this value. The diagonal terms in the Hamiltonian with a $(b_1)_1$ factor will thus vanish when $b_1=0$. The radius of each giant is determined by their momentum. Since $b_1$ is the difference in momentum of the two giants, $b_1=0$ corresponds to coincident giants. Thus, $(b_1)_n$ is switching off short distance interactions. The hop off Hamiltonian does not generate illegal Young diagrams from legal ones precisely because these interactions are switched off. It may seem puzzling that the boundary interaction has the universal strength $\sqrt{1-{b_0\over N}}$ regardless of which end the $Z$ peels off. Indeed, any local boundary interaction should only know about the boundary which is participating. Since the string end points are on branes of different sizes, one would expect two different strengths for the two endpoints. This universal strength is an artifact of the limit we consider. We take $b_0$ to be $O(N)$ and $b_1$ to be $O(1)$. The strength $\sqrt{1-{b_0\over N}}$ arises from the normalization of the Cuntz oscillator states for the string endpoint attached to the smaller giant graviton (see appendix D for these normalizations). Similarly, the strength $\sqrt{1-{b_0+b_1\over N}}$ arises from the normalization of the Cuntz oscillator states for the string endpoint attached to the larger giant graviton. In the limit we consider $$\sqrt{1-{b_0+b_1\over N}}-\sqrt{1-{b_0\over N}}=O\Big({1\over N}\Big).$$ Physically, taking $b_0=O(N)$ and $b_1=O(1)$ implies that the two branes are very nearly coincident. Finally, note that the structure of the hop on and hop off interactions, clearly reflect the fact that the open strings attached to the giants are orientable. Hop On Interaction ------------------ Since ${\cal N}=4$ super Yang-Mills theory is a unitary conformal field theory, we know that the spectrum of anomalous dimensions of the theory is real. This implies that the energy spectrum of our Cuntz chain Hamiltonian must be real and hence the Hamiltonian must be Hermitian. Thus, the hop on term in the Hamiltonian is given by the Hermitian conjugate of the hop off term. To give an example, we will now derive the term in the Hamiltonian describing the process in which a $Z$ from the brane hops into the first site of string 1. Let $\|\psi\rangle$ denote the state with a brane of momentum $P_{\rm brane}=P$ and a string of momentum $P_{\rm string}=p$ and $\|\phi\rangle$ denote the state with $P_{\rm brane}=P+1$ and $P_{\rm string}=p-1$. Then, $$H_{+1\to 1}\|\psi\rangle =-\lambda\sqrt{1-{b_0\over N}}M_1\|\phi\rangle ,$$ and $$\langle\phi' \|H_{+1\to 1}\|\psi\rangle =-\lambda\sqrt{1-{b_0\over N}}\langle\phi' \|M_1\|\phi\rangle = -\lambda\sqrt{1-{b_0\over N}} (M_1)_{\phi'\phi}.$$ Daggering we find (keep in mind that $M_1$ is real) $$\begin{aligned} \langle\psi \|H_{1\to +1}\|\phi'\rangle &=&(\langle\phi' \|H_{+1\to 1}\|\psi\rangle)^\dagger\nonumber\\ &=&-\lambda\sqrt{1-{b_0\over N}}\langle\phi \|(M_1)^T\|\phi'\rangle \nonumber\\ &=&-\lambda\sqrt{1-{b_0\over N}} \left( (M_1{})^T\right)_{\phi\phi'}.\nonumber\end{aligned}$$ Thus we obtain $$H_{1\to +1} \|\phi\rangle=-\lambda\sqrt{1-{b_0\over N}}N_1\|\psi\rangle ,$$ with $N_1=(M_1)^T$. Kissing Interaction ------------------- =16.0cm The kissing interaction corresponds to the Feynman diagram shown on the left in Figure \[fig:kissing.ps\]. Notice that the number of $Z$ fields in the giant is unchanged by this process so that the string and brane do not exchange momentum by this process. As far as the combinatorics goes, we can model the kissing interaction as a hop on (the string) followed by a hop off. We know both the hop on and hop off terms so the kissing interaction follows. This is illustrated by the Feynman diagram shown on the right in Figure 1. The kissing interaction must be included for both endpoints of both strings. A straight forward computation easily gives $$H_{\rm kissing}=\lambda \left(1-{b_0\over N}\right){\bf 1},$$ for each endpoint of either string. In this formula ${\bf 1}$ is the identity operator. The fact that the kissing interaction comes out proportional to the identity operator is a non-trivial check of our hop on and hop off interactions. Indeed, the contraction of the F term vertex which leads to the kissing interaction removes an adjacent $Z$ and $Y$ and then replaces them in the same order. Thus, the kissing interaction had to come out proportional to the identity. The careful reader may worry that this is not in fact true - indeed, the restricted Schur polynomial includes terms in which the open string word is traced and terms in which the two open string words are multiplied. For these terms there is no $Z$ next to the word to “do the kissing”. Precisely these terms were considered in Appendix C.5. They do not contribute at large $N$. Validity of the Cuntz Chain Hamiltonian --------------------------------------- We have made a number of approximations. When contracting the open string words, only the planar diagrams have been summed. The non-planar contributions can only be neglected if ${L^2\over N}\ll 1$. Contributions coming from contractions between $Z$s in the open strings and $Z$s associated to the brane system have been dropped. When computing two point functions in free field theory, if the number of boxes in the representation $R$ is less than $O(N^2)$ and the numbers of $Z$’s in the open string is $O(1)$, the contractions between any $Z$s in the open string and the rest of the operator are suppressed in the large $N$ limit[@recent]. Contractions between $Z$s in different open string words have been dropped because they are non planar and are hence subleading. No large combinatoric factors modify this. Finally, when $J$ is large, back reaction is important and the approximations we are employing are no longer valid. When $J$ becomes $O(\sqrt{N})$ the assumption that we can drop non-planar contributions when contracting the open string words breaks down. Interpretation ============== The operators we are studying are dual to giant gravitons with open strings attached. Since the giant gravitons have finite volume, the Gauss Law implies that the total charge on each giant must vanish - there must be the same number of strings leaving each brane as there are arriving on each brane. These operators do indeed satisfy these non-trivial constraints[@Balasubramanian:2004nb], providing convincing evidence for the proposed duality. The low energy dynamics of the open strings attached to the giant gravitons is a Yang-Mills theory. This new [emergent]{} $3+1$ dimensional Yang-Mills theory is not described as a local field theory on the $S^3$ on which the original Yang-Mills theory is defined - it is local on a new space, the world volume of the giant gravitons[@Balasubramanian:2004nb],[@Balasubramanian:2001dx]. This new space emerges from the matrix degrees of freedom participating in the Yang-Mills theory. Reconstructing this emergent gauge theory may provide a simpler toy model that will give us important clues into reconstructing the full AdS$_5\times$S$^5$ quantum gravity. In this section, our goal is to make contact with this emergent Yang-Mills dynamics. Dynamical Emergence of Chan-Paton Factors ----------------------------------------- Return to the $H_{+1\to 1}$ hop off interaction obtained in section 2.1. Recall that this corresponds to the interaction in which a $Z$ hops out of the first site of string 1. If we expand the matrix $M_1$ for large $b_1$, we find $$M_1= \sum_{n=0}^{\infty} M_1(n)b_1^{-n}.$$ The leading order $M_1(0)$ is simply $-{\bf 1}$ with ${\bf 1}$ the $6\times 6$ identity matrix. The $Z$ simply hops off the string and onto the brane without much rearranging of the system. This is the dominant process. Next, consider the term of order $b_1^{-1}$. It is simple to compute $$M_1(1)=\left[\matrix{ 0 &0 &0 &1 &1 &0 \cr 0 &0 &-1 &0 &0 &-1\cr 0 &1 &0 &0 &-1 &0 \cr -1 &0 &0 &0 &0 &1 \cr -1 &0 &1 &0 &0 &0 \cr 0 &1 &0 &-1 &0 &0 }\right].$$ The radius of the giant graviton $R_g$ is related to its momentum $P$ by $R_g=\sqrt{P\over N}$. The giant orbits with a radius $R =\sqrt{1-R_g^2}.$ For the two giants in the bound state we are considering we have $P_1=b_0$ and $P_2=b_0+b_1$. Using the fact that $b_0=O(N)$ and $b_1=O(1)$ it is simple to verify that both the difference in the radii of the two giants and the difference in the radii of their orbits is proportional to $b_1$. Thus, a $b_1^{-1}$ dependence indicates a potential with an inverse distance dependence which is the correct dependence for massless particles moving in $3+1$ dimensions. In Figure \[fig:interactions1.ps\] we have represented the transitions implied by $M_1(1)$ graphically. Transitions between any two adjacent Young diagrams are allowed. =18.0cm As an example, consider the transition $$\young({\,}{\,},{\,}{\,},{\,}{\,},{\,}{1},{\,},{\,},{\,},{2})\to \young({\,}{\,},{\,}{\,},{\,}{\,},{\,}{\twoone},{\,},{\,},{\,},{\,},{\onetwo}).$$ The upper label of string 1 has moved. In all of the transitions shown, the upper index of string 1 always moves, so that it is natural to associate the upper index of string 1 with the first site of string one, and to look for an interpretation of this interaction in terms of open string processes that involve the upper index of string 1. The figures between the Young diagram show that there is indeed a natural interpretation for these transitions. [It is clear that our Cuntz oscillator dynamics illustrates how the Chan-Paton factors for open strings propagating on multiple branes arise dynamically.]{} Drawing all possible ribbon diagrams correctly accounts for both $M_1(0)$ and $M_1(1)$. Physical Basis -------------- Although the interpretation of the $b_1^{-1}$ terms is encouraging, there are extra higher order corrections ($M_1(2)b_1^{-2}$, $M_1(3)b_1^{-3}$ and higher orders) that do not seem to have a natural open string interpretation. In addition to this, the interaction we have obtained depends on the open string words describing each open string, the Young diagram describing the brane bound state system as well as the order in which the strings were attached. This dependence on the order in which the strings are attached is not physically sensible. It is natural to expect that the resolution to these two puzzles is connected. Recall that when constructing the restricted Schur polynomial we have assumed that when computing reductions, string 1 is removed first and string 2 second. This arbitrary choice defines a basis for the Cuntz oscillator chain. We interpret the unphysical features of our interactions, described in the previous paragraph, as reflecting a property of the basis it is written in and not as an inherent problem with the interaction. In this section we will define a new physical basis, singled out by the requirement that the boundary interaction does not depend on the order in which the open strings are attached. A few comments are in order. A basis for the ${1\over 2}$ BPS states (giants with no open strings attached) is provided by the taking traces of $Z$ or by taking subdeterminants or by the Schur polynomials. These are three perfectly acceptable bases, since using any single one of these bases we can generate, by taking linear combinations of the elements of the basis considered, a member from every ${1\over 2}$ BPS multiplet[@Corley:2001zk]. From a physical point of view, these different bases are not on an equal footing: the Schur polynomial is the most useful. Indeed, the Schur polynomials diagonalize the matrix of two point correlators (Zamolodchikov metric) so that they can be put into correspondence with the (orthogonal) states of a Fock space. In the same way, the basis for excited giants gravitons we have been considering is a perfectly acceptable basis. However, it is the operators in the physical basis (defined below) that have a good physical interpretation. Denote our two strings by string $A$ and string $B$. The state obtained by attaching string $A$ first will be denoted by $\|b_0,b_1,x_A y_A, x_B y_B \rangle $, where $x_A y_A$ are the endpoints of string $A$ and $x_B y_B$ are the endpoints of string $B$. The state obtained by attaching string $B$ first will be denoted by $\|b_0,b_1,x_B y_B, x_A y_A \rangle\!\rangle $. In each subspace of sharp giant graviton momentum (definite $b_0$ and $b_1$), we can write the following relation between these two sets of states $$\left[\matrix{ \|b_0,b_1,bb,ll \rangle\cr \|b_0,b_1,ll,bb \rangle\cr \|b_0,b_1,bl,lb \rangle\cr \|b_0,b_1,lb,bl \rangle\cr \|b_0,b_1,ll,ll \rangle\cr \|b_0,b_1,bb,bb \rangle}\right]=PT \left[\matrix{ \|b_0,b_1,bb,ll \rangle\!\rangle\cr \|b_0,b_1,ll,bb \rangle\!\rangle\cr \|b_0,b_1,bl,lb \rangle\!\rangle\cr \|b_0,b_1,lb,bl \rangle\!\rangle\cr \|b_0,b_1,ll,ll \rangle\!\rangle\cr \|b_0,b_1,bb,bb \rangle\!\rangle }\right],$$ where $$P=\left[\matrix{ 0 &1 &0 &0 &0 &0\cr 1 &0 &0 &0 &0 &0\cr 0 &0 &0 &1 &0 &0\cr 0 &0 &1 &0 &0 &0\cr 0 &0 &0 &0 &1 &0\cr 0 &0 &0 &0 &0 &1}\right]\qquad {\rm and}$$ [$$T=\left[\matrix{ \left(1-{1\over (b_1+1)^2}\right) & {1\over (b_1+1)^2} &-{1\over (b_1+1)}\sqrt{1-{1\over (b_1+1)^2}} &-{1\over (b_1+1)}\sqrt{1-{1\over (b_1+1)^2}} &0 &0\cr {1\over (b_1+1)^2} & \left(1-{1\over (b_1+1)^2}\right) &{1\over (b_1+1)}\sqrt{1-{1\over (b_1+1)^2}} &{1\over (b_1+1)}\sqrt{1-{1\over (b_1+1)^2}} &0 &0\cr {1\over (b_1+1)}\sqrt{1-{1\over (b_1+1)^2}} &-{1\over (b_1+1)}\sqrt{1-{1\over (b_1+1)^2}} &\left(1-{1\over (b_1+1)^2}\right) &-{1\over (b_1+1)^2} &0 &0\cr {1\over (b_1+1)}\sqrt{1-{1\over (b_1+1)^2}} &-{1\over (b_1+1)}\sqrt{1-{1\over (b_1+1)^2}} &-{1\over (b_1+1)^2} &\left(1-{1\over (b_1+1)^2}\right) &0 &0\cr 0 &0 &0 &0 &1 &0\cr 0 &0 &0 &0 &0 &1} \right].$$ ]{} The matrix $T$ is determined by the subgroup swap rule of [@de; @Mello; @Koch:2007uu]. It is satisfying that $PT\times PT=1$. It is straight forward to check that $$H_{+1\to 1}=A_{2\to 1}\, PT\, H_{+2\to 2}\, A_{1\to 2}\, PT,$$ where $$\left[\matrix{ \|b_0-2,b_1+2,bb,ll \rangle\cr \|b_0-1,b_1,ll,bb \rangle\cr \|b_0-2,b_1+2,bl,lb \rangle\cr \|b_0-1,b_1,lb,bl \rangle\cr \|b_0-2,b_1+2,ll,ll \rangle\cr \|b_0-1,b_1,bb,bb \rangle}\right]=A_{2\to 1} \left[\matrix{ \|b_0-1,b_1,bb,ll \rangle\cr \|b_0-1,b_1,ll,bb \rangle\cr \|b_0-1,b_1,bl,lb \rangle\cr \|b_0-1,b_1,lb,bl \rangle\cr \|b_0-1,b_1,ll,ll \rangle\cr \|b_0-1,b_1,bb,bb \rangle }\right],\qquad {\rm and}$$ $$\left[\matrix{ \|b_0-2,b_1+1,bb,ll \rangle\cr \|b_0-1,b_1-1,ll,bb \rangle\cr \|b_0-2,b_1+1,bl,lb \rangle\cr \|b_0-1,b_1-1,lb,bl \rangle\cr \|b_0-2,b_1+1,ll,ll \rangle\cr \|b_0-1,b_1-1,bb,bb \rangle}\right]=A_{1\to 2} \left[\matrix{ \|b_0-2,b_1+1,bb,ll \rangle\cr \|b_0-2,b_1+1,ll,bb \rangle\cr \|b_0-2,b_1+1,bl,lb \rangle\cr \|b_0-2,b_1+1,lb,bl \rangle\cr \|b_0-3,b_1+3,ll,ll \rangle\cr \|b_0-1,b_1-1,bb,bb \rangle }\right].$$ Denote the similarity transformation which takes us to the physical basis by $S$. In this basis, we denote $H_{+1\to 1}$ by $\hat{H}_{+1\to 1}$ and $H_{+2\to 2}$ by $\hat{H}_{+2\to 2}$. Clearly $$\hat{H}_{+1\to 1} = SH_{+1\to 1}S^{-1},\qquad \hat{H}_{+2\to 2}=S H_{+2\to 2}S^{-1}.$$ The transformation $S$ is now determined by the requirement $$\hat{H}_{+1\to 1}=P\hat{H}_{+2\to 2}P .$$ We have not yet been able to solve this equation for $S$. Due to the presence of $A_{1\to 2}$ and $A_{2\to 1}$ in the relation between $H_{+1\to 1}$ and $H_{+2\to 2}$, it seems that $S$ must mix subspaces of different giant momenta $(b_0,b_1)$. In this case the physical basis will not have sharp giant momentum and hence the resulting states will not have a definite radius. This is not too surprising: the open strings will pull “dimples” out of the giant graviton’s world volume so that the giant with an open string attached does not have a definite radius. We leave the interesting question of determining the transformation $S$ for the future. Discussion ========== A bound state of giant gravitons can be excited by attaching open strings. The problem of computing the anomalous dimensions of these operators can be replaced with the problem of diagonalizing a Cuntz oscillator Hamiltonian. In this article we have developed the technology needed to construct this Cuntz oscillator Hamiltonian to one loop. Firstly, we have given an algorithmic construction of the operators dual to excitations described by open strings which stretch between the branes. This involved giving an explicit construction of the intertwiner which is used to construct the relevant restricted Schur polynomial. Secondly, we have developed methods that allow an efficient evaluation of any restricted character. Our method expresses the restricted character graphically as a sum of strand diagrams. Finally, we have explained how to derive the boundary interaction terms from identities satisfied by the restricted Schur polynomials. Since the excited giant graviton operators are small excitations of BPS states, we expect that our results can be extrapolated to strong coupling and hence can be compared with results from the dual string theory. The form of our Cuntz oscillator Hamiltonian provides evidence that the excitations of the giant gravitons have the detailed interactions of an emergent gauge theory. In particular, we have demonstrated the dynamical emergence of the Chan-Paton factors of the open strings. We have also started to clarify the dictionary relating the states of the Cuntz oscillator chain to the states of string field theory on D-branes in AdS$_5\times$S$^5$. Although we have mainly considered a bound state of two sphere giants with two open strings attached, our methods are applicable to an arbitrary bound state of giant gravitons with any number of open strings attached. Our result is a generalization of the spin chains considered so far in the literature: usually the spin chain gives a description of closed strings. Our Cuntz oscillator describes the dynamics of an open string interacting with a giant graviton. Both the state of the string (described by the Cuntz chain occupation numbers) and the state of the giant graviton (the shape of the Young diagram) are dynamical in our approach. It is worth emphasizing that the new emergent gauge symmetry is distinct from the original gauge symmetry of the theory[@Balasubramanian:2004nb]. The excited giant graviton operators[@Balasubramanian:2004nb] are obtained by taking a trace over the indices of the symmetric group matrix $\Gamma_R(\sigma)$ appearing in the sum $${1\over (n-k)!} \sum_{\sigma\in S_n} \Gamma_R(\sigma)\Tr(\sigma Z^{\otimes n-k}W^{(1)}\cdots W^{(k)}),\qquad {\rm where}$$ $$\Tr (\sigma Z^{\otimes n-k}W^{(1)}\cdots W^{(k)})= Z^{i_1}_{i_{\sigma (1)}}Z^{i_2}_{i_{\sigma (2)}}\cdots Z^{i_{n-k}}_{i_{\sigma (n-k)}}(W^{(1)})^{i_{n-k+1}}_{i_{\sigma (n-k+1)}}\cdots (W^{(k)})^{i_{n}}_{i_{\sigma (n)}}.$$ The color indices of the original super Yang-Mills theory are all traced: every term in the above sum is a color singlet with respect to the gauge symmetry of the original Yang-Mills theory. The color indices of the new gauge theory arise from the labeling of the partial trace over $\Gamma_R(\sigma)$. In some sense we are “substituting” symmetric group indices for the original gauge theory indices. We call this mechanism “[color substitution]{}”. There are a number of directions in which this work can be extended. For Young diagrams with $m$ columns we expect an emergent Yang-Mills theory with gauge group $U(m)$. It would be nice to repeat the calculations we performed here in that setting[^8]. Another interesting calculation would involve studying the dynamics of two giant gravitons with strings stretched between them. In general, the boundary terms will certainly have different values at each boundary (as anticipated in [@Berenstein:2006qk]) in which case there will be a net flow of $Z$s from one brane to the other. This flow of $Z$’s will produce a force between the two giants, conjectured to be an attractive force in[@Berenstein:2006qk]. A very concrete application of our methods is the construction of the gauge theory operator dual to the fat magnon[@Hirano:2006ti][^9]. The fat magnon is a bound state of a giant graviton and giant magnons (fundamental strings). Essentially, due to the background five form flux, the giant magnon becomes fat by the Myers effect[@Myers:1999ps]. The fat magnon has the same anomalous dimension as the giant magnon. It would be nice to explicitely recover this anomalous dimension using our technology[^10]. Finally, there is now a proposal for gauge theory operators dual to brane-anti-brane states[@Kimura:2007wy]. This proposal was made, at the level of the free field theory, by identifying the operators that diagonalize the two point functions of operators built from $Z$ and $Z^\dagger$. Since these states are non-supersymmetric, corrections when the coupling is turned on are expected to be important for the physics. It would be interesting to extend the technology developed in this article to this non-supersymmetric setting. $$$$ [Acknowledgements:]{} We would like to thank Rajsekhar Bhattacharyya, Norman Ives, Sanjaye Ramgoolam, João Rodrigues, Shahin Sheikh-Jabbari and Alex Welte for pleasant discussions and/or helpful correspondence. This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation. Any opinion, findings and conclusions or recommendations expressed in this material are those of the authors and therefore the NRF and DST do not accept any liability with regard thereto. This work is also supported by NRF grant number Gun 2047219. $$$$ [Navigating the Appendices:]{} In the appendices we will freely make use of results obtained in the previous two articles in this series[@de; @Mello; @Koch:2007uu; @de; @Mello; @Koch:2007uv]. A reader wishing to master the details of our analysis will need to review this background. We will now explain which results are used when. For a discussion of intertwiners see sections 2.2 and section C.1 of [@de; @Mello; @Koch:2007uu]. In appendix B we make frequent use of the subgroup swap rule which is derived in appendix D of [@de; @Mello; @Koch:2007uu]. This is perhaps the most technical result from [@de; @Mello; @Koch:2007uu; @de; @Mello; @Koch:2007uv] that is used in this article. For this reason, we have reviewed a concrete example in the first section of appendix B. We also use the character identity given at the end of section D.1 of [@de; @Mello; @Koch:2007uu]. The strategy for deriving the hopping identities of appendix C was given in [@de; @Mello; @Koch:2007uv]. Intertwiners ============ Intertwiners are used to construct operators dual to states with open strings stretching between giant gravitons. In this appendix we provide a general discussion of intertwiners and their construction. Strings stretching between two branes ------------------------------------- The Gauss Law is a strict constraint on the allowed excited brane configurations[@Balasubramanian:2004nb]: since the branes we consider have a compact world volume, the total charge on any given brane must vanish. This implies that to construct a state with strings stretching between two branes, we need at least two strings in the brane plus string system. Thus, in constructing the restricted Schur polynomial, we will need to remove at least two boxes. For concreteness, consider the case of two sphere giants, so that our restricted Schur polynomial is built with the Young diagram $R$ that has two columns and each column has $O(N)$ boxes. $R$ has a total of $n=O(N)$ boxes. Denote the two boxes to be removed in constructing the restricted Schur polynomial[^11] by box 1 and box 2. To attach strings stretching between these two giants, the two boxes must belong to different columns. Assume that box 1 belongs to column 1 and box 2 to column 2. After restricting $S_n$ to an $S_{n-1}$ subgroup, representation $R$ subduces irrep $R'$ (whose Young diagram is obtained by removing box 1 from $R$) and irrep $S'$ (whose Young diagram is obtained by removing box 2 from $R$). If we now further restrict to an $S_{n-2}$ subgroup, one of the irreps subduced by $R'$ is $R''$ (whose Young diagram is obtained by removing box 2 from $R'$) and one of the irreps subduced by $S'$ is $S''$ (whose Young diagram is obtained by removing box 1 from $S'$). Note that $R''$ and $S''$ have the same Young diagram (and hence the same dimension) but act on distinct states in the carrier space of $R$. The two possible intertwiners we can define map between the states belonging to $R''$ and the states belonging to $S''$. The precise form of the intertwiners depends on the basis used for the $S_{n-2}$ irreps $\Gamma_{R''}(\sigma)$ and $\Gamma_{S''}(\sigma)$. In writing down the intertwiner, we assume that $\Gamma_{R''}(\sigma)$ and $\Gamma_{S''}(\sigma)$ represent $\sigma$ with the same matrix. With this assumption, it is possible to put the elements of the basis of the carrier space of $R''$ into one to one correspondence with the elements of the basis of the carrier space of $S''$: $\|i,R''\rangle \leftrightarrow \|i,S''\rangle$. We will use this correspondence below. In a suitable basis, we have $$\Gamma_R (\sigma )=\left[ \matrix{\Gamma_{R''}(\sigma ) &0 &\cdots\cr 0 &\Gamma_{S''}(\sigma) &\cdots\cr \cdots &\cdots &\cdots }\right],$$ for $\sigma\in S_{n-2}$. In constructing the restricted Schur polynomial, we also consider more general $\sigma\in S_n$. In this case, if $\sigma\notin S_{n-2}$, $\Gamma_R(\sigma )$ will not be block diagonal. Even in this more general case, we will use the labels of the $S_{n-2}$ subduced subspaces to label the carrier space of irrep $R$. Denote the projection operator that projects from the carrier space of $R$ to the $R''$ subspace by $P_{R\to R'\to R''}$, and the projection operator that projects from the carrier space of $R$ to the $S''$ subspace by $P_{R\to S'\to S''}$. Clearly, the intertwiner which maps from $S''$ to $R''$ must take the form $$I_{R'',S''}=P_{R\to R'\to R''}OP_{R\to S'\to S''}=\left[ \matrix{0 &M &\cdots\cr 0 &0 &\cdots\cr \cdots &\cdots &\cdots }\right]. \label{intertwiner}$$ The second possible intertwiner that we can construct is given by $$I_{S'',R''}=P_{R\to S'\to S''}OP_{R\to R'\to R''}=\left[ \matrix{0 &0 &\cdots\cr M &0 &\cdots\cr \cdots &\cdots &\cdots }\right].$$ We want to find a unique specification for $O$ so that $M$ is simply the identity matrix. For $\sigma\in S_{n-2}$ we have $$\Gamma_R(\sigma )I_{R'',S''}=\left[ \matrix{0 &\Gamma_{R''}(\sigma)M &\cdots\cr 0 &0 &\cdots\cr \cdots &\cdots &\cdots }\right]$$ and $$I_{R'',S''}\Gamma_R(\sigma )=\left[ \matrix{0 &M\Gamma_{S''}(\sigma) &\cdots\cr 0 &0 &\cdots\cr \cdots &\cdots &\cdots }\right].$$ Now, by assumption, $\Gamma_{R''}(\sigma)=\Gamma_{S''}(\sigma)$ since we have $\sigma\in S_{n-2}$. Thus, $$\big[ \Gamma_R(\sigma ),I_{R'',S''}\big]=\left[ \matrix{0 &\big[\Gamma_{R''}(\sigma),M\big] &\cdots\cr 0 &0 &\cdots\cr \cdots &\cdots &\cdots }\right]. \label{offdiag}$$ Applying Schur’s Lemma (for irrep $R''$) to the right hand side implies that $M$ is the identity matrix if and only if $\big[ \Gamma_R(\sigma ),I_{R'',S''}\big]=0$ for all $\sigma\in S_{n-2}$. Clearly, for $\sigma\in S_{n-2}$ we have $\big[ \Gamma_R(\sigma ),P_{R\to R'\to R''}\big]=\big[ \Gamma_R(\sigma ),P_{R\to S'\to S''}\big]=0$ so that $$0=\big[ \Gamma_R(\sigma ),I_{R'',S''}\big]=P_{R\to R'\to R''}\big[ \Gamma_R(\sigma ),O\big] P_{R\to S'\to S''}.$$ Thus, we will require $$\big[ \Gamma_R(\sigma ),O\big]=0,\qquad \forall \sigma\in S_{n-2}. \label{determineO}$$ If we specify a condition that determines the normalization of the intertwiner, then this normalization condition and (\[determineO\]) provide the specification for $O$ that we were looking for. The normalization of the intertwiner is fixed by demanding that $$\Tr (M)={\rm dim}_{R''},$$ with ${\rm dim}_{R''}$ the dimension of irrep $R''$. This provides a unique definition of the intertwiner. For the example we are considering here, imagine that the $S_{n-1}$ subgroup is obtained as $${\cal G}=\{\sigma\in S_n \| \sigma (n)=n\},$$ and further that the $S_{n-2}$ subgroup is obtained as $${\cal H}=\{\sigma\in {\cal G} \| \sigma (n-1)=n-1\} .$$ Then the intertwiner is given by $$I_{R'',S''}={\cal N} P_{R\to R'\to R''}\Gamma_R (n,n-1) P_{R\to S'\to S''},$$ with $${\cal N}^{-1}={\Tr_{R'',S''}(\Gamma_R (n,n-1) )\over {\rm dim}_{R''}}\equiv\sum_{i=1}^{{\rm dim}_{R''}} {\langle R'',i \|\Gamma_R(n,n-1)\|S'',i\rangle\over {\rm dim}_{R''} }.$$ This last equation makes use of the correspondence between the bases of the carrier spaces $R''$ and $S''$. Using the technology developed in the next appendix, we find $${\Tr_{R'',S''}(\Gamma_R (n,n-1) )\over {\rm dim}_{R''}}=\sqrt{1-{1\over (c_1-c_2)^2}},$$ where $c_1$ and $c_2$ are the weights associated with box 1 and box 2 respectively. Note that the above trace is invariant under simultaneous similarity transformations of $R''$ and $S''$. It will however, change under general similarity transformations so that this last result is dependent on our choice of basis. The General Construction ------------------------ In the previous section we have developed our discussion of the intertwiner using a system of two branes with strings stretching between them. Our conclusion however, is completely general. For any system of branes with strings stretching between the branes, the intertwiner is always given, up to normalization, by the product (projection operator)$\times$(group element)$\times$(projection operator). The Gauss Law forces the net charge on any given brane’s worldvolume to vanish. This implies that for every string leaving a brane’s worldvolume, there will be a string ending on the worldvolume. Thus, starting with any particular brane with a stretched string attached, we can follow the string to the next brane, switch to the stretched string leaving that brane, follow it and so on, until we again reach the first brane. If we move along $k$ stretched strings before returning to the starting point, the group element is $\Gamma_R(n,n-k+1)$. The normalization factor easily follows using the results of Appendix B. Example ------- Consider the excited brane system described by the diagram (see Appendix E for a summary of our graphical notation) [$$\young({\,}{\,}{\,}{\,}{\,},{\,}{\,}{\,}{\,}{\onetwo},{\,}{\,}{\,},{\,}{\,}{\twothree},{\,},{\threeone}) .$$ ]{} The boxes are labeled by the upper index in each box and the weight of box $i$ is denoted $c_i$. The projector $P_{R\to R'''_1}$ projects through the following sequence of irreps [$$\yng(5,5,3,3,1,1)\to\yng(5,4,3,3,1,1)\to\yng(5,4,3,2,1,1)\to\yng(5,4,3,2,1).$$ ]{} The projector $P_{R\to R'''_2}$ projects through the following sequence of irreps [$$\yng(5,5,3,3,1,1)\to\yng(5,5,3,3,1)\to\yng(5,4,3,3,1)\to\yng(5,4,3,2,1) .$$ ]{} The intertwiner is now given by $$I_{12}={\cal N} P_{R\to R'''_2}\Gamma_R\left((n,n-2)\right)P_{R\to R'''_1},$$ where $${\cal N}^{-1}={\Tr_{R'''_2,R'''_1}\left(\Gamma_R\left((n,n-2)\right)\right)\over {\rm dim}_{R'''_1}}= {1\over c_2-c_3}\sqrt{1-{1\over (c_1-c_2)^2}}\sqrt{1-{1\over (c_1-c_3)^2}},$$ is easily computed using the methods of appendix B. To understand the order of the projection operators, note that $$\begin{aligned} \Tr _{R'''_1,R'''_2}\Big(\Gamma_R(\sigma )\Big)&=&\sum_{i}\langle i,R'''_1 \|\Gamma_R(\sigma)\|i,R'''_2\rangle \nonumber\\ &=&\Tr ({\cal N}^{-1} P_{R\to R'''_2}\Gamma_R(n,n-2)P_{R\to R'''_1}\Gamma_R(\sigma) ), \nonumber\end{aligned}$$ so that the row (column) index of the trace is column (row) index of the intertwiner respectively. Restricted Characters ===================== Starting from $S_n$, define a chain of subgroups ${\cal G}_i$ $i=1,...,d$ as follows $${\cal G}_1=\{\sigma\in S_n\|\sigma(n)=n\} \label{sgroup1}$$ $${\cal G}_i=\{\sigma\in {\cal G}_{i-1}\|\sigma(n-i+1)=n-i+1\},\qquad i=2,3,...,d. \label{sgroup2}$$ In this appendix we will give a simple algorithm for the computation of $$\chi_{R_1,R_2}\Big( (p_1,p_2,...,p_m) \Big)\equiv\Tr_{R_1,R_2} \Big(\Gamma_R\big( (p_1,p_2,...,p_m)\big) \Big)$$ with $R_1$ and $R_2$ irreps of ${\cal G}_d$ subduced from $R$, $(p_1,p_2,...,p_m)$ is an element of $S_n$ specified using the cycle notation and $n-d< p_i \le n$ $\forall i$. We call $\chi_{R_1,R_2}$ a [restricted character]{}. If $R_1=R_2$, we will simply write $\chi_{R_1}$. We have already seen that restricted characters determine the normalization of the intertwiners. Further, they are also needed in the derivation of the hopping identities that determine the interactions between strings and the branes to which they are attached. The first subsection of this appendix reviews the subgroup swap rule in the setting of a specific example. In the next subsection we will derive the algorithm for the computation of the restricted character. The third subsection of this appendix describes a graphical notation which considerably simplifies the computation. The remainder of the appendix then develops this diagrammatic notation further. Review of the Subgroup Swap Rule -------------------------------- In this appendix, we review the subgroup swap rule. The reader requiring a more detailed explanation can consult Appendix D of [@de; @Mello; @Koch:2007uu]. Consider the restricted Schur polynomial $$\chi^{(2)}_{R,R''}\Big\|_1\Big\|_2={1\over (n-2)!}\sum_{\sigma\in S_n}\mathrm{Tr}_{R''}\left(\Gamma_R(\sigma )\right)Z^{i_1}_{i_{\sigma (1)}}\cdots Z^{i_{n-2}}_{i_{\sigma (n-2)}}(W^{(2)})^{i_{n-1}}_{i_{\sigma (n-1)}}(W^{(1)})^{i_n}_{i_{\sigma (n)}}.$$ The labelling on the left hand side tells us to first restrict with respect to the subgroup that leaves the index of $W^{(1)}$ inert, and then with respect to the subgroup that leaves the index of $W^{(2)}$ inert. In general, we will get a different polynomial if we were to restrict first with respect to the subgroup that leaves the index of $W^{(2)}$ inert, and then with respect to the subgroup that leaves the index of $W^{(1)}$ inert. There is a relation between these two sets of polynomials, which is known as the “subgroup swap rule”. We use the weights of the boxes of the Young diagrams in the subgroup swap rule. All weights are defined by the Young diagram before the swap. The weight of the box labelled with upper index 1 is denoted by $c_1^U$ and the weight of the box labelled with lower index 1 is denoted by $c_1^L$. Similarly for index 2. The upper and lower no-swap factors are given by $$N_U = \sqrt{1-\frac{1}{(c_1^U-c_2^U)^2}}, \qquad N_L = \sqrt{1-\frac{1}{(c_1^L-c_2^L)^2}} .$$ The upper and lower swap factors are given by $$S_U = \frac{1}{c_1^U - c_2^U}, \qquad S_L = \frac{1}{c_1^L - c_2^L} .$$ Our example uses a restricted Schur with three strings attached. Swapping strings $2$ and $3$, the subgroup swap rule gives $$\begin{aligned} \chi_{\young({\,}{\,}{\onetwo},{\,}{\twothree},{{\threeone}})} (\sigma) \Big\|_1\Big\|_2\Big\|_3 &=&\left [ N_L N_U \chi_{\young({\,}{\,}{\onetwo},{\,}{\twothree},{{\threeone}})} (\sigma) + S_U N_L \chi_{\young({\,}{\,}{\onetwo},{\,}{3},{{\twoone}})} (\sigma) \right ] \Big\|_1\Big\|_3\Big\|_2 \cr &+&\left [ S_L N_U \chi_{\young({\,}{\,}{\onetwo},{\,}{\twoone},{{3}})} (\sigma) + S_U S_L \chi_{\young({\,}{\,}{\onetwo},{\,}{\threeone},{{\twothree}})} (\sigma) \right ] \Big\|_1\Big\|_3\Big\|_2\end{aligned}$$ where $$N_U = \sqrt{1-\frac{1}{(c_2^U-c_3^U)^2}} = \frac{\sqrt{3}}{2}$$ $$N_L = \sqrt{1-\frac{1}{(c_2^L-c_3^L)^2}} = \frac{\sqrt{3}}{2},$$ $$S_U = \frac{1}{c_2^U - c_3^U} = \frac{1}{2},$$ $$S_L = \frac{1}{c_2^L - c_3^L} = \frac{1}{2}.$$ Whenever an index is swapped, we include a swap factor, and whenever there is no swap, we include a no-swap factor. Computing Restricted Characters ------------------------------- Consider an irrep $R$ of $S_n$ labeled by a Young diagram which has at least two boxes, either of which can be dropped to leave a valid Young diagram. Label these two boxes by 1 and 2. Denote the weights of these boxes by $c_1$ and $c_2$. Denote the irrep of $S_{n-2}$ obtained by dropping box 1 and then box 2 by $R_1''$. Denote the irrep of $S_{n-2}$ obtained by dropping box 2 and then box 1 by $R_2''$. Our first task is to compute $$\Tr_{R''_1,R''_2}\left(\Gamma_R\left( (n,n-1)\right)\right).$$ Using the subgroup swap rule obtained in [@de; @Mello; @Koch:2007uu], we can write $$\begin{aligned} \chi_{R_1''}\left((n,n-1)\right)&=&\left[1-{1\over (c_1-c_2)^2}\right]\chi_{R_2''}\left((n,n-1)\right) +{1\over (c_1-c_2)^2}\chi_{R_1''}\left((n,n-1)\right)\label{ssr1}\\ &+&\sqrt{1-{1\over (c_1-c_2)^2}}{1\over c_1-c_2 } \left[\chi_{R_1'',R_2''}\left((n,n-1)\right)+\chi_{R_2'',R_1''}\left((n,n-1)\right)\right]. \nonumber\end{aligned}$$ A second application of the subgroup swap rule gives $$\begin{aligned} \chi_{R_2'',R_1''}\left((n,n-1)\right)&=&\left[1-{1\over (c_1-c_2)^2}\right]\chi_{R_1'',R_2''}\left((n,n-1)\right) +{1\over (c_1-c_2)^2}\chi_{R_2'',R_1''}\left((n,n-1)\right) \nonumber\\ &+&\sqrt{1-{1\over (c_1-c_2)^2}}{1\over c_1-c_2 } \left[\chi_{R_2''}\left((n,n-1)\right)-\chi_{R_1''}\left((n,n-1)\right)\right]. \label{ssr2}\end{aligned}$$ Now, substituting the results[@de; @Mello; @Koch:2007uu] $$\chi_{R_1''}\left((n,n-1)\right)={1\over c_1-c_2}{\rm dim}_{R_1''},\qquad \chi_{R_2''}\left((n,n-1)\right)={1\over c_2-c_1}{\rm dim}_{R_2''},$$ into (\[ssr1\]) and (\[ssr2\]) and solving, we obtain $$\chi_{R_1'',R_2''}\left((n,n-1)\right)=\sqrt{1-{1\over (c_1-c_2)^2}}{\rm dim}_{R_1''}=\chi_{R_2'',R_1''}\left((n,n-1)\right).$$ Next, consider an irrep of $S_n$ labeled by Young diagram $R$ . Choose three boxes in this Young diagram, and label them 1, 2 and 3 respectively. Choose the boxes so that dropping box 1 gives a legal Young diagram $R'$ labeling an irrep of $S_{n-1}$, dropping box 1 and then box 2 gives a legal Young diagram $R''$ labeling an irrep of $S_{n-2}$, and dropping box 1, then box 2 and then box 3 again gives a legal Young diagram $R'''$ labeling an irrep of $S_{n-3}$. We will compute $$\chi_{R'''}\left( (n,n-2)\right)=\Tr_{R'''}\left(\Gamma_R \left( (n,n-2)\right)\right).$$ In what follows, we will frequently need to refer to vectors belonging to the carrier spaces of specific representations subduced by $R$ when boxes are dropped from $R$. A convenient notation is to list the labels of the boxes that must be dropped from $R$ in the order in which they must be dropped. Thus, the ket $\|i,123\rangle$ is the $i^{\rm th}$ ket belonging to the carrier space of the $S_{n-3}$ irrep obtained by dropping box 1, then box 2 and then box 3 from $R$; the ket $\|j,231\rangle$ is the $j^{\rm th}$ ket belonging to the carrier space of the $S_{n-3}$ irrep obtained by dropping box 2, then box 3 and then box 1 from $R$ (assuming of course that the boxes can be dropped from $R$ in this order, giving a legal Young diagram at each step). Start by writing $$\begin{aligned} \chi_{R'''} ((&n&,n-2))=\sum_{i=1}^{{\rm dim}_{R'''}} \langle i,123\|\Gamma_R \left( (n,n-2)\right) \|i, 123\rangle \nonumber\\ &=&\sum_{i=1}^{{\rm dim}_{R'''}} \langle i,123\|\Gamma_{R'} \left( (n-1,n-2)\right) \Gamma_R \left( (n,n-1)\right)\Gamma_{R'} \left( (n-1,n-2)\right)\|i, 123\rangle . \nonumber\end{aligned}$$ Noting that $\Gamma_{R'} \left( (n-1,n-2)\right)\|i, 123\rangle $ must belong to the carrier space of $R'$, and using the completeness relation ($1_{R'}$ is the identity on the $R'$ carrier space) $$1_{R'}=\sum_{k=1}^{{\rm dim}_{R'}} \|k,1\rangle\langle k,1\|,$$ we have $$\chi_{R'''}\left( (n,n-2)\right)=\sum_{i=1}^{{\rm dim}_{R'''}}\sum_{j,k=1}^{{\rm dim}_{R'}} \langle i,123\|\Gamma_{R'} \left( (n-1,n-2)\right)\|k,1\rangle\langle k,1\| \Gamma_R \left( (n,n-1)\right) \|j,1\rangle$$ $$\times \langle j,1\|\Gamma_{R'} \left( (n-1,n-2)\right)\|i, 123\rangle .$$ Now, decompose $R'$ into a direct sum of $S_{n-2}$ irreps $ R'=\oplus R_\beta ''$. Use the label $\beta$ to denote the box that must be dropped from $R'$ to obtain $R_\beta''$. Thus, we can write $$1_{R'}=\sum_{k=1}^{{\rm dim}_{R'}} \|k,1\rangle\langle k,1\|=\sum_{\beta}\sum_{k=1}^{{\rm dim}_{R_\beta ''}} \|k,1\beta\rangle\langle k,1\beta\|,$$ and hence $$\chi_{R'''}\left( (n,n-2)\right)=\sum_{i=1}^{{\rm dim}_{R'''}}\sum_{\beta_1,\beta_2}\sum_{k=1}^{{\rm dim}_{R_{\beta_1} ''}} \sum_{j=1}^{{\rm dim}_{R_{\beta_2} ''}} \langle i,123\|\Gamma_{R'} \left( (n-1,n-2)\right)\|k,1\beta_1 \rangle$$ $$\times \langle k,1\beta_1 \| \Gamma_R \left( (n,n-1)\right) \|j,1\beta_2\rangle\langle j,1\beta_2 \|\Gamma_{R'} \left( (n-1,n-2)\right)\|i, 123\rangle .$$ Now, introduce the operator $O(2)$ obtained by summing all two cycles of the $S_{n-2}$ subgroup of which the $R_\beta''$ are irreps. This operator is a Casimir of $S_{n-2}$. If the Young diagram $R_\beta''$ has $r_i$ boxes in the $i^{\rm th}$ row and $c_i$ boxes in the $i^{\rm th}$ column, then when acting on the carrier space of $R_\beta''$ we have[@chen] $$O(2)\|i,1\beta\rangle =\left[\sum_i {r_i (r_i-1)\over 2}-\sum_j {c_j(c_j-1)\over 2}\right]\|i,1\beta\rangle\equiv \lambda_\beta \|i,1\beta\rangle .$$ Clearly, for the problem we study here, $\lambda_{\beta_1}=\lambda_{\beta_2}$ if and only if $R_{\beta_1}$ and $R_{\beta_2}$ have the same shape as Young diagrams. From the definition of the ${\cal G}_2$ subgroup given above, it is clear that $$\big[ O(2),\Gamma_R\left( (n,n-1)\right)\big]=0.$$ It is now a simple matter to see that $$\begin{aligned} \lambda_{\beta_1}\langle k,1\beta_1 \| \Gamma_R \left( (n,n-1)\right)\|j,1\beta_2\rangle &=& \langle k,1\beta_1 \|O(2) \Gamma_R \left( (n,n-1)\right) \|j,1\beta_2\rangle\nonumber\\ &=&\langle k,1\beta_1 \| \Gamma_R \left( (n,n-1)\right)O(2)\|j,1\beta_2\rangle\nonumber\\ &=&\lambda_{\beta_2}\langle k,1\beta_1 \| \Gamma_R \left( (n,n-1)\right)\|j,1\beta_2\rangle\nonumber\end{aligned}$$ so that $\langle k,1\beta_1 \| \Gamma_R \left( (n,n-1)\right)\|j,1\beta_2\rangle$ vanishes if $R_{\beta_1}$ and $R_{\beta_2}$ do not have the same shape. A completely parallel argument, using a Casimir of $S_{n-3}$, can be used to show that $\langle j,1\alpha_1\alpha_2 \|\Gamma_{R'} \left( (n-1,n-2)\right)\|i, 123\rangle$ is only non-zero if $\alpha_1=2$, $\alpha_2=3$ or $\alpha_1=3$, $\alpha_2=2$. Thus, $$\begin{aligned} \chi_{R'''}\left( (n,n-2)\right)&=&\sum_{i=1,j,k}^{{\rm dim}_{R'''}}\Big[ \langle i,123\|\Gamma_{R'} \left( (n-1,n-2)\right)\|k,123 \rangle \langle k,123 \| \Gamma_R \left( (n,n-1)\right) \|j,123\rangle\nonumber\\ &\times&\langle j,123 \|\Gamma_{R'} \left( (n-1,n-2)\right)\|i, 123\rangle+\langle i,123\|\Gamma_{R'} \left( (n-1,n-2)\right)\|k,132 \rangle \nonumber\\ &\times&\langle k,132 \| \Gamma_R \left( (n,n-1)\right) \|j,132\rangle\langle j,132 \|\Gamma_{R'} \left( (n-1,n-2)\right)\|i, 123\rangle\Big] \nonumber\\ &=&\left[{1\over (c_2-c_3)^2}{1\over c_1-c_2}+\left(1-{1\over (c_2-c_3)^2}\right){1\over c_1-c_3}\right]{\rm dim}_{R'''}. \nonumber\end{aligned}$$ This example illustrates the general algorithm to be used to compute restricted characters: - The group element whose trace is to be computed, can be decomposed into a product of two cycles of the form $\Gamma_R\left((i,i+1)\right)$. A complete set of states is inserted between each factor. - Using appropriately chosen Casimirs, one can argue that the only non-zero matrix elements of each factor, are obtained when the order of boxes dropped to obtain the carrier space of the bra matches the order of boxes dropped to obtain the carrier space of the ket, except for the $(n-i+1)^{\rm th}$ and $(n-i+2)^{\rm th}$ boxes, whose order can be swapped. - We can plug in the known value of the restricted character, which we have computed for precisely the two cases arising in the previous point. Strand Diagrams --------------- Strand diagrams are a graphical notation designed to compute restricted characters. Strand diagrams keep track of two things: - The order in which boxes are to be dropped and the identity (= position within the Young diagram) of the boxes. - The group element whose trace we are computing. If we are to drop $n$ boxes, we draw a picture with $n$ columns. The columns are populated by labeled strands - each strand represents one of the boxes that are to be dropped. We label the strands by the upper index in the box. The reader is strongly advised to read Appendix E for a summary of our graphical notation. Whatever appears in the first column is to be dropped first; whatever appears in the second column is to be dropped second and so on. The strands are ordered at the top of the diagram, according to the order in which they must be dropped to get the row index. The strands are ordered at the bottom of the diagram according to the column index. The strands move from the top of the diagram to the bottom of the diagram, without breaking, so that strands ends at the top connect to the corresponding strand ends at the bottom. To connect the strands (which in general are in a different order at the top and bottom of the diagram) we need to weave the strands, thereby allowing them to swap columns. The allowed swaps depends on the specific group element whose trace we are computing. To determine the allowed swaps, write the group element as a product of cycles of the form $(i,i+1)$. For example, we would write $$(n,n-2)=(n,n-1)(n-1,n-2)(n,n-1).$$ Each time we drop a box, we are considering a new subgroup. The action of the permutation group can be visualized as a permutation of $n$ indices. The subgroups are obtained by considering elements that hold certain indices fixed (see (\[sgroup1\]) and (\[sgroup2\])). Choose the subgroups involved so that when box $i$ is dropped, $n-i+1$ is held fixed. Clearly then, each column $j$ is associated with the index $n-j+1$. Each cycle $(i,i+1)$ is drawn as a box which straddles the columns associated with indices $i$ and $i+1$. When the strands pass through a box, they may do so without swapping or by swapping columns. Each box is associated with a factor. Imagine that the strands passing through the box, reading from left to right, are labeled $n$ and $m$. The weights associated with these boxes are $c_n$ and $c_m$ respectively. If the strands do not swap inside the box the factor for the box is $$f_{\rm no\,\, swap}={1\over c_n-c_m}.$$ If the strands do swap inside the box, the factor is $$f_{\rm swap}=\sqrt{1-{1\over (c_n-c_m)^2}}.$$ Denote the product of the factors, one from each box, by $F$. We have $$\Tr_{R_1,R_2}\Big(\Gamma_R(\sigma )\Big) = \sum_i F_i{\rm dim}_{R_1},$$ where the index $i$ runs over all possible paths consistent with the boundary conditions. With a little thought, the astute reader should be able to convince herself that this graphical rule is nothing but a convenient representation of the computation of the last subsection. Strand Diagram Examples ----------------------- In this section we will illustrate the use of strand diagrams in the computation of restricted characters. For our first example, we consider the computation of $$\chi_1=\Tr_{\young({\,}{\,}{\onethree},{\,}{\twoone},{\threetwo})}\Big(\Gamma_{\yng(3,2,1)}\big((6,4)\big)\Big).$$ =4.0cm Writing $(6,4)=(6,5)(4,5)(6,5)$ we obtain the strand diagram shown in Figure \[fig:strand1.ps\]. The factors for the upper most, middle and lower most boxes are $$\sqrt{1-{1\over (c_1-c_2)^2}},\qquad \sqrt{1-{1\over (c_1-c_3)^2}},\qquad {1\over c_2-c_3}$$ respectively. Thus, $$\begin{aligned} \chi_1&=&\sqrt{1-{1\over (c_1-c_2)^2}}\sqrt{1-{1\over (c_1-c_3)^2}}{1\over c_2-c_3}{\rm dim}_{\yng(2,1)} \nonumber\\ &=&2\sqrt{1-{1\over (c_1-c_2)^2}}\sqrt{1-{1\over (c_1-c_3)^2}}{1\over c_2-c_3}. \nonumber\end{aligned}$$ The alert reader may worry that our recipe is not unique. Indeed we could also have written $(6,4)=(4,5)(6,5)(4,5)$. In this case, we obtain the strand diagram given in Figure \[fig:strand2.ps\]. In this case, the factors for the upper most, middle and lower most boxes are $${1\over c_2-c_3},\qquad \sqrt{1-{1\over (c_1-c_2)^2}},\qquad \sqrt{1-{1\over (c_1-c_3)^2}}$$ respectively. This gives exactly the same value for $\chi_1$. =4.0cm Next, we consider the computation of $$\chi_2=\Tr_{\young({\,}{\,}{1},{\,}{2},{3})}\Big(\Gamma_{\yng(3,2,1)}\big((6,4)\big)\Big).$$ This example is interesting as more than one path contributes. Writing $(6,4)=(4,5)(6,5)(4,5)$ we obtain the strand diagrams shown in Figure \[fig:strand3.ps\]. The product of factors for the diagram on the left is $${1\over c_1-c_3}\left[ 1-{1\over (c_2-c_3)^2}\right].$$ The product of factors for the diagram on the right is $${1\over c_1-c_2} {1\over (c_2-c_3)^2}.$$ Thus, $$\begin{aligned} \chi_2&=&\left({1\over c_1-c_3}\left[ 1-{1\over (c_2-c_3)^2}\right]+{1\over c_1-c_2} {1\over (c_2-c_3)^2}\right){\rm dim}_{\yng(2,1)} \nonumber\\ &=&2\left({1\over c_1-c_3}\left[ 1-{1\over (c_2-c_3)^2}\right]+{1\over c_1-c_2} {1\over (c_2-c_3)^2}\right). \nonumber\end{aligned}$$ The reader can check that the same value for $\chi_2$ is obtained by decomposing $(6,4)=(6,5)(4,5)(6,5)$. Finally, consider $$\chi_3=\Tr_{\young({\,}{\,}{1},{\,}{2},{3})}\Big(\Gamma_{\yng(3,2,1)}\big( 1 \big)\Big).$$ Since we consider the identity element, the strand diagram has no boxes and hence $\chi_3={\rm dim}_{\tiny \yng(2,1)}=2$. Since $(4,5)(4,5)=1$ we could also have written $$\chi_3=\Tr_{\young({\,}{\,}{1},{\,}{2},{3})}\Big(\Gamma_{\yng(3,2,1)}\big( (4,5)(4,5) \big)\Big).$$ In this case there are two strand diagrams given in Figure \[fig:strand4.ps\]. Summing the contributions from these two strand diagrams we obtain $$\chi_3={1\over (c_2-c_3)^2}{\rm dim}_{\tiny \yng(2,1)}+\left(1-{1\over (c_2-c_3)^2}\right){\rm dim}_{\tiny \yng(2,1)} ={\rm dim}_{\tiny \yng(2,1)}=2.$$ Once again, the two ways of writing the restricted character give the same result. Note that the trace $$\chi_3=\Tr_{\young({\,}{\,}{\onetwo},{\,}{\twoone},{3})}\Big(\Gamma_{\yng(3,2,1)}\big( 1 \big)\Big),$$ clearly vanishes because we are tracing the identity over an off the diagonal block. This is reflected graphically by the fact that there is no strand diagram that can be drawn - the order of strands at the top of the diagram does not match the order of strands at the bottom of the diagram and since we consider the identity element, the strand diagram has no boxes. Tests of the Restricted Character Results ----------------------------------------- By summing well chosen restricted characters, one can recover the characters of $S_n$ which are known. This provides a number of tests that our restricted character formulas pass. As an example, consider the computation of $\chi_R\left( (6,7)\right)$ for $$R=\yng(6,1).$$ From the character tables for $S_7$ we find $\chi_R\left( (6,7)\right)=4$. In terms of restricted characters $$\chi_R\left( (6,7)\right)=\chi_{\young({\,}{\,}{\,}{\,}{2}{1},{\,})}\left( (6,7)\right)+ \chi_{\young({\,}{\,}{\,}{\,}{\,}{1},{2})}\left( (6,7)\right)+ \chi_{\young({\,}{\,}{\,}{\,}{\,}{2},{1})}\left( (6,7)\right).$$ Using the algorithm given above, it is straight forward to verify that $$\chi_{\young({\,}{\,}{\,}{\,}{2}{1},{\,})}\left( (6,7)\right)={\rm dim}_{\young({\,}{\,}{\,}{\,},{\,})}=4,$$ $$\chi_{\young({\,}{\,}{\,}{\,}{\,}{1},{2})}\left( (6,7)\right)={1\over 6},\quad \chi_{\young({\,}{\,}{\,}{\,}{\,}{2},{1})}\left( (6,7)\right)=-{1\over 6},$$ which do indeed sum to give 4. The reader is invited to check some more examples herself. As a further check of our methods, we have computed the restricted characters $\Tr_{R_1,R_2}\left(\Gamma_{R}\big[\sigma\big]\right)$ numerically. This was done by explicitly constructing the matrices $\Gamma_{R}\big[\sigma\big]$. Each representation used was obtained by induction. One induces a reducible representation; the irreducible representation that participates was isolated using projection operators built from the Casimir obtained by summing over all two cycles. See appendix B.2 of [@de; @Mello; @Koch:2007uu] for more details. The resulting irreducible representations were tested by verifying the multiplication table of $S_n$. The intertwiners were computed using the projection operators of [@de; @Mello; @Koch:2007uu] and the results of Appendix A; the normalization of the intertwiner was computed numerically. Representations of $S_n$ from Strand Diagrams --------------------------------------------- Using Strand diagrams, it is possible to write down the irreducible matrix representations of $S_n$. We will treat the simplest nontrivial example of $S_3$. First consider the $\yng(2,1)$ irrep. Start by numbering the boxes in the Young diagram labeling the irrep, with an ordering in which the boxes are to be removed, so that one is left with a legal Young diagram after each box is removed. These labeled Young diagrams are in one-to-one correspondence with the matrix indices of the matrices in the irrep. For our example, $$i=1, \leftrightarrow \young({3}{1},{2})\qquad\qquad\qquad i=2, \leftrightarrow \young({3}{2},{1}).$$ Each matrix element of $\Gamma_{\tiny \yng(2,1)}\left((12)\right)$ is given by a single strand diagram $$\left[\Gamma_{\tiny \yng(2,1)}\left((12)\right)\right]_{11}=\Tr_{\young({3}{1},{2})}\left( (12)\right)={1\over c_1-c_2}={1\over 2},$$ $$\left[\Gamma_{\tiny \yng(2,1)}\left((12)\right)\right]_{12}=\Tr_{\young({3}{\onetwo},{\twoone})}\left( (12)\right)= \sqrt{1-{1\over (c_1-c_2)^2}}={\sqrt{3}\over 2},$$ $$\left[\Gamma_{\tiny \yng(2,1)}\left((12)\right)\right]_{21}=\Tr_{\young({3}{\twoone},{\onetwo})}\left( (12)\right)= \sqrt{1-{1\over (c_1-c_2)^2}}={\sqrt{3}\over 2},$$ and $$\left[\Gamma_{\tiny \yng(2,1)}\left((12)\right)\right]_{22}=\Tr_{\young({3}{2},{1})}\left( (12)\right)={1\over c_1-c_2}=-{1\over 2},$$ so that $$\Gamma_{\tiny \yng(2,1)}\left((12)\right)=\left[ \matrix{{1\over 2} &{\sqrt{3}\over 2}\cr {\sqrt{3}\over 2} &-{1\over 2}}\right].$$ In exactly the same way we obtain $$\Gamma_{\tiny \yng(2,1)}\left((23)\right)=\left[ \matrix{-1 &0\cr 0 &1}\right].$$ These two elements can now be used to generate the complete irrep. Next consider $\yng(3)$. There is only one valid labeling $\young({3}{2}{1})$, so that the representation is one dimensional. It is straight forward to obtain $$\Tr_{\young({3}{2}{1})}\left( (12)\right)={1\over c_1 -c_2}=1,\qquad \Tr_{\young({3}{2}{1})}\left( (23)\right)={1\over c_2 -c_3}=1,$$ which are the correct results. Finally, consider $\yng(1,1,1)$. Again, there is only one valid labeling so that the representation is again one dimensional. We find $$\Tr_{\young({3},{2},{1})}\left( (12)\right)={1\over c_1 -c_2}=-1,\qquad \Tr_{\young({3},{2},{1})}\left( (23)\right)={1\over c_2 -c_3}=-1,$$ which are again the correct results. Hopping Identity ================ In this appendix, we derive identities that can be used to obtain the Cuntz chain Hamiltonian that accounts for the $O(g_{YM}^2)$ correction to the anomalous dimension of our operators. To construct the “hop off” process, we use the fact that whenever a $Z$ field hops past the borders of the open string word $W$, the resulting restricted Schur polynomial decomposes into a sum of two types of systems, one is a giant with a closed string and another is a string-giant system where the giant is now bigger. In the large $N$ limit only the second type needs to be considered. The identities we derive in this appendix express this decomposition. The irreps which play a role in the derivation of the identities are illustrated in Figure \[fig:irreps.ps\]. The basic structure of the derivation of these identities is very similar. For this reason, we explicitly derive an identity in the next subsection and simply state the remaining identities. In contrast to the case of a single string attached[@de; @Mello; @Koch:2007uv], here it does make a difference if the first or last sites of the string participate in the hopping. The identities needed in these two cases are listed separately. We have performed extensive numerical checks of the identities, which we describe next. Finally, we explain how to express the leading large $N$ form of the identities, in terms of states of the Cuntz chain. Derivation of a Hopping Identity -------------------------------- Our starting point is the restricted Schur polynomial $$\chi^{(2)}_{R,R''}\Big\|_1\Big\|_2={1\over (n-2)!}\sum_{\sigma\in S_n}\Tr_{R''}\left(\Gamma_R(\sigma )\right)Z^{i_1}_{i_{\sigma (1)}}\cdots Z^{i_{n-2}}_{i_{\sigma (n-2)}}(W^{(2)})^{i_{n-1}}_{i_{\sigma (n-1)}}(W^{(1)})^{i_n}_{i_{\sigma (n)}}.$$ There are two labeled boxes in $R$; dropping box 1 gives irrep $R'$; dropping box 2 gives irrep $R''$. Since $R'$ is an irrep of the $S_{n-1}$ subgroup ${\cal G}_1=\{\sigma\in S_n\|\sigma(n)=n\}$, we say that the open string described by the word $W^{(1)}$ is associated to box 1. Since $R''$ is an irrep of the $S_{n-2}$ subgroup ${\cal G}_2=\{\sigma\in {\cal G}_1 \|\sigma(n-1)=n-1\}$, we say that the open string described by the word $W^{(2)}$ is associated with box 2. Notice that, in the chain of subductions used to define the restricted Schur polynomial, the box associated with $W^{(1)}$ is dropped before the box associated to $W^{(2)}$. We have indicated this with the notation $\Big\|_1\Big\|_2$. Rewrite the sum over $S_n$ as a sum over ${\cal G}_1$ and its cosets $$\begin{aligned} \chi^{(2)}_{R,R''}(Z,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 &=& {1\over (n-2)!}\sum_{\sigma\in {\cal G}_1}\left[ \Tr_{R''}\left(\Gamma_{R'}(\sigma )\right)Z^{i_1}_{i_{\sigma (1)}}\cdots Z^{i_{n-2}}_{i_{\sigma (n-2)}}(W^{(2)})^{i_{n-1}}_{i_{\sigma (n-1)}}\Tr (W^{(1)})\right.\nonumber\\ &+&\Tr_{R''}\left(\Gamma_{R}((1,n)\sigma )\right)(W^{(1)}Z)^{i_1}_{i_{\sigma (1)}}\cdots Z^{i_{n-2}}_{i_{\sigma (n-2)}}(W^{(2)})^{i_{n-1}}_{i_{\sigma (n-1)}}+\cdots+\nonumber\\ &+&\Tr_{R''}\left(\Gamma_{R}((n-2,n)\sigma )\right)Z^{i_1}_{i_{\sigma (1)}}\cdots (W^{(1)}Z)^{i_{n-2}}_{i_{\sigma (n-2)}}(W^{(2)})^{i_{n-1}}_{i_{\sigma (n-1)}}+\nonumber\\ &+&\left. \Tr_{R''}\left(\Gamma_{R}((n-1,n)\sigma )\right)Z^{i_1}_{i_{\sigma (1)}}\cdots Z^{i_{n-2}}_{i_{\sigma (n-2)}}((W^{(1)}W^{(2)})^{i_{n-1}}_{i_{\sigma (n-1)}}\right].\nonumber\end{aligned}$$ The first term on the right hand side is $${1\over (n-2)!}\sum_{\sigma\in {\cal G}_1} \Tr_{R''}\left(\Gamma_{R'}(\sigma )\right)Z^{i_1}_{i_{\sigma (1)}}\cdots Z^{i_{n-2}}_{i_{\sigma (n-2)}}(W^{(2)})^{i_{n-1}}_{i_{\sigma (n-1)}}\Tr (W^{(1)})= \chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)}).$$ Using the methods of appendix B, we know that $$\Tr_{R''}\left(\Gamma_{R}((n-1,n)\sigma )\right)={1\over c_1-c_2}\Tr_{R''}\left(\Gamma_{R'}(\sigma )\right),$$ so that the last term on the right hand side is $${1\over (n-2)!}\sum_{\sigma\in {\cal G}_1} \Tr_{R''}\left(\Gamma_{R}((n,n-1)\sigma )\right)Z^{i_1}_{i_{\sigma (1)}}\cdots Z^{i_{n-2}}_{i_{\sigma (n-2)}}(W^{(1)}W^{(2)})^{i_{n-1}}_{i_{\sigma (n-1)}}$$ $$={1\over c_1-c_2}\chi^{(1)}_{R',R''}(Z,W^{(1)}W^{(2)}).$$ Focus on the remaining terms on the right hand side. Each of these terms makes the same contribution. We need to evaluate $$\Tr_{R''}\left(\Gamma_{R}((j,n)\sigma \right)=\sum_{i=1}^{{\rm dim}_{R''}} \langle i,12\|\Gamma_{R}((j,n))\Gamma_{R'}(\sigma )\|i,12\rangle .$$ Using the techniques of appendix B, it is straight forward to show that (the sum on $\alpha$ in the next equation is a sum over all boxes that can be removed from $R''$ to leave a valid Young diagram; the relevant $S_{n-3}$ subgroup is given by $\{\sigma\in {\cal G}_2\|\sigma(j)=j\}$) $$\begin{aligned} \Tr_{R''}\left(\Gamma_{R}((j,n)\sigma \right)&=&\sum_\alpha\sum_{i,k=1}^{{\rm dim}_{R_\alpha'''}} \langle i,12\alpha \|\Gamma_R((j,n))\|k,12\alpha\rangle\langle k,12\alpha \|\Gamma_{R'} (\sigma )\|i,12\alpha\rangle\nonumber\\ &+&\sum_\alpha\sum_{i,k=1}^{{\rm dim}_{R_\alpha'''}} \langle i,12\alpha \|\Gamma_R((j,n))\|k,1\alpha 2\rangle\langle k,1\alpha 2\|\Gamma_{R'} (\sigma )\|i,12\alpha\rangle\nonumber\\ &=&\sum_\alpha {1\over c_1-c_\alpha}\left[1+{1\over (c_1-c_2)(c_2-c_\alpha)}\right]\Tr_{R_\alpha'''}(\Gamma_{R'}(\sigma ))\nonumber\\ &+&\sum_\alpha {1\over c_1-c_2} {1\over c_1-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \Tr_{T_\alpha''',R_\alpha'''}(\Gamma_{R'}(\sigma )).\nonumber\end{aligned}$$ Thus, summing the remaining $n-2$ terms we obtain $$\begin{aligned} &\sum_\alpha& {1\over c_1-c_\alpha}\left[1+{1\over (c_1-c_2)(c_2-c_\alpha)}\right] \chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\Big\|_2\Big\|_1\nonumber\\ +&\sum_\alpha& {1\over c_1-c_2} {1\over c_1-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to T_\alpha''',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\Big\|_2\Big\|_1 .\nonumber\end{aligned}$$ A straight forward application of the subgroup swap rule gives $$\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\Big\|_2\Big\|_1 = \left[\left(1-{1\over (c_2-c_\alpha)^2}\right)\chi^{(2)}_{R',T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right.$$ $$+{1\over (c_2-c_\alpha)^2}\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)}) +\sqrt{1-{1\over (c_2-c_\alpha)^2}}{1\over c_2-c_\alpha}\left( \chi^{(2)}_{R'\to R_\alpha''' T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right.$$ $$\left.\left. +\chi^{(2)}_{R'\to T_\alpha''' R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right)\right]\Big\|_1\Big\|_2 ,$$ $$\chi^{(2)}_{R'\to T_\alpha''' R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\Big\|_2\Big\|_1 = \left[\left(1-{1\over (c_2-c_\alpha)^2}\right)\chi^{(2)}_{R'\to R_\alpha''' T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right.$$ $$-{1\over (c_2-c_\alpha)^2}\chi^{(2)}_{R'\to T_\alpha''' R_\alpha'''}(Z,W^{(1)}Z,W^{(2)}) +\sqrt{1-{1\over (c_2-c_\alpha)^2}}{1\over c_2-c_\alpha}\left( \chi^{(2)}_{R', R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right.$$ $$\left.\left. -\chi^{(2)}_{R', T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right)\right]\Big\|_1\Big\|_2 .$$ Thus, we finally obtain $$\begin{aligned} \chi^{(2)}_{R,R''}(Z,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 &=& \chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)})+{1\over c_1-c_2}\chi^{(1)}_{R',R''}(Z,W^{(1)}W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha}\left(1-{1\over (c_2-c_\alpha)^2}\right)\chi^{(2)}_{R',T_\alpha'''}(Z,W^{(1)}Z,W^{(2)}) \right.\nonumber\\ &+&{1\over c_1-c_2}{1\over (c_2-c_\alpha)^2}\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\label{mikesexample}\\ &+&{1\over c_1-c_2}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\nonumber\\ &+&\left. {1\over c_1-c_\alpha}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right]\Big\|_1\Big\|_2\nonumber \, .\end{aligned}$$ The above identity is relevant for interactions in which the impurity hops out of the last site of the string. For the hopping interaction in which the impurity hops out of the first site of the string, the right hand side of our identity should be written in terms of $ZW^{(1)}$. This identity is easily derived by rewriting the sum over $S_n$ in terms of right cosets of ${\cal G}_1$ instead of left cosets as we have done above. The identity derived above is relevant for the description of interactions in which string 1 exchanges momentum with the branes in the boundstate. To derive identities that allow string 2 to exchange momentum with the branes in the boundstate, we first use the subgroup swap rule to swap strings 1 and 2. We then rewrite the sum over $S_n$ in terms of a sum over $S_{n-1}$ and its cosets and then employ character identities as above. We give a complete set of identities in the next two subsections. On first inspection, our identity (\[mikesexample\]) may appear intimidating. For this reason, we conclude this section with a concrete example of the use of our identity. Consider for example $\chi^{(2)}_{R,R''} = $ [$ \young({\,}{\,}{1},{\,}{2},{\,})$]{}. In \[mikesexample\] the sum on $\alpha$ now yields one term for $\chi^{(2)}_{R',T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})$, two terms for $\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})$ and one term for $\chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})$ and $\chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})$. Explicitly: $$\begin{aligned} \chi^{(2)}_{R',T_\alpha'''}(Z,W^{(1)}Z,W^{(2)}) & = & \mbox{{\small $\young({\,}{\,},{\,}{2},{{\oneplus}})$}}, \\ \chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)}) & = & \mbox{{\small $\young({\,}{\,},{\,}{{\oneplus}},{2})$, $\young({\,}{2},{\,}{{\oneplus}},{\,})$ }},\\ \chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,W^{(1)}Z,W^{(2)}) & = & \mbox{{\small $\young({\,}{\,},{\,}{{\oneplustwo}},{\twooneplus})$}},\\ \chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,W^{(1)}Z,W^{(2)}) & = & \mbox{{\small $\young({\,}{\,},{\,}{\twooneplus},{\oneplustwo})$}},\end{aligned}$$ Now, $c_{1} = \mbox{N}+2$, $c_{2} = \mbox{N}$ and $c_{\alpha}$ (for a particular term in the identity) is equal to the weight of the labelled box in the restricted Schur polynomial of that term that does not correspond to either of the labelled boxes in the original Schur polynomial. The identity \[mikesexample\] therefore becomes: $$\begin{aligned} \mbox{{\small $ \young({\,}{\,}{1},{\,}{2},{\,})$}}\Big\|_1\Big\|_2 &=& \young({\,}{\,},{\,}{2},{\,}) \; \Tr (W^{(1)})+\frac{1}{2} \; \mbox{{\small $ \young({\,}{\,},{\,}{{\w12}},{\,})$}} +\frac{3}{16} \; \mbox{{\small $\young({\,}{\,},{\,}{2},{{\oneplus}})$}} \Big\|_{1^{+}}\Big\|_2 \nonumber\\ \\ &+&\frac{1}{8} \; \mbox{{\small $\young({\,}{\,},{\,}{{\oneplus}},{2})$}} \Big\|_{1^{+}}\Big\|_2 + \frac{1}{2} \; \mbox{{\small $\young({\,}{2},{\,}{{\oneplus}},{\,})$ }} \Big\|_{1^{+}}\Big\|_2 + \frac{\sqrt{3}}{16} \; \mbox{{\small $\young({\,}{\,},{\,}{\twooneplus},{\oneplustwo})$}} \Big\|_{1^{+}}\Big\|_2 + \frac{\sqrt{3}}{8} \; \mbox{{\small $\young({\,}{\,},{\,}{{\oneplustwo}},{\twooneplus})$}} \Big\|_{1^{+}}\Big\|_2. \end{aligned}$$ Identities Relevant to Hopping off the first site of the string --------------------------------------------------------------- $$\begin{aligned} \chi^{(2)}_{R,R''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)})+{1\over c_1-c_2}\chi^{(1)}_{R',R''}(Z,W^{(2)}W^{(1)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha}\left(1-{1\over (c_2-c_\alpha)^2}\right)\chi^{(2)}_{R',T_\alpha'''}(Z,ZW^{(1)},W^{(2)}) \right.\nonumber\\ &+&{1\over c_1-c_2}{1\over (c_2-c_\alpha)^2}\chi^{(2)}_{R',R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\label{firstone}\\ &+&{1\over c_1-c_2}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\nonumber\\ &+&\left. {1\over c_1-c_\alpha}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,ZW^{(1)},W^{(2)})\right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ The form of this identity is rather intuitive. The first term on the right hand side contributes to the process in which the bound state emits string 1; the second term describes the process in which the two open strings join to form one long open string. In both of these processes, the box which string 1 occupied on the left hand side does not appear on the right hand side. These two processes will not contribute to our Cuntz chain Hamiltonian; they are relevant for the description of interactions which change the number of open strings attached to the boundstate and do not contribute at the leading order of the large $N$ expansion. It is instructive to consider the form of this identity for well separated branes. For well separated branes, we have $\|c_1-c_2\|\gg 1$. For $\|c_1-c_\alpha \|\sim 1$, $\|c_2-c_\alpha \|\gg 1$ so that of the last four terms only the first one contributes, giving $\approx {1\over c_1-c_\alpha}\chi^{(2)}_{R',T_\alpha'''}(Z,ZW^{(1)},W^{(2)}) .$ Thus, string 2 stays in box 2 and string 1 is close to where it started. Note that dropping terms of order $(c_1-c_2)^{-1}$ or $(c_\alpha-c_2)^{-1}$ we obtain $$\chi^{(2)}_{R,R''}(Z,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 \approx \chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)})+\sum_\alpha {1\over c_1-c_\alpha}\chi^{(2)}_{R',T_\alpha'''}(Z,ZW^{(1)},W^{(2)}),$$ which is the identity of [@de; @Mello; @Koch:2007uv]. Next, consider the stretched string identities $$\begin{aligned} \chi^{(2)}_{R\to R'' S''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(1)}_{R',R''}(Z,W^{(2)}W^{(1)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha} {1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{R',R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\right.\label{firstwo}\\ &+&\left. {1\over c_1-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ $$\begin{aligned} \chi^{(2)}_{R\to S'' R''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(1)}_{S',S''}(Z,W^{(2)}W^{(1)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha} {1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{S',S_\alpha'''}(Z,ZW^{(1)},W^{(2)})\right.\label{firstthree}\\ &+&\left. {1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_\alpha)^2}}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{S'\to W_\alpha'''S_\alpha'''}(Z,ZW^{(1)},W^{(2)})\right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ Notice that in contrast to (\[firstone\]), (\[firstwo\]) and (\[firstthree\]) do not have a term on the right hand side corresponding to emission of string $1$. This is what we would expect for an operator dual to a state with two strings stretching between branes, since if string 1 is emitted, it leaves a state with string 2 stretched between branes; this state is not allowed as it violates the Gauss Law. The process in which the two open strings join at their endpoints is allowed. In this process, it is the box with the upper 1 label that is removed. Thus, we can identify the Chan-Paton label for the side of the string defining the first lattice site of the Cuntz chain with the upper label for the string, in our diagrammatic notation. This corresponds to the first label of the restricted Schur polynomial. We will see further evidence for this interpretation when we interpret the final form of the Hamiltonian. If we again consider the limit of two well separated branes, we find that (\[firstwo\]) becomes $$\chi^{(2)}_{R\to R'' S''}(Z,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 \approx \chi^{(1)}_{R',R''}(Z,W^{(2)} W^{(1)}) +\sum_\alpha {1\over c_1-c_\alpha} \chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\Big\|_1\Big\|_2 .$$ In this case, the box with upper 1 label and lower 2 label moves from box 1 to box $\alpha$ (which are close to each other in the Young diagram) and box with upper 2 label and lower 1 label stays where it is. The first three identities that we have discussed corresponded to an interaction in which an impurity from the first site of string 1 interacts with the brane. The next three identities that we discuss correspond to an interaction in which an impurity from the first site of string 2 interacts with the brane. The first three terms of the identity $$\begin{aligned} \chi^{(2)}_{R,R''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \left(1-{1\over (c_1-c_2)^2}\right)\chi^{(1)}_{S',S''}(Z,W^{(1)})\Tr (W^{(2)}) \nonumber\\ &+&{1\over (c_1-c_2)^2}\chi^{(1)}_{R',R''}(Z,W^{(1)})\Tr(W^{(2)}) +{1\over c_1-c_2}\chi^{(1)}_{R',R''}(Z,W^{(1)}W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_2-c_\alpha}\left(1-{1\over (c_1-c_2)^2}\right)\chi^{(2)}_{S',S_\alpha'''}(Z,W^{(1)},ZW^{(2)}) \right.\nonumber\\ &+&{1\over c_2-c_\alpha}{1\over (c_1-c_2)^2}\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)},ZW^{(2)})\label{firstfour}\\ &+&\left. {1\over c_1-c_2}{1\over c_1-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to R_\alpha''' T_\alpha'''}(Z,W^{(1)},ZW^{(2)}) \right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ change the number of open strings attached to the boundstate. The first two terms correspond to gravitational radiation; for both of these terms, string 2 is emitted as a closed string. The third term corresponds to a process in which the two open strings join to give a single open string. The order of the open string words in this term is not the same as the order in the corresponding term of (\[firstone\]). The term above is natural because it is the first site of string 2 that is interacting; the order in (\[firstone\]) also looks natural because in that case it is the first site of string 1 that is interacting. Notice that the above identity is rather different to (\[firstone\]). Physically this is surprising - since in both cases it is the first site of the string interacting, these identities should presumably look identical. This mismatch between the two identities is a consequence of the fact that we have treated string 1 and string 2 differently when constructing the operator. See section 3 for further discussion of this point. If we again consider the limit of two well separated branes, we find that (\[firstfour\]) becomes (take $\|c_1-c_2\|\gg 1$, $\|c_1-c_\alpha\|\gg 1$ and $\|c_2-c_\alpha\|\sim 1$) $$\chi^{(2)}_{R,R''}(Z,W^{(1)},W^{(2)})\Big\|_1\Big\|_2\approx \chi^{(1)}_{S',S''}(Z,W^{(1)})\Tr(W^{(2)}) +\sum_\alpha {1\over c_2-c_\alpha}\chi^{(2)}_{S',S_\alpha'''}(Z,W^{(1)},ZW^{(2)}).$$ This again reproduces the identity of [@de; @Mello; @Koch:2007uv]. Thus, the content of the formula for well separated branes matches the corresponding limit of (\[firstone\]). This is satisfying, because in this limit the order in which the strings are attached does not matter. This follows because the swap factor of [@de; @Mello; @Koch:2007uv] behaves as $\|c_1-c_2\|^{-1}$. The remaining two identities are stretched string identities. In contrast to what we found above, there are terms corresponding to gravitational radiation in these identities. We interpret this as a signal that there is some mixing between the operators we have defined (which as explained above, made some arbitrary choices) to get to a “physical basis”. See section 3 for more details. The first term in both identities $$\begin{aligned} \chi^{(2)}_{R\to R'' S''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(1)}_{S',S''}(Z,W^{(1)}W^{(2)}) \nonumber\\ &+&{1\over c_1-c_2}\sqrt{1-{1\over (c_1-c_2)^2}}\left( \chi^{(1)}_{R',R''}(Z,W^{(1)})-\chi^{(1)}_{S',S''}(Z,W^{(1)})\right)\Tr(W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha}{1\over c_2-c_1}\sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(2)}_{S',S_\alpha'''}(Z,W^{(1)},ZW^{(2)}) \right.\label{firstfive}\\ &+&{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \sqrt{1-{1\over (c_\alpha-c_1)^2}}\chi^{(2)}_{S'\to S_\alpha''' W_\alpha'''}(Z,W^{(1)},ZW^{(2)})\nonumber\\ &+&\left. {1\over c_1-c_2}{1\over c_1-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)},ZW^{(2)}) \right]\Big\|_1\Big\|_2,\nonumber\end{aligned}$$ $$\begin{aligned} \chi^{(2)}_{R\to S'' R''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(1)}_{R',R''}(Z,W^{(1)}W^{(2)}) \nonumber\\ &+&{1\over c_1-c_2}\sqrt{1-{1\over (c_1-c_2)^2}}\left( \chi^{(1)}_{R',R''}(Z,W^{(1)})-\chi^{(1)}_{S',S''}(Z,W^{(1)})\right)\Tr(W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_2-c_\alpha}{1\over c_1-c_2}\sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)},ZW^{(2)}) \right.\label{firstsix}\\ &+&{1\over c_1-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \sqrt{1-{1\over (c_\alpha-c_2)^2}}\chi^{(2)}_{R'\to R_\alpha''' T_\alpha'''}(Z,W^{(1)},ZW^{(2)})\nonumber\\ &+&\left. {1\over c_2-c_1}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{S',S_\alpha'''}(Z,W^{(1)},ZW^{(2)}) \right]\Big\|_1\Big\|_2,\nonumber\end{aligned}$$ corresponds to two open strings joining to form one long open string. The order of the open string words in these terms again looks natural given that it is the first site of string 2 that is interacting. They will again not contribute in the leading order of the large $N$ expansion. It is satisfying that the content of the large distance limit of (\[firstfive\]) $$\chi^{(2)}_{R\to R'' S''}(Z,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 \approx \chi^{(1)}_{S',S''}(Z,W^{(1)}W^{(2)})+\sum_\alpha{1\over c_2-c_\alpha}\chi^{(2)}_{S'\to S_\alpha''' W_\alpha'''}(Z,W^{(1)},ZW^{(2)}),$$ is in complete agreement with the large distance limit of (\[firstwo\]). Identities Relevant to Hopping off the last site of the string -------------------------------------------------------------- In this subsection, impurities hop between the last site of the strings and the threebrane. There are again six possible identities that we could consider. The first three identities describe an interaction between the last site of string 1 and the threebrane. The first identity $$\begin{aligned} \chi^{(2)}_{R,R''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)})+{1\over c_1-c_2}\chi^{(1)}_{R',R''}(Z,W^{(1)}W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha}\left(1-{1\over (c_2-c_\alpha)^2}\right)\chi^{(2)}_{R',T_\alpha'''}(Z,W^{(1)}Z,W^{(2)}) \right.\nonumber\\ &+&{1\over c_1-c_2}{1\over (c_2-c_\alpha)^2}\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\label{lastone}\\ &+&{1\over c_1-c_2}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\nonumber\\ &+&\left. {1\over c_1-c_\alpha}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ can be obtained from (\[firstone\]) by (i) swapping the labels on the twisted string states on the right hand side and (ii) swapping the order of the open string words in the second term on the right hand side. This is exactly what we would expect - it is now the last site of the string that is interacting; to swap the first and last sites, we must swap Chan-Paton indices i.e. we must swap the labels on the twisted string states. The discussion of this identity now parallels the discussion of (\[firstone\]) and is not repeated. Consider next the stretched string identities $$\begin{aligned} \chi^{(2)}_{R\to S'' R''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(1)}_{R',R''}(Z,W^{(1)}W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha} {1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right.\label{lasttwo}\\ &+&\left. {1\over c_1-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{R'\to R_\alpha''' T_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right]\Big\|_1\Big\|_2,\nonumber\end{aligned}$$ $$\begin{aligned} \chi^{(2)}_{R\to R'' S''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(1)}_{S',S''}(Z,W^{(1)}W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha} {1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{S',S_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right.\label{lastthree}\\ &+&\left. {1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_\alpha)^2}}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{S'\to S_\alpha''' W_\alpha'''}(Z,W^{(1)}Z,W^{(2)})\right]\Big\|_1\Big\|_2 .\nonumber\end{aligned}$$ It is satisfying that identity (\[lasttwo\]) can be obtained from (\[firstwo\]) and (\[lastthree\]) from (\[firstthree\]) by swapping the labels for stretched string states on both sides, and reversing the order of the open string words in the first term on the right hand side. The discussion of these identities now parallel the discussion of (\[firstwo\]) and (\[firstthree\]) and is not repeated. The remaining three identities describe an interaction between the last site of string 2 and the threebrane. The identity $$\begin{aligned} \chi^{(2)}_{R,R''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \left(1-{1\over (c_1-c_2)^2}\right)\chi^{(1)}_{S',S''}(Z,W^{(1)})\Tr (W^{(2)}) \nonumber\\ &+&{1\over (c_1-c_2)^2}\chi^{(1)}_{R',R''}(Z,W^{(1)})\Tr(W^{(2)}) +{1\over c_1-c_2}\chi^{(1)}_{R',R''}(Z,W^{(2)}W^{(1)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_2-c_\alpha}\left(1-{1\over (c_1-c_2)^2}\right)\chi^{(2)}_{S',S_\alpha'''}(Z,W^{(1)},W^{(2)}Z) \right.\nonumber\\ &+&{1\over c_2-c_\alpha}{1\over (c_1-c_2)^2}\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)},W^{(2)}Z)\label{lastfour}\\ &+&\left. {1\over c_1-c_2}{1\over c_1-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,W^{(1)},W^{(2)}Z) \right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ can be obtained from (\[firstfour\]) by (i) swapping the labels on the twisted string states on the right hand side and (ii) swapping the order of the open string words in the second term on the right hand side. Finally, the stretched string identities $$\begin{aligned} \chi^{(2)}_{R\to R'' S''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(1)}_{R',R''}(Z,W^{(2)}W^{(1)}) \nonumber\\ &+&{1\over c_1-c_2}\sqrt{1-{1\over (c_1-c_2)^2}}\left( \chi^{(1)}_{R',R''}(Z,W^{(1)})-\chi^{(1)}_{S',S''}(Z,W^{(1)})\right)\Tr(W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_2-c_\alpha}{1\over c_1-c_2}\sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)},W^{(2)}Z) \right.\label{lastfive}\\ &+&{1\over c_1-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \sqrt{1-{1\over (c_\alpha-c_2)^2}}\chi^{(2)}_{R'\to T_\alpha''' R_\alpha'''}(Z,W^{(1)},W^{(2)}Z)\nonumber\\ &-&\left. {1\over c_1-c_2}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{S',S_\alpha'''}(Z,W^{(1)},W^{(2)}Z) \right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ $$\begin{aligned} \chi^{(2)}_{R\to S'' R''}(&Z&,W^{(1)},W^{(2)})\Big\|_1\Big\|_2 = \sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(1)}_{S',S''}(Z,W^{(2)}W^{(1)}) \nonumber\\ &-&{1\over c_1-c_2}\sqrt{1-{1\over (c_1-c_2)^2}}\left( \chi^{(1)}_{S',S''}(Z,W^{(1)})-\chi^{(1)}_{R',R''}(Z,W^{(1)})\right)\Tr(W^{(2)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha}{1\over c_2-c_1}\sqrt{1-{1\over (c_1-c_2)^2}}\chi^{(2)}_{S',S_\alpha'''}(Z,W^{(1)},W^{(2)}Z) \right.\label{lastsix}\\ &+&{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \sqrt{1-{1\over (c_\alpha-c_1)^2}}\chi^{(2)}_{S'\to W_\alpha''' S_\alpha'''}(Z,W^{(1)},W^{(2)}Z)\nonumber\\ &+&\left. {1\over c_1-c_2}{1\over c_1-c_\alpha}\sqrt{1-{1\over (c_1-c_2)^2}} \chi^{(2)}_{R',R_\alpha'''}(Z,W^{(1)},W^{(2)}Z) \right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ can be obtained from (\[firstfour\]) and (\[firstfive\]) by swapping the labels for stretched string states on both sides, and reversing the order of the open string words in the first term on the right hand side. Numerical Test -------------- An important result of this article are the identities presented in the previous two subsections, since they determine the hop off interaction. The hop on interaction follows from the hop off interaction by Hermitian conjugation and the kissing interaction by composing the hop on and the hop off interactions. Thus, the complete boundary interaction and the corresponding back reaction on the brane are determined by these identities. For this reason, we have tested the identities numerically. In this subsection we will explain the check we have performed. Our formulas are identities between restricted Schur polynomials. They must hold if we evaluate them for [any]{}[^12] numerical value of the matrices $Z$ and $W$. Our check entails evaluating our identities for randomly generated matrices $W^{(1)}$, $W^{(2)}$ and $Z$, to check their validity. Evaluating a restricted Schur polynomial entails evaluating a restricted character as well as a product of traces of a product of the matrices $W^{(1)}$, $W^{(2)}$ and $Z$. The restricted character $\Tr_{R'',S''}\left(\Gamma_{R}\big[\sigma\big]\right)$ or $\Tr_{R''}\left(\Gamma_{R}\big[\sigma\big]\right)$ was computed by explicitly constructing the matrices $\Gamma_{R}\big[\sigma\big]$. Each representation used was obtained by induction. One induces a reducible representation; the irreducible representation that participates was isolated using projection operators built from the Casimir obtained by summing over all two cycles. See appendix B.2 of [@de; @Mello; @Koch:2007uu] for more details. The resulting irreducible representations were tested by verifying the multiplication table of $S_n$. The restricted trace is then evaluated with the help of a projection operator or an intertwiner. The intertwiner was computed using the results of appendix A. The trace $\Tr (\sigma Z^{\otimes n-1} W^{(1)}W^{(2)})= Z^{i_1}_{i_{\sigma(1)}}Z^{i_2}_{i_{\sigma(2)}}\cdots Z^{i_{n-2}}_{i_{\sigma(n-2)}}(W^{(2)})^{i_{n-1}}_{i_{\sigma(n-1)}} (W^{(1)})^{i_n}_{i_{\sigma(n)}}$ for any given $\sigma\in S_n$ is easily expressed as a product of traces of powers of $Z$, $W^{(1)}$ and $W^{(2)}$. In total we verified over 50 specific instances of our identities, which provides a significant check of each identity. Identities in terms of Cuntz Chain States ----------------------------------------- The state-operator correspondence is available for any conformal field theory. Using this correspondence, we can trade our (local) operators for a set of states. Concretely, this involves quantizing with respect to radial time. Considering a fixed “radial time" slice we obtain a round sphere. The states dual to the restricted Schur polynomial operators are the states of our Cuntz chain. Thus, we need to rewrite the identities obtained in this appendix as statements in terms of the states of the Cuntz oscillator chain. The states of the Cuntz oscillator chain are normalized. Normalized states correspond to operators whose two point function is normalized. Using the technology of [@de; @Mello; @Koch:2007uu] it is a simple task to compute the free equal time correlators of the restricted Schur polynomials. After making use of the free field correlators to write our identities in terms operators with unit two point functions, we find that not all terms are of the same order in $N$. We drop all terms which are subleading in $N$. These terms are naturally interpreted in terms of string splitting and joining processes, so that they will be important when interactions that change the number of open strings are considered. The discussion for all of the identities above is rather similar, so we will be content to discuss a specific example which illustrates the general features. Consider the right hand side of (\[firstone\]). From the equal time correlator (there are a total of $h_i$ fields in open string word $W^{(i)}$; $f_R$ is the product of the weights of the Young diagram $R$; $d_R$ is the dimension of $R$ as an irrep of the symmetric group; $n_R$ is the number of boxes in Young diagram $R$) $$\langle \chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)})\chi^{(1)}_{R',R''}(Z,W^{(2)})^\dagger\Tr (W^{(1)})^\dagger\rangle$$ $$=\left( {4\pi\lambda\over N}\right)^{h_1+h_2+n_{R''}}h_1 N^{h_1+h_2-1} n_{R''} f_{R'}{d_{R''}\over d_{R'}} \label{twopoint}$$ we know that the operator $\chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)})$ corresponds to the state (all Cuntz chain states are normalized to 1) $$\sqrt{\left( {4\pi\lambda\over N}\right)^{h_1+h_2+n_{R''}}h_1 N^{h_1+h_2-1} n_{R''} f_{R'}{d_{R''}\over d_{R'}}} \|R',R'',W^{(2)};W^{(1)}\rangle .$$ The result (\[twopoint\]) is not exact. When computing $\langle \Tr (W^{(1)})\Tr (W^{(1)})^\dagger\rangle$ we have only summed the leading planar contribution. When computing $\langle \chi^{(1)}_{R',R''}(Z,W^{(2)})\chi^{(1)}_{R',R''}(Z,W^{(2)})^\dagger\rangle $ we have only kept the $F_0$ contribution in the language of [@de; @Mello; @Koch:2007uu]. We have also factorized $\langle \chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)})\chi^{(1)}_{R',R''}(Z,W^{(2)})^\dagger\Tr (W^{(1)})^\dagger\rangle$ as $\langle \chi^{(1)}_{R',R''}(Z,W^{(2)})\chi^{(1)}_{R',R''}(Z,W^{(2)})^\dagger\rangle$ $\times \langle \Tr (W^{(1)})\Tr (W^{(1)})^\dagger\rangle$ which is valid at large $N$. Similarly, (again we sum only the leading order at large $N$) $$\langle\chi^{(1)}_{R',R''}(Z,W^{(2)}W^{(1)})\chi^{(1)}_{R',R''}(Z,W^{(2)}W^{(1)})^\dagger\rangle= \left( {4\pi\lambda\over N}\right)^{h_1+h_2+n_{R''}} N^{h_1+h_2-1} n_{R''} f_{R'}{d_{R''}\over d_{R'}}$$ implies that $\chi^{(1)}_{R',R''}(Z,W^{(2)}W^{(1)})$ corresponds to the state $$\sqrt{\left( {4\pi\lambda\over N}\right)^{h_1+h_2+n_{R''}} N^{h_1+h_2-1} n_{R''} f_{R'}{d_{R''}\over d_{R'}}} \|R',R'',W^{(2)}W^{(1)})\rangle .$$ Finally, the correlators (again we sum only the leading order at large $N$) $$\langle\chi^{(2)}_{R',T_\alpha'''}(Z,ZW^{(1)},W^{(2)})\chi^{(2)}_{R',T_\alpha'''}(Z,ZW^{(1)},W^{(2)})^\dagger \rangle = \left( {4\pi\lambda\over N}\right)^{h_1+h_2+1+n_{T_\alpha'''}} N^{h_1+h_2-1}n_{R'}^2 {d_{T_\alpha'''}\over d_{R'}}f_{R'},$$ $$\langle\chi^{(2)}_{R',R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\chi^{(2)}_{R',R_\alpha'''}(Z,ZW^{(1)},W^{(2)})^\dagger \rangle = \left( {4\pi\lambda\over N}\right)^{h_1+h_2+1+n_{T_\alpha'''}} N^{h_1+h_2-1}n_{R'}^2 {d_{R_\alpha'''}\over d_{R'}}f_{R'},$$ $$\langle\chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,ZW^{(1)},W^{(2)})^\dagger\rangle$$ $$= \left( {4\pi\lambda\over N}\right)^{h_1+h_2+1+n_{T_\alpha'''}} N^{h_1+h_2-1}n_{R'}^2 {d_{T_\alpha'''}\over d_{R'}}f_{R'},$$ $$\langle\chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,ZW^{(1)},W^{(2)})\chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,ZW^{(1)},W^{(2)})^\dagger\rangle$$ $$= \left( {4\pi\lambda\over N}\right)^{h_1+h_2+1+n_{T_\alpha'''}} N^{h_1+h_2-1}n_{R'}^2 {d_{T_\alpha'''}\over d_{R'}}f_{R'}$$ imply the correspondences $$\chi^{(2)}_{R',T_\alpha'''}(Z,ZW^{(1)},W^{(2)}) \longleftrightarrow \sqrt{\left( {4\pi\lambda\over N}\right)^{h_1+h_2+1+n_{T_\alpha'''}} N^{h_1+h_2-1}n_{R'}^2 {d_{T_\alpha'''}\over d_{R'}}f_{R'}} \|R',T_{\alpha'''},ZW^{(1)},W^{(2)}\rangle ,$$ $$\chi^{(2)}_{R',R_\alpha'''}(Z,ZW^{(1)},W^{(2)}) \longleftrightarrow \sqrt{\left( {4\pi\lambda\over N}\right)^{h_1+h_2+1+n_{T_\alpha'''}} N^{h_1+h_2-1}n_{R'}^2 {d_{R_\alpha'''}\over d_{R'}}f_{R'}} \|R',R_\alpha''',ZW^{(1)},W^{(2)}\rangle ,$$ $$\chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,ZW^{(1)},W^{(2)}) \longleftrightarrow \sqrt{\left( {4\pi\lambda\over N}\right)^{h_1+h_2+1+n_{T_\alpha'''}} N^{h_1+h_2-1}n_{R'}^2 {d_{T_\alpha'''}\over d_{R'}}f_{R'}} \|R',T_\alpha'''R_\alpha''',ZW^{(1)},W^{(2)}\rangle$$ $$\chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,ZW^{(1)},W^{(2)}) \longleftrightarrow \sqrt{\left( {4\pi\lambda\over N}\right)^{h_1+h_2+1+n_{T_\alpha'''}} N^{h_1+h_2-1}n_{R'}^2 {d_{T_\alpha'''}\over d_{R'}}f_{R'}} \|R',R_\alpha'''T_\alpha''',ZW^{(1)},W^{(2)}\rangle$$ Consider the factor $$n_{R'}^2 {d_{R_\alpha'''}\over d_{R'}}={({\rm hooks})_{R'}\over ({\rm hooks})_{R_\alpha'''}},$$ where (hooks)$_R$ is the product of the hook lengths of Young diagram $R$. It is straight forward to compute this ratio of hook lengths, which is generically of order $N^2$ implying that ${d_{R_\alpha'''}\over d_{R'}}$ is of order 1. Using this observation, it is equally easy to verify that ${d_{T_\alpha'''}\over d_{R'}}$ and ${d_{R''}\over d_{R'}}$ are also both $O(1)$. Given these results, it is simple to see that the sum of operators $$\begin{aligned} &&\chi^{(1)}_{R',R''}(Z,W^{(2)})\Tr (W^{(1)})+{1\over c_1-c_2}\chi^{(1)}_{R',R''}(Z,W^{(2)}W^{(1)})\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha}\left(1-{1\over (c_2-c_\alpha)^2}\right)\chi^{(2)}_{R',T_\alpha'''}(Z,ZW^{(1)},W^{(2)}) \right.\nonumber\\ &+&{1\over c_1-c_2}{1\over (c_2-c_\alpha)^2}\chi^{(2)}_{R',R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\nonumber\\ &+&{1\over c_1-c_2}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to T_\alpha'''R_\alpha'''}(Z,ZW^{(1)},W^{(2)})\nonumber\\ &+&\left. {1\over c_1-c_\alpha}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \chi^{(2)}_{R'\to R_\alpha'''T_\alpha'''}(Z,ZW^{(1)},W^{(2)})\right]\Big\|_1\Big\|_2\nonumber\end{aligned}$$ corresponds to the following sum of normalized states $$\begin{aligned} &&\sqrt{\left( {4\pi\lambda\over N}\right)^{h_1+h_2+n_{R''}} N^{h_1+h_2-1}n_{R'}^2 f_{R'}} \left[ \sqrt{h_1 d_{R''}\over n_{R'}d_{R'}}\|R',R'',W^{(2)};W^{(1)}\rangle\right.\nonumber\\ &+&{1\over c_1-c_2}\sqrt{d_{R''}\over n_{R'}d_{R'}}\|R',R'',W^{(2)}W^{(1)}\rangle\nonumber\\ &+&\sum_\alpha\left[{1\over c_1-c_\alpha}\left(1-{1\over (c_2-c_\alpha)^2}\right) \sqrt{d_{T_\alpha'''}\over d_{R'}}\|R',T_\alpha''',ZW^{(1)},W^{(2)}\rangle \right.\nonumber\\ &+&{1\over c_1-c_2}{1\over (c_2-c_\alpha)^2} \sqrt{d_{R_\alpha'''}\over d_{R'}}\|R',R_\alpha''',ZW^{(1)},W^{(2)}\rangle\nonumber\\ &+&{1\over c_1-c_2}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \sqrt{d_{T_\alpha'''}\over d_{R'}}\|R',T_\alpha'''R_\alpha''',ZW^{(1)},W^{(2)}\rangle\nonumber\\ &+&\left.\left. {1\over c_1-c_\alpha}{1\over c_2-c_\alpha}\sqrt{1-{1\over (c_2-c_\alpha)^2}} \sqrt{d_{T_\alpha'''}\over d_{R'}}\|R',R_\alpha''' T_\alpha''',ZW^{(1)},W^{(2)}\rangle\right]\right].\nonumber\end{aligned}$$ Recalling that $h_1=O(\sqrt{N})$ and $n_{R'}=O(N)$, it is clear that the first two terms are subleading. These two terms correspond to gravitational radiation (first term) and string joining (second term); they are the only terms that correspond to an interaction that changes the number of open strings attached to the excited giant system. Although we have illustrated things with an example, this conclusion is general - for all of the identities obtained in this appendix, terms that do not correspond to two strings attached to the giant system can be dropped in the leading large $N$ limit. State/Operator Map ================== In this section we will simply quote the six normalization factors that enter the relation between the restricted Schur polynomials and the normalized Cuntz chain states relevant for the excited two giant graviton bound state[^13]. The normalization factors are not exact - we simply quote the leading large $N$ value of these normalizations. These factors are determined completely by the $F_0^{(1)}F_0^{(2)}$ contribution in the language of [@de; @Mello; @Koch:2007uu]. The factor $f_R$ is the product of weights of the Young diagram $R$. The open string word $W^{(1)}$ contains a total number of $h_1$ Higgs fields; the open string word $W^{(2)}$ contains a total number of $h_2$ Higgs fields. State Normalization ----------------------------- -------------------------------------------------------------------------------------------------------------------------- $\|b_0-1,b_1,11,22\rangle$ $\left({4\pi\lambda\over N}\right)^{2b_0+b_1+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}$ $\|b_0-1,b_1,22,11\rangle$ $\left({4\pi\lambda\over N}\right)^{2b_0+b_1+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}$ $\|b_0-1,b_1,12,21\rangle$ $\left({4\pi\lambda\over N}\right)^{2b_0+b_1+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}$ $\|b_0-1,b_1,21,12\rangle$ $\left({4\pi\lambda\over N}\right)^{2b_0+b_1+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}$ $\|b_0-2,b_1+2,22,22\rangle$ $\left({4\pi\lambda\over N}\right)^{2b_0+b_1+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{b_1+3\over b_1+1}$ $\|b_0,b_1-2,11,11\rangle$ $\left({4\pi\lambda\over N}\right)^{2b_0+b_1+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{b_1-1\over b_1+1}$ Review of the Restricted Schur Polynomial Notation ================================================== In this appendix, we review the definition of the restricted Schur polynomial. The reader requiring more details can consult [@Balasubramanian:2004nb; @de; @Mello; @Koch:2007uu; @de; @Mello; @Koch:2007uv]. There is by now convincing evidence that the dual of a giant graviton is a Schur polynomial. Schur polynomials are labeled by Young diagrams. Excitations of giant gravitons can be described by attaching open strings to the giant graviton. Operators dual to excitations of giant gravitons are obtained by inserting words $(W^{(a)})^j_i$ describing the open strings (one word for each open string) into the operator describing the system of giant gravitons $$\chi_{R,R_1}^{(k)}(Z,W^{(1)},...,W^{(k)})={1\over (n-k)!} \sum_{\sigma\in S_n}\Tr_{R_1}(\Gamma_R(\sigma))\Tr(\sigma Z^{\otimes n-k}W^{(1)}\cdots W^{(k)}), \label{restrictedschur}$$ $$\Tr (\sigma Z^{\otimes n-k}W^{(1)}\cdots W^{(k)})= Z^{i_1}_{i_{\sigma (1)}}Z^{i_2}_{i_{\sigma (2)}}\cdots Z^{i_{n-k}}_{i_{\sigma (n-k)}}(W^{(1)})^{i_{n-k+1}}_{i_{\sigma (n-k+1)}}\cdots (W^{(k)})^{i_{n}}_{i_{\sigma (n)}}.$$ The representation $R$ of the giant graviton system is a Young diagram with $n$ boxes, i.e. it is a representation of $S_n$. $\Gamma_R(\sigma )$ is the matrix representing $\sigma$ in irreducible representation $R$ of the symmetric group $S_n$. The representation $R_1$ is a Young diagram with $n-k$ boxes, i.e. it is a representation of $S_{n-k}$. Imagine that the $k$ words above are all distinct, corresponding to the case that the open strings are distinguishable. Consider an $S_{n-k}\otimes (S_1)^k$ subgroup of $S_n$. The representation $R$ of $S_n$ will subduce a (generically) reducible representation of the $S_{n-k}\otimes (S_1)^k$ subgroup. One of the irreducible representations appearing in this subduced representation is $R_1$. $\Tr_{R_1}$ is an instruction to trace only over the indices belonging to this irreducible component. If the representation $R_1$ appears more than once, things are more interesting. The example discussed in [@Balasubramanian:2004nb] illustrates this point nicely. Suppose $R\to R_1\oplus R_2\oplus R_2$ under restricting $S_n$ to $S_{n-2}\times S_1\times S_1$. Choose a basis so that $$\Gamma_R (\sigma )=\left[ \matrix{\Gamma_{R_1}(\sigma)_{i_1 j_1} &0 &0\cr 0 &\Gamma_{R_2}(\sigma)_{i_2 j_2} &0\cr 0 &0 &\Gamma_{R_2}(\sigma)_{i_3 j_3}} \right],\qquad \forall \sigma\in S_{n-2}\times S_1\times S_1 ,$$ $$\Gamma_R (\sigma )=\left[ \matrix{A^{(1,1)}_{i_1 j_1} &A^{(1,2)}_{i_1 j_2} &A^{(1,3)}_{i_1 j_3}\cr A^{(2,1)}_{i_2 j_1} &A^{(2,2)}_{i_2 j_2} &A^{(2,3)}_{i_2 j_3}\cr A^{(3,1)}_{i_3 j_1} &A^{(3,2)}_{i_3 j_2} &A^{(3,3)}_{i_3 j_3}} \right],\qquad \sigma\notin S_{n-2}\times S_1\times S_1 .$$ There are four suitable definitions for $\Tr_{R_2}(\Gamma_R(\sigma ))$: $\Tr (A^{(2,2)})$, $\Tr (A^{(2,3)})$, $\Tr (A^{(3,2)})$ or $\Tr (A^{(3,3)})$. Interpret the operator obtained using $\Tr (A^{(2,3)})$ or $\Tr (A^{(3,2)})$ as dual to the system with the open strings stretching between the giants and the operator obtained using $\Tr (A^{(2,2)})$ or $\Tr (A^{(3,3)})$ as dual to the system with one open string on each giant. In general, identify the “on the diagonal" blocks with states in which the two open strings are each on a specific giant and the “off the diagonal" blocks as states in which the open strings stretch between two giants. As a consequence of the fact that the representation $R_2$ appears with a multiplicity two, there is no unique way to extract two $R_2$ representations out of $R$. The specific representations obtained will depend on the details of the subgroups used in performing the restriction. These subgroups are the set of elements of the permutation group that leave an index invariant, $\sigma(i)=i$. Choosing the index to be the index of an open string, we can associate the subgroups participating with specific open strings. The subgroups are specified by dropping boxes from $R$, so that we can now associate boxes in $R$ with specific open strings. This leads to a convenient graphical notation which has been developed in [@de; @Mello; @Koch:2007uu; @de; @Mello; @Koch:2007uv]. There is an obvious generalization to the case that a representation $R_1$ appears $n$ times after restricting to the subgroup. If any of the strings are identical, one needs to decompose with respect to a larger subgroup and to pick a representation for the strings which are indistinguishable. Thus, for example, if we consider a bound state of a giant system with three identical strings attached, we would consider an $S_{n-3}\otimes S_3$ subgroup of $S_n$. The restricted Schur polynomial would be given by $\chi^{(3)}_{R,R_1}$ with $R$ an irrep of $S_n$ and $R_1$ an irrep of $S_{n-3}\otimes S_3$. The $S_3$ subgroup would act by permuting the indices of the three identical strings; the $S_{n-3}$ subgroup would act by permuting the indices of the $Z$s out of which the giant is composed. Write $R_1=r_1\times r_2$ with $r_1$ are irrep of $S_{n-3}$ and $r_2$ an irrep of $S_3$. As an example, if we take $R$ to be an irrep of $S_9$ $$R=\yng(4,4,1),\qquad {\rm dim}_R= 84$$ then we can have $$R_1 = \yng(3,3)\otimes\yng(1,1,1),\quad {\rm dim}_{R_1}=5,\qquad R_1 = \yng(3,3)\otimes\yng(2,1),\quad {\rm dim}_{R_1}=10,$$ $$R_1 = \yng(4,2)\otimes\yng(3),\quad {\rm dim}_{R_1}=9,\qquad R_1 = \yng(4,2)\otimes\yng(2,1),\quad {\rm dim}_{R_1}=18,$$ $$R_1 = \yng(3,2,1)\otimes \yng(2,1),\qquad {\rm dim}_{R_1} = 32,$$ or $$R_1=\yng(4,1,1)\otimes\yng(3),\qquad {\rm dim}_{R_1}=10.$$ By summing the dimensions of these representations, it is easy to see that we have indeed listed all of the representations that are subduced by $R$. The giant graviton system is dual to an operator containing a product of order $N$ fields; the open strings are dual to an operator containing a product of order $\sqrt{N}$ fields. We have in mind the case that $k$ is $O(1)$, $n$ is $O(N)$ and the words $(W^{(a)})^j_i$ are a product of $O(\sqrt{N})$ fields. We call the operator (\[restrictedschur\]) a [restricted]{} Schur polynomial of representation $R$ with representation $R_1$ for the restriction. We end this appendix with a summary of the graphical notation of [@de; @Mello; @Koch:2007uu], which is used heavily in this article. An operator dual to an excited giant graviton takes the form $$\chi_{R,R_1}^{(k)}(Z,W^{(1)},...,W^{(k)}) ={1\over (n-k)!}\sum_{\sigma\in S_n}\Tr (\Pi \Gamma_R(\sigma))\Tr(\sigma Z^{\otimes n-k}W^{(1)}\cdots W^{(k)}),$$ where $\Pi$ is a product of projection operators and/or intertwiners, used to implement the restricted trace. $\Pi$ is defined by the sequence of irreducible representations used to subduce $R_1$ from $R$, as well as the chain of subgroups to which these representations belong. Since the row and column indices of the block that we trace over (denoted by $R_1$ in the above formula) need not coincide, we need to specify this data separately for both indices. The graphical notation summarizes this information. For the case that we have $k$ strings, we label the words describing the open strings $1,2,...,k$. Denote the chain of subgroups involved in the reduction by ${\cal G}_k\subset {\cal G}_{k-1}\subset\cdots\subset {\cal G}_2\subset {\cal G}_1\subset S_n$. ${\cal G}_m$ is obtained by taking all elements $S_n$ that leave the indices of the strings $W^{(i)}$ with $i\le m$ inert. To specify the sequence of irreducible representations employed in subducing $R_1$, place a pair of labels into each box, a lower label and an upper label. The representations needed to subduce the row label of $R_1$ are obtained by starting with $R$. The second representation is obtained by dropping the box with upper label equal to 1; the third representation is obtained from the second by dropping the box with upper label equal to 2 and so on until the box with label $k$ is dropped. The representations needed to subduce the column label are obtained in exactly the same way except that instead of using the upper label, we now use the lower label. For further details and explicit examples, we refer the reader to [@de; @Mello; @Koch:2007uu]. Boundstate of three Sphere Giants ================================= In this appendix, we will compute the $+1\to 1$ interaction for two strings attached to a bound state of three sphere giants. This example is interesting because, firstly, it does partially illustrate our claim that the methods we have developed apply to any bound state of giants and secondly, in this situation, we expect an emergent $U(3)$ gauge theory. The three sphere giant boundstate is described by a Young diagram with three columns. When labeling the open string endpoints we will use the labels ‘b’, ‘m’ and ‘l’ for the first column (‘b’ for big brane), second column (‘m’ for medium brane) and third column (‘l’ for little brane) respectively. The relevant Cuntz chain states together with their normalizations are shown in the table below. State Normalization ----------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------- $\|b_0,b_1-1,b_2,bb,mm\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+b_2+1)b_1\over (b_1+b_2+2)(b_1+1)}$ $\|b_0-1,b_1+1,b_2-1,bb,ll\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+2)b_2\over (b_2+1)(b_1+1)}$ $\|b_0,b_1-1,b_2,mm,bb\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+b_2+1)b_1\over (b_1+b_2+2)(b_1+1)}$ $\|b_0-1,b_1,b_2+1,mm,ll\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_2+2)(b_1+b_2+3)\over (b_2+1)(b_1+b_2+2)}$ $\|b_0-1,b_1+1,b_2-1,ll,bb\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+2)b_2\over (b_2+1)(b_1+1)}$ $\|b_0-1,b_1,b_2+1,ll,mm\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_2+2)(b_1+b_2+3)\over (b_2+1)(b_1+b_2+2)}$ $\|b_0,b_1,b_2-2,bb,bb\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_2-1)(b_1+b_2)\over (b_2+1)(b_1+b_2+2)}$ $\|b_0,b_1-2,b_2+2,mm,mm\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_2+3)(b_1-1)\over (b_2+1)(b_1+1)}$ $\|b_0-2,b_1+2,b_2,ll,ll\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+3)(b_1+b_2+4)\over (b_1+1)(b_1+b_2+2)}$ $\|b_0,b_1-1,b_2,bm,mb\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+b_2+1)b_1\over (b_1+b_2+2)(b_1+1)}$ $\|b_0,b_1-1,b_2,mb,bm\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+b_2+1)b_1\over (b_1+b_2+2)(b_1+1)}$ $\|b_0-1,b_1+1,b_2-1,bl,lb\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+2)b_2\over (b_2+1)(b_1+1)}$ $\|b_0-1,b_1+1,b_2-1,lb,bl\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_1+2)b_2\over (b_2+1)(b_1+1)}$ $\|b_0-1,b_1,b_2+1,ml,lm\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_2+2)(b_1+b_2+3)\over (b_2+1)(b_1+b_2+2)}$ $\|b_0-1,b_1,b_2+1,lm,ml\rangle$ $\left({4\pi\lambda\over N}\right)^{3b_0+2b_1+b_2+h_1+h_2-2\over 2}b_0\sqrt{f_R} \sqrt{N^{h_1+h_2-2}}\sqrt{(b_2+2)(b_1+b_2+3)\over (b_2+1)(b_1+b_2+2)}$ The labels $b_0$, $b_1$ and $b_2$ again determine the momenta of the giants. The giant corresponding to the first column has a momentum of $b_0+b_1+b_2$, the giant corresponding to the second column has a momentum of $b_0+b_1$ and the giant corresponding to the third column has a momentum of $b_0$. We take $b_0$ to be $O(N)$ and $b_1,b_2$ to be $O(1)$. To determine the boundary interactions, we start by rewriting the identities of Appendix C for the case that we have a Young diagram with three columns. To obtain the boundary interaction terms in the Hamiltonian, these identities are then inverted and rewritten in terms of normalized Cuntz chain states. The term in the Hamiltonian describing the process in which a $Z$ hops out of the first site of string 1 is given by $$H_{+1\to 1}\left[ \matrix{ \|b_0,b_1-1,b_2,bb,mm\rangle\cr \|b_0-1,b_1+1,b_2-1,bb,ll\rangle\cr \|b_0,b_1-1,b_2,mm,bb\rangle\cr \|b_0-1,b_1,b_2+1,mm,ll\rangle\cr \|b_0-1,b_1+1,b_2-1,ll,bb\rangle\cr \|b_0-1,b_1,b_2+1,ll,mm\rangle\cr \|b_0,b_1,b_2-2,bb,bb\rangle\cr \|b_0,b_1-2,b_2+2,mm,mm\rangle\cr \|b_0-2,b_1+2,b_2,ll,ll\rangle\cr \|b_0,b_1-1,b_2,bm,mb\rangle\cr \|b_0,b_1-1,b_2,mb,bm\rangle\cr \|b_0-1,b_1+1,b_2-1,bl,lb\rangle\cr \|b_0-1,b_1+1,b_2-1,lb,bl\rangle\cr \|b_0-1,b_1,b_2+1,ml,lm\rangle\cr \|b_0-1,b_1,b_2+1,lm,ml\rangle} \right]=-\lambda\sqrt{1-{b_0\over N}}M \left[ \matrix{ \|b_0,b_1-1,b_2+1,bb,mm\rangle\cr \|b_0-1,b_1+1,b_2,bb,ll\rangle\cr \|b_0,b_1,b_2-1,mm,bb\rangle\cr \|b_0-1,b_1+1,b_2,mm,ll\rangle\cr \|b_0,b_1,b_2-1,ll,bb\rangle\cr \|b_0,b_1-1,b_2+1,ll,mm\rangle\cr \|b_0,b_1,b_2-1,bb,bb\rangle\cr \|b_0,b_1-1,b_2+1,mm,mm\rangle\cr \|b_0-1,b_1+1,b_2,ll,ll\rangle\cr \|b_0,b_1-1,b_2+1,bm,mb\rangle\cr \|b_0,b_1,b_2-1,mb,bm\rangle\cr \|b_0-1,b_1+1,b_2,bl,lb\rangle\cr \|b_0,b_1,b_2-1,lb,bl\rangle\cr \|b_0-1,b_1+1,b_2,ml,lm\rangle\cr \|b_0,b_1-1,b_2+1,lm,ml\rangle} \right],$$ where the non-zero elements of $M$ are given by $$M_{1\, 1}=-(b_2)_1^2 (b_1+b_2)_2 ,\qquad M_{3\, 1}=-{(b_1+b_2)_2\over (b_2+1)^2 (b_2+2)},\qquad M_{6\, 1}=-{\frac {\left (b_1+2\right )\sqrt {b_2+2}\sqrt {b_1}}{\sqrt {b_2+1}\left (b_1+1\right )^{3/2}\left (b_1+b_2+2\right )}},$$ $$M_{4\, 1}={\frac {-b_1-b_2-3}{\sqrt {b_2+1}\left (b_1+1\right )^{3/2}\left (b_1+b_2+2\right )\sqrt {b_1}\sqrt {b_2+2}}},\qquad M_{8\, 1}=-{\frac {\sqrt {b_1-1}\sqrt {b_2+3}\sqrt {b_1+b_2+3}}{\sqrt {b_2+1}\sqrt {b_1+b_2+2}\left (b_2+2\right )\sqrt {b_1}}},$$ $$M_{10\, 1}= -{(b_1+b_2)_2 (b_2)_1\over (b_2+1)(b_2 +2)}, \qquad M_{11\, 1}=-{(b_1+b_2)_2 (b_2)_1\over (b_2+1)}, \qquad M_{14\, 1}= {\frac {\sqrt {b_2+2}\sqrt {b_1+2}}{\left (b_1+1\right )^{3/2}\sqrt {b_2+1}\left (b_1+b_2+2\right )}},$$ $$M_{15\, 1}= {\frac {\left (b_1+b_2+3\right )\sqrt {b_1+2}}{\left (b_1+1\right )^{3/2}\sqrt {b_2+1}\left (b_1+b_2+2\right )\sqrt {b_2+2}}}, \qquad M_{2\, 2}=-(b_1+b_2)_2^2 (b_2)_1,$$ $$M_{5\, 2}={(b_2)_1\over (b_1+b_2+2)^2 (b_1+b_2+3)},\qquad M_{4\, 2}= -{\frac {b_1\,\sqrt {b_1+b_2+3}\sqrt {b_1+2}}{\left (b_1+1\right )^{3/2}\left (b_2+1\right )\sqrt {b_1+b_2+2}}},$$ $$M_{6\, 2}= {\frac {-b_2-2}{\left (b_2+1\right )\left (b_1+1\right )^{3/2}\sqrt {b_1+b_2+2}\sqrt {b_1+2}\sqrt {b_1+b_2+3}}},\qquad M_{13\, 2}=-{(b_2)_1(b_1+b_2)_2\over (b_1+b_2+2)},$$ $$M_{9\, 2}= -{\frac {\sqrt {b_1+b_2+4}\sqrt {b_1+3}\sqrt {b_2+2}}{\sqrt {b_2+1}\sqrt {b_1+b_2+2}\sqrt {b_1+2}\left (b_1+b_2+3\right )}}, \qquad M_{12\, 2}=-{(b_2)_1 (b_1+b_2)_2\over (b_1+b_2+2)(b_1+b_2+3)}$$ $$M_{14\, 2}= -{\frac {\left (b_2+2\right )\sqrt {b_1}}{\left (b_1+1\right )^{3/2}\left (b_2+1\right )\sqrt {b_1+b_2+2}\sqrt {b_1+b_2+3}}}, \qquad M_{1\, 3}={(b_1)_1\over b_2 (b_2+1)^2},$$ $$M_{15\, 2}= -{\frac {\sqrt {b_1+b_2+3}\sqrt {b_1}}{\left (b_1+1\right )^{3/2}\left (b_2+1\right )\sqrt {b_1+b_2+2}}}, \qquad M_{3\, 3}=-(b_2)_1^2 (b_1)_1 ,$$ $$M_{2\, 3}= {\frac {b_1+2}{\sqrt {b_2+1}\left (b_1+1\right )\left (b_1+b_2+2\right )^{3/2}\sqrt {b_1+b_2+1}\sqrt {b_2}}}, \qquad M_{10\, 3}={(b_1)_1 (b_2)_1\over (b_2+1)},$$ $$M_{5\, 3}= -{\frac {\left (b_1+b_2+3\right )\sqrt {b_2}\sqrt {b_1+b_2+1}}{\sqrt {b_2+1}\left (b_1+1\right )\left (b_1+b_2+2\right )^{3/2}}}, \qquad M_{11\, 3}={(b_1)_1 (b_2)_1\over b_2(b_2+1)},$$ $$M_{7\, 3}= {\frac {\sqrt {b_2 -1}\sqrt{b_1+b_2}\sqrt {b_1+2}}{\sqrt {b_2+1}\sqrt {b_1+1}b_2\,\sqrt {b_1+b_2+1}}}, \qquad M_{12\, 3}= {\frac {\sqrt {b_2}\sqrt {b_1+b_2+3}}{\left (b_1+b_2+2\right )^{3/2}\left (b_1+1\right )\sqrt {b_2+1}}},$$ $$M_{13\, 3}= -{\frac {\left (b_1+2\right )\sqrt {b_1+b_2+3}}{\left (b_1+b_2+2\right )^{3/2}\left (b_1+1\right )\sqrt {b_2+1}\sqrt {b_2}}}, \qquad M_{2\, 4}= {\frac {\sqrt {b_1+2}\left (b_1+b_2+1\right )\sqrt {b_1+b_2+3}}{\left (b_2+1\right )\sqrt {b_1+1}\left (b_1+b_2+2\right )^{3/2}}},$$ $$M_{4\, 4}=-(b_1)_1^2 (b_2)_1, \qquad M_{5\, 4}= -{\frac {b_2}{\sqrt {b_1+1}\left (b_2+1\right )\left (b_1+b_2+2\right )^{3/2}\sqrt {b_1+b_2+3}\sqrt {b_1+2}}},$$ $$M_{6\, 4}= -{\frac {\sqrt {b_2+2}\sqrt {b_2}}{\left (b_1+1\right )^{2}\left (b_2+1\right )\left (b_1+2\right )}}, \qquad M_{9\, 4}= -{\frac {\sqrt {b_1+b_2+4}\sqrt {b_1+3}\sqrt {b_2}}{\sqrt{b_2+1}\sqrt {b_1+1}\left (b_1+2\right )\sqrt{b_1+b_2+3} }},$$ $$M_{12\, 4}= -{\frac {b_2\,\sqrt {b_1+b_2+1}}{\left (b_1+b_2+2\right )^{3/2}\left (b_2+1\right )\sqrt {b_1+1}\sqrt {b_1+2}}}, \qquad M_{13\, 4}= {\frac {\sqrt {b_1+2}\sqrt {b_1+b_2+1}}{\left (b_1+b_2+2\right )^{3/2}\left (b_2+1\right )\sqrt {b_1+1}}},$$ $$M_{14\, 4}=-{(b_2)_1(b_1)_1\over (b_1+1)(b_1+2)},\qquad M_{1\, 5}= {\frac {b_1}{\left (b_2+1\right )^{3/2}\left (b_1+1\right )\sqrt {b_1+b_2+2}\sqrt {b_2}\sqrt {b_1+b_2+1}}},$$ $$M_{15\, 4}=-{(b_2)_1(b_1)_1\over (b_1+1)}, \qquad M_{2\, 5}={(b_1)_1\over (b_1+b_2+2)^2 (b_1+b_2+1)},$$ $$M_{3\, 5}= {\frac {\sqrt {b_1+b_2+1}\left (b_2+2\right )\sqrt {b_2}}{\left (b_2+1\right )^{3/2}\left (b_1+1\right )\sqrt {b_1+b_2+2}}}, \qquad M_{5\, 5}=-(b_1)_1 (b_1+b_2)_2^2,$$ $$M_{7\, 5}= {\frac {\sqrt{b_2-1}\sqrt{b_1+b_2}\sqrt {b_1}}{\sqrt {b_1+1}\sqrt {b_1+b_2+2}\left (b_1+b_2+1\right )\sqrt {b_2}}}, \qquad M_{10\, 5}= -{\frac {\sqrt {b_1+b_2+1}\sqrt {b_2+2}}{\left (b_2+1\right )^{3/2}\left (b_1+1\right )\sqrt {b_1+b_2+2}}},$$ $$M_{11\, 5}= -{\frac {b_1\,\sqrt {b_2+2}}{\left (b_2+1\right )^{3/2}\left (b_1+1\right )\sqrt {b_1+b_2+2}\sqrt {b_1+b_2+1}}}, \qquad M_{12\, 5}={(b_1)_1(b_1+b_2)_2\over b_1+b_2+2},$$ $$M_{13\, 5}=-{(b_1)_1(b_1+b_2)_2\over (b_1+b_2+2)(b_1+b_2+1)}, \qquad M_{1\, 6}= {\frac {\sqrt {b_1}b_2\,\sqrt {b_2+2}}{\sqrt {b_1+1}\left (b_2+1\right )^{3/2}\left (b_1+b_2+2\right )}},$$ $$M_{3\, 6}= {\frac {b_1+b_2+1}{\sqrt {b_1+1}\left (b_2+1\right )^{3/2}\left (b_1+b_2+2\right )\sqrt {b_2+2}\sqrt {b_1}}}, \qquad M_{4\, 6}={(b_1+b_2)_2\over b_1 (b_1+1)^2},$$ $$M_{6\, 6}=-(b_1)_1^2(b_1+b_2)_2,\qquad M_{8\, 6}= {\frac {\sqrt {b_1-1}\sqrt {b_2+3}\sqrt {b_1+b_2+1}}{\sqrt {b_1+1}\sqrt{b_1+b_2+2}\sqrt{b_2+2}b_1}},$$ $$M_{10\, 6}= {\frac {\left (b_1+b_2+1\right )\sqrt {b_2}}{\left (b_2+1\right )^{3/2}\sqrt {b_1+1}\left (b_1+b_2+2\right )\sqrt {b_1}}}, \qquad M_{11\, 6}= {\frac {\sqrt {b_1}\sqrt {b_2}}{\left (b_2+1\right )^{3/2}\sqrt {b_1+1}\left (b_1+b_2+2\right )}},$$ $$M_{14\, 6}={(b_1)_1 (b_1+b_2)_2\over b_1+1}, \qquad M_{1\,7}= -{\frac {\sqrt {b_1}\sqrt{b_2+2}\sqrt{b_1+b_2+3}}{\left (b_2+1\right )^{2}\sqrt {b_1+1}\sqrt {b_1+b_2+2}\sqrt {b_2}}},$$ $$M_{15\, 6}=-{(b_1)_1 (b_1+b_2)_2\over b_1(b_1+1)}, \qquad M_{2\, 7}= -{\frac {\sqrt {b_1+2}\sqrt{b_2+2}\sqrt{b_1+b_2+3}}{\sqrt {b_2+1}\sqrt {b_1+1}\left (b_1+b_2+2\right )^{2}\sqrt {b_1+b_2+1}}},$$ $$M_{3\, 7}= -{\frac {\sqrt {b_1}\sqrt{b_2+2}\sqrt{b_1+b_2+3}\sqrt {b_2}}{\sqrt {b_1+1}\left (b_2+1\right )^{2}\sqrt {b_1+b_2+2}}}, \qquad M_{5\, 7}= -{\frac {\sqrt {b_1+2}\sqrt{b_2+2}(b_1+b_2)_2}{\sqrt {b_1+1}\sqrt {b_2+1}\left (b_1+b_2+2\right )}},$$ $$M_{7\, 7}=-{\sqrt{b_1+b_2+3}\sqrt{b_2+2}\sqrt{b_2-1}\sqrt{b_1+b_2}\over\sqrt{b_2}\sqrt{b_1+b_2+1}\sqrt{b_2+1}\sqrt{b_1+b_2+2}}, \qquad M_{10\, 7}= {\frac {\sqrt {b_1}\sqrt {b_1+b_2+3}}{\left (b_2+1\right )^{2}\sqrt {b_1+1}\sqrt {b_1+b_2+2}}},$$ $$M_{11\, 7}= {\frac {\sqrt {b_1}\left (b_2+2\right )\sqrt {b_1+b_2+3}}{\left (b_2+1\right )^{2}\sqrt {b_1+1}\sqrt {b_1+b_2+2}}}, \qquad M_{12\, 7}= {\frac {\sqrt {b_1+2}\sqrt {b_2+2}}{\left (b_1+b_2+2\right )^{2}\sqrt {b_2+1}\sqrt {b_1+1}}},$$ $$M_{13\, 7}= {\frac {\sqrt {b_1+2}\sqrt {b_2+2}\left (b_1+b_2+3\right )}{\left (b_1+b_2+2\right )^{2}\sqrt {b_2+1}\sqrt {b_1+1}}}, \qquad M_{1\, 8}= {\frac {\sqrt {b_1+2}\sqrt {b_1+b_2+1}(b_2)_1}{\left (b_2+1\right )\sqrt {b_1+1}\sqrt {b_1+b_2+2}}},$$ $$M_{3\, 8}= -{\frac {\sqrt {b_1+2}\sqrt {b_1+b_2+1}\sqrt {b_2}}{\left (b_2+1\right )^{2}\sqrt {b_1+1}\sqrt {b_1+b_2+2}\sqrt {b_2+2}}}, \qquad M_{4\, 8}= -{\frac {\sqrt {b_1+2}\sqrt {b_1+b_2+3}\sqrt {b_2}}{\left (b_1+1\right )^{2}\sqrt{b_2+1}\sqrt{b_1+b_2+2}\sqrt {b_1}}},$$ $$M_{6\, 8}= -{\frac {\sqrt {b_1+2}\sqrt {b_1+b_2+3}\sqrt {b_2}\sqrt {b_1}}{\sqrt{b_2+1}\left (b_1+1\right )^{2}\sqrt{b_1+b_2+2}}}, \qquad M_{8\, 8}= -{\frac {\sqrt {b_1-1}\sqrt {b_2+3}\sqrt {b_1+2}\sqrt {b_2}}{\sqrt {b_1+1}\sqrt {b_2+1}\sqrt {b_1}\sqrt {b_2+2}}},$$ $$M_{10\, 8}= -{\frac {\sqrt {b_1+2}\sqrt {b_1+b_2+1}b_2}{\left (b_2+1\right )^{2}\sqrt {b_1+1}\sqrt {b_1+b_2+2}}}, \qquad M_{11\, 8}= {\frac {\sqrt {b_1+2}\sqrt {b_1+b_2+1}}{\left (b_2+1\right )^{2}\sqrt {b_1+1}\sqrt {b_1+b_2+2}}},$$ $$M_{14\, 8}= {\frac {\sqrt {b_1+b_2+3}\sqrt {b_2}}{\left (b_1+1\right )^{2}\sqrt{b_2+1}\sqrt{b_1+b_2+2}}}, \qquad M_{15\, 8}= {\frac {\left (b_1+2\right )\sqrt {b_1+b_2+3}\sqrt {b_2}}{\left (b_1+1\right )^{2}\sqrt{b_2+1}\sqrt{b_1+b_2+2}}},$$ $$M_{2\, 9}= {\frac {\sqrt {b_1}\sqrt {b_2}(b_1+b_2)_2}{\sqrt {b_1+1}\sqrt {b_2+1}\left (b_1+b_2+2\right )}}, \qquad M_{4\, 9}= {\frac {\sqrt {b_1}\sqrt {b_1+b_2+1}\sqrt {b_2+2}\sqrt {b_1+2}}{\sqrt{b_1+b_2+2}\sqrt{b_2+1}\left (b_1+1\right )^{2}}}$$ $$M_{5\, 9}= -{\frac {\sqrt {b_1}\sqrt {b_1+b_2+1}\sqrt {b_2}}{\sqrt {b_1+1}\sqrt {b_2+1}\left (b_1+b_2+2\right )^{2}\sqrt {b_1+b_2+3}}}, \qquad M_{6\, 9}= -{\frac {\sqrt {b_1}\sqrt {b_1+b_2+1}\sqrt {b_2+2}}{\sqrt{b_2+1}\left (b_1+1\right )^{2}\sqrt{b_1+b_2+2}\sqrt {b_1+2}}},$$ $$M_{9\, 9}= -{\frac {\sqrt {b_1+b_2+4}\sqrt {b_1+3}\sqrt {b_1}\sqrt {b_1+b_2+1}}{\sqrt {b_1+1}\sqrt {b_1+b_2+2}\sqrt {b_1+b_2+3}\sqrt {b_1+2}}}, \qquad M_{12\, 9}= -{\frac {\sqrt {b_1}\left (b_1+b_2+1\right )\sqrt {b_2}}{\left (b_1+b_2+2\right )^{2}\sqrt {b_1+1}\sqrt {b_2+1}}},$$ $$M_{13\, 9}= {\frac {\sqrt {b_1}\sqrt {b_2}}{\left (b_1+b_2+2\right )^{2}\sqrt {b_1+1}\sqrt {b_2+1}}}, \qquad M_{14\, 9}= -{\frac {b_1\,\sqrt {b_1+b_2+1}\sqrt {b_2+2}}{(b_1+1 )^{2}\sqrt{b_2+1}\sqrt{b_1+b_2+2}}},$$ $$M_{15\, 9}= {\frac {\sqrt {b_1+b_2+1}\sqrt {b_2+2}}{\left (b_1+1\right )^{2}\sqrt{b_2+1}\sqrt{b_1+b_2+2}}}, \qquad M_{3\, 10}=-{\sqrt{b_2+3}(b_1+b_2)_2\over (b_2+2)\sqrt{b_2+1}},$$ $$M_{4\, 10}= {\frac {\sqrt {b_2+3}}{\left (b_1+b_2+2\right )\sqrt {b_2+2}\sqrt {b_1}\sqrt {b_1+1}}}, \qquad M_{8\, 10}= {\frac {\sqrt {b_1-1}\sqrt {b_1+b_2+3}}{\sqrt {b_1+b_2+2}\left (b_2+2\right )\sqrt {b_1}}},$$ $$M_{10\, 10}= -{\frac {\sqrt {b_2+3}\sqrt {b_1+b_2+1}\sqrt {b_1+b_2+3}\sqrt {b_2}}{\sqrt {b_2+1}\sqrt {b_2+2}\left (b_1+b_2+2\right )}}, \qquad M_{15\, 10}= -{\frac {\sqrt {b_2+3}\sqrt {b_1+2}}{\sqrt {b_1+1}\left (b_1+b_2+2\right )\sqrt {b_2+2}}},$$ $$M_{1\, 11}= {\frac {\left (b_2-1\right )\sqrt {b_1}\sqrt {b_1+2}}{\left (b_1+1\right )\sqrt {{b_2}^{2}-1}b_2}}, \qquad M_{2\, 11}= {\frac {\sqrt {b_2-1}}{\left (b_1+1\right )\sqrt {b_2}\sqrt {b_1+b_2+1}\sqrt {b_1+b_2+2}}},$$ $$M_{7\, 11}= -{\frac {\sqrt {b_1+b_2}\sqrt {b_1+2}}{\sqrt {b_1+1}b_2\,\sqrt {b_1+b_2+1}}}, \qquad M_{11\, 11}= -{\frac {\sqrt {b_2-1}\sqrt {b_1}\sqrt {b_1+2}\sqrt {b_2+2}}{\sqrt {b_2+1}\sqrt {b_2}\left (b_1+1\right )}},$$ $$M_{13\, 11}= -{\frac {\sqrt {b_2-1}\sqrt {b_1+b_2+3}}{\sqrt {b_1+b_2+2}\left (b_1+1\right )\sqrt {b_2}}}, \qquad M_{5\, 12}= -{\frac {\sqrt{b_1+b_2+4}\sqrt {b_2+2}\sqrt {b_2}}{(b_2+1)\sqrt {b_1+b_2+2}\left (b_1+b_2+3\right )}},$$ $$M_{6\, 12}= -{\frac {\sqrt {b_1+b_2+4}}{\left (b_2+1\right )\sqrt {b_1+b_2+3}\sqrt {b_1+2}\sqrt {b_1+1}}}, \qquad M_{9\, 12}= {\frac {\sqrt {b_1+3}\sqrt {b_2+2}}{\sqrt {b_2+1}\left (b_1+b_2+3\right )\sqrt {b_1+2}}},$$ $$M_{12\, 12}= -{\frac {\sqrt {b_1+b_2+4}\sqrt {b_2+2}\sqrt {b_2}\sqrt {b_1+b_2+1}}{\sqrt {b_1+b_2+2}\sqrt {b_1+b_2+3}\left (b_2+1\right )}}, \qquad M_{14\, 12}= -{\frac {\sqrt {b_1+b_2+4}\sqrt {b_1}}{\sqrt {b_1+1}\left (b_2+1\right )\sqrt {b_1+b_2+3}}},$$ $$M_{1\, 13}= -{\frac {\sqrt {b_1+b_2}}{\left (b_1+1\right )\sqrt {b_1+b_2+1}\sqrt {b_2}\sqrt {b_2+1}}}, \qquad M_{2\, 13}= {\frac {\sqrt{b_1+b_2}\sqrt {b_1}\sqrt {b_1+2}}{(b_1+1)\sqrt {b_1+b_2+2}\left (b_1+b_2+1\right )}},$$ $$M_{7\, 13}= -{\frac {\sqrt {b_2-1}\sqrt {b_1}}{\sqrt {b_1+1}\left (b_1+b_2+1\right )\sqrt {b_2}}}, \qquad M_{11\, 13}= {\frac {\sqrt {b_1+b_2}\sqrt {b_2+2}}{\sqrt {b_2+1}\left (b_1+1\right )\sqrt {b_1+b_2+1}}},$$ $$M_{13\, 13}= -{\frac {\sqrt {b_1+b_2}\sqrt {b_1}\sqrt {b_1+2}\sqrt {b_1+b_2+3}}{\sqrt {b_1+b_2+1}\sqrt {b_1+b_2+2}\left (b_1+1\right )}}, \qquad M_{5\, 14}= {\frac {\sqrt {b_1+3}}{\left (b_2+1\right )\sqrt {b_1+2}\sqrt {b_1+b_2+3}\sqrt {b_1+b_2+2}}},$$ $$M_{6\, 14}= -{\frac {\left (b_1+3\right )\sqrt {b_2+2}\sqrt {b_2}}{\left (b_2+1\right )\sqrt {{b_1}^{2}+4\,b_1+3}\left (b_1+2\right )}}, \qquad M_{9\, 14}= {\frac {\sqrt {b_1+b_2+4}\sqrt {b_2}}{\sqrt{b_2+1}\left (b_1+2\right )\sqrt{b_1+b_2+3} }},$$ $$M_{12\, 14}= {\frac {\sqrt {b_1+3}\sqrt {b_1+b_2+1}}{\sqrt {b_1+b_2+2}\left (b_2+1\right )\sqrt {b_1+2}}}, \qquad M_{14\, 14}= -{\frac {\sqrt {b_1+3}\sqrt {b_2+2}\sqrt {b_2}\sqrt {b_1}}{\sqrt {b_1+1}\sqrt {b_1+2}\left (b_2+1\right )}},$$ $$M_{3\, 15}= {\frac {\sqrt {b_1-1}}{\left (b_1+b_2+2\right )\sqrt {b_1}\sqrt {b_2+2}\sqrt {b_2+1}}}, \qquad M_{4\, 15}= {\frac {\left (b_1-1\right )(b_1+b_2)_2}{\sqrt {{b_1}^{2}-1}b_1}},$$ $$M_{8\, 15}= -{\frac {\sqrt {b_2+3}\sqrt {b_1+b_2+1}}{\sqrt{b_1+b_2+2} b_1\,\sqrt{b_2+2} }}, \qquad M_{10\, 15}= {\frac {\sqrt {b_1-1}\sqrt {b_2}}{\sqrt {b_2+1}\left (b_1+b_2+2\right )\sqrt {b_1}}},$$ $$M_{15\, 15}= -{\frac {\sqrt {b_1-1}\sqrt {b_1+b_2+1}\sqrt {b_1+b_2+3}\sqrt {b_1+2}}{\sqrt {b_1+1}\sqrt {b_1}\left (b_1+b_2+2\right )}}.$$ For large $b_1$ and $b_2$, we find that $M=-{\bf 1}$ with ${\bf 1}$ the $15\times 15$ identity matrix. We can also identify terms in $M$ that behave as $b_1^{-1}$ $$M_1={1\over b_1}\left[ \matrix{ 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0 &1\cr 0 &0 &-1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &-1 &0 &0 &0 &0 &0 &-1 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &-1\cr 0 &0 &0 &-1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &-1 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &1 &0 &0 &-1 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &-1 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0} \right],$$ terms that behave as $b_2^{-1}$ $$M_2={1\over b_2}\left[ \matrix{ 0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &1 &0 &0 &0 &0\cr 0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &-1 &0 &0 &-1 &0 &0 &0 &0 &0\cr 0 &-1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &-1 &0 &0 &0 &0\cr -1 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &1 &0 &0 &0 &0 &-1 &0 &0 &0 &0 &0 &0 &0\cr -1 &0 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &-1 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0} \right],$$ and terms that behave as $(b_1+b_2)^{-1}$ $$M_3={1\over b_1+b_2}\left[ \matrix{ 0 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0 &1 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &-1 &0 &0 &0 &0 &-1 &0 &0 &0\cr -1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &-1 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &-1 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &1\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &1 &0 &0 &0 &-1 &0 &0 &0 &0 &0 &0\cr 0 &-1 &0 &0 &0 &0 &1 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0 &0\cr 0 &0 &0 &0 &0 &0 &0 &0 &0 &-1 &0 &0 &0 &0 &0} \right].$$ By looking at the Cuntz chain states, it is straight forward to see that $M_1$ is reproduced by ribbon diagrams in which a pair of labels undergoes a $l\leftrightarrow m$ transition, that $M_2$ is reproduced by ribbon diagrams in which a pair of labels undergoes a $b\leftrightarrow m$ transition and that $M_3$ is reproduced by ribbon diagrams in which a pair of labels undergoes a $l\leftrightarrow b$ transition. 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B [528]{}, 111 (2002) \[arXiv:hep-th/0111163\]. S. Hirano, “Fat magnon,” JHEP [0704]{} (2007) 010 \[arXiv:hep-th/0610027\]. R. C. Myers, “Dielectric-branes,” JHEP [9912]{} (1999) 022 \[arXiv:hep-th/9910053\]. Y. Kimura and S. Ramgoolam, “Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality,” arXiv:0709.2158 \[hep-th\]. J.-Q. Chen, [Group Representation Theory for Physicists]{}, Singapore, World Scientific (1989). [^1]: See [@Berenstein:2006qk],[@Strings],[@Shahin] for further studies of non-BPS excitations that have been interpreted as open strings attached to giant gravitons. [^2]: We review the definition of the restricted Schur polynomial in Appendix E. [^3]: An exception to this is an open string attached to a maximal giant graviton[@Maxg]. [^4]: For some earlier related work, see[@Corley:2002mj]. [^5]: In Appendix F we consider a boundstate of three sphere giants with two open strings attached. [^6]: When the number of operators in the Young diagram is $O(N^2)$, the operator is dual to an LLM geometry[@LLM]. [^7]: The number of primes on the label of the restricted Schur polynomial indicates how many boxes are dropped, i.e. $R''$ is obtained by dropping two boxes from $R$. [^8]: For the $m=3$ case, see Appendix F. [^9]: The fat magnon in the plane wave background is the hedgehog of [@Shahin] [^10]: We would like to thank Shahin Sheikh-Jabbari for suggesting this to us. [^11]: See appendix E for a quick review of restricted Schur polynomials and [@Balasubramanian:2004nb; @de; @Mello; @Koch:2007uu; @de; @Mello; @Koch:2007uv] for a detailed discussion. [^12]: In particular, not necessarily Hermitian. [^13]: See the introduction for the restricted Schur polynomials corresponding to these states.
Host-parasite relationships in amebiasis: conference report. Entamoeba histolytica has been redescribed as the separate species E. histolytica and Entamoeba dispar. E. dispar is apparently never invasive in humans, while E. histolytica is the etiologic agent of amebic colitis and liver abscess. Virulence factors that may enable E. histolytica to invade include a galactose-specific adhesin, secreted proteases, extracellular matrix receptors, and a cell surface lipophosphoglycan. Progress in vaccine development includes the identification of the cysteine-rich domain of the adhesin and the serine-rich surface protein as protective antigens.
Question Posted by: anon \| 2011-04-21 can''t get married man out of my head Hi, I don''t why but i cannot get this married man out of my head. 4 years ago i met this guy which i was crazy about but not knowing that he is engaged. we were seeing each other for a few weeks only to find out he is engage. i immediately ended things. we saw each other often because we then had mutual friends but nothing happened between us in that time. we really liked each developed strong feelings for each other he was everything i wanted in a guy. he then told me he''s getting married, he''s fiance was pregnant and she was muslim but he wasn''t happy in the relationship, i think he was pressured to take responsibility but asked me if i wanted to be with him in that case he will not get married. i said no cause i could not break up a family and she was expecting his child. it was hard for me to let go but i knew that it could not work if he cheated on his fiance then he could cheat on me too. i cut off all ties from him and only after a few months i saw him again and did something stupid that i''m not proud of at all. but he looked miserable and we were so happy to see other and then we got intimate. i don''t know what i was thinking coz that is not like me. i''ve only before him been with one guy which i spent 7 years with. he then wanted to leave his wife for me but i refused and decided it''s best that we don''t see each other anymore. i moved on with my life and met my boyfriend which i love to bits and have been with for 3 years and we were always happy. and then he came back again went looking my cell number and said he just needed to talk to someone. we hooked up and he told me he is seperated from his wife and it ended up with us being intimate again. i felt terrible of what i did to my boyfriend as i''m not the type to cheat but somehow this guy has this effect on me i just cannot control my feelings for him. he then again insisted that we leave the people we are with to be together and i actually considered it but then again cut all ties from him up untill today. i was not sure about him we did not date and the fling we had didn''t last too long so i'' decided to stay with my boyfriend even though i will always love this other guy and i know he feels the same way. and i still think about him alot and i sometimes wish that i can just see him again. he is still with his wife now. i don''t know why i can''t get him out of my head....i believe that it will and can never be ....why can''t i get him out of my mind? how can i just forget about him and concentrate on my relationship with my boyfriend ....pls advise Our expert says: Firstly, try to avoid giving yourself negative instructions and predictions, like " I can't get..." You haven't done so SO FAR. YOu could. And face the FACTS. He was cheating on his fiancee ; he lied to you and to her. IS that really "everything you ever wanted in a guy " ? And he had gotten his fiancee pregnant ( knowing especially what this would mean to a muslim ) and THEN decided he didn't much care for her ? Then you felt sorry for him ( though he had been busy hurting OTHER people ) and gave him a chance to get you pregnant, too. And he didn't worry about the possible consequences for you. What on EARTH do you find so irresistable about this rat ? Of he needs to talk to someone, tell him to see a counsellor, who won't let him sleep with him or her. If he loved you there is no way he would have taken advantage of you so often. Are you really desperately keen to help him to get you into more trouble and misery ? You are workin hard to ignore all the ugly truths about him, and you are in love not with this unpleasant guy,, you are in love with your fantasies of who you dream he might be and which he will never be. You say you're not proud of what you did, but you keep on doing it. You CAN stop those feelings. You can stop being in love with a rosy fantasy, and start smelling the stinkblaar. The information provided does not constitute a diagnosis of your condition. You should consult a medical practitioner or other appropriate health care professional for a physical exmanication, diagnosis and formal advice. Health24 and the expert accept no responsibility or liability for any damage or personal harm you may suffer resulting from making use of this content. Our users say: Posted by: Anon \| 2011-04-28 thanks for the advise CS and everyone for your input i think i''m starting to look at things more clearer now and feeling a lot of regret and really stupid for degrading myself in that way and for what i''ve done and allowed Posted by: Pat \| 2011-04-21 Perhaps if more men and women practice a little self discipline, a lot of heartache can be avoided. I feel sorry for the child in this marriage as the dad is not a dedicated family man. He will not be dedicated to you if you do decide to have a relationship, as he is weak willed with no idea of what he wants in life. How can he impregnate a woman, marry her then decide this is not what he wants? Posted by: anon \| 2011-04-21 to romany i said WE COULD NEVER BE i don''t want him to leave his wife. and you have a right to your opinion and believe me ''im not proud of what i did at all. i have accepted the fact that he is married and don''t intend of leaving my boyfriend for him. and the last time i saw him was more than a year ago but i still can''t stop thinking of him. i know what i feel and i cannot change my feelings you can''t just switch off your feelings and stop loving someone Posted by: Anon \| 2011-04-21 Posted by: Romany \| 2011-04-21 Hi, you are giving yourself lots of UNDUE credit by making remarks such as:- &quot i''''m not the type to cheat &quot &quot i said no cause i could not break up a family and she was expecting his child&quot etc etc.The bottom line here is that HE IS MARRIED regardless to whom. Religion, race everything else aside. He made a CHOICE to marry her and now, instead of paying a prostitute in hard earned cash..... he is getting it free and for nothing from you.If you insist that the both of you FEEL for each other and are meant to be together bla bla bla.... tell him to divorce his wife/family legally and only THEN will you make a commtment and give the relationship a go.I will bet money on the fact that this will not happen.You are into the deceipt, the mystery, the whole scene with this guy and you THINK you love him, but looking at the hard facts here, you really cannot be that naive? Or can you.Then on the other hand (and this is something you should do always). Place yourself in the wife''s position..... would you like someone to do this to you?No, believe me, do this and it will come back to you like a ton of bricks. Posted by: cybershrink \| 2011-04-21 Firstly, try to avoid giving yourself negative instructions and predictions, like " I can't get..." You haven't done so SO FAR. YOu could. And face the FACTS. He was cheating on his fiancee ; he lied to you and to her. IS that really "everything you ever wanted in a guy " ? And he had gotten his fiancee pregnant ( knowing especially what this would mean to a muslim ) and THEN decided he didn't much care for her ? Then you felt sorry for him ( though he had been busy hurting OTHER people ) and gave him a chance to get you pregnant, too. And he didn't worry about the possible consequences for you. What on EARTH do you find so irresistable about this rat ? Of he needs to talk to someone, tell him to see a counsellor, who won't let him sleep with him or her. If he loved you there is no way he would have taken advantage of you so often. Are you really desperately keen to help him to get you into more trouble and misery ? You are workin hard to ignore all the ugly truths about him, and you are in love not with this unpleasant guy,, you are in love with your fantasies of who you dream he might be and which he will never be. You say you're not proud of what you did, but you keep on doing it. You CAN stop those feelings. You can stop being in love with a rosy fantasy, and start smelling the stinkblaar. Get a daily health tip Stay in touch The information on Health24 is for educational purposes only, and is not intended as medical advice, diagnosis or treatment. If you are experiencing symptoms or need health advice, please consult a healthcare professional. See additional information.
Functional role of cysteine residues in the (Na,K)-ATPase alpha subunit. The structural-functional roles of 23 cysteines present in the sheep (Na,K)-ATPase alpha1 subunit were studied using site directed mutagenesis, expression, and kinetics analysis. Twenty of these cysteines were individually substituted by alanine or serine. Cys452, Cys455 and Cys456 were simultaneously replaced by serine. These substitutions were introduced into an ouabain resistant alpha1 sheep isoform and expressed in HeLa cells under ouabain selective pressure. HeLa cells transfected with a cDNA encoding for replacements of Cys242 did not survive ouabain selective pressure. Single substitutions of the remaining cysteines yielded functional enzymes, although some had reduced turnover rates. Only minor variations were observed in the enzyme Na(+) and K(+) dependence as a result of these replacements. Some substitutions apparently affect the E1<-->E2 equilibrium as suggested by changes in the K(m) of ATP acting at its low affinity binding site. These results indicate that individual cysteines, with the exception of Cys242, are not essential for enzyme function. Furthermore, this suggests that the presence of putative disulfide bridges is not required for alpha1 subunit folding and subsequent activity. A (Na,K)-ATPase lacking cysteine residues in the transmembrane region was constructed (Cys104, 138, 336, 802, 911, 930, 964, 983Xxx). No alteration in the K(1/2) of Na(+) or K(+) for (Na,K)-ATPase activation was observed in the resulting enzyme, although it showed a 50% reduction in turnover rate. ATP binding at the high affinity site was not affected. However, a displacement in the E1<-->E2 equilibrium toward the E1 form was indicated by a small decrease in the K(m) of ATP at the low affinity site accompanied by an increase in IC(50) for vanadate inhibition. Thus, the transmembrane cysteine-deficient (Na,K)-ATPase appears functional with no critical alteration in its interactions with physiological ligands.
The Alabama House of Representatives has advanced a bill that would allow probate judges to refuse to issue marriage licenses to gay couples – because the document would no longer be required to get married. Instead, couples would file an affidavit that they were married and it would be recorded. Judges in the state have been using a loophole to refuse to issue marriage licenses to gay couples already. The law says probate judges “may” issue licenses but does not require them to do so. Some judges refuse and couples have to go to a different judge to get the license. “This will allow everyone to be married in their home county,” Republican state senator Greg Albritton said. Albritton has sponsored the legislation for years, but this is the first time it has advanced through both chambers. “There’s still counties that will not issue marriage licenses,” Albritton said. “They take the word may to the extreme, if you will.” Related: Did a lesbian former legislator just out Alabama’s Republican Governor Kay Ivey? The state senate passed Albritton’s bill by a vote of 26-0 on March 21. It cleared the House Judiciary Committee yesterday, clearing it for final passage on the House floor. Albritton’s bill says probate judges “shall” record every marriage with proper documentation. These would include affidavits saying they are of legal age to wed, are not already married, are not related, and are mentally competent to make the decision to get married. It would also eliminate the requirement that the marriage be “solemnized” by a judge, minister, or other official during a ceremony. “I would suggest this is the end of the state telling people who they can and cannot marry. A license is permission,” Albritton said. Only Democrat Merika Coleman voted against the bill. “I do remember the original dialogue where it came from,” Coleman said. “So that was my no vote. It was still one of those kind of protest votes against what I felt was the original reason why we were here with this bill in the first place.”
EVERYTHING is an adventure Pregnancy yoga for my baby, I mean me, I mean… I can’t actually tell if my pregnancy yoga is for me, for my baby or for the bond between me and my baby. Isn’t that an amazing confusion? I started prenatal yoga at about 9 weeks into my pregnancy and even though I could have continued with my normal yoga (with modifications), I just didn’t feel confident enough that I knew enough about pregnancy to know what’s safe and what’s not. So prenatal yoga it was. With no belly to show and nausea to spice things up a bit, I entered into the pregnancy yoga world not knowing what to expect. A bunch of pregnant woman just lying around and stretching and arm or a leg here and there? A whole lot of child’s pose? Will we even move? It was everything I didn’t expect. Having been an ashtanga and vinyasa yogi for years and continuously pushing my body and my mind through yoga flow, this was a strange new world to me. This is a world where you don’t push yourself. You don’t see how deep you can take a pose, you don’t try and stretch that little bit further, you don’t try and take your mind into deeper place. You “just be” and move with yourself and your baby in a way that soothes your soul, your baby and your body. When we found out that we were pregnant, a friend gave me a card with a quote in and at the time, it didn’t sink in how powerful it really was, until I had actually spent time with my pregnancy, through yoga. I’m going to end off with this quote and let it sink in for you. To be pregnant is to be vitally alive, thoroughly woman, and distressingly inhabited. Soul and spirit are stretched – along with the body – making pregnancy a time of transition, growth, and profound beginnings.” – Anne Christian Buchanan
BARCELONA, SPAIN—Spain’s top court on Tuesday officially ruled that Catalonia’s disputed independence referendum was illegal because a regional law that backed it was against Spain’s constitution. The Catalan regional parliament passed the so-called “self-determination referendum law” in early September. Regional leaders went on to stage the Oct. 1 referendum on whether the region should separate from Spain. They say the “Yes” side won and that the result gave the region a mandate to declare independence. Spain’s constitutional Court had earlier suspended the law temporarily while judges assessed the Spanish government’s objection to it. In its ruling Tuesday, the court says the law was against national sovereignty and the “indissoluble unity of the Spanish nation.” The court says that the parliamentary session that approved the law also violated the country’s constitution. Read more: Spain’s government awaits decision on independence from Catalan leader Infighting threatens to derail Catalan independence efforts in Spain The ruling was not surprising — Spain’s government had already repeatedly insisted the vote was illegal. “We are facing an executive power in the state that uses the judiciary branch to block the legislative,” Catalan government spokesman Jordi Turull told reporters shortly after the ruling was announced. Catalan President Carles Puigdemont made an ambiguous statement about the region’s future last week, saying he has the mandate to declare independence — but would not immediately move to put it into effect to allow time for talks and mediation. The president of the Catalonia region Carles Puigdemont said on Oct. 10 that he was proceeding with a declaration of independence but was suspending it for several weeks to facilitate negotiations. (The Associated Press) Puigdemont now has until Thursday to backtrack on any steps the region has taken toward secession. If he refuses, the central government has said it would invoke constitutional authority to restrict or revoke the areas of self-governance Catalonia has now. Tuesday’s ruling came a day after a Madrid judge provisionally jailed two Catalan independence leaders, Jordi Sanchez and Jordi Cuixart, in a sedition probe. The judge ruled they were the orchestrators of massive demonstrations Sept. 20-21 in Barcelona that hindered a police operation against preparations for the Oct. 1 independence referendum. Protesters were gathering for a fresh round of demonstrations in Barcelona Tuesday to demand their release. Loading... Loading... Loading... Loading... Loading... Loading... Some 500 students left classrooms in one of Barcelona’s main universities to join the demonstrations. “We urge the release of our political prisoners and call on Catalan authorities to revoke the suspension of the independence declaration and proclaim the Catalan republic,” said Aina Delgado Morell, a representative of Universitats per la Republica, a pro-independence student organization. Students would keep protests going to “stop the repression by the Spanish state,” she added. Read more about:
Q: ¿ Cómo poner un relative con un fondo difuminado como en la imagen adjunta? ¿ Hay algún Theme en Eclipse que haga esto o alguien ha usado este tipo de fondo ? Es exactamente lo que busco pero con cualquier color que uso lógicamente se me queda mate, no es el resultado, debe ser translúcido. UPDATE: Mi código xml donde tengo un botón que es el que tengo que modificar para que se aplique a todos, ya que tengo una lista como en el ejemplo: <RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android" android:layout_width="match_parent" android:layout_height="match_parent" > <RelativeLayout android:layout_width="wrap_content" android:layout_height="wrap_content" android:layout_alignParentLeft="true" android:layout_alignParentRight="true" android:layout_alignParentTop="true" android:layout_marginTop="0dp" android:background="@drawable/translucido" > <TextView android:id="@+id/cargo" android:layout_width="wrap_content" android:layout_height="wrap_content" android:layout_alignParentTop="true" android:layout_centerHorizontal="true" android:layout_marginTop="57dp" android:gravity="center" android:text="Medium Text" android:textAppearance="?android:attr/textAppearanceMedium" android:textColor="#FFFFFF" /> <TextView android:id="@+id/nombre" android:layout_width="match_parent" android:layout_height="wrap_content" android:layout_alignBottom="@+id/cargo" android:layout_alignParentLeft="true" android:layout_marginBottom="21dp" android:gravity="left" android:text=" Large Text" android:textAppearance="?android:attr/textAppearanceLarge" android:textColor="#FFFFFF" android:textStyle="bold" android:typeface="serif" /> </RelativeLayout> </RelativeLayout> A: El efecto se conoce como blur. No es muy recomendado utilizarlo por el gran consumo de memoria que tiene. Pero hay librerías que te ayudan a generar dicho efecto. Si te interesa puedes puedes ver esta librería: https://github.com/faradaj/BlurBehind
Gaston's War Gaston's War is a 1997 drama film directed by Robbe De Hert and starring Werner De Smedt, Mapi Galán and Peter Firth. Based on a novel by Allan Mayer, the film is set many decades after the Second World War, and tells the story of a Belgian resistance fighter, Gaston Vandermeerssche, who tries to discover who betrayed them to the Nazis. Main cast Werner De Smedt ... Gaston Vandermeerssche Mapi Galán ... Veronique Stuart Laing ... Harry Oliver Windross ... Doug Peter Firth ... Major Smith Christian Crahay ... Hachez Olivia Williams ... Nicky Lukas Smolders ... Louis Clive Swift ... General James Marilou Mermans ... Farmer's wife René van Asten ... Van der Waals Sylvia Kristel ... Miep Visser Stefan Perceval ... German soldier Gert-Jan Dröge ... Cohen Serge Marechal ... Frenchman References External links Category:Danish films Category:Dutch films Category:Belgian films Category:1990s drama films Category:English-language films Category:Dutch-language films Category:Films directed by Robbe De Hert Category:1997 films
We make use of cookies to enhance your user experience. By clicking "OK" without altering your cookie preferences, you are giving us your consent to use cookies. For further information, please read our information on the use of cookies.OK Well-oiled Bayern gearing up for Bundesliga restart vor 2 Stunden Several members of the Bayern squad braved the freezing temperatures in shorts at their first training session back in Munich2014 Ballon d'Or bronze medalist Manuel Neuer performs some strengthening exercises during the one-hour sessionHowever, centre-back Medhi Benatia trained individually after suffering with back complaints recently Munich - The pained expressions on the faces of some of the FC Bayern München players said it all as they emerged from the changing room into the freezing afternoon air at the club’s Säbener Straße complex for their first training session back in Germany following a nine-day jaunt in the Middle East. Bayern took an overnight flight back to Munich on 17 January and after resting on Sunday, the players - wrapped in scarves, hats and gloves to fend off the chill - set about the tasks assistant coach Lorenzo Buenaventura set them with gusto, with Pep Guardiola watching eagle-eyed from the sidelines. Quintet missing Long-standing absentees Philipp Lahm, Thiago Alcantara and Javi Martinez played no part in the session, while Mario Götze and Medhi Benatia were the only other players missing from the 21-man first-team party, although the latter duo did undergo individual exercises in an effort to shake off adductor and back complaints respectively. Holger Badstuber and David Alaba, recent returnees from injury themselves, were both able to complete the session unscathed. After Buenaventura gave brief instructions to the group, in impressive German, the Bayern players began a series of stretching, balancing and strengthening exercises for around 15 minutes, before boyish shouts of excitement filled the air when they moved on to the ‘boxes’: a keep-ball drill played in a confined space. One-touch passing Watching Bastian Schweinsteiger, Xabi Alonso and Co. up close as they pinged the ball around at a furious pace in an approximately five metre by five metre area, with two players in the middle desperately trying to intercept, it was plain to see why the Bavarians are unbeaten this season. They regularly reached a tally of between 35 and 40 one-touch passes, as Rafinha gleefully reminded his colleagues in the middle by loudly keeping count. The only dampener on an intense training session, in which players threw themselves whole-heartedly into tackles, was when Schweinsteiger limped off early, clutching his right boot in his hand after receiving a knock on his ankle, although it is not thought to be a serious injury. The rest of the squad proceeded to the final segment of the session, a series of interval running exercises across the length of the pitch. Ready to go It was an impressive demonstration of muscle-flexing, and having already won two friendlies by a 4-1 scoreline this calendar year, it is impossible not to feel a twinge of sympathy for the club's next friendly opponents VfL Bochum, whom they face this coming Friday. Regardless of the outcome of that game, Bayern already look primed and ready to defend their Bundesliga lead when they travel to VfL Wolfsburg for the Rückrunde curtain raiser on 30 January. Jonathan Stockitt reporting from Säbener Straße Free! Get the Bundesliga newsletter delivered straight to your inbox. Sign up today!
Q: Shell script to change digits with strings I need to write a shell script using sed command to change digits with their words, for example 1->one, 2->two, ..., but when i got 2 digits ( 11, 25) do not change. Any idea about this? thank you A: Assuming that, like me, you are running a version of sed which doesn't support regexp assertions, you could run sed -rf myscript with a script like this: s/(^\|[^[:digit:]])1($\|[^[:digit:]])/\1one\2/g s/(^\|[^[:digit:]])2($\|[^[:digit:]])/\1two\2/g ...continuing through the other digits. Breaking this down: s starts the substitute command. /(^\|[^[:digit:]])1($\|[^[:digit:]])/ is the regular expression to replace. (^\|[^[:digit:]]) means capture either the beginning of the line or a character which isn't a digit. 1 is a literal 1. ($\|[^[:digit:]]) means capture either the end of the line or a character which isn't a digit. \1one\2 is the replacement string. \1 adds the content of the first capture group. one adds a literal one. \2 adds the second capture group. The g at the end indicates that the substitute operation should repeat as many times as possible on each line.
/* * Copyright (c) 2017-2018 THL A29 Limited, a Tencent company. All Rights Reserved. * * 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 com.tencentcloudapi.iot.v20180123.models; import com.tencentcloudapi.common.AbstractModel; import com.google.gson.annotations.SerializedName; import com.google.gson.annotations.Expose; import java.util.HashMap; public class GetDeviceDataResponse extends AbstractModel{ /* * 设备数据 / @SerializedName("DeviceData") @Expose private String DeviceData; /* * 唯一请求 ID，每次请求都会返回。定位问题时需要提供该次请求的 RequestId。 / @SerializedName("RequestId") @Expose private String RequestId; /* * Get 设备数据 * @return DeviceData 设备数据 / public String getDeviceData() { return this.DeviceData; } /* * Set 设备数据 * @param DeviceData 设备数据 / public void setDeviceData(String DeviceData) { this.DeviceData = DeviceData; } /* * Get 唯一请求 ID，每次请求都会返回。定位问题时需要提供该次请求的 RequestId。 * @return RequestId 唯一请求 ID，每次请求都会返回。定位问题时需要提供该次请求的 RequestId。 / public String getRequestId() { return this.RequestId; } /* * Set 唯一请求 ID，每次请求都会返回。定位问题时需要提供该次请求的 RequestId。 * @param RequestId 唯一请求 ID，每次请求都会返回。定位问题时需要提供该次请求的 RequestId。 / public void setRequestId(String RequestId) { this.RequestId = RequestId; } /* * Internal implementation, normal users should not use it. */ public void toMap(HashMap<String, String> map, String prefix) { this.setParamSimple(map, prefix + "DeviceData", this.DeviceData); this.setParamSimple(map, prefix + "RequestId", this.RequestId); } }
Join us in a round of applause for Mr. Tuvok, a 14-year-old, 10-pound Terrier mix who’s the light of his family’s life. In 2002, while living in Dallas, Hélène Côté and Mike Charlasch decided they needed a dog, one small enough to travel easily and spry enough to take part in outdoor adventures. They found their match in Mr. Tuvok, a pint-sized charmer they adopted from the Protective Animal League and named for the stoic Vulcan lieutenant commander on Star Trek Voyager. They adopted Tuvok with a bum leg and bad teeth, but those were soon fixed. In the process, it was discovered that not only had his back leg been broken and never set, he’d also been shot with an air rifle; the surgeon found three pellets in his body. Mr. T now leads an adventure-filled life with his family in Los Angeles, and this photo by L.A. photographer and award-winning art director Grace Chon catches his jaunty, spirited nature and winsome smile to perfection.
-5, -48, 0.8? b Let x = 39372.94 - 39373. Which is the smallest value? (a) -0.042 (b) 0.05 (c) x c Let f = 151 - 1357/9. Let g = -1562.8 + 1563. Which is the third smallest value? (a) f (b) g (c) 7.5 c Let z = 58 - 288/5. Let a be (9/(-6) - -4) + (-2)/4. Suppose -al = -4x - 10, x + 2x + 15 = 4l. What is the second smallest value in l, z, -3? z Let a = -7 - -15. Let m = -27 + a. What is the second smallest value in 5, -6/5, 0.3, m? -6/5 Let v be -15 + 23 + (-94)/6. Let y = 0.06 + 2.94. What is the second biggest value in -4, y, v? -4 Let y be 25 + (1672/(-77) - 5). What is the third smallest value in -3, -7.9, y? y Suppose w - 466 = 2v, 0 = -0v + 5v - 2w + 1163. Let h = v + 235. Which is the fourth biggest value? (a) 1/5 (b) 1 (c) 1/7 (d) h c Let k = -1051/4770 - 1/530. Which is the second smallest value? (a) k (b) 10 (c) -0.05 c Let o be (-4605)/(-1535) + (-5 - (-2 - -2)). What is the third smallest value in o, -0.4, -0.07, 187? -0.07 Suppose 4y - n = 196, 4y = 9n - 7n + 200. Let v be 3/4 + 188/y + -5. Let x = -5/4 + 13/12. What is the second smallest value in 4, 11, v, x? x Let r = 354/53 - 1327/159. What is the fourth smallest value in -2/3, r, -0.4, -0.69? -0.4 Let p = -19851 - -19849. What is the biggest value in 87, 2/5, p? 87 Let u = -14953 - -14956. Let v = -0.4 - -1.4. Let b = -5 + v. What is the fourth smallest value in u, b, -8, 1/5? u Let q be (-18)/155/(-1). Let x = 100.65 - 6.55. Let f = x - 94. Which is the third smallest value? (a) f (b) q (c) 1/3 b Suppose 5x - 43 = 4x + 5s, x - 35 = 4s. Which is the second biggest value? (a) x (b) 202 (c) -0.2 a Let r = 4202 - 4205.5. Which is the fourth biggest value? (a) 0 (b) -2/7 (c) 4 (d) r d Let p be (10 - 243/24 - (-79)/(-8)) + 7. What is the third smallest value in p, -0.4, 1, 4, 0.02? 0.02 Let j = 5.2 + -0.1. Let r = 2.1 + 2.9. Let n = r - j. What is the third smallest value in 2/11, -2/25, n? 2/11 Let l = 3.7 + 11.3. Let h = -1.423 + 1.823. Which is the second smallest value? (a) h (b) l (c) -0.4 a Let m = 1.7039 - 1.3039. What is the third biggest value in -0.7, m, -0.05, 2/7? -0.05 Let h = -5220 - -5214. Which is the smallest value? (a) 2/5 (b) -2/11 (c) h c Let k = -5/355221 + 12117773/56124918. Let g = -1/158 - k. Let z(q) = -q - 1. Let j be z(2). Which is the biggest value? (a) j (b) g (c) -1.7 b Let h = -14.445 + -11.855. Which is the biggest value? (a) h (b) 6/7 (c) 4 c Let x = -3170 - -41212/13. What is the fifth biggest value in 0, -0.2, 0.2, -0.5, x? -0.5 Let s = 1 + -0.4. Let m = -209492 - -209491. What is the fourth biggest value in 0.5, s, m, -3? -3 Let m be (-4)/(-2) - 30/14. Let f be (-3)/(-15) - 180/150. Which is the biggest value? (a) m (b) f (c) -5 (d) 0.5 d Let z be (45/105)/(7/((-56)/12)). Let c = -0.24 - 0.06. Let q = -8.1 + 0.1. What is the smallest value in c, z, q? q Let h = 523 + -1502. Let l = -1019 - h. What is the second biggest value in 1, l, -0.3? -0.3 Let y(m) = -4m*2 + 3m - 4. Let k be y(-3). Let q = k - -48. Let u = 234 - 230. Which is the second smallest value? (a) 1/4 (b) q (c) u a Let r = 80 - 103. Let z = 11.2 - -11.3. Let i = r + z. What is the fourth biggest value in -1/8, 0.2, 2/7, i? i Let d = -0.96919 - -0.06919. What is the second smallest value in d, -26, 0.2? d Let n = 26.7 - 26.9. Let l = -198 - -198.2. Which is the biggest value? (a) n (b) l (c) 19 c Let i be (-1978)/(0 - -1) + (-4)/2. Let c be 1267/i + (-7)/(-28). Let f = c + -1/99. What is the smallest value in 3, f, -3, 0? -3 Let g = 3.8 - 4.1. Let f = -55.75 + 56. Let t = f - 5.25. What is the fourth smallest value in 1, t, g, -2/13? 1 Let o = -69.4 + 14.4. Which is the biggest value? (a) -4 (b) 3 (c) o b Let v = -0.04 + 99.04. Let p be 240/64 + 4/161. What is the third biggest value in v, p, -0.3? -0.3 Suppose 0 = 2k + 3g - 57, -2g = -3k - 8 + 87. Let w be (-6 - 0) + 180/k. Which is the third smallest value? (a) 5 (b) w (c) 1 a Let w = 2 - 4. Let g = -3 - w. Let u(t) = -2t*3 + 33t*2 - 18t + 33. Let h be u(16). What is the biggest value in h, 5, g? 5 Let j = 12 + -75.9. Let v = j + 62. Let w = 3.9 + v. Which is the second smallest value? (a) w (b) 4 (c) 1/3 a Let o be (1 - -1)(10/365)/2. Let r = -152/219 + o. Let t = 14 + -13.91. Which is the second smallest value? (a) t (b) r (c) 4 a Let h = -121332 - -363994/3. Let n be (4 - 2) + (-1313)/656. Let m = n - -1979/7216. What is the third biggest value in h, m, -4? -4 Let w = -7068 - -7067.89. Which is the third smallest value? (a) -5 (b) -0.1 (c) w (d) -11 c Let b = 25215 - 25212. Let k = -0.5 + 0.8. What is the second smallest value in 5, 5/3, b, k? 5/3 Let t be 225/105 - 3 - (-4)/7. Which is the second biggest value? (a) -1 (b) 3/4 (c) t (d) -0.343 c Let f = 3456 - 3461. Which is the second smallest value? (a) -0.1 (b) 0.192 (c) f (d) -2 d Let w = -9576 + 9576.0475. Which is the smallest value? (a) w (b) 4 (c) -4 (d) -3/4 (e) -0.4 c Let x = -7 - -10. Let z = 1704 - 1703. Which is the second biggest value? (a) 5 (b) x (c) -30 (d) z b Let i = 1/38 - 49/418. Let a = -6.35 - -0.25. Let d = a + 6.1. What is the second biggest value in i, d, 1/2, -5? d Let h be ((-2)/(-4))/((-3)/2). Let c = 159651 + -159641. What is the third smallest value in c, 2, h? c Let x = 192 - 182. Suppose -xb + 18b = -264. What is the smallest value in 0, 1/2, b? b Let i = 24.533 - 29.533. What is the fourth biggest value in 3/4, -1/20, -3/8, 0.3, i? -3/8 Let j = -216/77 - -205/77. What is the third biggest value in 3/2, 1, j, 0.047, -0.1? 0.047 Let x = 3321 + -3320.66. Which is the second biggest value? (a) 5 (b) x (c) 3 c Let o = -3593 + 3592.9. What is the fourth smallest value in -1/13, -0.3, -2, o, -7? o Let w = 343 - 341.93. Let o = 2.93 + w. Suppose 0 = 3y - 0y. What is the fourth smallest value in o, 1/6, y, -4? o Let m = 3 - 2.6. Suppose 8n = 26n - 17n + 5. Let r = 0.1 + 0.1. Which is the biggest value? (a) r (b) m (c) n b Let v = -2.02 + 0.02. Let f(g) = -59g - 69. Let z be f(-6). Let s be 1/(z/(-207) + 16/12). Which is the third smallest value? (a) -0.1 (b) v (c) s a Let k = 175 + -171.865. Let n = 0.135 - k. Which is the second biggest value? (a) n (b) 0.1 (c) -90 a Let v = 14893 - 15002.41. Let s = v + 110. Let w = -0.09 + s. Which is the second biggest value? (a) -4 (b) w (c) 2 b Let m = -18965.831 + 18966. Which is the second biggest value? (a) 2 (b) -2 (c) m (d) -3/4 (e) 5 a Let v = -0.6 + -0.4. Let s = 3 + v. Let o = -1054 - -1053.99. What is the smallest value in s, o, 0? o Let z = -4.6811 - 0.3189. Which is the third smallest value? (a) z (b) 1 (c) 2 (d) -0.02 (e) -3 d Let f = 781/6 - 773/6. Which is the biggest value? (a) 2/59 (b) -0.1 (c) f c Let a be 8/(-10)115/(-2). Let p = a + -320/7. Let b = -1385.2 + 1385. What is the third smallest value in -16, b, p? p Let i = 55.2 - 1.2. Let v = -22 + 78. Let b = i - v. What is the third smallest value in b, -0.1, -2/5? -0.1 Suppose 33w + 7730 = -190. Which is the biggest value? (a) 0.3 (b) w (c) -1 a Let o = 712 + -743. What is the smallest value in o, 1, -5? o Let u = -25734 + 25729. Which is the third biggest value? (a) u (b) -8 (c) 12 b Suppose 4l - 10 = 5v - l, -v - 2l = -13. Suppose -7x + 3x - 8 = 4y, 6 = -x - vy. Which is the smallest value? (a) 7 (b) -5 (c) x b Let h be (43420/16)/5 + (-11)/(-44). Let p = h + -2712/5. Let i be 3/12 + (-5)/(-28). Which is the biggest value? (a) p (b) i (c) 11 c Let i = -5 + 6. Let n be 7 - 9/9 - 17/3. Which is the second smallest value? (a) n (b) -1.1 (c) 5 (d) i a Let j = 2737 - 3125. Which is the smallest value? (a) j (b) 0.5 (c) -3 a Let n = -292.44 - -292. Let i = n + 0.94. Which is the third smallest value? (a) -2 (b) i (c) -7 b Let z = -30571/7 + 21812/5. Let f = z - -30/7. What is the second smallest value in -2, f, 0.1? f Let f = 44281/36 - 11068/9. Let w be (-4)/(-6) - (-14)/(-12). What is the third smallest value in f, w, -1/5? f Let s = 2068/1273 - 130/67. What is the smallest value in 8, 5, s, 3? s Let f = -763/264 + 65/24. What is the smallest value in -0.1, -1206, f? -1206 Let n = 707.75 - -0.25. Let y = 707 - n. Which is the second smallest value? (a) y (b) 0.01 (c)
Aluminium’s credentials as a green metal, which its rival steel in many applications will be shy of claiming, rest primarily on its endless recyclability. Unlike in North America and Europe where recyclers command respect from the community for environment caring, recycling of domestically produced and used aluminium is yet to gain momentum.A sore point with the country’s three aluminium makers is that of total imports of 1.9 million tonnes (mt) of the silvery white metal during 2017-18 as much as 1.1 mt were scrap. Large arrivals of foreign origin scrap in India are … Source: Business Standard
Demons Training Session Natalie did a surprise appearance at a Demons AFL training session in Melbourne this Wednesday. In town for this weekend’s NGV Gala, she took time out to check out how the Dees were coming along in pre-season. Apparently, Natalie’s best friend, a big Demons supporter, was the reason behind her visit. Their children took part in the warm-up with the players. Natalie also donned an AFLW guernsey and there were plenty of fans on social media who were happy with her choice of club. As usual, Zimbio has several photos:
The Changing Dynamics of the Syria Crisis Summary: The two-year-old Syrian conflict sharply escalated in recent weeks, hence necessitating a renewed U.S.-Russian effort to find a solution to the crisis and solve inner tensions within the Syrian opposition. The two-year-old conflict in Syria escalated in recent weeks with the direct engagement of Hezbollah in the fight for Qusair, Israeli missile strikes near Damascus, and bombings in Turkey. A renewed U.S.-Russian effort to convene an international conference in June is threatened by the deep divisions within the Syrian opposition over participation in the Geneva peace talks. Rafaël LeFèvre, an expert on the Syrian branch of the Muslim Brotherhood, joined the Carnegie Middle East Center’s Paul Salem and Yezid Sayigh and Carnegie Moscow’s Dmitri Trenin to discuss the changing dynamics of the Syrian crisis in a special event held in Beirut. Syria’s Battle Ground Significance of Qusair: Sayigh argued that the fight for the rebel-held city of Qusair had become a defining battle in the course of the conflict. While prior to this victory the warring factions maintained a strategic balance, he argued that a tipping point is approaching. Opposition Leadership: The opposition’s defeat in Qusair is due to its inability to unite under one cohesive leadership, Sayigh said. The Syrian National Council had become a reactor instead of a shaper in areas such as diplomacy and militarization. Adaptation and Resilience: The Syrian regime has ‘sub-contracted’ the war by allowing people to fight in and around their hometowns, essentially diminishing the cost of mobilization, Sayigh explained. He implied that these developments, coupled with the regime’s resilient strategy, may lead to the determination of a victor by the year’s end. Local Opposition Faction LeFèvre highlighted three major trends that have emerged recently and are currently influencing the political strategy of the Muslim Brotherhood of Syria: Cooperation with Opposing Groups: Although Saudi Arabia and the Muslim Brotherhood have a history of mistrust, they have both come to the realization that they need to cooperate in order to try and topple President Bashar al-Assad. Political Solution: A political solution will be needed at some point in order to stop the bloodshed. This realization came after the brutal defeat of the rebels in the battle of Qusair and the acknowledgment of the regime’s military resilience, LeFèvre added. Global Actors: The shift from a regional to a seemingly global war, involving not only Russia and the United States but also the United Kingdom and France, has placed the exiled opposition under increased foreign influence. LeFèvre further explained that dissatisfaction with internal opposition politics may cause the Brotherhood to freeze its membership from the coalition or even withdraw completely. Although risky, this would solidify its base and grant further autonomy. LeFèvre concluded by predicting an increased fragmentation within the exiled opposition before the Geneva II convention. Regional Friction and Development Salem shared insight into the broader political view for the region and Lebanon in particular. Regional Order: Salem declared that the Levant was ‘broken’ at the state and national level. States are failing even as they manage to survive, he explained, and with these failures come the fracture of national identities, a project in the making since the establishment of most of these regimes in the 1950s. International Relations: Salem also lamented the end of the business-first approach to international relations, as exemplified by Turkey and Qatar’s foreign policy agenda prior to the ‘Arab Spring’. Governments have been siding with or against the Assad regime at the expense of this ‘third way’ in settling foreign affairs. Repercussions in Lebanon: The conflict has polarized opinions since the outset, Salem remarked. For a while, relative calm persisted, due in part to the Mikati government’s dissociation policy and the previous lack of Islamist factions. However, the collapse of the government, Hezbollah’s increased involvement, and threats made by Islamist group Jabhat al-Nusra are all signs that the conflict’s spillover in Lebanon is gradually becoming a threat to national cohesion and security, Salem concluded. The Contrasting Perspective Trenin examined the motivations behind the Russian approach to the Syrian crisis: World Order Policy: Moscow holds that the use of force should be mandated and directed through the United Nations charter. Additionally, the Russian government adheres to a strict interpretation of respect for state sovereignty and non-intervention. As a result, it strongly opposes any meddling in Syria’s internal affairs. Assessing the Arab Spring: As the Arab Spring is considered first and foremost an Islamist revolution in Russia, Moscow is very concerned about its own domestic Chechen population. Trenin added that the Libyan experience, which left Russia out in terms of trade agreements, is still vividly remembered by the Kremlin. The Kremlin’s Interests: Trenin noted that the Kremlin views some of the rebel groups as a potential ‘enemy-in-the-making’ and is more than ready to assist in undermining them. However, he concluded on a positive note, stating that the Russians were making a comeback on the diplomatic scene, with the United States recently hinting at a joint effort to find a political solution to the conflict. End of document Comments Post your comments 2500 character limit. No links or markup permitted. Comments are moderated and may not appear immediately. Screen names appear with your comment. Screen Name Follow the conversation—Sign up to receive email updates when comments are posted to this article. Comment Policy Comments that include profanity, personal attacks, or other inappropriate material will be removed. Additionally, entries that are unsigned or contain "signatures" by someone other than the actual author will be removed. Finally, steps will be taken to block users who violate any of the posting standards, terms of use, privacy policies, or any other policies governing this site. You are fully responsible for the content that you post.
--- abstract: 'We conducted a high-sensitivity radio detection survey for forty narrow-line Seyfert 1 (NLS1) galaxies using very-long-baseline interferometry (VLBI) at 22 GHz through phase-referencing long-time integration and using a newly developing recorder with a data rate of 8 Gbps, which is a candidate of the next generation VLBI data recording systems for the Japanese VLBI Network. The baseline sensitivity was typically a few mJy. The observations resulted in a detection rate of 12/40 for our radio-selected NLS1 sample; 11 out of the detected 12 NLS1s showed inverted radio spectra between 1.4 and 22 GHz on the basis of the Very Large Array flux densities and the VLBI detections. These high fractions suggest that a compact radio core with a high brightness temperature is frequently associated with NLS1 nuclei. On the other hand, at least half of the sample indicated apparently steep spectra even with the limited VLBI sensitivity. Both the inverted and steep spectrum radio sources are included in the NLS1 population.' author: - 'Akihiro <span style="font-variant:small-caps;">Doi</span>, Tomoaki <span style="font-variant:small-caps;">Oyama</span>, Yusuke <span style="font-variant:small-caps;">Kono</span>, Aya <span style="font-variant:small-caps;">Yamauchi</span>, Syunsaku, <span style="font-variant:small-caps;">Suzuki</span>, Naoko <span style="font-variant:small-caps;">Matsumoto</span>, and Fumie <span style="font-variant:small-caps;">Tazaki</span>' title: 'A Radio Detection Survey of Narrow-Line Seyfert 1 Galaxies using Very-Long-Baseline Interferometry at 22 GHz' --- Introduction ============ The radio natures of narrow-line Seyfert 1 (NLS1s) galaxies potentially provide us key understandings of outflowing mechanisms in the growing phase of active galactic nuclei (AGNs). NLS1s as a class are thought to be fed at high mass accretion rates onto relatively small-mass black holes, potentially connecting between stellar-mass and supermassive black hole systems in the mass function. The first systematic studies in radio bands by interferometric observations were carried out at arc-second resolutions using the Very Large Array (VLA), and indicated little difference between NLS1s and Seyfert galaxies: similar radio luminosities, steep radio spectra, and scarcely resolved radio morphology suggest the presence of weak nonthermal jets as a radio emitting source [@Ulvestad:1995; @Moran:2000], although several optical/X-ray properties are clearly different. NLS1s were thought to be radio-quiet objects as a class with only a few exceptions of known radio-loud objects (e.g., @Grupe:2000 [@Oshlack:2001; @Siebert:1999]); subsequent systematic studies based on large database, such as the VLA Faint Images of the Radio Sky at Twenty-centimeters (FIRST; @Becker:1995) and the NRAO VLA Sky Survey (NVSS; @Condon:1998) in radio and the Sloan Digital Sky Survey (SDSS) in optical, have revealed a lower fraction of radio-loud objects ($\sim7$%; @Komossa:2006, see also @Zhou:2006 [@Whalen:2006; @Yuan:2008]) compared to that of broad-line Seyfert galaxies. Recently, gamma-ray detections by [Fermi Gamma-Ray Space Telescope]{} toward six NLS1s galaxies with high significance [@Abdo:2009a; @Abdo:2009; @DAmmando:2012; @DAmmando:2015a] have offered a new population of gamma-ray emitting AGNs other than blazars and radio galaxies. The radio observations at high angular resolutions using very-long-baseline interferometry (VLBI) for the first discovered $\gamma$-ray emitting NLS1 SDSS J094857.31+002225.4 (PMN J0948+0022) had revealed the presences of a one-sided pc-scale jet and a rapidly variable, very high brightness radio core showing an inverted spectrum at the nucleus [@Doi:2006]. PMN J0948+0022 also shows a core-dominant structure with two-sided kpc-scale radio emissions [@Doi:2012]. The combination of these radio/gamma-ray properties is reminiscent of blazars, which are characterized by Doppler-beaming on relativistic jets viewed from pole-on typically at parsec (pc) scales and by decelerated components at from kpc to Mpc scales. VLBI observations of the other several gamma-ray emitting NLS1s also indicate the presence of beamed jets at pc scales [@DAmmando:2012; @DAmmando:2013a; @Doi:2011a; @Doi:2013a; @Wajima:2014]; some of them also show two-sided kpc-scale radio structures [@Anton:2008; @Doi:2011a; @Doi:2012]. However, the radio jets are mildly relativistic and their powers are comparable to the least energetic blazars, on the basis of single-dish monitoring [@Angelakis:2015]. On the other hand, VLBI observations of radio-loud NLS1s including gamma-ray detections/non-detections have revealed that the radio-loud aspect is possibly attributed not only to a beaming effect but also an intrinsically large radio power. Intrinsic radio powers that are corrected for the beaming effect using estimated Doppler factors suggest that radio-loud NLS1s include both intrinsically radio-loud and intrinsically radio-quiet cases [@Doi:2011a; @Doi:2012]. An extended pc-scale jet showing a steep spectrum dominates a total radio power, which suggests being not so relativistic and/or sufficiently inclined with respect to our line of sight for the jet [@Gu:2010; @Gu:2015]. Seven out of known ten NLS1s with kpc-scale radio structures (@Richards:2015, see also @Gliozzi:2010 [@Doi:2012; @Doi:2015]) are not still gamma-ray detected. This situation suggests that jet powers may be intrinsically large sufficient to escape the core regions of host galaxies, but not so beamed because of relatively large viewing angles. For several nearby radio-quiet NLS1s, VLBI observations have also revealed pc-scale jet-like structures showing steep spectra, which are presumably generated through the same process as that of radio-loud NLS1s, but probably with an only difference in power or viewing angle for nonthermal jets [@Giroletti:2005; @Doi:2013a; @Doi:2015]. Thus, at least a fraction of NLS1 nuclei has an ability to generate nonthermal jets, which have a wide range of radio powers; in some cases, the signatures of beaming effect on relativistic jets viewed from pole-on are observed. However, a limited number of NLS1s has still been investigated at milli-arcsecond (mas) resolutions so far, because NLS1s are relatively weak radio sources in comparison with the other AGN classes. Systematic VLBI observations have been started by the other authors [@Gu:2015], whose targets are sixteen radio-loud NLS1s selected from several parent samples with 105 sources; fourteen sources were detected at 5 and 6.7 GHz, which were relatively low frequencies and may tend to be biased to the contribution of an extended jet component. The present paper reports the result of a new VLBI detection survey as a systematic study for NLS1s in the radio band at a higher frequency (22 GHz), where an inner jet component is potentially focused on. Our observation was planned before the publication of @Gu:2015. Our sample selection was relatively similar to theirs; the differences are (1) the combination of parent samples, (2) including radio-quiet NLS1s as well, and (3) at a higher observing frequency. Section \[section:sample\] presents the sample selection. In Sections \[section:observation\] and \[section:reduction\], VLBI observations and the procedures of data reductions are described. These results are presented and its implications are briefly discussed in Section \[section:result\]. Sample {#section:sample} ====== We selected NLS1 radio sources by position-matching between the catalog of the Very Large Array (VLA) 1.4-GHz Faint Images of the Radio Sky at Twenty cm (FIRST) survey [@Becker:1995] and source lists in the following NLS1 studies: (1) 64 sources in @Veron-Cetty:2001a, (2) 2011 sources in @Zhou:2006, (3) 23 sources in @Yuan:2008, and (4) 62 sources in @Whalen:2006. We found several sources that were counted redundantly; the number of uniquely selected sources resulted in 233 sources (734–0.8 mJy beam$^{-1}$). We clipped these sources into 41 sources with an intensity higher than 10 mJy beam$^{-1}$. The NLS1 radio source catalogue that is a target list in the present study is listed in Table \[table:sample\]. The sample selection criteria are similar to those of the previous systematic VLBI study by @Gu:2015, which was also based on the radio selected samples with flux densities of $>10$ mJy in the FIRST. The parent samples were restricted to only radio-loud objects from @Komossa:2006 [@Zhou:2006; @Yuan:2008; @Foschini:2011], which were slightly different from ours including radio-quiet ones as well. Six radio-quiet objects are included in our sample ($\log{RL}<1$, see Col. (7) in Table \[table:sample\]). Observation {#section:observation} =========== The observations are performed as a part of the experimental observations to test a developing OCTAVE-DAS (Data Acquisition System, @Oyama:2012). It is a candidate of the next generation data recording system for OCTAVE (Optically Connected Array for VLBI Exploration, @Kono:2012), JVN (Japanese VLBI Network, @Fujisawa:2016) and other VLBI arrays. OCTAVE-DAS consists of three key components. The first is a high speed analog-to-digital (A/D) converter at a sampling rate of 8 gigabits per second (Gbps) of 3 bit quantization. It is called OCTAD (OCTave A/D converter). It is able to sample signals at a radio frequency (RF) directly. In addition, it has digital base-band converter (DBBC) functions for the VLBI Global Observing System (VGOS) observation. The second key component is a media converter between single 10 GigE (Gigabit Ethernet) port and four VSI-H (Vlbi Standard Interface-Hardware) I/O ports. It is called OCTAVIA (OCTave Vlbi Interface Adapter) or OCTAVIA2 depending on its version. The last key component is a recorder. It is able to record the data stream at the rate from 4.5 Gbps up to 32 Gbps. It is called OCTADISK (OCTave DISK recorder), OCTADISK2 or VSREC (Vlbi Software Recorder) depending on its version. OCTAVE-DAS is being developed at the Mizusawa VLBI observatory, a branch of the National Astronomical Observatory of Japan. The test observations using OCTAVE-DAS were conducted on April 21 and 28, 2014 using four radio telescopes of the VLBI Exploration of Radio Astrometry project (VERA; @Kobayashi:2003); Mizusawa, Ogasawara, Iriki, and Ishigaki stations participated in the experiment. The polarization is the left-circular-polarization. VERA has a dual-beam receiving system. The dual beams are called A- and B-beam. For the dual beam observation in this paper, A-beam was used for the target sources. B-beam was used for the reference sources. The received radio signals of dual beams are converted to IF frequency, respectively. The bandwidth is 512 MHz. The IF signals are sampled by two A/D converters (ADS-1000s). The sampling rate is 1.024 GHz. The quantization bit number is two. The data streams are recorded by OCTADISK. The aggregated bit rate is 4.096 Gbps. In addition to this current VERA observation system, we installed OCTAVE-DAS in order to expand the bandwidth. We also installed the analog signal converters with wider bandwidth. The new system was installed on A-beam for this test observation to increase the sensitivity of target sources. The received signal of A-beam was divided to two signals for the current and the new system. The signal for the new systems is divided to four IF channels of which bandwidth is 512 MHz. The starting frequencies of the four IFs are 21.459, 21.971, 22.483, and 22.995 GHz. The four IF signals are A/D converted by ADS-3000+ which was developed by NICT (National Institute of Information and Communications Technology) instead of OCTAD for the observation in this paper. The sampled data stream was recorded by VSREC. The aggregated recording rate is 8.192 Gbps. The dual beam systems with the current VERA system and OCTAVE-DAS can work simultaneously. We utilized “dual-beam phase referencing” in order to increase coherent integration time by elimination of the atmospheric phase fluctuation of the targets with the phases of the calibrators. For several targets (SBS 0846+513, SDSS J103727.44+003635.5, B3 1441+476, \[HB89\] 1519-065, \[HB89\] 1546+353), proper calibrators cannot be found within a separation angle of 2.1 degrees. We used a nodding style phase-referencing. A-beam pointing was switched between a target and a reference calibrator. On-source tracking was used for PMN J0948+0022, which was expected to be detected without phase-referencing. SDSS J124634.64+023809.0 was mis-allocated in our observation. The number of observed targets resulted in 40. The A/D converter ADS1000 at Ishigaki station was unlocked to a reference signal during both of the two observations unfortunately. The solutions of phase reference from the B-beam were unavailable. Data reduction {#section:reduction} ============== The correlations were processed with the software correlator OCTACOR2 (OCTAve CORrelator), which was developed at the Mizusawa VLBI observatory and NICT [@Oyama:2012]. The correlated data were integrated every one second. The frequency channel number per an IF channel is 512. Data reduction procedures were performed using the Astronomical Image Processing System (AIPS; @Greisen:2003). Amplitude calibration using a priori gain values together with the system noise temperatures measured during the observations were applied. The calibration accuracy had not been evaluated in this new system, probably less than 20%, which was inferred from the comparison of results of known strong sources in the data. The delay differences among the four IF channels were calibrated using the fringe-fitting solutions of a bright calibrator (”manual-pcal”). This solution allowed us to adopt a small fringe-finding window in subsequent fringe fitting procedures. For dual-beam phase-referencing, the fringe-fitting solution in phase for the reference calibrator was obtained with the B-beam data at first. Next, we applied the solution to the four channels of the A-beam. Calibrators for five targets were not detected. The difference between the center frequencies of two beams is 256 MHz ($\sim1$% with respect to the radio frequency). In the case of residual phase variation of $\sim100$ deg (typically observed during VERA dual-beam observations) after a fringe-rate removal, the coherence loss is expected to be only 0.02% when we apply fringe-phase solutions to data at a $\sim1$%-different frequency. With the dual beam phase referencing, we were able to extend the fringe-fitting solution interval to 720 seconds. The interval is equivalent to a scan duration time of the antenna schedule. As a result, six out of 29 targets were detected at signal-to-noise ratios ($SNRs$) higher than 3 in this observing mode. We also performed fringe-fitting on the five target that observed in the manner of nodding style phase-referencing with a cycle of 40 seconds. The solution interval was 720 seconds with a net accumulation of 240 seconds on a target. As a result, two out of the five targets were detected at $SNR>3$ in this observing mode. PMN J0948+0022, which was observed without phase-referencing, was detected with a solution interval of 120 sec. Fringe findings for five targets whose calibrators were not detected in B-beam were also attempted with a solution interval of 120 sec. As a result, three out of the five were detected at $SNR>3$. \[table:sample\] Col. (1) Source Name in NED; Col. (2) redshift; Col. (3) right ascension; Col. (4) declination; Col. (5) peak intensity in mJy beam$^{-1}$ in VLA FIRST; Col. (6) parent sample; Col. (7) radio loudness from reference listed in Col. (6), except for sources from @Veron-Cetty:2001a that includes no value for radio loudness. Note that the definition of radio loudness differs from reference to reference. We calculated radio loudness for sources in @Veron-Cetty:2001a by the ratio of FIRST 1.4 GHz radio to SDSS $g$-band PSF optical flux densities, according to @Veron-Cetty:2001a. Sources denoted by $\dagger\dagger$ represent the use of $B$-band magnitudes listed in @Veron-Cetty:2001a because their SDSS results are not available; Col. (8) reference of previous VLBI observation; Col. (9) observation mode in the present study. ”ND” and ”2B” represent nodding-style and VERA’s dual-beam phase referencing, respectively. ”1B” represents an on-source observation with a single beam. SDSS J124634.64+023809.0 was mis-allocated in our observation; Col. (10) phase-referencing calibrator used in the present study. Calibrators denoted by $\dagger$ represent non-detection in B-beam; Col. (11) correlated flux density in mJy measured in the present study.\ References — a: @Veron-Cetty:2001a , b: @Whalen:2006 , c: @Yuan:2008 , d: @Zhou:2006 , e: @Gu:2015 , f: @DAmmando:2013 , g: @Doi:2006 , h: @Abdo:2009b , i: @Giroletti:2011 , j: @Doi:2013a , k: @Doi:2015 , l: @Giroletti:2009 , m: @Fey:2000 , n: @DAmmando:2013a , o: @Orienti:2015 , p: @Doi:2007 , q: @Gu:2010 , r: @Doi:2011a , s: @Doi:2012 Result and Discussion {#section:result} ===================== Correlated flux densities averaged through baselines with detection are listed in the last column of Table \[table:sample\]; the table includes the references for sources for which previous VLBI studies exist. Upper limits of correlated flux density, ranging from $7$ mJy to $23$ mJy depending on the observing mode (Sect. \[section:reduction\]), were determined by $SNR=3$ on the most sensitive baseline during observations. Twelve out of 40 observed targets were detected with VERAs’ baselines ranging from $\sim1000$ km to $\sim2300$ km, which imply a brightness temperature of the order of $10^7$ Kelvin or more for high-frequency radio emissions associated with these NLS1s. Even if we adopted a detection limit of $5\sigma$ instead of $3\sigma$, only \[HB89\] 1546+353, which is the weakest detection in our sample, would get into non-detection. The two sources, FBQS J114654.2+323652 and FBQS J1713+3523, are for the first detected with very long baselines. FBQS J114654.2+323652 was presumably detected with the MIZUSAWA–IRIKI baseline in the dual-beam phase reference mode; we also confirmed the fringe detection in a normal fringe fitting, without a calibrator, with a shorter integration (2 min). Around this source, there is no strong source potentially confusing to our observation. FBQS J1713+352 was positively detected with baselines of all the four antennas in fringe fitting without a calibrator (because its calibrator was not detected in B-beam). Around this source, there is no strong source potentially confusing to our observation. Both the two sources are weak radio sources at 1.4 GHz in the FIRST (15.42 mJy and 11.24 mJy for FBQS J114654.2+323652 (1994.4) and FBQS J1713+352 (1994.5), respectively); on the other hand, they are relatively strong at 22 GHz in our observation (104 mJy and 138 mJy). These sources should be inverted spectrum sources with $\alpha=+0.7$ and $\alpha=+0.9$, where $\alpha$ is the spectral index ($F_\nu \propto \nu^\alpha$), assuming that the 1.4 GHz FIRST (and the 22 GHz) fluxes do not vary significantly in $\sim20$ years. Such a weak source showing an inverted spectrum has also been previously reported by @Doi:2007 for FBQS J1629+4007, which is also in the list of the present study and has been detected (11.95 mJy at 1.4 GHz (1994.6) and 145 mJy at 22 GHz). In the first place, relatively weak radio emissions at 1.4 GHz and a limited baseline sensitivity at 22 GHz were supposed to strongly bias VLBI detections toward inverted spectrum sources. In fact, all the detected sources except for one (11/12) show flat or inverted spectra ($\alpha=-0.1$–$+0.9$) between 1.4–22 GHz, if variability in the time interval between measurements at 1.4 and 22 GHz is assumed insignificant. Although this is a sort of artificial effect, it is noteworthy that not so small fraction of NLS1 radio sources (12/40) have been detected at such a high frequency even with very long baselines. On the other hand, at least half of the sources indicate apparently steep spectra ($\alpha<-0.2$) between 1.4 GHz and 22 GHz on the basis of the FIRST flux densities and the VLBI upper limits. Both the inverted and steep spectrum radio sources are included in the NLS1 population, as previously pointed out by several authors [@Doi:2007; @Gu:2010; @Doi:2011a]. Particularly, $[$HB89$]$ 1044+476 is the strongest radio source (767.44 mJy at 1.4 GHz in the FIRST (1997.2)) in our sample but not detected with the VLBI at 22 GHz ($<7$ mJy). Only a weak radio emission (19.4 mJy) with a core-jet structure in the east-west direction has been previously found in VLBI images at 5 GHz while VLA images at 8.4 and 22 GHz show significantly large radio flux densities; a bulk of total flux must be resolved out with very long baselines and originate in extended components of a compact steep spectrum source [@Gu:2015]. B3 1702+457 is in the similar situation (118.64 mJy at FIRST 1.4 GHz (1997.2) and $<9$ mJy at VLBI 22 GHz); the previous VLBI studies revealed an extended radio structure with a steep spectrum for B3 1702+457 [@Doi:2007; @Doi:2011a]. Hence, our negative detections with a limited sensitivity at 22 GHz are genuine even for these sources relatively strong at 1.4 GHz. Consequently, the systematic study by our VLBI detection survey has revealed that NLS1s are one of AGN subclasses that can possess compact radio components with high brightness temperatures ($\gtrsim10^7$ Kelvin) even at the high frequency (22 GHz). These compact components show inverted spectra in almost all the VLBI-detected cases, which account for a significant fraction in our radio-selected NLS1 sample. These properties may be related to NLS1s’ blazer-like aspects such as gamma-ray detections in several NLS1s in contrast to normal broad-line Seyfert galaxies. This study was partially supported by Grants-in-Aid for Scientific Research (B) (24340042, AD) and Grant-in-Aid for Scientific Research on Innovative Areas (26120537, AD) from the Japan Society for the Promotion of Science (JSPS). We are grateful to all the staffs and students involved in the development and operation of the Japanese VLBI network (JVN) and the VLBI Exploration of Radio Astrometry project (VERA). The JVN project is led by the National Astronomical Observatory of Japan (NAOJ), which is a branch of the National Institutes of Natural Sciences (NINS), Yamaguchi University, Hokkaido University, Gifu University, Kagoshima University, Tsukuba University, Osaka Prefecture University, and Ibaraki University, in collaboration with the Geographical Survey Institute (GSI), the Japan Aerospace Exploration Agency (JAXA), and the National Institute of Information and Communications Technology (NICT). The VERA is operated by the Mizusawa VLBI observatory, a branch of the National Astronomical Observatory of Japan. We used the US National Aeronautics and Space Administration’s (NASA) Astrophysics Data System (ADS) abstract service and NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory (JPL). In addition, we used the Astronomical Image Processing System (AIPS) software developed at the National Radio Astronomy Observatory (NRAO), a facility of the US National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
Anonymous, Aquitanian Repertory born in Limoges, France, composed during the Medieval period The Aquitanian Repertory is a blanket term used to identify music produced in the French region of Aquitaine in Southwest France between the tenth and early thirteenth centuries, most in manuscripts originating from the abbey of St. Martial in Limoges. The Aquitanian repertory contains the oldest sizeable literature of polyphonic music in Europe, the earliest of which predates Notre Dame Organa by at least a century, and likewise includes a wealth of important monophonic pieces. It is notated in a unique and tidy-looking system of Neumes that resembles Braille and is easily readable, although the polyphonic sources are rhythmically ambiguous and any realization of such music is necessarily conjectural to some degree. All of the Aquitanian composers and scribes are anonymous save one -- Adémar de Chabannes (988-1034), whose monophonic Apostolic Mass for St. Martial is the earliest music manuscript in Europe known to be in the hand of the composer. Musicologists still use the term "Aquitanian School" or "School of St. Martial" to describe the general musical activity at St. Martial, although it has become archaic. It is clear that the music transcribed at St. Martial was picked up from a variety of sources and that its literature does not constitute a coherent "school" of the kind that the Notre Dame School represents starting in the middle of the twelfth century. Nevertheless, the local productions of St. Martial composers are easily distinguishable from foreign material, given its high investment in sequences, tropes, conductus, and other special pieces venerating local saints. The works of thirteenth century troubadour Bertran de Born are preserved in Aquitanian manuscripts, but to describe him as belonging to the "School of St. Martial" is incorrect. There are six basic manuscript sources for Aquitanian music; three in the Bibliothèque Nationale in Paris, one in Santiago de Compostela (the "Codex Calixtinus"), one in the British Library in London, and one in Cambridge, England. Although some optimistic scholars have attempted to place part of the monophonic sources in the ninth century, no music manuscript from St. Martial appears to predate the early tenth. Other scholars have cited the possibility that Aquitanian sources may contain melodies from the mostly lost body of Gallican chant (the predecessor to Gregorian), but it appears that the Gallican tradition had mostly died out by the time the monks at St. Martial first began working at producing manuscripts. Although Aquitanian Neumes probably went into disuse in the early thirteenth century due to the rise in popularity of square notation, the abbey itself began to suffer from a severe credibility problem at that time owing to its repeated efforts to establish its third century founder, St. Martial, as an apostle to the historical Jesus. The basis for this was on documents forged by Adémar de Chabannes himself. In the tenth and eleventh centuries, Limoges had been a major pilgrimage site for worshipers, but by the thirteenth, the order was largely discredited as heretical. In the sixteenth century, the abbey fell on hard times, and the manuscripts now in the Bibliothèque Nationale were sold to King Louis XV, ensuring their survival; the Codex Calixtinus had been made to order for Santiago de Compostela, and it is not known how the others wound up in their current locations. The Abbey of St. Martial in Limoges was condemned in 1793 during the French Revolution and by the early nineteenth century was reduced to a pile of rubble. Excavations of St. Martial's crypt in the 1960s yielded nothing of the Abbey and its fabled scriptorium, but a number of architectural ruins were discovered from the time Limoges was the Roman outpost of Augustoritum. ~ Uncle Dave Lewis , Rovi
The diagnosis of thoracic malignant mesothelioma: practical considerations and recent developments. Pleural biopsies for the evaluation of malignant mesothelioma can be some of the most challenging cases faced by the practicing surgical pathologist. We review the epidemiology, clinical presentation, and imaging studies in patients with malignant mesothelioma, and then present a practical approach to the diagnosis using the cytologic features for malignancy and whether there is an epithelioid or spindled morphology; four main scenarios are discussed. The pertinent immunohistochemical work-up is reviewed for each scenario. Following this general overview, more unusual histologic patterns are compared and unusual presentations are discussed. Brief mention of grading systems for malignant mesothelioma and the use of electron microscopy and molecular studies is made. Practical considerations in the diagnosis of malignant mesothelioma are made throughout.
Six Decades of Music Making - our origins and the conductors who have led us. The Guernsey Choral Society was formed in 1948 by John Longmire. John Longmire, who was born in Lincolnshire, moved to Guernsey prior to the Second World War. He joined the evacuatiuon from the Island in anticipationof the German occupation but returned after 1945. He was a prolific composer of piano music and also wrote for solo voice and choirs. Much of his output is still available. At around the time of the outbreak of the Second World War British composer and organist John Ireland lived briefly in Guernsey and he and John Longmire became friends. John Longmire subsequently published a respected biography of John Ireland. The orchestra was formed in 1971 and the Society name changed to the present form. Roll-Call of Conductors 1948 - 1954 John Longmire 1954 - 1962 Winifred Perkins 1963 - 1964 Gordon Hugh 1964 (Dec) - 1976 Marian Blondel 1977 - 1979 Malcolm Vivyan 1979 (Dec) - 1983 Roger Surcombe 1983 (Dec) - 2001 Alan Gough 2001 (Dec) Bruce Cornelius 2002 (May) Roger Brooks 2002 (June - Dec) Keith Dawber 2003 - 2005 Stephen Le Prevost 2006 - 2014 Helen Grand 2014 - present Alan Gough In 2008 the Society published A Brief History of the Guernsey Choral and Orchestral Society to mark the 60th anniversary. The history was written by Stephen Oliphant, then the immediate past chairman of GCOS. OUR CONCERT VENUE: ST JAMES It was at a public meeting on 30 October 1815 that Admiral Sir James Saumarez, later Lord de Saumarez, conceived the idea of building St James. The church was to provide a place of worship for the British garrison in Guernsey, where services could be held in English. At that time, services in the Town Church were heldin French. The building was completed in 1818. After a full life, which included its use as the Elizabeth College chapel for many years, the building finally became redundant in 1970 and fell into partial decay. In1981 The Friends of St James Association was formed to achieve St James' restoration and then to administer the building as a concert and assembly hall. The States agreed to pay for its full restoration in 1983 and the building re-opened in July1985. Since that time, St James has provided the island with a unique and versatile venue for concerts and public events covering a broad range of tastes for both residents and visitors. In early 2002, the Dorey Centre opened after a fifteen month building period and years of fund raising by the Friends of St James Association. The resulting three-storey annexe now houses a reception and box office, fourfunction rooms, bar and café as well as the prestigious Guernsey Tapestry. These additional facilities provide St James with the increased versatility itrequires to cater for many different types of functions and also provides theAssociation with further let-able income from local businesses and organisations. The Friends of St James receive an annual grant from the States of Guernsey to help towards the administration of the building while fund raisingand income from Membership of the Association help them further to meet their financial obligations. OUR ISLAND Guernsey is an island that covers approximately 24 square miles and is located in the Gulf of St Malo, 60 miles south west of England and about 30 miles west of Northern France. It has a population of around 60,000 people.English speaking, with a centuries-old tradition of political stability and good governance. Guernsey is in the same time zone as London and frequent air links to London and other United Kingdom airports permit one-day business trips. But for those wishing to stay longer, a wide range of top quality hotels and restaurants is available to meet all the needs of the business traveller. The island has its own parliament, the States of Deliberation, which is democratically elected. There are no political parties in Guernsey and therefore the island is not prone to pendulum swings in regime or policy. The States is responsible for domestic affairs, its economy and tax regime. Guernsey enjoys full fiscal autonomy in tax and regulatory matters. As a Crown Dependency, the island's ties to the UK are through the Crown rather than the British Parliament, where Guernsey has no representation. The Lieutenant Governor is Her Majesty's personal representative and official channel of communication between the Crown and the UK Government and Guernsey.
الثلاثاء، 28 يونيو، 2011 Speech by Alan Shatter TD Minister for Justice, Equality and Defenceon Friday 24th June 2011 -Citizenship Ceremony -Dublin Castle Conference Centre, Dublin 2Ladies and Gentlemen,Welcome to Dublin Castle on this very special occasion. It is an important and remarkable event for two reasons. This is the first time the Irish State has marked the granting of citizenship with a formal civic ceremony to welcome our new citizens. And of course it is a personal and happy day for all of you, your families and friends, some of whom are here with you today, as you become fully naturalised Irish citizens. So I think you deserve a special Céad Míle Fáilte to honour this historic occasion.The granting of citizenship to a person who has come to our country from a foreign land is quite clearly a major event in his or her life. It is a time of celebration, a rite of passage and a moment for all of you to cherish. It is also a solemn event for this State in granting it.As Minister for Justice and Equality, I am in law given the duty of deciding who should be awarded the privilege of citizenship. In doing so, I have to carefully apply the citizenship laws enacted by our Parliament and consider the individual circumstances of those who seek Irish citizenship. I take that duty very seriously, as I am acting on behalf of all Irish people in deciding who should be granted the privilege of Irish citizenship. That is why, within days of becoming Minister in March, I decided that we as a State needed to do more – a lot more – to mark in a formal way the significance of the granting of citizenship. We do not award citizenship lightly and it is right that it’s granting is marked by a sense of occasion that serves to underscore its importance to you, the person receiving it, and to us who, on behalf of the people of Ireland, grant it to you.You have waited a long time for this moment – too long in many cases. You came to our country and chose to live among us; we welcome you and we hope that you will continue to contribute to our communities, to our neighbourhood and to our society. As a people we have been enriched by your presence and in making you citizens of our ancient and proud land we are acknowledging that contribution.I intend today’s pilot ceremony to be the first of many such events. Our ceremony today is greatly enhanced by the presence of Bryan McMahon, a highly respected lawyer and very recently retired High Court Judge and a greatly respected patron of the arts. Bryan will lend great dignity to the proceedings in his role as presiding officer and his presence will signify in a very public way the importance of the occasion. I want to thank you most sincerely, Bryan, for taking on this task. I also want to thank the Band of the 4th Western Brigade, conducted by Captain Declan Whitston, for joining us today for this important ceremony. As Minister of two important government departments, Justice and Equality and also Defence I appreciate the cooperation and interaction that takes place between both of my Departments and between An Gardai Siochana and our Defence Forces. The Army Band’s presence today is an important symbolic contribution to our proceedings. I also want to thank my Department of Justice officials who have organised today’s event.I referred earlier to the length of time that many of you here today will have waited for your citizenship applications to be processed.When the new Government came into office on 9th March there was a backlog of approximately 22,000 citizenship applications awaiting decision, approximately 17,000 of which had been waiting for in excess of 6 months with an average waiting time of 25 months. Some, indeed, had waited longer. It is entirely inappropriate, and completely out of step with other countries, that people wishing to become Irish citizens should be required to wait an average of 25 months for a decision on their applicationOn taking up office, I immediately initiated steps within my Department to deal with the huge backlog of citizenship applications and today there remain 13,500 applications awaiting decision in excess of 6 months. Over 6,000 citizenship applications have been dealt with in the past 3 months which exceeds the full year total for 2010 which was 5,038. I expect that the current backlog will be dealt with by Spring of next year. From that time on my aim is that, under new measures I announced on 16th June, save in exceptional circumstances, persons applying for citizenship will be given a decision on their application within six months.I was astonished to discover, on taking office in March, that approximately 55% of all citizenship applications received by the Immigration and Naturalisation Service had to be returned to applicants due to their being incorrectly completed. It was evident, prior to my appointment as Minister, that citizenship application forms were unnecessarily complex and obtuse and I took immediate steps to remedy this. Since last Friday, 17th June. new application forms have been available on the Irish Naturalisation and Immigration Service (INIS) website of the Department of Justice. I want to thank the officials in my Department for the work undertaken by them, in which I was also personally engaged, in the preparation of these new, more user friendly, application forms. These new forms should dramatically reduce the numbers incorrectly completed and substantially contribute to more efficient processing times.Other measures to improve the system include streamlined and accelerated checking procedures for certain categories of applicants such as spouses of Irish citizens and applicants recently granted long term residency who, as part of that process, underwent checks similar to those in place for naturalisation.It is planned to recruit an appropriate number of interns under the new Internship Programme announced in the Government’s Jobs Initiative to assist in areas dealing with naturalisation applications such as the Citizenship Section of the Department of Justice and Equality and the Garda Vetting Office.These are major changes to the current system which will yield positive results; they also are a strong signal from me on behalf of the new Government that we are serious about our commitment to address inefficient administrative processes and to deliver cost effective public services.Very shortly you will be invited to publicly declare your loyalty to our nation - your new home - and fidelity to our State. Having completed that legal formality under the guidance of Bryan Mc Mahon, retired Judge of the High Court, I will then present you with a certificate of naturalisation – at this point you will be a constitutionally recognised citizen of this State which you have made your home.73 of you from 24 countries across 5 continents have joined us here today in the historic precincts of Dublin Castle to become Irish Citizens. These buildings were once the seat of British rule in Ireland and, in the courtyard outside in January 1922, a famous ceremony took place which saw the transfer of British rule to us as an independent nation. Almost 90 years later, our ceremony today on the award of citizenship is maintaining in a very public way one of the very potent and powerful manifestations of our independence as a nation.The history of this State is now your history and the narrative of your life is now part of our history. For those of you granted citizenship today your future is now interwoven with the future of this State, its citizens across the globe and, in particular, all of us who live on this island.I wish to congratulate you, one and all, on becoming our newest Irish Citizens – we welcome you to our national family.I now formally introduce Bryan Mc Mahon and call upon him to administer the declaration of Fidelity, in which you publicly declare your loyalty to our Nation and Fidelity to our State.ends AIMS and Objectives: Aims 1.To support, advise and assist Libyan living in Ireland. 2.To facilitate and promote the integration and adaptation of Libyan living in Ireland and to help them keep their identity. 3.To promote and advance community development projects to alleviate poverty and improving living conditions of Libyan living in Ireland. Objectives The Libyan Community in Ireland is a social organization directs its activities towards social events only and its objectives are: 1.To contribute to the cultural and educational development of the Libyan community. 2.To provide family advice and counseling. 3.To organize cultural, sport and entertainment events for children and adults. 4.To facilitate young people to understand their cultural identity. 5.To develop strategies to cooperate with Irish society. 6.To build a positive and active Libyan personality to participate in the Irish society. 7.To co-operate with other communities in Ireland who have similar projects. 8.To support the Libyan women to participate in the development of the society. 9.To equip our youth with the necessary skills and abilities towards a more successful professional career. 10.To teach the youngsters their customs and heritage.
--- abstract: 'Casimir interaction between topological insulators with opposite topological magnetoelectric polarizabilities and finite surface band gaps has been investigated. For large surface band gap limit$(m\rightarrow\infty)$, we can obtain results given in \[Phys. Rev. Lett. 106, 020403 (2011)\]. For small surface band gap limit$(m\rightarrow0)$, Casimir interaction between topological insulators is attractive and analogy to ideal mental in short separation limit. Generally, there is a critical value $m_c$ and when the surface band gap is greater than the critical value, the Casimir force is repulsive in an intermediate separation region. We estimate the critical surface band gap $m_c \sim 1/(2a)$, where $a$ is a critical separation where Casimir force vanishes.' author: - Liang Chen - Shaolong Wan title: Casimir interaction between topological insulators with finite surface band gap --- Introduction ============ Time reversal invariant topological insulator(TI)[@Qi_physToday_2010; @Moore_nature_2010; @Hasan_rmp_2010] is a new quantum state of matter which has a full insulating gap in the bulk, but has gapless surface states protected topologically. This material has been extensively studied experimentally[@Hsieh_nature_2008; @YLChen_science_2009; @YXia_nature_2009; @Hsieh_nature_2009; @Hsieh_prl_2009; @YLChen_science_2010] and theoretically[@Fu_prl_2007; @Fu_prb_2007; @Moore_prb_2007; @Qi_prb_2008]. Two dimensional TI has been observed in $\text{HgTe}$ quantum well[@Bernevig_science_2006; @Konig_science_2007], $\text{Sb}_{1-x}\text{Te}_x$ is the first material has been reported to be 3-dimensional TI, and $\text{Bi}_2\text{Se}_3$, $\text{Bi}_2\text{Te}_3$, $\text{Sb}_2\text{Te}_3$ have been predicted[@HJZhang_nature_2009] to be TI with single Dirac cone on the surface. Novel properties of TI have been predicted, for instance, effective monopole[@Qi_science_2009] and topological magnetoelectric effect[@Qi_prb_2008], superconductor proximity effect induced Majorana fermion states[@Fu_prl_2008] etc. Recently, an interesting property of TI, tunable repulsive Casimir interaction between TIs with opposite topological magnetoelectric polarizability $\theta$ has been proposed[@Grushin_PRL], and the robustness of this repulsion in small separation limit against finite temperature and uniaxial anisotropy has also been analyzed[@Grushin_arXiv]. Repulsive Casimir interaction has been discussed in a few proposals, with special geometry[@Levin_prl_2010] or chiral metamaterials[@Zhao_prl_2009], or filling high-refractive liquid between dielectrics[@Zwol_pra_2010]. The repulsion between TIs is analogy to metamaterials, however, time reversal invariant TI is protected by gapless surface states. In order to observe the repulsive Casimir interaction, one need cover the TI surfaces with magnetic coating to open the band gap. The effect of finite surface band gap on this repulsive force is considerable. In this paper, we analyze the influence of finite surface band gap on Casimir force between TIs with opposite topological magnetoelectric polarizability $\theta$, we show that there is a minimal surface band gap $m_c$ and when surface band gap $m<m_c$, repulsive Casimir force will disappear. We also estimate this critical surface band gap numerically. Let us formulate the model. When time reversal symmetry is protected in the bulk, the topological nontrivial term $\alpha/(4\pi^2)\int{d^3}{x}{d}t\theta\bm{E}\cdot\bm{B}$ can be reexpressed as spin-momentum locked fermions on the interface of TI and normal insulator, in this paper we consider only one kind of fermion corresponding to $\theta=\pi$ or $-\pi$, generalization to multi-fermions is straightforward. Action of Dirac fermion on TI surface is $$S_D={\int}d^{3}x\,\bar{\psi}\left[i \gamma^a (\partial_a+ i e A_a) - m \right]\psi,$$ where $a=0,x,y$, $\gamma^0=\sigma^z$, $\gamma^x=iv_{F}\sigma^y$, $\gamma^y=-iv_{F}\sigma^x$. $\sigma^{x,y,z}$ are Pauli matrices of spin, $v_F$ is the Fermi velocity of surface fermion, which has a magnitude of $10^{-3}$ speed of light(we set $\hbar=c=1$ in this paper) and takes different values for different materials[@YLChen_science_2009; @YXia_nature_2009], ie, $v_F=1.3\times10^{-3}$ for $\text{Bi}_{2}\text{Te}_{3}$, and $1.7\times10^{-3}$ for $\text{Bi}_{2}\text{Se}_{3}$. Parameter $m$ is surface band gap opened by magnetic coating on TI and we assume chemical potential has been tuned into the surface band gap. $A_a$ present the first three components of vector-potential, while electromagnetic field is described by Maxwell action: $$\label{eq:S_em_2} %\mathcal{L}_V &=& -\frac{1}{8\pi}(\mathbf{E}^2 - \mathbf{B}^2)\\ S_{EM} = -\frac{1}{8\pi}{\int}d^4x(\varepsilon\bm{E}^2-\frac{1}{\mu}\bm{B}^2),$$ where $\bm{E}$ and $\bm{B}$ are electric and magnetic fields, $\varepsilon$ and $\mu$ are permittivity and permeability of TI in the bulk and equal to 1 in the vacuum. This paper is organized as follows: In Sec. \[sec:section2\], we evaluate an effective action for electromagnetic field on TI surface by quantum field theory approach and give the Maxwell equations of electromagnetic field with proper boundary conditions. In Sec. \[sec:section3\], we analyze the Casimir interaction between TIs via Lifshitz theory. We discuss the results in Sec. \[sec:section4\], and give a conclusion in Sec. \[sec:section5\]. \[sec:section2\]Effective Lagrangian on TI Surface and Maxwell Equations ======================================================================== In order to calculate the Casimir interaction caused by quantum fluctuation of electromagnetic field between TIs, one need to integrate the contribution from surface fermion. An effective action for external electromagnetic field in (2+1)-dimension can be found by standard quantum field theory approach[@chay1993; @kim1997; @novotny2002], $S_{eff}(A)=-i\ln\det[i\gamma^a(\partial_a+ieA_a)-m]$. We introduce a Feynman parameter, integrate out the fermion field up to one-loop correction and get the effective action in the following form: $$\begin{aligned} \label{eq:S_surface_3} S_{eff}(A) &=& \int{d}^3{x} \left[ - \frac{\phi (\lambda)}{8 \pi} \epsilon_{abc} A^{a} \partial^{b} A^{c} \right. \nonumber\\ &+& \left. \frac{\Phi(\lambda)}{4 {\pi} \|m\|} \left(F_{0j} F^{0j} + v_F^{2} F_{xy} F^{xy} \right) \right],\end{aligned}$$ with dimensionless parameters $\phi$ and $\Phi$ which take the forms: $$\begin{aligned} \label{eq:phi} \phi(\lambda) &=& \text{sign}(m )\alpha \int_0^1{dx} \frac{1}{\sqrt{1 - x ( 1- x) \lambda}}, \\ \label{eq:Phi} \Phi(\lambda) &=& \alpha \int_0^1{dx} \frac{(1-x) x}{\sqrt{1 - x (1 - x) \lambda}},\end{aligned}$$ where $\text{sign}(m)$ gives the sign of surface band gap, which corresponding to different signs of topological magnetoelectric polarizability. $\alpha=1/137$ is the fine structure constant of electromagnetic interaction, $\lambda=\left[k_0^2-v_F^2\left(k_x^2+k_y^2 \right)\right]/{m^2}$, and $k_0$, $k_x$, $k_y$ are frequency and momentum of electromagnetic fields on TI surface. A detailed derivation and a short discussion on this effective action(\[eq:S\_surface\_3\]) have been given in the appendix. We also note that in both limit, $m^2\rightarrow0$ and $m^2\rightarrow\infty$, $\phi$ and $\Phi$ are convergent. For the sake of Eq.(\[eq:Lifshitz\]), we derive expressions of $\phi$ and $\Phi$ in imaginary time formalism: $$\begin{aligned} \tilde{\phi} (\gamma) &=& \text{sign}(m) \frac{2 \alpha}{\sqrt{\gamma}} \arctan \left(\frac{\sqrt{\gamma}}{2} \right), \\ \tilde{\Phi} (\gamma) &=& \frac{\alpha}{2 \gamma} + \left( \frac{\alpha}{4 \sqrt{\gamma}} - \frac{\alpha}{\gamma^{3/2}} \right) \arctan \left(\frac{\sqrt{\gamma}}{2} \right),\end{aligned}$$ where $\gamma=(k_0^2+v_F^2\left(k_x^2+k_y^2\right))/{m^2}$. For the large surface band gap limit $(\|m\|\rightarrow\infty)$, $\tilde{\phi}(\gamma)\rightarrow{\text{sign}(m)}\alpha$, the term proportional to $\phi(\lambda)$ in Eq.(\[eq:S\_surface\_3\]) is topological and the term proportional to $\Phi(\lambda)$ in Eq.(\[eq:S\_surface\_3\]) is vanishing. For the small gap limit $(\|m\|\rightarrow0)$, $\tilde{\phi}(\gamma)\rightarrow0$ and $\tilde{\Phi}(\gamma)\rightarrow1/6$. ![Schematic illustration of Casimir interaction between TIs with opposite topological magnetoelectric polarizability $\theta$. We assume the thickness of magnetic coating is much smaller than the separation between TIs. \[fig:setup\]](set_up.eps){width="5cm"} Add the surface term Eq.(\[eq:S\_surface\_3\]) to standard action of electromagnetic fields Eq.(\[eq:S\_em\_2\]), one can get the Maxwell equations with surface corrections: $$\begin{aligned} &&\frac{1}{4\pi} \nabla \cdot \bm{D} = - \delta (z - z_i) \left(\frac{\phi_i}{4 \pi} B_z - \frac{\Phi}{2 \pi \|m\|} \nabla \cdot \bm{E} \right), \\ &&\frac{1}{4\pi} \left[\partial_t \bm{D} - (\nabla \times \bm{H}) \right] \nonumber\\ &&= \delta (z -z_i) \left[\frac{\phi_i}{4 \pi} \tilde{\bm{E}} + \frac{\Phi}{2 \pi \|m\|} \left(\partial_t \bm{E} - v_F^2 \nabla \times \bm{B} \right) \right],\\ &&\nabla \cdot \bm{B} = 0,\\ &&\partial_t \bm{B} + (\nabla \times \bm{E}) = 0,\end{aligned}$$ where $\bm{D}=\varepsilon\bm{E}$ and $\bm{H}=\bm{B}/\mu$ are electric displacement field and magnetizing field, $\tilde{E}_j=\epsilon_{jk}E_{k}$ ($j,k=x,y$), ($i=1,2$), $z_1=0$ and $z_2=a$ are positions of TI-surfaces (as shown in Fig.\[\[fig:setup\]\]), $\phi_1$ and $\phi_2$ are corresponding values of $\phi$. Without loss of generality, we assume the absolute values of surface band gaps on two TIs are equal, different signs of surface band gaps stand for different signs of the topological term $\alpha\theta\bm{E}\cdot\bm{B}/(4\pi^2)$ in Lagrangian of electromagnetic fields in TIs. We also note that in large band gap limit $(\|m\|\rightarrow\infty)$, these Maxwell equations are equal to those given in Refs.[@Qi_science_2009; @Karch_prl_2009] by redefine the electric displacement and magnetizing field as $\bm{D}=\varepsilon\bm{E}+{\alpha}\frac{\theta}{\pi}\bm{B}$, $\bm{H}=\frac{1}{\mu}\bm{B}-{\alpha}\frac{\theta}{\pi}\bm{E}$. From above Maxwell equations, we get the following discontinuous boundary conditions: $$\begin{aligned} D_z (z_i^+) - D_z(z_i^-) &=& - {\phi_i} B_z + \frac{2\Phi}{\|m\|} \left(\partial_x E_x + \partial_y E_y \right) \\ H_x(z_i^+) - H_x(z_i^-) &=& {\phi_i} E_x - \frac{2 \Phi}{\|m\|} \left(\partial_t E_y + v_F^2 \partial_x B_z \right)\\ H_y(z_i^+) - H_y(z_i^-) &=& {\phi_i} E_y + \frac{2\Phi}{\|m\|} \left(\partial_t E_x - v_F^2 \partial_y B_z \right),\end{aligned}$$ where $z_i^{\pm}$ means $z_i\pm0$. And $E_x$, $E_y$, $B_z$ are continuous on the interfaces. \[sec:section3\]Casimir Interaction =================================== Now we analyze the Fresnel coefficients of reflection light on the TI-vacuum interface. Incident TE-mode from vacuum with wave-vector $(k_x, k_y, k_z)$ will induce reflected TE and TM-mode, we assume the reflection coefficients are $r_{ee}$ and $r_{em}$ respectively, then the electromagnetic waves in the vacuum read: $$\begin{aligned} \bm{E} &=& (1 + r_{ee}) k_0 ( -k_y \bm{e}_x + k_x \bm{e}_y ) + r_{em}(-k_z \bm{k} - k^2 \bm{e}_z ), \nonumber\\ \bm{B} &=& (-k_z \bm{k} + k^2 \bm{e}_z) + r_{ee} (k_z \bm{k} + k^2 \bm{e}_z) \nonumber\\ &&+ r_{em} k_0 (- k_y \bm{e}_x + k_x \bm{e}_y ),\end{aligned}$$ and the refracted light with TE, TM-mode in TI take the forms: $$\begin{aligned} \bm{E}&=&t_{ee} k_0(-k_y\bm{e}_x + k_x\bm{e}_y )+c\,t_{em}(p_z\bm{k}-k^2\bm{e}_z),\nonumber\\ \bm{B}&=&t_{ee}(-p_z\bm{k}+k^2\bm{e}_z) + \frac{t_{em}}{c}k_0( -k_y \bm{e}_x + k_x \bm{e}_y ),\end{aligned}$$ where $t_{ee}$ and $t_{em}$ are refraction coefficients of TE and TM-mode, $c$ is the relative velocity of light in TI bulk, $\bm{k}=k_x\bm{e}_x+k_y\bm{e}_y$, $k^2=k_x^2+k_y^2$ and $p_z$ is $z$-component of wave vector in TI. For the injected TM-mode, one can write the analogy equations with reflection coefficients $r_{me}$, $r_{mm}$ and refraction coefficients $t_{me}$, $t_{mm}$. After some tedious derivation, we obtain the Fresnel coefficients matrix $\mathcal{R}$ in imaginary time formalism: $$\label{eq:fresnel_coefficients} \mathcal{R}=\left( \begin{array}{cc} r_{ee} & r_{em} \\ r_{me} & r_{mm} \\ \end{array} \right),$$ with $$\begin{aligned} r_{ee}&=&-1+\frac{2}{D}\left(1+\varepsilon\frac{k_z}{p_z}+2\tilde{\Phi}\frac{k_z}{m}\right), \nonumber\\ r_{em}&=&r_{me}=\frac{2}{D} \tilde{\phi}, \nonumber\\ r_{mm}&=&1-\frac{2}{D}\left(1+\frac{1}{\mu} \frac{p_z}{k_z}+2\lambda\tilde{\Phi}\frac{m}{k_z}\right), \nonumber\\\end{aligned}$$ where the denominator $$\begin{aligned} D& & = \left(1+\varepsilon\frac{k_z}{p_z} \right) \left(1+2\gamma\tilde{\Phi} \frac{m}{k_z}\right) + \left(1+\frac{1}{\mu }\frac{p_z}{k_z}\right) \nonumber\\ & &\times\left(1+2\tilde{\Phi} \frac{k_z}{m}\right) +\left(\frac{\epsilon }{\mu }+\tilde{\phi} ^2\right)-\left(1-4 \gamma\tilde{\Phi} ^2\right).\end{aligned}$$ For the large surface band gap limit, we can obtain the same Kerr rotation and Faraday rotation angle as given in Ref.[@Qi_prb_2008; @Karch_prl_2009]. In imaginary time formalism, Casimir energy density between two parallel dielectric semispaces can be expressed in a closed form of dielectric permittivity: $$\label{eq:Lifshitz} \frac{E_C(a)}{A}=\int_0^{\infty} \frac{d k_0}{2\pi} \int \frac{{d}^2k_{\parallel}}{(2 \pi)^2} \log\det\left[ 1 - \mathcal{R}^{(1)} \mathcal{R}^{(2)} \bm{e}^{-2 k_3 a} \right]$$ where $A$ is the surface area of TIs, $\mathcal{R}^{(1,2)}$ are Fresnel coefficients on the surfaces, $k_3=\sqrt{\bm{k}_{\parallel}^2+k_0^2}$. In order to calculate the Casimir energy density numerically, we also need a form of frequency-dependent dielectric permittivity $\varepsilon$ (we assume the permeability $\mu = 1$), this can be modeled by[@Bordag_book; @Bordag_report_2001]: $$\label{eq:dielectric_permittivity} \varepsilon(i k_0) = 1+\sum_{J=1}^{K}\frac{g_J}{k_{0}^{2}+\omega_{J}^{2}+\gamma_{J} k_0},$$ we consider only one oscillator ($K=1$) with oscillator strength $g_J$, oscillator frequency $\omega_{J}$ and damping parameter $\gamma_{J}$. $\gamma_{J}\ll\omega_J$ and we omit the contribution from damping parameter here. \[sec:section4\]Results and Discussion ====================================== ![The ratio $E_C^{(\alpha)}/E_C^{(0)}$ as a function of dimensionless separation $a \omega_J$ for different oscillator strength $g' = \sqrt{g_J}/\omega_J$ in the closed surface band gap limit, $m = 0$. Where $E_C^{(\alpha)}$($E_C^{(0)}$) is the Casimir energy with(without) surface correction. Here fermion velocity $v_F = 1.0\times10^{-3}$.\[fig:zero\_mass\]](velocity1000.eps){width="9cm"} In this paper, we analyze Casimir interaction between TIs with finite surface band gap. First, for large surface band gap limit $(m \rightarrow \infty)$, we can obtain same results given in \[Phys. Rev. Lett. 106, 020403 (2011)\][@Grushin_PRL] from equations (\[eq:fresnel\_coefficients\])-(\[eq:dielectric\_permittivity\]). Second, for small surface band gap limit $(m \rightarrow 0) $, the off-diagonal terms in Fresnel coefficients matrices will vanish and Casimir energy can be rewritten in imaginary time formalism as: $$\begin{aligned} \label{eq:Lifshitz_zero_mass} \frac{E_C(a)}{A} &=& \int_0^\infty \frac{{d}k_0}{2 \pi} \int \frac{d^2k_{\parallel}}{(2 \pi)^2} \left[\log \left(1 - e^{-2 k a} r_{TE}^{(1)}r_{TE}^{(2)} \right) \right. \nonumber\\ &&+ \left.\log \left(1 - e^{-2 k a} r_{TM}^{(1)} r_{TM}^{(2)} \right) \right],\end{aligned}$$ with $$\begin{aligned} \label{eq:re_zero_mass} r_{TE} &=& - 1 + \frac{2}{1 + \frac{p_3}{k_3} + \frac{\pi \alpha}{4} \sqrt{\cos^2 \theta + v_F^2 \sin^2 \theta}},\\ \label{eq:rm_zero_mass} r_{TM} &=& 1 - \frac{2\frac{p_3}{k_3} \sqrt{\cos^2 \theta + v_F^2 \sin^2 \theta}}{\frac{\pi \alpha}{4} \frac{p_3}{k_3} + (\frac{p_3}{k_3} + \varepsilon) \sqrt{\cos^2 \theta + v_F^2 \sin^2 \theta}} ,\end{aligned}$$ where $k_3=\sqrt{k_0^2+\bm{k}_{\parallel}^2}$, $p_3=\sqrt{\varepsilon{k_0^2}+\bm{k}_{\parallel}^2}$, and $\theta=\cos^{-1}(k_0/k_3)$. The Casimir energy between dielectric materials without special boundary conditions, $\alpha\rightarrow0$ in Eq.(\[eq:re\_zero\_mass\]) and Eq.(\[eq:rm\_zero\_mass\]), has been studied[@Bordag_book; @Bordag_report_2001; @Lambrecht_NJP]. Considering correction from surface interaction, for large separation limit, we obtain the correction up to first order of fine structure constant: $$\begin{aligned} &&\frac{E_C^{(1)}(a)}{E_0} = - \frac{\pi \alpha}{4 d^3} \left[\frac{\varepsilon(0) - 1}{(\varepsilon(0) + 1)^3} \log{\frac{1}{v_F}} \right. \nonumber\\ &&+ \left. \frac{\log \left[\frac{1}{2} \left(1 + \sqrt{\varepsilon(0)} \right) \right]}{\varepsilon(0) - 1} - \frac{3 + 5 \sqrt{\varepsilon(0)}}{4 \left(1 + \sqrt{\varepsilon(0)} \right)^3} \right],\end{aligned}$$ where $E_0=A\omega_J^3/(2\pi)^2$ which is set as the unit of Casimir energy, $d=a\omega_J$ is the dimensionless separation. For small separation limit, in order to make the physics more clear, we also formally expand Eq.(\[eq:Lifshitz\_zero\_mass\]) in powers of $\alpha$, up to first order correction, the Casimir energy takes the following form(here we assume the relative oscillator strength $g_J/\omega_J^2\ll1$): $$\begin{aligned} \frac{E_C^{(1)}(a)}{E_0} & &= - \frac{g_J}{\omega_J^2} \frac{\pi \alpha}{64 d^3} \int_0^{\infty} d y y^2 e^{- y} \nonumber\\ &&\left[\frac{\theta(t)}{\sqrt{t}} \text{arctan} \sqrt{t} + \frac{\theta (-t)}{\sqrt{-t}} \text{arctanh} \sqrt{-t} \right],\end{aligned}$$ where $t=-1+{v_F^2y^2}/{4d^2}$ and $\theta(t)$ is the Heaviside unit step function. Casimir energy is dominated by surface Dirac fermion and turns into the ideal conductor case which is proportional to $1/a^3$. This conclusion is also confirmed numerically in Fig.\[\[fig:zero\_mass\]\]. ![Boundary of repulsive and attractive Casimir interaction in the plane of dimensionless separation $d=a\omega_J$ and product $\|m\|a$ for different oscillator strengths $g'=\sqrt{g_J}/\omega_J$. When the parameters $d$ and $\|m\|a$ have been taken in the left-up region over these lines, the Casimir interaction is attractive, when $d$ and $\|m\|a$ have been taken in the lower-right region of these lines, the Casimir interaction is repulsive. (The relative Fermi velocity $v_F$ has been taken to be $1.0\times10^{-3}$).\[fig:phase\_boundary\]](phase_boundary.eps){width="9cm"} Finally, for general surface band gap, we have two dimensionless parameters: $m/\omega_J$ and $d=\omega_J{a}$ (there are two other parameters in our model, the Fermi velocity of surface fermion, $v_F$, and optical oscillator strength in TIs, $g_J/\omega_J^2$, which both have quantitatively influence on Casimir energy). For the large separation limit $(a\gg\text{max}(1/\omega_J,1/\|m\|))$, we expand the integral in Eq.(\[eq:Lifshitz\]) in power of fine structure constant[@alpha] $\alpha$ and consider the correction up to $\alpha$. In this case, the dielectric permittivity $\varepsilon(ik_0)$ can be approximated by long wave length limit value $\varepsilon(0)$, and the Casimir energy correction from interaction between surface fermions and electromagnetic field reads: $$\frac{E_{C}^{(1)}(a)}{E_0} = - \frac{\|m\| \alpha}{\omega_{J}d^2} \int_0^1 \frac{dx}{v_F^2+x^2} \left[\frac{r^2(\varepsilon(0) - r)}{(\varepsilon(0) + r)^3} + \frac{x^2(1 - r)}{(1 + r)^3} \right],$$ where $ r= \sqrt{1 + (\varepsilon(0)-1) x^2}$, and $v_F \ll 1$. For the small separation limit $(d\rightarrow0)$, in order to make the physics more clear, we also formally expand the Casimir energy in power series of $\alpha$. In this case, the Casimir energy is dominated by surface terms, the term which contains $\tilde{\Phi}^2$ and is proportional to $1/m^2a^5$ is important. However this dominant term will be suppressed if $\|m\|a\rightarrow\infty$, the topological term which contains $\text{sign}(\theta_1\theta_2)\tilde{\phi}^2$ and is proportional to $1/a^3$ will provide a large repulsive potential between TIs when $\text{sign}(\theta_1\theta_2)=-1$. So the surface terms in Casimir energy will dominate and $\|m\|a$ is a good parameter to estimate the Casimir force: when $\|m\|a\gg1$, the Casimir force will be repulsive and when $\|m\|a\ll1$, the Casimir force will be attractive. ![Casimir energy density $E_C$ (in units of $E_0=\omega_J^2/(2\pi)^2$) as a function of the dimensionless distance $d=a\omega_J$ with different surface band gaps $m/\omega_J$. Here we take the dimensionless oscillator strength $g_J/\omega_J^2=0.45^2$ and Fermi velocity $v_F=1.0\times10^{-3}$.\[fig:finite\_gap\]](casimir_finite6lines.eps){width="8.5cm"} In Fig.\[\[fig:phase\_boundary\]\], we give the boundary of repulsive and attractive Casimir interaction, as a function of dimensionless separation $d=a\omega_J$ and product $\|m\|a$. We find that there is a critical value $(\|m\|a)_{c}\sim1/2$, when $\|m\|a<(\|m\|a)_{c}$, the Casimir interaction is attractive for any separation length. The independence of $(\|m\|a)_{c}$ on oscillator strength $g_J/\omega_J^2$ shows that Casimir interaction, in small separation limit, is dominated by surface terms. More intuitively, we calculated the Casimir energy as a function of dimensionless separation $d=a\omega_J$ for different surface band gaps, as shown in Fig.\[\[fig:finite\_gap\]\], for given parameters, $g_J/\omega_J^2=0.45^2$ and $v_F=1.0\times10^{-3}$. We find the critical surface band gap, where the repulsive peak disappears, $m_c\approx300\omega_J$ (the blue-square dotted line in Fig.\[\[fig:finite\_gap\]\]). We note that our calculations can be generalized to multi-value of topological magnetoelectric polarizability $\theta=(2n+1)\pi$ ($n$ is an integer) straightforward by introducing multi-fermion on TI surface, and the critical value $(\|m\|a)_{c}$ is independent on the absolute value of $\theta$ (as shown in Fig.\[\[fig:phase\_boundary\_pi\]\]), this is because in short separation limit, Casimir interaction is dominated by surface terms and each species fermion will contribute both repulsive and attractive Casimir interaction if $\text{sign}(\theta_1) = - \text{sign}(\theta_2)$. We can use this relationship to estimate the critical surface band gap for repulsive Casimir interaction. For $\text{Tl} \text{Bi} \text{Se}_2$ suggested in Ref.[@Grushin_PRL], the minimum of Casimir energy appears at a separation of $a \sim 0.1{\mu}m$, and the corresponding surface band gap needs to be greater than $1eV$, which reflects that the width of surface band gap opened by magnetic coating is non-ignorable and unaccessible experimentally. ![Boundary of repulsive and attractive Casimir interaction in the plane of dimensionless separation $d=a\omega_J$ and product $\|m\|a$ for different topological magnetoelectric polarizability. (The relative Fermi velocity $v_F$ and oscillator strength $g_J/\omega_J^2$ has been taken to be $1.0\times10^{-3}$ and $0.45^2$ respectively).\[fig:phase\_boundary\_pi\]](phase_boundary_pi.eps){width="9cm"} \[sec:section5\]Conclusion ========================== We studied the Casimir energy between TIs with opposite topological magnetoelectric polarizability and finite surface band gap via Lifshitz formula, we found that, in small separation limit, Casimir force is dominated by interaction between surface fermion and electromagnetic field in the vacuum, and a great surface band gap $m>m_c\sim1/(2a)$ is essential for repulsive Casimir interaction. This work is supported by NSFC Grant No.10675108. Effective action {#app:effective_action} ================ We give a detailed derivation of the effective action(\[eq:S\_surface\_3\]) in this appendix. The effective action from quantum field theory is: $$\label{app:S_eff} S_{eff}(A) = \frac{1}{2}\int \frac{d^3k}{(2\pi)^3} A_{a}(k)\Pi^{ab}(k)A_{b}(k),$$ where $\Pi(k)$ is the polarization tensor, which takes the form: $$\label{app:polar} i\Pi^{ab}(k) = -e^2\int\frac{d^3p}{(2\pi)^3}\text{tr}[(-i\gamma^a)G(k+p)(-i\gamma^b)G(k)],$$ and $G(k) = i/(\gamma^a k_a + m)$ is the propagator of fermion on TI surface. From the standard calculation in quantum field theory, one can get the exact form of polarization tensor: $$\begin{aligned} \Pi(k) &=& \Pi_1(k) + \Pi_2(k)\\ \label{app:Pi_1} \Pi_1^{ab}(k) &=& \frac{\phi(\lambda)}{4\pi}\epsilon^{abc}ik_c\\ \label{app:Pi_2} \Pi_2(k) &=& \frac{\Phi(\lambda)}{2\pi\|m\|}\left( \begin{array}{ccc} k_x^2+k_y^2 & -k_0 k_x & -k_0 k_y \\ -k_0 k_x & k_0^2- v_F^2 k_y^2 & v_F^2 k_x k_y \\ -k_0 k_y & v_F^2 k_x k_y & k_0^2-v_F^2 k_x^2 \end{array} \right)\nonumber\\\end{aligned}$$ where $\phi(\lambda)$ and $\Phi(\lambda)$ has been given in Eq.(\[eq:phi\]) and Eq.(\[eq:Phi\]), $k_{1,2}(k_0)$ are the momentum(frequency) of electromagnetic field. One can check that the polarization tensor satisfies Ward identity, $\sum_a k_a \Pi^{ab}(k) = \sum_b\Pi^{ab}(k) k_b = 0 $. The Fourier transformation of Eq.(\[app:S\_eff\]) gives Eq.(\[eq:S\_surface\_3\]).\ We take $\Pi^{xy}(k)$ as an example to show more detailed calculations of polarization tensor. Taking the trace in Eq.(\[app:polar\]), one can get $$i\Pi^{xy}(k) %&=&-e^2 \int \frac{d^3p}{(2\pi)^3}\text{tr}\left[ %(-i\gamma^x) \frac{i}{\gamma^a(k_a+p_a)+m} (-i\gamma^y) \frac{i}{\gamma^b p_b+m}\right]\nonumber\\ =-e^2 \int \frac{d^3p}{(2\pi)^3}\frac{2v_F^2[-im k_0 + v_F^2(2k_x k_y + k_x p_y + k_y p_x)]} {[(p_0 + k_0)^2 + m^2 -v_F^2(\bm{p}+\bm{k})^2][k_0^2 + m^2 -v_F^2\bm{k}^2]}.$$ One can get the following form of $i\Pi^{xy}(k)$ by introducing a Feynman parameter $x$ and redefining the integration variables $l_a '=p_a+xk_a$, $l_0 = l_0 '$, and $\bm{l}=v_F\bm{l}'$: $$i\Pi^{xy}(k) =-2e^2\int_0^1dx\int\frac{d^3l}{(2\pi)^3}\frac{i m k_0+2x(1-x)v_F^2k_xk_y}{\left(l_0^2-\bm{l}^2-\Delta\right)^2},$$ where $\Delta= m^2-x(1-x)(k_0^2-v_F^2\bm{k}^2)= m^2[1-\lambda x (1-x)]$. Making Wick rotation $l_0\rightarrow{il_0^E}$ and integration over $l$, we find: $$\begin{aligned} i\Pi^{xy}(k)&=&ie^2\left[imk_0\int\frac{ d x }{4\pi\sqrt{\Delta}}+v_F^2k_xk_y\int dx\frac{x(1-x)}{2\pi\sqrt{\Delta}}\right]\nonumber\\ &=&i\left(\frac{i k_0}{4\pi}\phi(\lambda)+\frac{v_F^2k_xk_y}{2\pi\|m\|}\Phi(\lambda)\right)\end{aligned}$$ Comparing with the effective action of electromagnetic field in monolayer graphene system as shown in Ref.[@graphene], we find that there is an additional topological term Eq.(\[app:Pi\_1\]) together with the normal vacuum polarization Eq.(\[app:Pi\_2\]), the first term is essential for TI because this parity-odd term reflects the fact that there are always odd species of surface fermions which are spin-momentum locked, the contribution from second term is analogy to Dirac fermion in monolayer graphene system and reflects the dynamical response of TI surface state to extra electromagnetic field.\ [arxiv]{} X. L. Qi and S. C. Zhang, Phys. 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With advance of science and technology and maturity of fabric industry, various new fabrics having the quality distinct from that of the traditional fabrics, have been developed. Further, with economic promotion, people pay more attention to dressing and pursue style. Therefore, to meet diversified dressing designs, sewing method has to advance further. In earlier times, the translation gear of a single-translation-gear sewing machine was only to feed fabric into the sewing position. Under constant rotation speed of the motor, if the number of the needle reciprocation was also constant, changing the sewing thread pitch would be achieved via only changing the travel range of the translation gear, which determines the fabric feeding quantity. However, confronting current new-type fabrics (such as an elastic fabric) and various dressing designs (such as a dress with wrinkles intentionally formed on the sewing thread), the above mentioned single-translation-gear sewing machine cannot satisfy the demand obviously. Therefore, double-translation-gear sewing machine is adopted in most cases nowadays. The function of the rear translation gear thereof is equivalent to the above mentioned single translation gear, and the sewing thread pitch can be adjusted via changing the travel range of the rear translation gear. The function of the front translation gear is to determine the ratio between the delivered-out fabric amount and the feed-in fabric amount to form different patterns of the fabric neighboring the sewing thread, such as plane, tension or wrinkled pattern, i.e. so-called differential ratio, via that the front translation gear translates the fabric in speed equal to, higher or less than the feeding speed of the rear translation gear. Thus, the double-translation-gear sewing machine can meet the demand of current elastic fabrics and diversified dressing designs. Nevertheless, none of the current transverse shuttle-type sewing machines can separately adjust the travel ranges of the front and rear translation gears, i.e. the sewing thread pitch and the differential ratio, for example, a R.O.C. Patent Publication No. 541377 of the inventor, entitled “Sewing Machine with an Adjust Mechanism of the Front Differential Feeding”, which uses an adjust mechanism of the front differential feeding to adjust the speed of the front translation gear and comprises: a swing element, four linking-up elements, an adjust mechanism, and a transmission shaft. In this patent, the adjust mechanism of the front differential feeding is actuated by the transmission mechanism of the rear differential feeding and drives the front translation gear to move to and fro. The adjust mechanism of the front differential feeding has an adjust mechanism, which can change the ranges of the planar to-and-fro feeding travel of the front translation gear. When the user shifts the adjust mechanism during operation, he can modify the travel range of the front translation gear. Although the travel range of the front translation gear can be adjusted in this invention, the travel range of the rear translation gear cannot be adjusted but is determined by the front translation gear. Therefore, the travel ranges of the front and rear translation gears cannot be separately adjusted. Thus, the sewing thread pitch and the differential ratio cannot be adjusted separately and arbitrarily as the user demands. Accordingly, it is a problem the sewing machine manufacturers desire to solve to provide a sewing machine wherein the user can arbitrarily and separately adjust the sewing thread pitch and the differential ratio to meet the cases that a special fabric is used, special sewing thread pitch is needed or wrinkles are demanded.
3-Dimensional susceptibility testing of beta-lactam antibiotics. A technique for demonstrating the substrate specificities of bacterial beta-lactamases is presented. Enzymatic degradation of beta-lactam antibiotics can be detected by cutting a wall of inoculum into the agar 3 mm from an antibiotic disc. Inactivation of the drug as it diffuses through the wall of inoculum results in distortion of the resulting inhibition zone. This procedure can be applied to the Stokes, Bauer-Kirby, International Collaborative Study (ICS) and Calibrated Dichotomous Sensitivity Test (CDS) methods so that they provide information about any detrimental effect of a pathogen on beta-lactam antibiotics, in addition to the effect the antibiotics have on the pathogen. The additional information generated by this simple procedure should increase the predictive value of in-vitro tests.
Q: CTC + BLSTM Architecture Stalls/Hangs before 1st epoch I am working on a code which recognizes online handwriting recognition. It works with CTC loss function and Word Beam Search (custom implementation: githubharald) TF Version: 1.14.0 Following are the parameters used: batch_size: 128 total_epoches: 300 hidden_unit_size: 128 num_layers: 2 input_dims: 10 (number of input Features) num_classes: 80 (CTC output logits) save_freq: 5 learning_rate: 0.001 decay_rate: 0.99 momentum: 0.9 max_length: 1940.0 (BLSTM with variable length time stamps) label_pad: 63 The problem that I'm facing is, that after changing the decoder from CTC Greedy Decoder to Word Beam Search, my code stalls after a particular step. It does not show the output of the first epoch and is stuck there for about 5-6 hours now. The step it is stuck after: tensorflow/stream_executor/platform/default/dso_loader.cc:42] Successfully opened dynamic library libcublas.so.10 I am using a Nvidia DGX-2 for training (name: Tesla V100-SXM3-32GB) A: Here is the paper describing word beam search, maybe it contains some useful information for you (I'm the author of the paper). I would look at your task as two separate parts: optical model, i.e. train a model that is as good as possible at reading text just by "looking" at it language model, i.e. use a large enough text corpus, use a fast enough mode of the decoder To select the best model for part (1), using best path (greedy) decoding for validation is good enough. If the best path contains wrong characters, chances are high that also beam search has no chance to recover (even when using language models). Now to part (2). Regarding runtime of word beam search: you are using "NGramsForecast" mode, which is the slowest of all modes. It has running time O(W*log(W)) with W being the number of words in the dictionary. "NGrams" has O(log(W)). If you look into the paper and go to Table 1, you see that the runtime gets much worse when using the forecast modes ("NGramsForecast" or "NGramsForecastAndSample"), while character error rate may or may not get better (e.g. "Words" mode has 90ms runtime, while "NGramsForecast" has over 16s for the IAM dataset). For practical use cases, I suggest the following: if you have a dictionary (that means, a list of unique words), then use "Words" mode if you have a large text corpus containing enough sentences in the target language, then use "NGrams" mode don't use the forecast modes, instead use "Words" or "NGrams" mode and increase the beam width if you need better character error rate
Q: How to set an option from multiple options or array with different values to views as selected in select box using PHP An option value is taken from the database and included in a select box along with other options. How can I set the value taken from the database as selected? The value from the database is set as $row['value'] and equals s. In HTML the options look like so... <select name="select"> <option value='xxs'>Extra, Extra small</option> <option value='xs'>Extra small</option> <option value='s'>Small</option> <option value='m'>Medium</option> <option value='l'>Large</option> <option value='xl'>Extra Large</option> <option value='xxl'>Extra, Extra small</option> </select> What I want is the $row['value'] (Small) option to be displayed on page load... Is this possible? A: The good news is, this is possible and in PHP is quite simple really. First we put all of our options and their respective values in an array like so: <?php $options=array('Extra, Extra small'=>'xxs','Extra small'=>'xs','Small'=>'s','Medium'=>'m','Large'=>'l','Extra Large'=>'xl','Extra, Extra Large'=>'xxl'); Follow this by opening the select box and calling upon the options array in a foreach loop... echo '<select>'; foreach($options as $view=>$value){ As you may have noticed the array contains fields that look like 'Large'=>'l' and the for each loop is calling upon the options as $view=>$value. $view represents the name field, in this case 'Large' and $value represents the value field 'l'. This is important if you expect the user to see different options in the select box than what the values are set at. Next we create the variable $selected which is going to be used to determine if there is a match between $row['value'] and $value... $selected=($row['value'] == $value)? "selected" : ""; This is the same as using an if and else statement to set the variable, but shorter. The first section after the variable is asking if $row['value'] is equal to $value, if it does then $selected="selected" else (:) $selected is set to blank. Next we include the options. Because it is in the foreach loop, we only need one line to insert all of the options... echo '<option '.$selected.' value="'.$value.'">'.$view.'</option>'; Remember the $selected variable in the last step? Each time the foreach loop goes through a section of the options array set at the beginning, it checks to see if $row['value'] equals $value. If it does then $selected will be set as selected and that particular option will be the one that is shown on page load. It continues through the rest of the array until all views and values have been scanned and returns their respective options. Finally we close the foreach loop and the select box... } echo '</select>'; And there you have it, an automatic way to make a select box option set as selected. A similar pattern can be used for check-boxes, radio selectors, tabs and more. The full code... <?php $options=array('Extra, Extra small'=>'xxs','Extra small'=>'xs','Small'=>'s','Medium'=>'m','Large'=>'l','Extra Large'=>'xl','Extra, Extra Large'=>'xxl'); echo '<select>'; foreach($options as $view=>$value){ $selected=($row['value'] == $value)? "selected" : ""; echo '<option '.$selected.' value="'.$value.'">'.$view.'</option>'; } echo '</select>';
Q: Holding in an atmosphere primarily using a magnetic field Assuming it was possible to create an artificial magnetic shield on the moon, would it be possible that a sufficiently powerful field could hold onto an atmosphere despite the low gravity. Thanks A: Shorter answer: No. Magnetic fields don't hold electrically neutral gases and almost all of the gases in the atmosphere except ozone are electrically neutral. You'd have to come up with some other solution. Now, if you are talking about "the Moon" rather than a moon, I'm not sure that the gravity is too low to support some sort of atmosphere under the right circumstances. The Moon still has one-sixth of Earth gravity and an escape velocity of 2.38 km/s v. 11.2 km/s for Earth. The moon has 85% of the gravity of Titan (which has a thick hydrocarbon atmosphere). Chris in a prior stack exchange post (shit my apologies, I closed it before getting the link) noted that: The escape velocity at the moon's surface is about 2.4 km/s. The mean speed of oxygen at 293 K is about 0.48 km/s. A commonly quoted rule of thumb says that the escape velocity needs to be 6 times the gas's mean velocity in order for that gas to remain captive to gravity and the values I quoted are related by a factor of only 5. The air would contain water (since dry air is very uncomfortable to breath) and carbon dioxide (as a by-product if not also needed to sustain the cyanobacteria/plants you would want in place of planetary size mechanical carbon dioxide scrubbers, then there are the nutrients you would need to sustain those) which would readily exacerbate an atmospheric greenhouse effect and, with the moon being at about the same distance from the sun as is earth, you would expect the air to warm up to similar to earth temperatures, though without the moderating effect of oceans, and so cause the oxygen to dissipate. As nitrogen is lighter it's mean speed at the same temp is higher, v_rms something like 0.51 km/s IIRC, so it too would dissipate as would water vapour. In short, it doesn't seem likely that it would be possible on the moon. But, while everything he says is true, I think the conclusion doesn't follow automatically because 273 K and 760 mmHG pressure are not reasonable assumptions for the Moon. While the Moon's gravity could not sustain an atmosphere at close to room temperature on Earth, it could sustain a cooler atmosphere that was still warm enough to have gas form oxygen. W = 3kT/2 where W is average kinetic energy, k is the boltzmann constant (=1.38x10^(-23) J/K or 8.617x10^(-5) eV/K) and T is temperature (K). W = m*v^2/2 where m is the molecular mass and v is the average molecular speed. So basically temperature in kelvin is proportional to speed squared. To reduce speed to the 5/6th of Earth speed necessary to allow the Moon to hold an atmosphere, you need to reduce temperature to 25/36th of 273 K, which is about 190 K (i.e. about -83 °C). This is Antarctica winter cold, but not uninhabitable and is above the freezing and boiling points of oxygen. The freezing point oxygen (O2) is 54.36 K (−218.79 °C) and the boiling point of liquid oxygen is 90.19 K (−182.96 °C) at 101.325 kPa (760 mmHg). The average temperature on the Moon (at the equator and mid latitudes) varies from -183 °C (about 90 K), at night to 106 °C (about 379 K) during the day, which is an average of 235 K, just a bit over our 190 K target. The existence of an atmosphere itself would probably buffer these extremes of temperature, preventing oxygen from going to liquid form a night, but the problem would be that the daytime temperature would cause the temperature to exceed escape velocity. So, the real trick would be to see how to control the temperature on the Moon to prevent it from rising above 190 K or below 95 K or so. Thus the real issue is how to prevent about 50% of the solar energy that currently reaches the Moon in the daytime from doing so, ideally in a manner that shifts that solar energy to the night. The most obvious way to do that would be to get high winds going from the light side to the dark side at a sufficient speed. On Earth, the distances are too great to accomplish this, but the lunar day is much longer (29 days, 12 hours and 44 minutes) and the Moon's circumference is about a quarter of the Earth's. So, if you could get winds going strong in the atmosphere and reduce the average amount of solar energy penetrating the atmosphere by about 20% plus a little more for a buffer (perhaps by somehow increasing its albedo, e.g. with the right kind of clouds perhaps by inserting water vapor or some other highly reflective colored gas), you could get a stable atmosphere on the Moon. It would have to be very cold, but it could otherwise work. So, rather than magnetic fields, you might need vaporizers to create clouds and fans to keep the air circulating fast enough, rather than any kind of artificial magnetic field. A: As others have pointed out, a magnetic field does you no good with most gasses as they are no electrically charged. However, you do not need a magnetic field to hold an atmosphere on the moon. The moon's gravity is sufficient. The proof of this is that Titan, which has a lower surface gravity than the moon, has a denser atmosphere than Earth. In addition, Titan's atmosphere is primarily nitrogen, the same primary component of Earth's atmosphere. Titan is even able to hold onto helium and hydrogen, which despite being the lightest gas there is and the most likely to escape into space, still has a concentration of 1000 ppm on Titan. Now there are definately geochemical processes on Titan that we do not understand yet which are contributing to this atmosphere, so I imagine that the moon would not hold an atmosphere indefinitely, but assuming human action is taken to put an atmosphere on the moon, that same atmosphere could plausibly be maintained on the moon.
/* * Licensed to the Apache Software Foundation (ASF) under one or more * contributor license agreements. See the NOTICE file distributed with * this work for additional information regarding copyright ownership. * The ASF licenses this file to You 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 org.apache.gobblin.converter.string; import org.apache.gobblin.configuration.ConfigurationKeys; import org.apache.gobblin.configuration.WorkUnitState; import org.apache.gobblin.converter.DataConversionException; import java.util.Iterator; import org.testng.Assert; import org.testng.annotations.Test; /* * Tests for {@link StringFilterConverter}. / @Test(groups = { "gobblin.converter.string" }) public class StringFilterConverterTest { /* * Test for {@link StringFilterConverter#convertRecord(Class, String, WorkUnitState)} with a blank regex. / @Test public void testConvertRecordWithNoRegex() throws DataConversionException { WorkUnitState workUnitState = new WorkUnitState(); StringFilterConverter converter = new StringFilterConverter(); converter.init(workUnitState); String test = "HelloWorld"; Iterator<String> itr = converter.convertRecord(String.class, test, workUnitState).iterator(); Assert.assertTrue(!itr.hasNext()); } /* * Test for {@link StringFilterConverter#convertRecord(Class, String, WorkUnitState)} with a regex that is only a * sequence of letters. / @Test public void testConvertRecordWithSimpleRegex() throws DataConversionException { WorkUnitState workUnitState = new WorkUnitState(); workUnitState.setProp(ConfigurationKeys.CONVERTER_STRING_FILTER_PATTERN, "HelloWorld"); StringFilterConverter converter = new StringFilterConverter(); converter.init(workUnitState); // Test that HelloWorld matches the pattern HelloWorld String test = "HelloWorld"; Iterator<String> itr = converter.convertRecord(String.class, test, workUnitState).iterator(); Assert.assertTrue(itr.hasNext()); Assert.assertEquals(itr.next(), test); Assert.assertTrue(!itr.hasNext()); // Test that Hello does not match the pattern HelloWorld test = "Hello"; itr = converter.convertRecord(String.class, test, workUnitState).iterator(); Assert.assertTrue(!itr.hasNext()); } /* * Test for {@link StringFilterConverter#convertRecord(Class, String, WorkUnitState)} with a regex that actually uses * regex features, such as wildcards. / @Test public void testConvertRecordWithComplexRegex() throws DataConversionException { WorkUnitState workUnitState = new WorkUnitState(); workUnitState.setProp(ConfigurationKeys.CONVERTER_STRING_FILTER_PATTERN, "."); StringFilterConverter converter = new StringFilterConverter(); converter.init(workUnitState); // Test that HelloWorld matches the pattern .* String test = "HelloWorld"; Iterator<String> itr = converter.convertRecord(String.class, test, workUnitState).iterator(); Assert.assertTrue(itr.hasNext()); Assert.assertEquals(itr.next(), test); Assert.assertTrue(!itr.hasNext()); // Test that Java matches the pattern .* test = "Java"; itr = converter.convertRecord(String.class, test, workUnitState).iterator(); Assert.assertTrue(itr.hasNext()); Assert.assertEquals(itr.next(), test); Assert.assertTrue(!itr.hasNext()); } }
Effect of n-hexane on the disposition and toxicity of the 1,3-butadiene metabolite 3-butene-1,2-diol. 3-Butene-1,2-diol (butenediol), a major metabolite of 1,3-butadiene (butadiene), can undergo either detoxification or biotransformation to potentially toxic metabolites, including 3,4-epoxy-1,2-butanediol and hydroxymethylvinyl ketone (HMVK). Butadiene exposure can occur concomitantly with hexanes, which share common biotransformation pathways with butadiene. To determine the potential influence of hexane co-exposure on butadiene toxicity, the present study examined the effect of n-hexane on butenediol disposition [as measured by urinary excretion of (N-acetyl-S-(3,4-dihydroxybutyl)-L-cysteine) (MI level)] and genotoxicity (as measured by the frequency of bone marrow micronucleated erythrocytes) and acute toxicity (as measured by body weight changes) in the rat. The results show that butenediol was not genotoxic to adult or immature rats but was acutely toxic to adult but not immature rats. The results also suggest that n-hexane co-exposure may attenuate the acute toxicity by butenediol in adult rats and that immature rats may be less sensitive than adults to the acute toxicity.
All Politics is now Global Tag Archives: AKP Almost a century has passed since the Ottoman Empire was dismembered and Mustafa Kemal set out to build the modern Turkish state on its ruins. Twenty years ago, no one in the West would have called into question the achievement of the man who eventually, with considerable justice, styled himself Atatürk (“Father of the Turks”). But many now fear that the political and cultural revolution he instigated in the 1920s will be overturned and that Turkey will cease to function as normal nation state, turn on the West, and try to upend the existing order in the eastern Mediterranean, the Balkans, and the Middle East. Continue reading → Turkish President Recep Tayyip Erdoğan has said that Turkey “gave away” Greek islands that “used to be ours” and are “within shouting distance”. “There are still our mosques, our shrines there,” he said, referring to the Ottoman occupation of the islands. (Photo by Carsten Koall/Getty Images) Turkish propagandists also have been twisting facts to try to portray Greece as the aggressor. Although Turkey knows that the islands are legally and historically Greek, Turkish authorities want to occupy and Turkify them, presumably to further the campaign of annihilating the Greeks, as they did in Anatolia from 1914 to 1923 and after. Any attack against Greece should be treated as an attack against the West. There is one issue on which Turkey’s ruling Justice and Development Party (AKP) and its main opposition, the Republican People’s Party (CHP), are in complete agreement: The conviction that the Greek islands are occupied Turkish territory and must be reconquered. So strong is this determination that the leaders of both parties have openlythreatened to invadethe Aegean.Continue reading → While most would agree “it is high time for the West wake up and take Ankara to task”, then what? The megalomaniac running Turkey will only turn to China and Russia, further emboldening them. He has already purchased S-400’s from Russia in Turkey’s biggest hint to the West/NATO that its loyalty lies elsewhere and can be officially transfered quickly. They also don’t care if the equipment isn’t compatible with NATO equipment. It will be compatible overnight (with the axis powers) if they so choose. This is one of those situations where a problem has gone on too long without a correction. The West is going to have to grow a spine or this will result in Turkey’s Hitler reestablishing the Ottoman Empire through bloodshed. It also is likely that it’s too late and Turkey won’t be stopped without going to war against it — which it also will likely foresee and officially align itself with the Sino-Soviet alliance beforehand. (Photo by Elif Sogut/Getty Images) Turkey’s ruling party, and even much of the opposition, seem intent on, if not obsessed with, invading and conquering these Greek islands, on the grounds that they are actually Turkish territory. “The things we have done so far [pale in comparison to the] even greater attempts and attacks [we are planning for] the coming days, inshallah [Allah willing].” – Turkish President Recep Tayyip Erdoğan, February 12, 2018. The head of the state-funded Directorate of Religious Affairs, the Diyanet, has openly described Turkey’s recent military invasion of Afrin as “jihad.” This designation makes sense when one considers that Muslim Turks owe their demographic majority in Asia Minor to centuries of Turkish persecution and discrimination against the Christian, Yazidi and Jewish inhabitants of the area. In an incident that took place less than two weeks after the Greek Defense Ministry announced that Turkey had violated Greek airspace 138 times in a single day, a Turkish coast guard patrol boat on February 13 rammed a Greek coast guard vessel off the shore of Imia, one of many Greek islands over which Turkey claims sovereignty. Continue reading → Empowered to issue decrees with the “power of law” authorized by the state of emergency declared after the July 15 coup attempt, the ruling Justice and Development (AKP) government is frantically busy with changes that will radically affect the structure of the Turkish Armed Forces (TSK) and the civilian-military relations of the country. Judging from the pace and scope of the changes, this can well be characterized as “revolutionary civilian transformation.” The profound changes that have been introduced to the TSK with the decree issued July 31 include that from now on deputy prime ministers and the ministers of justice, interior and foreign affairs will participate in the Supreme Military Council (SMC), which decides on promotions of generals and other important issues in regard to the TSK. The role of civilians in the SMC used to be restricted to the prime minister and minister of defense. Continue reading → WikiLeaks released the emails in response to President Erdogan’s brutal backlash to the failed military coup last week. Erdogan has rounded up political enemies, including high-ranking military personnel and senior judges, while others have been detained in a move many feel is the Turkish President seizing the opportunity to tighten his rule. Parliament Speaker Ismail Kahraman unexpectedly sparked controversy in Turkey when on April 25 he declared that Turkey’s new constitution should forgo mention of “secularism” and instead be a “religious constitution” referencing God. His words reignited Turkey’s always tense “secularism debate,” which has been amplified since 2002 when the Justice and Development Party (AKP) came to power. Kahraman’s remarks led to protests in a number of cities, a call by the main opposition leader for him to resign and allegations by secular pundits that the Speaker had shown the AKP’s “true face,” its “real intentions.” Because Kahraman is a known confidant of President Recep Tayyip Erdogan, many also suspected that his statement was part of a scheme being orchestrated by Turkey’s leader. Continue reading → Following months of monetary and diplomatic appeasement of Erdogan, which culminated with a migration deal according to which Turkey would hold Syrian refugees within its borders instead of allowing them to continue onward to Central Europe, things promptly fell apart. As a reminder, less than a month ago, a high-ranking deputy for Turkey’s ruling AKP party, Burhan Kuzu (also a former adviser to President Erdogan) issued an explicit threat to Europe which was at that time discussing whether or not to grant Turkey visa-free travel within the continent. Specifically, he tweeted that “The European Parliament will discuss the report that will open Europe visa-free for Turkish citizens. If the wrong decision is taken, we will unleash the refugees!.” Many read that as tacit blackmail. Continue reading → The Turkish president has wilfully cut himself off from any free flow of critical information President Recep Tayyip Erdogan last week pushed out Ahmet Davutoglu, the prime minister he himself had handpicked, seemingly to clear his way towards the untrammelled one-man rule he has sought since he moved from the premiership to Turkey’s presidency two years ago. Conventional wisdom says Mr Erdogan is surrounding himself with loyalists. But the man he has just defenestrated is a loyalist. He joins a long list of those jettisoned from the president’s inner circle over the past two years, in a processional purge that is starting to look like standard political procedure. Continue reading → The Russian bear stamps out terror, but Erdogan prepares to stab it in the back (Sputniknews.com, November 24, 2015) The Russian-Turkish conflict is reflected not only in the military, political and economic tension between the two countries but also in the Russian media, which expresses extreme hostility towards Turkey and its president. This is evident, for example, in articles in English published recently on the Russian websites NEO[1] and Pravda.[2] One of these articles cites “a leading military expert” as saying that, in the event of a war between the two countries, “Russia will have to use nuclear weapons immediately, because the existence of the nation will be at stake.” The others focus on Turkish president Recep Tayyip Erdogan, presenting him as an enabler and supporter of the Islamic State (ISIS) and calling him a “madman” and a “murderer.” One even suggests that Turkey was “a prime mover in the [November 13] Paris attack.” On the right, Hayrettin Karaman , the main Fatwa giver in Turkey who is announcing to prep Erdogan as Caliph of the Muslim World Below we will discuss a multitude of biblical references to show how far this one man matches what Scripture refers to as “the man of sin,” but before we do, 2016 will yield much to monitor Turkey’s rise to a Caliphate system which its initiation was sparked when on this Friday, Hayrettin Karaman, Erdogan’s main Fatwa giver issued some very strange declarations. As he wrote for Yeni Safak, the pro-Erdogan main newspaper under the control of Erdogan in Istanbul. In his article regarding the new presidential system which Erdogan wants to establish, Karaman desperately defended Erdogan and declared what we were saying all along they will do; that Erdogan will soon become the Caliph for all Muslims. The following is a presentation of the exciting part in an article Hayrettin Karaman wrote: “During the debate on the presidential system, here is what everyone must do so while taking into account the direction of the world’s national interest and the future of the country and not focus on the party or a particular person. What this [presidential system] looks like is the Islamic caliphate system in terms of its mechanism. In this system the people choose the leader, the Prince, and then all will pledge the Bay’ah [allegiance] and then the chosen president appoints the high government bureaucracy and he cannot interfere in the judiciary where the Committee will audit legislation independent of the president. ” Hayrettin Karaman Although it was fairly obvious since the refugee crisis started, you can now officially add Turkey to the list of nations successfully blackmailing and destroying Europe. Those already on the list include Greece, Libya, and Russia. Of all these, Russia is the most sinister of all. As Kevin Freeman points out, this is economic warfare via migration. Moreover, the aim is of divide and disintegrate Europe to the point where it can be conquered because there is no unified approach to keeping the European continent secure while the nation states are busy bickering at one another. It’s a simple game of divide and conquer. Don’t ever allow for the last few decades of peace to lull you into a false sense of security or think large-scale war can’t happen again. The next world war is already underway and this generation will live to see it. History always repeats itself and Europe seems to be leading the way to the next dark ages. Historically, it has always been home to the world’s bloodiest wars. The resounding win by the Adalet ve Kalkinma Partisi (Justice and Development Party: AKP) in the Nov. 1 parliamentary elections in Turkey relied heavily on the support given to President Recep Tayyip Erdogan and the AKP because of his promise to resolve the strategic challenge to Western Europe caused by the influx of illegal migration from Syria, Iraq, and Afghanistan through Turkey, and from Libyan ports. But evidence is now mounting that the upsurge in the migratory wave was the result of deliberate efforts by Erdogan to facilitate and push the flow of migrants in order to blackmail and punish the EU into supporting him. Continue reading → On Friday we checked in on two of the world’s most important conflicts: 1) that which is unfolding in Turkey where President Recep Tayyip Erdo?an has effectively granted Washington access to Incirlik (you know, for “anti-terror” sorties) in exchange for NATO’s acquiescence to a brutal crackdown on the Kurds as AKP looks to usurp Turkey’s fragile deomcracy, and 2) that which is unfolding in Yemen, where a Saudi-led coalition is fighting to restore the government of Abd Rabbuh Mansur Hadi. In Turkey, Erdogan has successfully undermined the coalition building process necessitating new elections in November when he hopes the escalation of violence across the country will prompt voters to restore AKP’s parliamentary majority allowing the President to rewrite the constitution and consolidate his power. Journalists are being arrested, a terror “tip line” has been set up, a 24-hour Erodgan Presidential TV channel is in the works, and the country has, for all intents and purposes, been plunged into civil war with ISIS acting as a smokescreen for Erdogan’s power grab. Continue reading → It appears as if the Turkish government is using ISIS as a pretext to attack the PKK (Kurdistan Workers’ Party). Turkey just announced that its air base at Incirlik will soon be open to coalition forces, presumably to fight ISIS. But the moment Turkey started bombing, it targeted Kurdish positions in Iraq, in addition to targeting ISIS positions in Syria. In Turkey, millions of indigenous Kurds are continually terrorized and murdered, but ISIS terrorists can freely travel and use official border crossings to go to Syria and return to Turkey; they are even treated at Turkish hospitals. If this is how the states that rule over Kurds treat them, why is there even any question as to whether the Kurds should have their own self-government? Turkey’s government seems to be waging a new war against the Kurds, now struggling to get an internationally recognized political status in Syrian Kurdistan. On July 24, Turkish media sources reported that Turkish jet fighters bombed Kurdish PKK (Kurdistan Workers’ Party) bases in Qandil, in Iraqi Kurdistan, as well as the Islamic State (ISIS) in Syria. Turkey is evidently unsettled by the rapprochement the PKK seems to be establishing with the U.S. and Europe. Possibly alarmed by the PKK’s victories against ISIS, as well as its strengthening international standing, Ankara, in addition to targeting ISIS positions in Syria, has been bombing the PKK positions in the Qandil mountains of Iraqi Kurdistan, where the PKK headquarters are located.
Q: WPF curpos in textbox databinding to label This Morning i came across a slight problem, now as I'm relatively new to WPF i wanted to find out how to do this. On my form i have a a textbox, and i have a label that i want to bind the current curpos of the textbox to in realtime (as the cursor moves the table updates but only for the textbox). Has anyone got any idea of how to do this? Here is some sample code of my textbox in wpf and what i have attempted in c#. wpf: <Window x:Class="WpfApplication1.MainWindow" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" Title="MainWindow" Height="465" Width="681"> <Grid> <ListBox x:Name="listbox1" HorizontalAlignment="Left" Height="405" Margin="10,10,0,0" VerticalAlignment="Top" Width="208" PreviewMouseDown="listbox1_PreviewMouseDown"> <ListBoxItem Content="Gordon"/> <ListBoxItem Content="Nico"/> <ListBox.Resources> <Style TargetType="ListBoxItem" BasedOn="{StaticResource {x:Type ListBoxItem}}"> <Style.Triggers> <DataTrigger Binding="{Binding IsMouseOver,RelativeSource={RelativeSource Self}}" Value="True"> <Setter Property="IsSelected" Value="True" /> </DataTrigger> </Style.Triggers> </Style> </ListBox.Resources> </ListBox> <TextBox x:Name="textbox1" HorizontalAlignment="Left" Height="405" Margin="289,10,0,0" TextWrapping="Wrap" VerticalAlignment="Top" Width="364" SpellCheck.IsEnabled="True" Cursor="IBeam" AcceptsReturn="True" AllowDrop="True" DragEnter="textbox1_DragEnter" Drop="textbox1_Drop" PreviewMouseUp="textbox1_PreviewMouseUp"/> <Label x:Name="label1" Content="" HorizontalAlignment="Left" Margin="241,10,0,0" VerticalAlignment="Top"/> </Grid> C# My events fire in the PreviewMouseDown event private void listbox1_PreviewMouseDown(object sender, MouseButtonEventArgs e) { Point curpos = e.GetPosition(textbox1); if (listbox1.SelectedItems.Count > 0) { ListBoxItem mySelectedItem = listbox1.SelectedItem as ListBoxItem; if (mySelectedItem != null) { label1.Content = curpos.ToString(); DragDrop.DoDragDrop(listbox1, "%" + mySelectedItem.Content.ToString()+"%", DragDropEffects.Copy); } } } Thanks in advance. A: i added the following code: private void textbox1_PreviewMouseMove(object sender, MouseEventArgs e) { Point curpos = e.GetPosition(textbox1); int pos1; pos1 = textbox1.GetCharacterIndexFromPoint(curpos, true); label1.Content = pos1.ToString(); }
Q: ImageView Max Size iOS MonoTouch I am creating an image from a byte array using a UIImageView control. I need to ensure that the max size of the image is 600 x 600. How can I do that? I have tried SizeThatFits() and SizeToFit(), however, that just moves the image around on the screen. I have tried setting the Bound property to new RectangleF(0, 0, 600, 600), however, that also does no good. A: You could check UIImage Size property for exceeding your limits. If so, scale it: const int limit = 600; if ((View.Frame.Size.Width > limit) \|\| (View.Frame.Size.Height > limit)) { // Scale as on link above. } Alternatively, you could set Frame and ContentMode of your UIImageView to desirable values.
We see a lot of PID controllers around here, like this router based espresso machine add-on. Proportional-Integral-Derivative Controllers are a way to make sure the control you intended to get from your devices is actually achieved in practice. They monitor a process and accumulate results over time in order to account for future events. From what we’ve just described you can see why the subject needs to be demystified. Get yourself elbow-deep into [Brett’s] article. He does a great job of discussing each issue, and uses a multitude of easily understandable graphs to show the hurdles each portion of code is meant to overcome. 18 thoughts on “Demystifying PID Control with a look at the new Arduino PID library” I think that Brett has done a great job. Congratulations, it’s a great way to make PID easier. Anyway, I’ve always thought that the simplest (simplest final product) way to make a PID is the traditional one (the only shitty thing is that some more (not much) knowledge is required): ·Calculate the transfer function knowing what’s your desired maximum error, damping, overshoot, etc… in a continuous system (most easy using Laplace Transform (I repeat, don’t scare, it’s quite easy, a (well) trained monkey could do it)) ·Convert your transfer function to a discrete one with the method you prefer (MATLAB, paper and pencil…etc) ·Convert it to a discrete temporal system, with its delays and all. That’s what, in a scenario of a assembler programming for example, will be the simplest solution. Just sums, products, and delays :) I was just preparing to code my first PID, and this easily the best tutorial I’ve seen. The task looks a lot less intimidating now. I especially love how you show the complete code as it is incrementally changed to accommodate each improvement. Will definitely be reading again and studying in detail. This is a real asset to all of us. I would love to see you go further and explore: 1) Feed forward. It seems fairly simple in concept, but an example in your style of writing would make it crystal clear. 2) Reset tiebacks. I haven’t heard this one before and couldn’t find anything on it. What is it? 3) Velocity instead of position. Again, an example would be great. 4) Different PID forms. Maybe touch briefly on this. Are there any that have notable benefits/drawbacks in any given situation? Having that info would be a good start for individuals to further explore them on their own. Integer math is really a topic of its own. Although I’m sure you would do it justice, it’s not specific to PID; and probably adequately explained elsewhere. @Colecoman1982: That is right for my first point, the continuous (‘s’ or Laplace Transform) transfer function. But once you switch it to the discrete (‘z’ transform) transfer function (by using the Residue Theorem on pencil&paper, or any of the functions as ‘c2d’ on MATLAB/Octave on PC), such transfer function “works” (sorry proffessors, but the transform domains involve much math stuff) only on certain discrete values of time, such as iterations of a microcontroller. You end up with a ‘Action[k] = 2*Error[k-1] + Error[k]’ thing for your transfer function (‘k’ would be the current iteration), which obviously a microcontroller can solve efficiently :) The advantage with this method is that you can use a P, PD, PI, II, PID, or just any other controller you want, because YOU define your own transfer function, whether for (Hey, @Chris!) position, velocity, accelleration…and any with a % of error, or zero error (adding an integral factor (‘s’ or ‘z-1′) to the transfer function). I’ve made like 2 systems I can remember using PID, and after having done the calculations, the PID itself didn’t take more than 5 lines in the code… ;) I’m leaving for a 20 days backpack trip in some hours. If I can help you with PID, find my email on the link and let me know. Have fun with volts! @Stunt21: Actually I was trying to make a joke. I was drawing attention to the fact that you called your version of a PID “traditional”. PIDs pre-date digital logic. In fact, according to Wikipedia, they date back to the 1890’s and were mechanical in nature back then and for a long time after. After that, they were, also for a long time, designed using all analog electrical components. In neither case was it necessary to deal with the system in a discreet manner. Wow, that’s great. I looked into a PID controller for my robot and eventually settled on a kalman filter because I heard arduino couldn’t handle PID. But, now there’s a PID library?! That’s awesome because I could never get my kalman filter working. @Chris it’s going to be a while before I get to those things. It took me months to refine the library and writeup, and I haven’t even started thinking about how to best explain those topics. @George as part of my employment agreement I’m not supposed to give pid tuning advice without my company getting paid. This is also why there is no auto-tune for the pid library. If you’re specifically interested in tunings for your process, try the diy pid control google group. there’s a growing community that should be able to give you some tuning help @ed there’s a link to the Arduino library in the first paragraph. that should give you a working c++ library that you can use. Also, if you’re looking for Arduino-specific, there are examples included on that page, and bundled with the library. QUOTE: “They monitor a process and accumulate results over time in order to account for future events.” I think I know what you are trying to say but this is wrong -One huge drawback of a PID control system is that it is a purely reactionary – it doesn’t account for future events, only what has happened. Perhaps you are talking about the derivative term which helps to prevent overshoot but it still doesn’t account for future events. Interesting link but for those new with the concept I will suggest to start with the excellent paper called “PID without a PhD” by Tim Wescot (first answers by google, prefer the Pdf file here: http://www.eetimes.com/ContentEETimes/Documents/Embedded.com/2000/f-wescot.pdf ) also linked on the wikipedia page for PID. Very practical approach, which help me a lot to understand the tuning part for example (for which, the author of your linked page cannot explain much) (And sorry for my poor english which is only my third language :-)
This invention relates to puzzles and more specifically to magic square puzzles wherein components are assembled in an effort to achieve a solution.
WASHINGTON -- Senate leaders Wednesday jointly announced an agreement on a bipartisan proposal to extend the nation’s debt limit and end the partial shutdown of the federal government. Congress is expected to approve the package, which would prevent an economically dangerous U.S. default. Senate Majority Leader Harry Reid (D-Nev.) and Minority Leader Mitch McConnell (R-Ky.) revealed the agreement shortly after the Senate session began. “The eyes of the world have been on Washington all this week,” Reid said. “Today, they will also see Congress reaching a historic bipartisan agreement to reopen the government and avert a default on the nation’s bills. The compromise we reached will provide our economy with the stability it desperately needs.” McConnell said he was “confident” both those goals would be reached Wednesday. FULL COVERAGE: The U.S. government shutdown “It has been a long, challenging few weeks for Congress and for the country,” he said. “It is my hope that today we can put some of those most urgent issues behind us.” [Updated, 10:35 a.m. PDT Oct. 16: The Senate is expected to vote on the budget deal Wednesday evening, sending the measure to the House, which is expected to give the final approval later in the night. House Republican leaders plan a caucus with their members Wednesday afternoon to review the deal and discuss procedures.] A filibuster in the Senate was unlikely as Sen. Ted Cruz (R-Texas) indicated that he would not hold up the package. Cruz was one of the leaders of a group of Republicans who had demanded a halt or delay in President Obama’s healthcare law in exchange for a bill to keep the government running. Passage of the Senate proposal by Congress could send the legislation to President Obama’s desk but it was unclear if that would happen by Thursday’s deadline to extend the nation’s borrowing capacity. Experts have said that as long as passage is expected, the nation would likely not risk a debt default. The proposal makes no substantial changes to the president’s healthcare law, which Republicans had hoped to stop or stall by using the budget crisis as leverage. PHOTOS: 2013’s memorable political moments A minor provision on the healthcare law was included in the legislation, requiring those Americans who purchase insurance on the new healthcare exchanges to verify their income. The agreement would allow the government to continue borrowing to pay its bills through Feb. 7 and would provide funding to reopen the government and keep it running through Jan. 15. Congress would need to draft a new agreement at that time to avoid another budget crisis. Follow Politics Now on Twitter and Facebook Twitter: @LisaMascaroinDC lisa.mascaro@latimes.com Twitter: @MikeMemoli michael.memoli@latimes.com Times staff writer Brian Bennett in the Washington bureau contributed to this report.
RESAOLAB today Building on our strengths RESAOLAB today Building on our strengths Today we are bolstering RESAOLAB’s regional approach by taking into account each country’s national priorities with a renewed focus on clinical diagnostics. To build a strong network we focus on 3 pillars: Annual meetings with all 15 national project teams Support to develop laboratory policies and documents Enhanced capacity to fight antimicrobial resistance Pillar 1: regional meetings to track progress and share ideas To implement our ambitious program, RESAOLAB stakeholders meet twice a year with other participants in the network. They share feedback about ongoing projects, update each other on initiatives to harmonize practices, and report on progress in each country. They also examine opportunities for replication between countries and determine strategies based on identified needs, calling on national and international stakeholders for additional expertise as needed. Pillar 2: policies and strategic plans for the laboratory sector The RESAOLAB Program aims to support countries as they develop national policies to structure the laboratory sector and implement operational plans on quality, training programs, equipment maintenance, etc. The international team pays particular attention to ensuring standardized documents and promoting a participative approach. Pillar 3: Strengthening AMR diagnostic testing capacities Antimicrobial resistance (AMR) is a growing global health concern. What role can RESAOLAB play to address this challenge? Working with regional experts, the program focuses on building laboratory capacity by supporting laboratories as they implement quality antimicrobial susceptibility testing and share national data to contribute to regional surveillance. How our program is run The RESAOLAB association which represents professionals of the medical biology sector in West Africa Laboratory Directors (or their equivalent) in each of the countries of West Africa Technical & financial partners including the Mérieux Foundation Each stakeholder makes a unique contribution to the program. The RESAOLAB association constitutes a pool of professionals with specific know-how and represents the profession in West Africa. The laboratory directors represent the health authorities and national networks, providing key input on the policy dimension. The Mérieux Foundation brings to the table its expertise, experience, international renown and financial management capacity. The Foundation puts forward ideas and provides funding for cross-sector activities.
Understanding nursing scope of practice: a qualitative study. The past decade has seen increased patient acuity and shortened lengths of stays in acute care hospitals resulting in an intensification of the work undertaken by nursing staff in hospitals. This has ultimately led to a reconsideration of how nursing staff manage their work. The aim of this study was to understand how medical and surgical nurses from two Australian hospitals conceive their scope of practice in response to the available grade and skill mix of nurses and availability of unlicensed health care workers and other health care professionals. By exploring these meanings, this study aimed to build an understanding of how nursing work patterns were shifting in the face of changing patient acuity, patient profiles and nursing skill mix. A constructivist methodology, using critical incident technique (CIT) was used to explore nurses' role and scope of practice. Twenty nurses, 16 registered nurses (RNs) and four enrolled nurses (ENs), discussed significant events during which they perceived they were undertaking either patient care activities they should be undertaking, or activities that should have either been delegated or undertaken by a higher level of care provider. Five themes emerged from the data: (1) good nurses work in proximity to patients providing total patient care; (2) safeguarding patients; (3) picking up the slack to ensure patient safety; (4) developing teamwork strategies; and (5) privileging patients without mental illness or cognitive impairment. A pattern woven throughout these themes was the idea of negotiation. RNs were struggling with the notions that direct patient care was sometimes not the best use of their time, and delegation did not equate with laziness. Negotiation has become a fundamental aspect of nursing practice given the variety of nursing care providers currently employed in acute care settings. Negotiation has allowed nurses to redefine appropriate nurse-patient proximity, promote patient safety and find innovative ways of working in nursing teams.
Agents related to a potent activator of the acetylcholine receptor of Electrophorus electricus. The synthesis of a number of compounds related to trans-3,3'-bis[alpha-(trimethylammonium)methyl]azobenzene dibromide (trans-3,3'-BisQ) (1) is described. Among the compounds are: [14C]-trans-3,3'-BisQ (1) diiodide, cis-3,3'-BisQ (2) dibromide, the trans-2,2' (7) and 4,4' (11) isomers of BisQ, 2,2', (12), 3,3' (13) and 4,4' (14) isomers of bis-benzyldimethylammonium analogues, and related compounds in which the azo bridge between the two aromatic rings is replaced by diketo and amide bridges. Of them all trans-3,3'-BisQ (1) was the most active cholinergic compound in the electroplax system of Electrophorus electricus; the pure cis isomer (2) was without activity. Intermediate activities were found for some of the other compounds and others were inhibitors. The relationship of the structure of these agents to a proposed conformation and topography of the binding site of the acetylcholine receptor (AChR) is discussed.
The present invention relates to apparatus for monitoring and/or controlling plasma processes. Plasma processes are used on an industrial scale in many technical fields. For example, by means of plasmas it is possible to deposit, atomize or sputter materials, e.g. in sputtering processes, to etch materials, e.g. in ionic etching and plasma etching, and to apply coatings, e.g. in plasma chemical-vapor deposition. A further special application is plasma polymerization. A considerable problem arising when performing plasma processes is their monitoring and control. It is known to use optical emission spectroscopy for monitoring such plasma processes. The parameter monitored is the light emission of atoms or molecules in the plasma which are stimulated to produce light. It is generally not possible to obtain quantitative results in optical emission spectroscopy.
James Chamberlain Crawford James Chamberlain Crawford (1880–1950) was an American entomologist. Biography Life Crawford was born August 24, 1880 in West Point, Nebraska, to Judge James Chamberlain Crawford and Catherine Moore. He attended the University of Nebraska and graduated in 1904. He headed the biology department while there. He died in December 20, 1950, the same year that he retired. Career In 1904, Crawford joined the Bureau of Entomology as a research specialists, in the United States Department of Agriculture. He worked there from 1904 to 1919, after which he worked in a private business for four years, then joined the North Carolina Department of Agriculture. He left the North Carolina Department in 1930, and returned to the Bureau of Entomology and stayed there until his retirement. In 1907, Crawford became an Assistant Curator in the Division of Insects, in the United States National Museum, and became an Associate Curator in 1911. He continued in this position until 1917, and specialized in the taxonomy of Hymenoptera. From 1921 until 1930, he studied the Mexican bean beetle, in Black Mountain, North Carolina. He then returned to the Bureau of Entomology until his retirement. References Category:1880 births Category:1950 deaths Category:American entomologists Category:Hymenopterists Category:University of Nebraska alumni Category:United States Department of Agriculture people
My wife and I ordered your Cardio C and have a concern about possible interactions with prescriptions, vitamins and herbs. My wife is diabetic II and was told it was dangerous to take over 300mg of vitamin C a day because it could possibly cause a heart attack, is this true? Any person who says that taking more than 300 mg will "cause a heart attack" in diabetics is lying. For some people, I say, taking less than 10,000 mg daily will lead to a heart attack. Anyway, the way to think about this is that the nutrients in Cardio-C are all required in some amount for life, with the possible exception of proline - which the body makes for itself. But it may be that as we age, we make less proline, leading to a great risk of heart disease. Vitamin C and lysine are required for life and have no known toxic dose, and people who are taking scores of heart medications have gotten well following LInus Pauling's advice since we began promoting his theory around 1994. Finally, if your wife has Type II diabetes, it can and should be reversed, and this should make Pauling's therapy more effective (since glucose and vitamin C may compete for entry into cells. Glucose wins, and crowds out vitamin C, so high blood glucose levels are not good for this reason.) Here is an article that explains the issue and his entire web site is devoted to naturally curing Type II http://healingmatters.com/deception.htm which he says science knows is caused by processed food containing trans fatty acids. Rereading I notice that you take a stomach acid blocker!? I recommend Jonathan Wright's book WHY STOMACH ACID IS GOOD FOR YOU and it turns out that for vitamin C to be absorbed through the stomach lining (ascorbic acid) there has to be stomach acid, so this is yet another way these acid blockers are harmful. I have found that a product NOGERD (from LetsTalkHealth) can reduce and/or eliminate GERD if taken daily. And looking at your list of supplements. Where is the multi vitamin/multi mineral? Vitamin C?Vitamin E? Vitamin A? B-complex!? Please read Linus Pauling's book HOW TO LIVE LONGER AND FEEL BETTER. You might adopt his regimen (as I did in 1986) ) with a few additions (e.g. Magnesium) and try to wean yourself off as many of those drugs as possible!
Q: Apache Spark reads for S3: can't pickle thread.lock objects So I want my Spark App to read some text from Amazon's S3. I Wrote the following simple script: import boto3 s3_client = boto3.client('s3') text_keys = ["key1.txt", "key2.txt"] data = sc.parallelize(text_keys).flatMap(lambda key: s3_client.get_object(Bucket="my_bucket", Key=key)['Body'].read().decode('utf-8')) When I do data.collect I get the following error: TypeError: can't pickle thread.lock objects and I don't seem to find any help online. Have perhaps someone managed to solve the above? A: Your s3_client isn't serialisable. Instead of flatMap use mapPartitions, and initialise s3_client inside the lambda body to avoid overhead. That will: init s3_client on each worker reduce initialisation overhead
Inches network to left, boosts self Credit: AP In taking on Fox favorite Newt Gingrich, Megyn Kelly has staked out new ground for the hard-right network — and propelled her own career in the process. The popular news host’s dramatic on-air confrontation with the former House speaker — a Trump surrogate — went viral and positioned Kelly as an independent voice on Fox and a hero among women. It comes as Kelly, who has famously tangled with Trump himself, is reportedly demanding a new contract that would pay her more than $20 million per year amid speculation she could bolt Fox for another network. The article you requested has been archived All coverage within bostonherald.com from the last 14 days remains free of charge. Articles do not always include original photos, charts or graphics.
Q: Rails jquery native vs rails gem I'm using jquery more and more. But, one thing confuses me. What benefit do you get from using a rails gem that implements a jquery module, over just installing the pieces without the gem? For instance bootstrap-editable-rails for x-editable. Or twitter-bootstrap-rails for Bootstrap. Thanks! A: I don't need to download them manually and they work seamlessly with asset pipeline right away. Since it's just a gem, I can use Bundler to take care of updating, checking for new version, resolving dependencies. They usually provide some sort of integration with Rails. Take a look at the twitter-bootstrap-rails gem. It provides generators for layouts, scaffolds, helpers for working with breadcrumb etc.
Q: Is it possible to select data with a function call using EF Code First and an Oracle Database? I'm using EF Code First on an Oracle Database. Given a table like this public class Entity { public int Id { get; set; } } is it possible to construct a where clause that contains a call to a function? e.g MyDatabase database = new MyDatabase(); var results = database.Entity.Where(c => c.Id < 1000 && "Schema.Package.Function(" + c.Id + ")); A: You can use SqlQuery method var results = database.Entity .SqlQuery("select c.* from Entity c where c.Id < 1000 and Schema.Package.Function(c.Id)");
Base of Operations First Appearance Web Serial Contents Black Kaze is described as an "ordinary looking" Japanese woman with her hair in a ponytail in prison sweats[3]. Her fingers constantly twitched, as if searching for a weapon they expected to find[3]. She was very measured in her movements during combat[4]. It was theorized that the Endbringer attack on Kyushu broke her psychologically. When she was captured and put on trial she remained cognizant and controlled,[3] and she defaults to cold non-emotion in all situations, with no ability to socialize.[5] When in an altered mental state - whether natural (tired, stressed) or power-induced - she risks entering a homicidal frenzy.[5] In none of her appearances has Black Kaze spoken. Black Kaze is capable of teleporting by using her weapon's movement.[6] The greater the arc of her swing, the greater distance she can cover with a maximum range of about 50 feet. She is capable of striking an approximately 40 foot radius with ten feet of leeway from her start and end point. While teleporting, innumerable versions of herself occupy space in the area between her departure and arrival point[7], moving for a fraction of a second (not long enough to be seen[4]) which lets her cut people with her ever present katana.[1] Black Kaze has an enhanced physique and is highly skilled in fighting with in depth awareness of her surroundings brought on from years of practice and untreated PTSD[5]. In actual combat she is able to moderate the swings she makes with her weapon, for example multiple small swings allow for multiple short range teleports. She is also able to strike the ground a hundred times, kicking up clouds of dust, moving chaotically within the created effect, executing available targets with one final swing of her blade, or focus[8] to absolutely shred a single target with a thousand small cuts by teleporting past them.[7] Her experience left her with a superb connection to her Agent, though this has heavily damaged her ability to interact with others[8]. Following Leviathan's attack on Kyushu, Black Kaze went around killing anyone she saw. She purportedly killed twenty-thousand people,[9] killing survivors, killing rescuers, boarding the ships that approached too close to the ruined area and killing the crews, and rendering a widespread area devoid of life. She was considered an urban legend.[3] Living on her own, scavenging, and possibly as a result of health problems that went untreated with her isolation, she started to slip. She may or may not have fainted during combat[8]. She was captured and sentenced to the Birdcage[3], where she became a cell block leader.[10] Black Kaze attended a meeting of cell block leaders in the Birdcage, but did not speak.[10] She was one of the twelve cell block leaders to engage in dialogue with the various factions at the Cauldron forum. She was given the okay for release from the Birdcage to fight against Zion,[3] she stayed close to Masamune during these events.[11] In the final stages she directly engaged Zion alongside Acidbath[4] before the various parahumans began coordinating. ↑Power: Katana Flash - When she would attack, she may instead travel up to 40’, attacking everyone between her and her destination (with 10’ leeway to either side). Works with bonus attacks from Finesse. - Playtest Capes ↑ 7.07.1Black Kaze can teleport. While teleporting, innumerable versions of herself occupy space in the area between herself and the target point (with some leeway to either side), moving for a fraction of a second (not long enough to be seen). She teleports past you, you get shredded by a thousand cuts. - Private Email by Wildbow, archived on Spacebattles ↑ 8.08.18.2Black Kaze teleported by using her weapon - any movement of the weapon could teleport her. Bigger swing, more distance covered. Swing multiple times, teleport multiple times. Strike the ground a hundred times, raise up clouds of dust, move unpredictably, cover the distance between herself and her target, execute multiple targets in one final teleport. At the end of the day, though, she was human, and living on one's own, scavenging, possibly getting sick, or having tooth problems, or missing nutrients, she started to slip. Maximum connection to passenger, minimum quality of care for her own body. Might well have passed out or fainted in the midst of a confrontation. - Comment by Wildbow on Reddit ↑There’s something to be said for someone who gets a body count of 20,000 with a sword, and something to be said for leader of a Birdcage cell block. Odd that that something is ‘she is to be pitied’. - Playtest Capes
U.S. to push for 'reciprocal tax' on trade partners: Trump WASHINGTON (Reuters) - U.S. President Donald Trump said on Monday he would push for a "reciprocal tax" against countries, including U.S. allies, that levy tariffs on American products, but officials did not provide details on how such a tax would be structured or what goods it would apply to. (Reuters Politics) More
/** * oscP5bundle by andreas schlegel * an osc broadcast server. * example shows how to create and send osc bundles. * oscP5 website at http://www.sojamo.de/oscP5 / import oscP5.; import netP5.; OscP5 oscP5; NetAddress myRemoteLocation; void setup() { size(400,400); frameRate(25); / start oscP5, listening for incoming messages at port 12000 / oscP5 = new OscP5(this,12000); / myRemoteLocation is a NetAddress. a NetAddress takes 2 parameters, * an ip address and a port number. myRemoteLocation is used as parameter in * oscP5.send() when sending osc packets to another computer, device, * application. usage see below. for testing purposes the listening port * and the port of the remote location address are the same, hence you will * send messages back to this sketch. / myRemoteLocation = new NetAddress("127.0.0.1",12000); } void draw() { background(0); } void mousePressed() { / create an osc bundle / OscBundle myBundle = new OscBundle(); / createa new osc message object / OscMessage myMessage = new OscMessage("/test"); myMessage.add("abc"); / add an osc message to the osc bundle / myBundle.add(myMessage); / reset and clear the myMessage object for refill. / myMessage.clear(); / refill the osc message object again / myMessage.setAddrPattern("/test2"); myMessage.add("defg"); myBundle.add(myMessage); myBundle.setTimetag(myBundle.now() + 10000); / send the osc bundle, containing 2 osc messages, to a remote location. / oscP5.send(myBundle, myRemoteLocation); } / incoming osc message are forwarded to the oscEvent method. / void oscEvent(OscMessage theOscMessage) { / print the address pattern and the typetag of the received OscMessage */ print("### received an osc message."); print(" addrpattern: "+theOscMessage.addrPattern()); print(" typetag: "+theOscMessage.typetag()); println(" timetag: "+theOscMessage.timetag()); }
Richard Brandt of Chicago, Illinois, writes: Marilyn: If we had never fought in any wars, what would the U.S. population be now? Marilyn responds: I’ve answered this question before, but because readers send it frequently, I think the reply is worth repeating: You may be surprised to hear that our population would be roughly the same if we had never fought in any wars. The great majority of wartime casualties have been male, and demographers say that population growth is generally determined by the number and child-bearing capacity (called fecundity, pronounced feh-KUHN-dih-tee) of the females. Fecundity is affected by hardship factors such as disease and a lack of food and water, but having fewer men—who remain fertile throughout their entire lives—doesn’t make a significant dent in population growth.
Advocacy in pediatric neurosurgery: results from a 2017 survey of the American Society of Pediatric Neurosurgeons. Pediatric neurosurgeons are unswerving advocates for public health-related issues in children, with most providers participating in local, regional, national, or international efforts. Collective advocacy efforts by organized pediatric neurosurgeons have not been undertaken to date. A 10-item survey was administered to members of the American Society of Pediatric Neurosurgeons (ASPN) in order to evaluate attitudes and opinions regarding the development of a formal advocacy effort by the organization. Seventy-nine of 178 registered members of the ASPN (44.38%) participated in the survey. Participants were 82.61% male, with age, stage of career, and practice type varied. Although there was unequivocal support for participation in organized advocacy, respondents were divided on methods and topics for advocacy. In this survey, the ASPN membership prioritized public health and clinical issues over economic issues that affected children. Most respondents favored the drafting of position statements on key issues and partnerships with larger organizations to pursue an advocacy agenda. The survey provides data regarding pediatric neurosurgeons' attitudes that may assist with the design of a successful advocacy program.
Trypanosoma cruzi: modulation of HSP70 mRNA stability by untranslated regions during heat shock. Gene regulation in trypanosomatids occurs mainly by post-transcriptional mechanisms modulating mRNA stability and translation. We have investigated heat shock protein (HSP) 70 gene regulation in Trypanosoma cruzi, the causal agent of Chagas' disease. The HSP70 mRNA's half-life increases after heat shock, and the stabilization is dependent on protein synthesis. In a cell-free RNA decay assay, a U-rich region in the 3' untranslated region (UTR) is a target for degradation, which is reduced when in the presence of protein extracts from heat shocked cells. In a transfected reporter gene assay, both the 5'- and 3'-UTRs confer temperature-dependent regulation. Both UTRs must be present to increase mRNA stability at 37 degrees C, indicating that the 5'- and 3'-UTRs act cooperatively to stabilize HSP70 mRNA during heat shock. We conclude that HSP70 5'- and 3'-UTRs regulate mRNA stability during heat shock in T. cruzi.
/* message.c / int msg __ARGS((char_u s)); int msg_attr __ARGS((char_u s, int attr)); char_u msg_strtrunc __ARGS((char_u s)); int emsg __ARGS((char_u s)); int emsg2 __ARGS((char_u s, char_u a1)); int emsgn __ARGS((char_u s, long n)); char_u msg_trunc_attr __ARGS((char_u s, int force, int attr)); char_u msg_may_trunc __ARGS((int force, char_u s)); void ex_messages __ARGS((void)); void wait_return __ARGS((int redraw)); void msg_start __ARGS((void)); void msg_starthere __ARGS((void)); void msg_putchar __ARGS((int c)); void msg_putchar_attr __ARGS((int c, int attr)); void msg_outnum __ARGS((long n)); void msg_home_replace __ARGS((char_u fname)); void msg_home_replace_hl __ARGS((char_u fname)); int msg_outtrans __ARGS((char_u str)); int msg_outtrans_attr __ARGS((char_u str, int attr)); int msg_outtrans_len __ARGS((char_u str, int len)); int msg_outtrans_len_attr __ARGS((char_u str, int len, int attr)); void msg_make __ARGS((char_u arg)); int msg_outtrans_special __ARGS((char_u str, int from)); char_u str2special __ARGS((char_u *sp, int from)); void str2specialbuf __ARGS((char_u sp, char_u buf, int len)); void msg_prt_line __ARGS((char_u s)); void msg_puts __ARGS((char_u s)); void msg_puts_title __ARGS((char_u s)); void msg_puts_long __ARGS((char_u longstr)); void msg_puts_long_attr __ARGS((char_u longstr, int attr)); void msg_puts_long_len_attr __ARGS((char_u longstr, int len, int attr)); void msg_puts_attr __ARGS((char_u s, int attr)); void msg_moremsg __ARGS((int full)); void repeat_message __ARGS((void)); void msg_clr_eos __ARGS((void)); void msg_clr_cmdline __ARGS((void)); int msg_end __ARGS((void)); void msg_check __ARGS((void)); void give_warning __ARGS((char_u message, int hl)); void msg_advance __ARGS((int col)); int do_dialog __ARGS((int type, char_u title, char_u message, char_u buttons, int dfltbutton)); void display_confirm_msg __ARGS((void)); int vim_dialog_yesno __ARGS((int type, char_u title, char_u message, int dflt)); int vim_dialog_yesnocancel __ARGS((int type, char_u title, char_u message, int dflt)); int vim_dialog_yesnoallcancel __ARGS((int type, char_u title, char_u message, int dflt)); char_u do_browse __ARGS((int saving, char_u title, char_u dflt, char_u ext, char_u initdir, char_u filter, BUF *buf));

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