Rainbow Riots' plans to establish an LGBT community center in Uganda, the first of its kind in East Africa, have recently been publicly condemned by the country's famously homophobic Minister of State for Ethics & Integrity, Simon Lokodo.
The organization remains defiant against the remarks, made in an interview with The Guardian newspaper. Loko deemed the center "illegal" in a story which also featured an interview with Rainbow Riots founding director, Petter Wallenberg.
In The Guardian's article, Neela Ghoshal, of Human Rights Watch, was quoted stating that the Center is now more crucial than ever for the quality of life for LGBT people in Uganda.
Crowdfunding for the project continues despite this threat to the center. The activists within the organization Rainbow Riots, plan to establish a safe space for LGBT people in Uganda. The center is to be opened in a secret location in Kampala, and welcomes the country's LGBT people as a refuge for advice on safety, health and HIV issues.
Even though the threat is judged to be real, Rainbow Riots are intending to move forward with the center, which will host workshops and creative projects; arts and music being central to the activities allowing visitors to express themselves in ways they are now allowed to do anywhere else.
Rainbow Riots believe that art and music are a powerful means of decreasing homophobia and transphobia in the regions where LGBT people are condemned as non-African. Rainbow Riots has been part of the Ugandan LGBT movement since 2015. They have organized secret pride celebrations after the police stopped Pride Uganda 2017 and Wallenberg has recorded the internationally acclaimed music album "Rainbow Riots", featuring LGBT Ugandan artists, to give this most vulnerable group a voice in a country where they are considered to be illegal.


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Check out Fast Company's 100 most creative, not richest, not smartest, not powerful – creative people.
Really. It's probably not who you think they are, JJ Abrams is number 14, go check it out.


Here is our 18th edition of our to-do list that runs from Tuesday to Monday. How did we do last week?
Maybe sew a bit on the second ABC quilt so it gets off the design wall – nope!
We not only started sewing this jigsaw quilt, we found the border material we are going to use. It was hard to start sewing until we knew which color direction we want to focus on. We went with a white polka-dotted fabric. We love dots!
This was silly – I should have never put this on the to-do list. Sue wants it off the design wall. Pieces of the fabric float to the floor, often to be placed in a new (improved?!) spot. I see no reason to sew this quickly. We have one in our Etsy shop – we don't need to rush on another. I guess it could be leaders/enders though . . .
We found fabric for Sue's sister (sometimes called Sissy or Janice) housewarming gifts. She requested a new topper for her table and runner for her breakfast bar. She wants to pull out gray and taupe in her granite and wall colors, and gave us a paint chip to use for matching colors. The topper needs to be 19″ x 19″ and the runner 11″ x 48″. We are leaning toward our new favorite HSTs like we used in the Airplane quilt layout choices. More on this project soon!
Update the sewing room layout – new sewing table coming – yippee!
Our Linky Parties can be found by clicking the link for more quilting fun. Check out what our friends are up to. Like/follow us on our Facebook page and share your GK blocks or whatever you're working on. We would love to see it!
You accomplished a good bit. Love the #7 Grandma's Kitchen block. A new sewing table sounds very exciting.
I am liking what I see of your confetti quilt, fun and bright.
Next story T&J Quilt – Eagle, Deer, Wolf, Bear – Oh My!


For doctors Steve Gilchrist and Louise Draper, finding a bank to finance their dream home was hard. Then they called BOQ Specialist.
Dr Steve Gilchrist, a sports-loving Scot, fell in love with Australia—and Aussie Rules football—on a WA work placement during his medical school training at Edinburgh University. Back in Scotland, at Dundee Hospital, he fell in love with fellow emergency department intern Dr Louise Draper. So when he decided to move Down Under, his fiancée came with him.
A year ago, the pair married in the UK and "spent a lot of money on the wedding and a huge honeymoon", Dr Draper recalls. That, along with the costs of relocation and renting, "ate away most of our deposit". Nevertheless, the newlyweds were keen to buy a home of their own large enough to raise a family in.
But to purchase a three-bedroom house in a suburb close to the city, she admits, "you're pushing over the million-dollar mark". And with savings amounting to less than 10 per cent of that, the couple were finding it difficult to secure the loan they needed.
"We'd been to a few mainstream banks but they weren't that flexible, and wanted us to have a certain amount for the deposit," recalls Dr Draper.
So they turned to BOQ Specialist.
"Many friends have used BOQ Specialist and recommended them," Dr Draper explains. "Krista, our BOQ Specialist consultant, was great; she managed to sort everything for us really quickly. She came to our house and helped us get the loan sorted. Initially, she just gave us confirmation they'd help us—and then by coincidence, we saw 'the house' the same night, so then we had to move quite quickly on it.
"We'd never bought a house before so we knew nothing about the process. Krista guided us every step of the way. We had to send her lots of paperwork in the weeks afterwards, which was more complicated than usual because we had quite a few income sources. But Krista made it really easy for us.
With a 30-year loan, repayments "haven't been a strain", adds Dr Gilchrist. "We were putting away more every month, saving for the deposit, than we're paying in mortgage costs now. Along with the mortgage, we have what's called a 'top-up loan'. After we've paid off a certain amount we can drop it to a lower repayment rate.
In the market for a home loan? Click on the link to find out more about our tailored financial solutions for home loans. Ready to take the next step? Contact us to find out how we can tailor a finance solution for you, or call us on 1300 131 141.
Kicking goals: For doctors Steve Gilchrist and Louise Draper, finding a bank to finance their dream home was hard. Then they called BOQ Specialist.


I worry about my fate when I can't recall what movies I have and haven't seen over the past year. When I remember movies from a few years ago and think, oh, that was just last spring… but maybe not. When did I take over QFD, when was that last trip? What happens to those memories? Are they gone, or just irretrievable, hopefully temporarily? When I'm old and growing backwards, will those names and faces recall themselves? My world goes so fast that days and weeks blend into a blur, yet when I look outside myself, everybody is thinking so slowly, painstakingly picking their way through the machinations of today's 'benevolent' society. Life moves on, and as fast as I can consume it, I am still left behind, straggling, hearing the faint, faraway call of passionate roses picking up their roots and stalking away in disgust. I wish I could walk with them.
I look at my desires for movement, freedom, travel and I wonder if they relate to basic human needs of safety in movement and the desire to look for better foraging. Humanity can be so simple, and yet so complex. Is it amazing how we humans are built upon flesh and bone and genetics. How we have these physical needs that bubble up within us. I think many people feel humans are governed by our conscious thought. I can't agree. My engineering mentor was always encouraging me to step back from the problem in order to find a better understanding of what I was trying to achieve and potentially find a simpler more efficient solution. I try to do the same with my thoughts, to step back and observe the roiling mass, watching for patterns and directions. I don't see purely conscious thoughts, logically ordered as much as the engineer in me would like. I see a stream of consciousness that is buffeted and directed and hijacked by human needs and desires. What do you find attractive, what do you fear, how do you relate to a challenge, what soothes pain, what brings tears of joy to your eyes, what drives the passion in life? All those questions require the conscious to answer and to sort, yet all the answers are derived from subconscious, neurological, human needs. Attraction can be so physical – smell, sight, feel, taste and sound. Senses all tied into the core of the brain, senses sometime interpreted by the conscious brain. Security and safety are another almost physical feeling. It is very difficult to overcome those instincts and be with somebody who doesn't smell right, look right, or worse that could or does threaten your security and safety. Or in some cases, threaten our freedom – movement being yet another biologically hardwired desire. I wonder just how close that animal kingdom is, the kingdom that doesn't store information in books or PDAs, but that genetically knows what to do. Why flap my wings? Because I'm supposed to. My little fuzzy bird head says this feels right.
I say, that little bird sometimes has got it good. This vacation thing let me have some of that instinctual life back, so I'm not complaining! I may not be walking with the roses, but I'm mostly okay with that... right now.


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Search https://www.georgesoros.com/
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Remarks delivered at the World Economic Forum
Davos, Switzerland, January 25, 2012
I have just published a book which tries to explain and, to the extent possible, predict the outcome of the euro crisis. It follows the same pattern as my other books: it contains an updated version of my conceptual approach, the application of that approach to a particular situation and some kind of real time experiment to test the validity of my argument.
The book is not complete because the crisis is still ongoing. Indeed, what I am saying today is a part of the real time experiment. I won't repeat or summarize what's in the book. You'll have to read it for yourselves. All I can do is to bring you up to date.
The measures introduced by the European Central Bank in December, including the LTRO, have relieved the liquidity problems of European banks but they did not cure the financing disadvantage from which the highly indebted member states suffer. Since the high risk premiums on Italian and Spanish bonds endanger the capital adequacy of the banks which hold those bonds, half a solution is not enough. It leaves the weaker members of the eurozone relegated to the status of third world countries that became highly indebted in a foreign currency. Instead of the IMF, Germany is acting as the task master imposing tough fiscal discipline. This will generate both economic and political tensions that could destroy the European Union.
I have proposed a plan that would allow Italy and Spain to refinance their debt by issuing treasury bills at around 1%. I named it after Tommaso Padoa-Schioppa, in memory of my friend who as central banker helped to stabilize Italy's finances in the 1990's. The plan is rather complicated, but it is legally and technically sound. It allows the ECB in partnership with the EFSF and the ESM to do what the ECB couldn't do on its own: act as lender of last resort. I describe it in detail in my new book.
The authorities rejected this plan in favor of the LTRO which provides unlimited amounts of liquidity to the banking system for up to three years. That allows Italian and Spanish banks to buy the bonds of their own country and engage in a very profitable arbitrage at practically no risk because if the country defaulted the banks would become insolvent anyhow.
The difference between the two schemes is that mine would provide an instant reduction in interest costs to governments while the one actually adopted has kept the countries and their banks hovering on the edge of a precipice. I am not sure whether the authorities have deliberately prolonged the crisis atmosphere in order to maintain the pressure on these countries or if they have been driven to their course of action by divergent views which they could not reconcile in any other way. Which interpretation is correct is not inconsequential because the Padoa-Schioppa plan is still available and could be implemented at any time as long as the available funds of the EFSF are not otherwise committed.
Either way, it is Germany that dictates European policy because at times of crisis the creditors are in the driver's seat. The trouble is that the austerity that Germany wants to impose will push Europe into a deflationary debt spiral. Reducing the budget deficit will put both wages and profits under downward pressure, the economy will contract and tax revenues will fall. So the debt burden, which is a ratio of the accumulated debt to the GDP, will actually rise, requiring further budget cuts, and setting in motion a vicious circle.
To be sure, I am not accusing Germany of acting in bad faith. Germans genuinely believe in the policies they are advocating. Germany is the most successful economy in Europe. Why should not the rest of Europe be like Germany? But that is impossible. In a closed system like the euro-clearing system, creditors must always be balanced by debtors.
The fact that an unattainable target is being imposed creates a very dangerous political dynamic. Instead of bringing the member countries closer together it will drive them to mutual recriminations. There is a real danger that the euro will undermine the political cohesion of the European Union.
Interestingly, the evolution of the European Union is following a course that resembles a boom-bust sequence or financial bubble. That is no accident. Both processes are reflexive and are largely driven by mistakes and misconceptions.
In the boom phase the European Union was what British psychologist David Tuckett calls a "fantastic object" – an unreal but attractive object of desire. To my mind, it was the embodiment of an open society –an association of nations founded on the principles of democracy, human rights, and the rule of law in which no nation or nationality dominated. Its creation was a feat of piecemeal social engineering. It was led by a group of far-sighted statesmen who understood that the fantastic object was not within their reach. They set limited objectives and firm timelines and then mobilized the political will for a small step forward, knowing full well that when they accomplished it, its inadequacy would become apparent and require a further step. That is how the coal and steel community was gradually transformed into the European Union, step by step.
During the boom period Germany was the main driving force. When the Soviet empire started to fall apart, Germany's leaders realized that reunification was possible only in the context of a more united Europe. They needed the political support of the other countries and they were willing to make considerable sacrifices to obtain it. When it came to bargaining they were willing to contribute a little more and take a little less than the others, thereby facilitating agreement. At that time, German statesmen used to assert that Germany had no independent foreign policy, only a European policy.
The boom period culminated with the Maastricht Treaty and the introduction of the euro. It was followed by a period of stagnation which turned into a process of disintegration after the crash of 2008.
The architects of the euro knew that it was an incomplete currency when they designed it. The Maastricht Treaty established a monetary union without a political union. The euro boasted a common central bank but it lacked a common treasury. The architects had good reason to believe, however, that when the time came, further steps would be taken towards a political union. Unfortunately, the euro also had some other defects that the architects ignored and that remain poorly understood even today. These defects set in motion a process of disintegration that makes a political union more difficult to achieve today than it was when the euro was introduced.
The euro was built on an outdated theory of financial markets which assumed that only the public sector produces imbalances because market excesses are corrected by the invisible hand. In addition, it was believed that the safeguards against public sector imbalances were adequate. Therefore, government bonds were treated as riskless assets that banks could hold without allocating any capital reserves against them.
When the euro was introduced, the ECB accepted all government bonds at its discount window on equal terms. This gave banks an incentive to gorge themselves on the bonds of the weaker countries in order to earn a few extra basis points on the higher yielding bonds. That caused interest rates to converge and that, in turn, caused economic performance to diverge. Germany, struggling with the burdens of reunification, undertook structural reforms and became more competitive. Other countries, benefiting from lower interest rates, enjoyed a housing boom that made them less competitive. So the introduction of the euro caused the divergence in competitiveness which became one of the main components of the euro crisis. It also left the banks loaded with the government bonds of less competitive countries which is another component.
The tipping point was reached when a newly elected Greek government revealed that the previous government had cheated and the deficit was much bigger than had been announced. The Greek crisis revealed two defects in the Maastricht Treaty which could prove fatal: first, that when member countries become heavily indebted they become like third world countries that have borrowed too much in a foreign currency. Second, that there are no provisions for correcting errors in the euro's design. There is neither an enforcement mechanism nor an exit mechanism and member countries cannot resort to printing money.
Unfortunately the European authorities had little understanding of how financial markets really work and did everything wrong. Financial markets far from combining all the available knowledge, as economic theory claims, are ruled by emotions and they abhor uncertainty. What was needed was a comprehensive solution and ample financial resources to implement it. But Germany did not want to become the deep pocket for bad debtors. Consequently Europe always did too little too late and the Greek crisis snowballed. The bonds of other heavily indebted countries, such as Italy and Spain, were hit by contagion and the European banks suffered losses that remained unrecognized on their balance sheets.
Germany aggravated the situation by imposing draconian conditions and insisting that Greece should pay penalty rates on its rescue package. The Greek economy collapsed, capital fled, and Greece kept failing to meet the conditions. Eventually Greece became patently insolvent. Germany then further destabilized the situation by insisting on private sector participation. This pushed the risk premiums on Italian and Spanish bonds through the roof and endangered the solvency of the banking system. The authorities then ordered the European banking system to be recapitalized. This was the coup-de-grace. It created a powerful incentive for the banks to reduce their balance sheets by calling in loans and getting rid of risky government bonds, rather than selling shares at a discount.
That is where we are today. The credit crunch started to affect the real economy in the last quarter of 2011. The ECB responded by reducing interest rates, buying government bonds in the open market and aggressively supplying liquidity to the banking system. This relieved the credit crunch but left Italian and Spanish bonds dangerously exposed – although the last few days brought some relief.
What lies ahead? Economic deterioration and a process of political and social disintegration will mutually reinforce each other. Up to the introduction of the euro, the European leadership was in the forefront of further integration; now they are clinging to the status quo. Treaties and laws that were meant to be stepping stones have turned into immovable rocks. This drives all those who find the status quo unsustainable or intolerable into an anti-European stance. What is happening in Hungary today is a precursor of what is in store.
This outlook is truly dismal. But there must be some way to avoid it – after all, history is not predetermined. I do see an alternative. It would recapture the European Union as the "fantastic object" which used to be so alluring when it was only an idea.
The European Union as a reality bears little resemblance to that fantastic object. It is undemocratic to the point where the electorate is disaffected and ungovernable to the point where it cannot deal with the crisis that it has created.
This is unacceptable but it can be changed. All we need to do is to reassert the principles of open society and recognize that the prevailing order is not cast in stone and rules are constantly in need of improvement. In short, we must reform the euro and the European Union according to the principles of open society. That is a program that should appeal to the silent majority that is disaffected and disoriented but at heart still pro-European.
When I look around the world I see people aspiring to an open society. I see it in the Arab spring, in various African countries; I see stirrings in Russia, and as far away as Burma and Malaysia. Why not in Europe?
To be a little more specific, let me give you the outlines of a European solution to the crisis. It involves a delicate two-phase maneuver, similar to the one that got us out of the crash of 2008. When a car is skidding, you first have to turn the steering wheel in the direction of the skid, and only after you have regained control can you correct your direction. In this case, you must first impose strict fiscal discipline on the deficit countries and encourage structural reforms but then you must find some stimulus to get you out of the deflationary spiral – because structural reforms alone will not do it. With individual countries under strict fiscal constraints, the stimulus will have to come from the European Union and it will have to be guaranteed jointly and severally. That will require Eurobonds in one guise or another. It is important, however, to outline the path well in advance. Without a clear game plan Europe will remain mired in a larger vicious circle in which economic decline and political disintegration mutually reinforce each other.
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Born in Budapest in 1930, George Soros is chair of Soros Fund Management LLC. As one of history's most successful financiers, his views on investing and economic issues are widely followed. This is the official site for information about George Soros.
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Super Girl / It is a pictorial design schema customized for the Super Girl propagation, mainly noting each one's personal information and features from this session of Super Girl such like Li Yuchun, Hejie. The outer package is of pink soft fur-skinned quality, with the coverage spotlighted in its brand image, symbolic of cute, lively-hood, young, sunshine. There are still plus of simplicity, liveliness, and generosity.


When choosing a vision center in the Somerville, MA area, individuals will ultimately want to make an appointment with Parrelli Optical. With a number of eminently qualified optometrists to choose from, men and women can quickly procure prescriptions that will surely improve their eyesight. Both glasses and contacts will be available, and patients will ultimately be able to choose frames that are elegant and stylish. In nearly all cases, they will be given an eye exam at the first appointment. Once optometrists have the results, they can put together a treatment plan that should allow patients to see more clearly going forward.
The qualified eye doctors at Parrelli Optical are capable of uncovering a number of unsavory health conditions. By examining the eyes in detail, optometrists will be able to diagnose glaucoma, cataracts, and other abnormalities. In some cases, blood pressure and cholesterol problems will also be evident. If any serious health problems are noted, men and women will be advised to visit a specialist in the appropriate field. Ultimately, optometrists are quite capable of heading off health conditions that would have grown perpetually worse without proper treatment.
Individuals who are outdoors quite a bit might also be considering prescription sunglasses. With the appropriate lenses, people can avoid ultraviolet rays. This should ultimately keep their vision intact for many years. Proper eye protection will also help guard against cataracts later in life.
Optometrists might also want people to wear glasses while they are performing specific activities. Bifocals, for example, might be worn while reading books. Likewise, individuals who are having trouble seeing clearly at night might be advised to wear glasses when driving. By visiting the best vision center in the Somerville, MA area, local residents can count on immaculate eyesight in the years ahead.


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Dr Phene's House of Mystery
Posted on January 25, 2016 January 30, 2018 by James
Although I don't normally collect postcards of old buildings, this one caught my eye in an antique shop late last year – and with a title like 'Dr Phene's House of Mystery, Chelsea', I simply could not resist.
At first glance I (mis)read the caption as 'Dr Phibes', the vengeful protagonist played by Vincent Price in The Abominable Dr Phibes (Fuerst, 1971) but there's a good case to be had for making an equally memorable film about the man who built the House of Mystery.
Dr John Samuel Phene FRIBA, FRGS (1824-1912) – architect, property developer, traveller, collector, scholar and antiquarian – studied at Kings Lynn Grammar School, Durham University and Trinity College Cambridge before being articled to the firm of an architect by the name of Hardwick.
He seems to have inherited some property in Chelsea sometime before 1850, and in the following years he had constructed a number of buildings in what would become Oakley Street, Margaretta Street and Terrace (both named after his wife Margaretta Forysth, whom he married in 1850), Phene Terrace and Upper Cheyne Row. The Phene Arms was built in 1853 and is still a popular pub to this day. Phene had it built to provide a social hub for local tenants and he seems to have been a progressive thinker, planting trees on both sides of Oakley Street 'to purify the air and help prevent epidemics.'
From his house at 32 Oakley Street he supervised the construction of 'The House of Mystery' on the corner of Upper Cheyne Row. Work seems to have begun in the early 1900s, and its curious appearance led locals to call it the 'Gingerbread Castle.' Phene, however, called it 'The Chateau' and a close-up of the lettering above the doorway reveals the words: 'Renaissance du Chateau de Savenay' – rebirth of the castle of Savenay – in honour of the area in France's Loire valley that Phene claimed as his ancestral home.
Despite the murkiness surrounding facts about his ancestry, it is clear that Dr Phene maintained an interest in the traditions of old France, for in 1885 he was one of the founders of the Huguenot Society of London. Despite the wealth of (often) apocryphal stories that circulate regarding this mysterious man, he was a serious scholar who published numerous research papers and gave both his services and artefacts to museums around the country. He was managing director of the Royal Polytechnic Institution before being succeeded by John Henry Pepper (of Pepper's Ghost fame), and when Sir Peter Coats presented the town of Paisley with a Museum and Library in September 1870 it was Dr Phene who gave the inaugural address. Nonetheless there is often a tinge of eccentricity clinging to his publications, such as the pamphlet On Prehistoric Traditions and Customs in Sun and Serpent Worship (1875), an illustration from which is given below:
It's a curious (albeit impressive) piece of work that examines the links between diverse traditions of sun and serpent worship around the world, from the Scottish Hebrides (where Phene spent several years and considerable expense looking for carved stones depicting serpents) to Egypt, America, Mexico, Greece and the west coast of Africa. The insights into ancient history might (or might not be) valuable, but the paper reveals some intriguing details about contemporary events: a footnote on p.4 informs us that 'A curious illustration of fondness for serpents exists at Chelsea at the present time, which has led to alarm in the neighbourhood.'
A full list of his published work would be too long to detail here, but as a Life Member of the British Association for the Advancement of Science he presented papers at a number of their annual meetings, including 'On some Evidences of a Common Migration from the East' (Brighton, 1872) and 'On the District of Mycene and its early Occupants.' (Plymouth, 1877.) The British Library lists five publications:
Reptile Tumuli. A lecture … Reprinted from the 'Paisley and Renfrewshire Gazette.' [16 pages]
 Paisley : J. & J. Cook, 1871
Records of the Past. A lecture. [16 pages]
Paisley : J. & J. Cook, 1873
On the Causes of Art: with an outline of the origin and progress of art from prehistoric to modern times … A discourse … Reprinted from 'The British Architect.' [19 pages]
Manchester ; London ; Glasgow, 1874
Victoria Queen of Albion : an idyll of the world's advance in her life and reign.
London: Blades, East and Blades, 1897. [165 pages]
This was written in verse, with twelve pages of plates, plus an appendix carrying article on Roman London – presumably by Phene – which appeared in several newspapers and magazines in 1896
Exhibits by Dr. Phene in the Ecclesiastical & Educational Exhibition in the Imperial Institute, Kensington, October 7th to 14th 1899. [8 pages]
His long-standing interest in Scottish antiquities confirmed by a 'Photograph of wooden idol from deep peat in Scotland' taken by Phene in 1900 and registered with the Copyright Office. At the same time he also registered his 'Photograph of the Great Stone Ship Temple in Minorca. (Plate 1 of group of ten)' and 'Photograph of remains of pre-Roman and Old Roman London, sculptured masonry now in the Guildhall Museum, to illustrate Mr Roach Smith's discovery of Sculptured Masonry in the foundations of the old Roman wall of London, testifying to a Pre-Roman stone built city of the Trinobantes (Plate 5 of group of five)' – further evidence of his fascination with ancient stones.
Although sometimes referred to as a reclusive character, there seems to be plenty of evidence of social activities, including a photograph of him taken by Sir Benjamin Stone outside the House of Commons on 2 July 1907 in the company of Mark Twain and other gentlemen. His membership of numerous activities actually suggests a gregarious nature, and he was also an active member of the Royal Geographical Society and the Royal Society of Literature; following his death tribute was paid to him by Sir Edward William Brabrook (1839–1930) that offers further proof of his diverse interests:
'I must first mention my dear old friend Dr. John Samuel Phene, who had reached his eighty-ninth year. He had been a member of the British Association since the year 1863 was elected a Fellow of the Society of Antiquaries in 1872, and Joined our Society in 1875. In the year 1892, when Lord Halsbury became President, Dr. Phene and I were added to the list of Vice-Presidents, of which list, as it then stood, I am now the last survivor. His deep interest in the Society was manifested by his contributing not fewer than eight papers to our Transactions, in which he brought great erudition and shrewd observation to bear upon a variety of subjects, viz.: 'Linguistic Synonyms in the Pre-Roman Languages of Britain and of Italy' (vol. xv), 'King Arthur and St. George' (vol. xvii), 'Ethical and Symbolical Literature in Art' (vol. xviii), ' δενδροϕορία or Tree Transporting' (vol. xix), 'Place Names in and around Rome, Latium, Etruria, Britain, etc., with Earthworks and Other Works of Art illustrating: such Names' (vol. xx), 'The Rise, Progress, and Decay of the Art of Painting in Greece' (vol. xxi), and 'The Influence of Chaucer on the Language and Literature of England' (vol. xxii). There was thus, in recent times, hardly a year in which he did not make some communication to our Society: he was regular in attendance at our Councils up to the last year of his life.'
– Report of the Royal Society of Literature, (1912) pp.12-13.
The stories about his reclusiveness may have some truth, for it seems that the doctor began building Cheyne House for his wife, and after her death he lost interest in the project and began to spend more time alone. He rarely left his Oakley Street residence after this, while the House of Mystery and Cheyne House in Upper Cheyne Row – now a storeroom for his collection of stones – were both boarded up and abandoned. The four acre garden behind the house was strewn with large statues and other curios.
For those interested in reading more about Dr Phene, there's an article on him in the July 2013 edition of Fortean Times (which I must confess I have not yet read), and also a nicely-illustrated blog post here.
Posted in All, Books, Egyptology, Gothic.
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St. Maximilian Kolbe was a Polish Franciscan who volunteered to die in place of a stranger in the Nazi concentration camp of Auschwitz in Poland.
Jesus has a magnetic draw, and because of Him, so do you. Father Burns reflects on the Gospel Readings for the Feast of the Epiphany.
Should Pope Francis Change the Catechism on the Death Penalty?
How can you make sense of and respond to the announced changes to the Catechism regarding the death penalty?


Elissa is one of the first students off the bus in the morning wearing her sparkly, light up shoes! She brings such a great attitude and is just a bright spot in everyone's day. She really enjoys painting pots and chocolate chip cookies are her favorite BrightStone product. In her leisure time, she loves going to the Predators and Titans games with her family. She's a joy to have at BrightStone and a great friend to everyone. Congratulations, Elissa!
Reggie is one of our newest students and this is a his first time to be awarded "Class Star!" Reggie tackles each day at BrightStone with lots of energy and enthusiasm. He made lots of new friends right away and has been a great addition. Reggie has enjoyed learning the packaging process with Mr. Randy and also making platters in Ceramics. His favorite restaurant is Taco Bell and he likes watching football. Way to go, Reggie!
Philip is a very special guy who is thought highly of at BrightStone by his peers and staff. He has a gentle way about him and demonstrates all the qualities of a "Class Star." He enjoys our Friday field trips to Chick-Fil-A and working in the Paint area. He loves watching old DVD's of our annual Christmas programs and playing UNO with his friends. He is a great asset to BrightStone and we are blessed to have him here. Way to go, Philip!
Kim had a birthday this week and we were fortunate to have the opportunity to celebrate with her. She loves BrightStone and being around her friends. Kim has such good manners and always introduces herself to anyone new who comes in the building. She enjoys making bowls in Ceramics class and her favorite BrightStone product is fudge. She loves when Judy comes and she can lead "Doggie in the Window." Congratulations, Kim!
Jock is our resident meteorologist. He is fascinated by the weather and keeps us up to date on important things like when Daylight Savings time starts and other red letter dates on the calendar. Jock says that his favorite daily living job is praying and he liked Taco Salad at lunch. He enjoys eating out at Olive Garden and listening to the Oak Ridge Boys version of "Elvira." Congratulations, Jock!
Cathy is known as our "coupon lade," She clips coupons every Sunday and distributes them throughout the week to the staff. She is very thoughtful that way and has a great laugh when she "gets tickled." Her favorite work area is Packaging with Mr. Randy and she is always up for a game of Uno. She enjoys helping out in the kitchen and leading "Church in the Wildwood" during music. Way to go, Cathy!


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text:
My Meeting With Ian Smith
by Laura Seay | Nov 23, 2007 | Opinion
Ian Smith, the former white minority president of Southern Rhodesia, has died. Smith and his supporters unilaterally (and illegally) declared independence from the United Kingdom in 1965 and ran a white minority regime for 14 years, until an insurgency led by Robert Mugabe finally forced him into peace talks at Lancaster House in 1979.
The Lancaster House Agreement led to the creation of independent Zimbabwe, which has been led by Mugabe ever since.
I met Ian Smith in 2001. Jesse Helms introduced us. Of all the people and things in life I never expected to encounter, Ian Smith was right up there, but one day I found myself stuck in a room with Helms, who told me he was about to meet his friend Smith. Helms asked if I knew who Smith was, and I told him that since I study African politics, I did. He proceeded to inform me that Smith was "a prophet," because "exactly what he said was going to happen to that country did happen."
And in teetered Ian Smith. I stood in the shadows, as good interns are supposed to do, and watched the two men greet one another. Smith took a look around and said, "You sure have a lot of pretty girls working for you," and Helms grabbed my arm, pulled me over, and said, "This one knows all about what a prophet you are, because she studies African history," and Smith smiled and stretched out his hand to greet me.
I shook Ian Smith's hand. My upbringing and manners won out over my sense of injustice.
I don't really remember what happened after that, until later that day, when a staff member who'd witnessed the whole exchange said to me, "You've never heard anyone say anything nice about Ian Smith before, have you?" "Well," I replied, "there was that whole 'white minority regime' thing."
"Well, sure, it wasn't one-man, one-vote," responded the staff member, "but he was fighting the Communists!"
Smith was a complicated man. I don't feel right about speaking ill of those who have died, but he was, as his New York Times obituary put it, "committed all the while to an unshakable belief that Africa without whites would not work." He and Helms were friends and allies in part because they shared certain values about race. And, as the Times points out, he clearly saw the events of the past few years in Zimbabwe (in which President Mugabe's expropriation of white-owned farms for his political allies and bad economic policies have caused unbelievable inflation rates and a near-total collapse of the national economy) as a vindication of his views which Helms saw as so prophetic.
What do you say about an unrepentant racist? There's no question that his insistence on white minority rule set up the problems the country is having today. Land should not have been so heavily concentrated in the hands of whites, and if a liberation war hadn't been necessary, Mugabe wouldn't be able to spew vitriolic hatred of whites as a justification for his policies. Mugabe's last eight years of rule has been a disaster, but I would argue, however, that the bulk of the problem is not rule by black Africans, but rather rule by Mugabe. Zimbabwe is a complicated place, and too many people, both black and white, are responsible for messing it up.
What we can be grateful for, however, is that it's no longer socially acceptable in the bulk of the world to be so blatantly racist as Smith and others of his ilk were in their primes. In no sense have we solved the race issue in our society, but you can't stand on the international stage and proclaim that whites are superior to others and get away with it. So may Ian Smith rest in peace, and may we all work to build a better society than the one he left behind.
Laura Seay is a Ph.D. candidate at the University of Texas studying social services in the Democratic Republic of Congo. Her college internships included the U.S. State Department. She writes a blog titled Texas in Africa.
Laura Seay
Laura Seay is an Assistant Professor of Government at Colby College. She studies African politics, conflict and development, with a focus on central Africa.
texasinafrica.blogspot.com/
Tags: Laura Seay, Politics, Violence, War
The Fragile State of Democracy by Mitch Randall January 6, 2022
S. Sudan Baptists Minister Amid Gov't Instability, Hunger by Zach Dawes Jr July 8, 2021
U.S. Wage Inequality Continues to Increase by Zach Dawes Jr January 4, 2022


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Factory78 Presents Red Carpet moments at the Beffta Awards 2011.
Factory78tv was live on the red carpet for the just concluded 2011 annual Beffta awards ceremony held at The LightHouse centre Camberwell London. The glamorous affair was attended by some of the UK's most celebrated Afro-Caribbean personalities in the entertainment ( music, film, fashion and art) industry. Watch Factory78tv's highlights of the red carpet coverage right here.
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text:
Maryland Football Recruiting Update: Terps Score Commitment From 2016 WR
By Dustin Hawkins January 24, 2015
Maryland is still putting the finishing touches on their 2015 recruiting class, but that isn't stopping Randy Edsall from casting an eye to the future.
Maryland scored a commitment from in-state WR/ATH Darryl 'D.J.' Turner on Saturday, becoming the third player from his recruiting class to commit to the Terrapins. Turner attends Maryland HS powerhouse DeMatha Catholic, and his close relationships with other Maryland targets will serve as a huge boost to the 2016 class. From SB Nation's Testudo Times:
Turner is a part of a loaded DeMatha rising senior class that includes four-star wide receiver Tino Ellis, four-star offensive guard Terrance Davis, four-star offensive tackle JP Urquidez and Harrison. Maryland is very much interested in all of them (as well as close friends Dwayne Haskins and Trevon Diggs), and adding another player from that group should only help the Terps' chances with the rest of them.
At 5'10 and 175 lbs, Turner isn't the biggest WR out there, but his speed and surprising strength make him a high-potential target. It'll be very interesting to see how this adds to Maryland's existing momentum.
Back to the Maryland Terrapins Newsfeed
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text:
THE BLUE MARBLE REPORT
Atmospheric CO2 level for February, 2022 high 421.24
Doug's Column
Article & Report Links
FUTURCIDE
The social, environmental and economic components of civilization form the three pillars of sustainable development. At present the economy ignores the necessity of the other two. That must change. You cannot consume your way out of growing scarcity.
When TV Was Actually Informative about Reality: Now "Reality TV" has little to do with "reality." Science was big news in the 50s and 60s, attracting film giants like Frank Capra (yes, that Academy Award winning Frank Capra) to produce four films for Bell Science Films featuring educator and science host Frank Baxter ("Dr. Research"). Not only were these films informative but also prescient to today's climate crisis.
"Man may be unwittingly changing the world's climate through the waste products of his civilization," warned Dr. Research. "Due to our release through factories and automobiles every year of more than 6 billion tons of carbon dioxide, which helps air absorb heat from the sun, our atmosphere seems to be getting warmer."
Every year there have been sterner warnings as the science became ever more clear.
Pope Francis explored Climate affects on The World's Poor: In 2015, U.N. Secretary General Ban Ki-Moon brought all of his U.N. program leaders to the Vatican to meet Pope Francis. These two global institutions are showing their muscle on a topic that they both believe threaten their greatest interest, the welfare of life on planet Earth; and, a sustainable and prosperous future. Pope Francis expressed Papal concern that degradation was already impacting the poor. On June 18th, 2015, Pope Francis delivered a Papal encyclical teaching the impacts of climate change upon the world's poor. This is thought to be a major milestone, placing the Vatican at the forefront of a new coalition between the church and science. Pope Francis holds a Master's degree in Chemistry, and is the first Jesuit Pope. The Jesuits emphasize missionary work and education.
ENCYCLICAL LETTER
OF THE HOLY FATHER
ON CARE FOR OUR COMMON HOME
The Blue Marble Report goes To Mt. Si High School:
The Editor of the BMR has been the keynote presenter on Earth Day at Mt. Si High School for eight years. The entire Junior and Senior student body take their regular science period to participate in a discussion of climate change and sustainability. This year the focus was on "Planetary Boundaries." Climate Change is already happening. Global warming and subsequent changes in the climate are taught in science classes around the nation. Students often know more about the science than their parents. The inaction by parents and leaders scares them, and it should. Students wanted to know how they could get involved in getting the message out. Students want older generations to pay attention. Their children will pay the price of adult inaction to prevent permanent and irreparable damage to the planet. The window of opportunity is nearly shut. The photo (left) shows the first of 6 classes held throughout the annual Earth Day event.
Photo credit: Doug Smith


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[W]hile film incentive programs were once universally applauded as great economic development tools and tourism boosters, their merits are now being rigorously debated. At a minimum, film incentive programs should be required to report how many dollars in incentives were provided per each Full-Time Equivalent (FTE) job created by qualified productions. Programs should be reviewed periodically for their effectiveness by legislative oversight or a third party.
The report details recent suspensions or eliminations in Arizona, Arkansas, Idaho, Iowa, Kansas, Maine, New Jersey, and Washington. Additionally, programs are facing additional restrictions or scrutiny in Alaska, Connecticut, Georgia, Hawaii, Michigan, Missouri, New Mexico, Rhode Island, and Wisconsin.
On the other hand, officials have extended, protected, or expanded film incentive programs in California, Minnesota, Nevada, Ohio, Pennsylvania, Utah, Virginia, and Wyoming.
Governors Rick Snyder (R-MI), Susanna Martinez (R-NM), and Lincoln Chafee (I-RI) have been particuarly critical. Advocates of their film incentive programs have included Governors Mark Dayton (DFL-MN), John Kasich (R-OH), Tom Corbett (R-PA), and Bob McDonnell (R-VA).


text:
\section{Introduction}
It is well known that theories with general covariance are
constrained systems \cite{refDirac1,ref
Dirac2,refHRT,refBergman1}. In other words, their equations of
motion in Lagrangian formalism lead to acceleration-free
relations. On the other hand, constructing the Hamiltonian
formulation for such theories needs care in order to consider
the constraints. The {\textit{primary}} constraints emerge in the phase
space whenever the momenta are not independent functions
of velocities. The {\textit{secondary}} constraints come out as the
result of the consistency of primary constraints.

The most difficulty in Hamiltonian treatment of general
covariant theories is that the action depends on the second
derivatives of the metric, as well. In this situation a wellbehaved
Hamiltonian system is not recognized, or at least is
not agreed upon, even when a system is not constrained.
However, for Einstein-Hilbert gravity
\cite{refSundermeyer} or, for instance, Ho\v{r}ava gravity
\cite{refhorava} one may use one may use the Arnowitt-Deser-Misner
variables\cite{refADM} whose advantage is that the Lagrangian does not
contain accelerations when written in terms of these variables.
This may not happen for an arbitrary general covariant
Lagrangian.

 The other possibility is using the so-called Palatini
formalism in which the Christoffel symbols are considered
as independent variable. For Einstein-Hilbert gravity, this
approach does work well. The reason is the relation between
the Christoffel symbols and the derivatives of the
metric results naturally from the equation of motion of
Christoffel symbols. It was shown recently
\cite{ref2} that for a
gravitation theory of the Lovelock-type, the Palatini formalism
is fine. However, for an arbitrary model the equations
of motion give no guaranty about the relations of
Christoffel symbols and derivatives of the metric.
Therefore, one needs to add them to the Lagrangian using
Lagrange multipliers, which should be considered as additional
variables in the Lagrangian formalism.

The three-dimensional gravity has attracted intensive
interest in recent years. One reason is that it is possible
to construct nontrivial renormalizable models in three dimensions.
Among so many attractive features, investigating
the Hamiltonian structure of the models is noticeable.
The topological massive gravity
\cite{refTMG}, which is generally covariant on a closed manifold, is
one of the most important ones. The Hamiltonian structure of TMG
is discussed in some papers\cite{refcgmb}.

Recently Begshoeff, Hohm and Townsend proposed a model\cite{ref0}
for three dimensional massive gravity (the so called new massive
gravity) which preserves parity and possesses general covariance
on an arbitrary manifold. Linearization around the flat metric of
this model leads to Pauli-Fierz action describing massive
graviton. Then Deser\cite{refdeser} showed that this model is
finite and ghost-free. Oda and Nakasone\cite{refodanakasone}
showed afterward that the model is unitary and renormalizable.
Clem\`{e}nt also gave some black hole solutions of the
model\cite{refclement}.
The Lagrangian of new massive gravity (NMG), at one
hand, includes accelerations (i.e. second order derivatives
of the metric), which make it necessary to use Christoffel
symbols (or combinations of them) as auxiliary fields. On
the other hand, the model is not of the Lovelock-type.
These peculiarities make the Hamiltonian treatment and
constraint structure of NMG much more difficult.
Moreover, the existence of quadratic terms with respect
to $R_{\mu\nu}$ makes it difficult to use the Arnowitt-Deser-Misner
variables. However, in spite of complicated calculations,
the Hamiltonian treatment of the theory can be followed
carefully. This is what we have done in this paper.

Our main task in this work is counting the physical
degrees of freedom of this model. Since the Einstein gravity
in three dimensions has zero degrees of freedom, one
expects roughly that the NMG action, which contains two
more derivatives, should have 2 degrees of freedom; in the
same way as TMG with one more derivative than Einstein-
Hilbert action possesses 1 degree of freedom. This result is
in agreement with the number of massive gravitons in the
linearized model. However, from a theoretical point of
view, it is better to check the validity of such rough arguments
by a careful Hamiltonian analysis.

In Section 2 we introduce the model in the Hamiltonian formalism
and find the primary constraints. In Section 3 we follow the
consistency conditions of the constraints and find the secondary
constraints of system. Section 4 is devoted to our conclusions.

In our work we use Greek indices for space-time components and
Latin indices
 for space components.

\section{Lagrangian and Hamiltonian}
The action of NMG is given as:
\begin{eqnarray}\label{12}
 S=\frac{1}{16\pi G}\int {d^3x \sqrt g\left[\ R-2\Lambda+\frac{1}{m^2} (R_{\mu\nu}
R^{\mu\nu}-\frac{3}{8} R^2)\right]\ },
\end{eqnarray}
where $g$ is the metric determinant, $R_{\mu\nu}$ is the Ricci
tensor and $R$ is the Ricci scalar. We assume that 3d
space-time is torsion-free and the Christoffel symbols
$\Gamma^\lambda_{\mu\nu}$ are symmetric with respect to $\mu$ and
$\nu$. This allows us to introduce new variables
$\xi^\lambda_{\mu\nu}$ via
\begin{eqnarray}\label{11}
 \Gamma^{\lambda}_{\mu\nu}=\xi^{\lambda}_{\mu\nu}-\frac{1}{2} (\delta^{\lambda}_{\mu}\xi^{\sigma}_{\nu\sigma}+
 \delta^{\lambda}_{\nu}\xi^{\sigma}_{\mu\sigma}),
\end{eqnarray}
as in reference \cite{ref1}. The Ricci tensor in terms of
$\xi$ variables contains derivatives in the form of total
3-divergence as
\begin{eqnarray}\label{15-6}
  R_{\mu\nu}=\xi^{\lambda}_{\mu\nu,\lambda}-\xi^{\lambda}_{\mu\sigma}\xi^{\sigma}_{\nu\lambda}+\frac{1}{2}
  \xi^{\sigma}_{\mu\sigma}\xi^{\lambda}_{\nu\lambda}.
\end{eqnarray}
This is, in fact the advantage of using $\xi$'s in comparison with
$\Gamma$'s. In this way, $\xi^0_{\mu\nu}$ are the only variables
whose velocities are present in the Lagrangian.
  As is well known,
in 3 dimensions an action containing higher order derivatives can
not be of Lovelock-type. So the Palatini approach can not be used
without imposing explicitly the relation between the metric
$g_{\mu\nu}$ and auxiliary variables $\xi^\lambda_{\mu\nu}$. Using
the Eq. (\ref{11}) and the definition of Christoffel symbols as
\begin{eqnarray}
\Gamma^\lambda_{\mu\nu}=\frac{1}{2}g^{\lambda\rho}
(g_{\mu\rho,\nu}+g_{\nu\rho,\mu}-g_{\mu\nu,\rho}),
\end{eqnarray}
we have
 \begin{eqnarray}\label{13}
 \Psi_{\alpha\lambda\beta}\equiv g_{\lambda\rho}(\xi^{\rho}_{\alpha\beta}-
\frac{1}{2}(\delta^{\rho}_{\alpha}\xi^{\sigma}_{\beta\sigma}+
 \delta^{\rho}_{\beta}\xi^{\sigma}_{\alpha\sigma}))
 -\frac{1}{2}(g_{\lambda\beta,\alpha}+g_{\lambda\alpha,\beta}-
 g_{\alpha\beta,\lambda})=0.
\end{eqnarray}
Expressions $\Psi_{\alpha\lambda\beta}$ should be considered as
external Lagrangian constraints which should be put by hand in the
Lagrangian with Lagrange multipliers. These Lagrange multipliers
then should be taken into account as new variables in addition to
$g_{\mu\nu}$ and $\xi^\lambda_{\mu\nu}$. In this way, the
following action should be considered instead of the original one
(\ref{12}):
\begin{eqnarray}\label{4}
 S&=&\int d^3x\mathcal{L}=\int d^3x \sqrt {g}[R-2\Lambda+\frac{1}{m^2}(R_{\mu\nu}
R^{\mu\nu}-\frac{3}{8} R^2)]\nonumber \\
  &+&\int d^3x A^{\alpha\lambda\beta}\left(\ g_{\lambda\rho}
  (\xi^{\rho}_{\alpha\beta}-
\frac{1}{2}(\delta^{\rho}_{\alpha}\xi^{\sigma}_{\beta\sigma}+
 \delta^{\rho}_{\beta}\xi^{\sigma}_{\alpha\sigma}))
 -\frac{1}{2}(g_{\lambda\beta,\alpha}+g_{\lambda\alpha,\beta}-
 g_{\alpha\beta,\lambda})\right)\ .
\end{eqnarray}
where $A^{\alpha\lambda\beta}$ is Lagrange multiplier.
Let us enumerate different degrees of freedom before considering
the details of the dynamics of the system. We have six degrees of
freedom $g_{\mu\nu}$ and $3\times 6=18$ auxiliary variables
$\xi^\lambda_{\mu\nu}$, taking into account the $\mu
\leftrightarrow\nu$ symmetry in both cases. In other words, by
adding the auxiliary variables,
number of Lagrangian degrees of freedom are multiplied by 4 to
avoid higher order derivatives (greater than 2) in the equations
of motion. We have also introduced 18 more degrees of freedom
$A^{\alpha\lambda\beta}$, since Eq. (\ref{13}) is symmetric with
respect to indices $\alpha$ and $\beta$ and we have
$A^{\alpha\lambda\beta}=A^{\beta\lambda\alpha}$. Putting all these
points together we have a priory $18+18+6=42$ Lagrangian variables which
is equivalent to $84$ phase space variables.\\
Now we proceed to the Hamiltonian formalism. The canonical momenta
conjugate to $g_{\mu\nu}$, $\xi^\lambda_{\mu\nu}$ and
$A^{\alpha\lambda\beta}$ are defined respectively as
\begin{eqnarray}\label{15}
&&\Pi^{\mu\nu}_{\gamma}=\frac{\partial \mathcal{L}}{\partial \dot
   \xi^{\gamma}_{\mu\nu}}=\sqrt{g}\delta^0_{\gamma}(g^{\mu\nu}+
   \frac{2}{m^2}G^{\mu\alpha\nu\beta}R_{\alpha\beta}),
\end{eqnarray}
\begin{eqnarray}\label{15-1}
  \pi^{\mu\nu}=\frac{\partial \mathcal{L}}{\partial \dot
  g_{\mu\nu}}=-\frac{1}{2}(A^{0\mu\nu}+A^{0\nu\mu}-A^{\mu 0 \nu}),
 \end{eqnarray}
 \begin{eqnarray}\label{15-2}
  P_{\alpha\lambda\beta}=\frac{\partial \mathcal{L}}{\partial \dot
  A^{\alpha\lambda\beta}}=0.
\end{eqnarray}
  where $G^{\mu\alpha\nu\beta}$ is the generalized metric defined
  by
  \begin{eqnarray}
  G^{\mu\alpha\nu\beta}=g^{\mu\alpha}g^{\nu\beta}-\frac{3}{8}g^{\mu\nu}g^{\alpha\beta}.
  \end{eqnarray}
  From eq.(\ref{15}), with $\gamma=0$, we have
  \begin{eqnarray}\label{15-3}
  R_{\mu\nu}=\frac{1}{2}m^2\mathcal{G}_{\mu\alpha\nu\beta}(g^{-1/2}\Pi_0^{\alpha\beta}-g^{\alpha\beta}).
  \end{eqnarray}
  where $\mathcal{G}_{\mu\alpha\nu\beta}$ is the inverse  of the
generalized metric $G^{\mu\alpha\nu\beta}$ such that $\mathcal
{G}_{\mu\alpha\nu\beta} G^{\mu\sigma\nu\gamma}=
\delta_\alpha^\sigma \delta_\beta^\gamma$. Hence, using
(\ref{15-6}) we find
  \begin{eqnarray}\label{15-4}
  \dot\xi^0_{\mu\nu}=\frac{1}{2}m^2g^{-1/2}\mathcal{G}_{\mu\alpha\nu\beta}\Pi_0^{\alpha\beta}+4m^2g_{\mu\nu}
  -\xi^i_{\mu\nu,i}+\xi^{\lambda}_{\mu\sigma}\xi^{\sigma}_{\nu\lambda}-\frac{1}{2}
  \xi^{\sigma}_{\mu\sigma}\xi^{\lambda}_{\nu\lambda}.
  \end{eqnarray}
  Using eqs.(\ref{15-3}) and (\ref{15-4}) the canonical Hamiltonian
density can be derived in the usual way as
$H_C=\int{d^2x\mathcal{H}_C}$, where
\begin{eqnarray}\label{24}
   \mathcal{H}_C&=&\pi^{\mu\nu}\dot g_{\mu\nu}+\Pi_\gamma^{\mu\nu}\dot
   \xi^{\gamma}_{\mu\nu}+ P_{\alpha\lambda\beta}\dot
   A^{\alpha\lambda\beta}-\mathcal{L}\nonumber\\ &=&
   \frac{1}{4}m^2 g^{-1/2}\mathcal{G}_{\mu\alpha\nu\beta}
   \Pi_0^{\alpha\beta}\Pi_0^{\mu\nu}+2\sqrt{g}(\Lambda-3m^2)\nonumber\\
    &+&\frac{1}{2}(A^{i\mu\nu}+A^{i\nu\mu}-A^{\mu i
  \nu})g_{\mu\nu,i}-\Pi_0^{\mu\nu}\left[\ \xi^i_{\mu\nu,i}-
  \xi^{\lambda}_{\mu\sigma}\xi^{\sigma}_{\nu\lambda}+\frac{1}{2}
  \xi^{\sigma}_{\mu\sigma}\xi^{\lambda}_{\nu\lambda} \right]\ \nonumber\\
  &-& A^{\alpha\lambda\beta}g_{\lambda\rho}\left (\ \xi^{\rho}_{\alpha\beta}-
\frac{1}{2}(\delta^{\rho}_{\alpha}\xi^{\sigma}_{\beta\sigma}+
 \delta^{\rho}_{\beta}\xi^{\sigma}_{\alpha\sigma})\right )\  .
   \end{eqnarray}
  In deriving the
Canonical Hamiltonian the following primary constraints resulted
from Eqs. (\ref{15}-\ref{15-2}) are imposed:
   \begin{eqnarray}\label{16}
  &&\phi^{\mu\nu}:=\pi^{\mu\nu}+\frac{1}{2}(A^{0\mu\nu}+A^{0\nu\mu}
  -A^{\mu 0 \nu})\approx 0,\nonumber\\
  &&\Phi_i^{\mu\nu}:=\Pi_i^{\mu\nu}\approx 0 ,\\
  &&\Omega_{\mu\lambda\nu}:=P_{\mu\lambda\nu}\approx
  0, \nonumber
\end{eqnarray}
where the symbol "$\approx$" means weak equality, i.e., equality on
the constraint surface. We recall that primary constraints are
identities amongst coordinates and momenta which follow directly
from the definition of Canonical momenta.
 The total Hamiltonian reads
\begin{eqnarray}
 &&H_T=\int d^3x\mathcal{H}_T\nonumber\\
&&\mathcal{H}_T=\mathcal{H}_C+U_{\mu\nu}\phi^{\mu\nu}
+\lambda^i_{\mu\nu}\Phi_i^{\mu\nu}
+V^{\mu\alpha\nu}\Omega_{\mu\alpha\nu},
\end{eqnarray}
where $U_{\mu\nu}$, $\lambda^i_{\mu\nu}$ and $V^{\mu\alpha\nu}$
are Lagrange multipliers (in the context of Hamiltonian
constrained systems) corresponding to the primary constraints
(\ref{16}) respectively.\\
The fundamental Poisson brackets of field variables are
\begin{eqnarray}
  &&\{g_{\mu\nu}(x),\pi^{\alpha\beta}(y)\}=\Delta^{\alpha\beta}_{\mu\nu}\delta^{(3)}(x-y), \nonumber\\
  &&\{\xi^\lambda_{\mu\nu}(x)
  ,\Pi_\gamma^{\alpha\beta}(y)\}=\delta^\lambda_\gamma
  \Delta^{\alpha\beta}_{\mu\nu}\delta^{(3)}(x-y), \\
  &&\{A^{\alpha\lambda\beta}(x),P_{\mu\gamma\nu}(y)\}=\delta^\lambda_\gamma
  \Delta^{\alpha\beta}_{\mu\nu}\delta^{(3)}(x-y),\nonumber
\end{eqnarray}
where
$\Delta^{\alpha\beta}_{\mu\nu}\equiv\frac{1}{2}(\delta_{\mu}^{\alpha}
\delta_{\nu}^{\beta}+\delta_{\nu}^{\alpha}\delta_{\mu}^{\beta})$.
\section{Constraint dynamics and counting physical degrees of freedom\label{sec3}}
The number of primary constraints as well as their corresponding Lagrange
multipliers are as follows:
\begin{center}
 \# $\phi^{\mu\nu}$ corresponding to $U_{\mu\nu}=6$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\ \\
 \# $\Phi_i^{\mu\nu}$ corresponding to $\lambda^i_{\mu\nu} =2 \times
    6=12$\;\;\;\;\;\;\;\ \\
 \# $\Omega_{\mu\lambda\nu}$ corresponding to
    $V^{\mu\lambda\nu} =3 \times 6 =18$ \;\;\;\ \\
 \# total primary constraints $= 36$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\
\end{center}
As in all constrained systems, the primary constraints should be
valid in the course of time. This means that their Poisson
brackets with the total Hamiltonian, which is responsible for the
dynamics of the system, should vanish. This process is the so
called "consistency of the constraints."\\
  It is important to remind the reader that at each step of consistency,
  two main things may happen. If a given constraint has
  non-vanishing Poisson bracket with some primary constraints, the
  corresponding Lagrange multiplier would be determined in terms
  of phase space variables. This is the case when the related
  constraint is second class \footnote {Remember that a set of
  constraints are second class if the matrix of their mutual
  Poisson brackets is non-singular. On the other hand, first
  class constraints have vanishing Poisson brackets with all of
  the constraints (at least on the constraint surface).}. TThe other possibility is that a new constraint
emerges as the consistency of the given constraint
and corresponding Lagrange multiplier is not determined.
These constraints at different levels of consistency are
called second level, third level, and so forth, which altogether
are remembered as secondary constraints. The process
of consistency will continue up to the last level in
which either a Lagrange multiplier is determined (when we
have a chain of second class constraints) or the consistency
is established identically (when the constraints in the corresponding
chain are first class). Now, we follow the consistency
procedure for our problem.

Consistency of $\Phi_i^{\mu\nu}$'s causes the following
 expressions vanish:
\begin{eqnarray}\label{7}
\chi_i^{\mu\nu}\equiv\{\Phi_i^{\mu\nu},H_T\}&=&-\frac{1}{2}
(\partial_i\Pi_0^{\mu\nu}-\frac{1}{2}\Pi_0^{\lambda\mu}
\xi_{\sigma\lambda}^\sigma\delta_i^\nu-\frac{1}{2}(g_{\lambda
i}A^{\mu\lambda\nu}-g_{\lambda\sigma}A^{\sigma\lambda\mu}\delta^\nu
_i)\nonumber\\&+&2\Pi_0^{\lambda\mu}\xi_{\lambda
i}^\nu)+\mu\longleftrightarrow\nu\ .
\end{eqnarray}
Since $\Phi_i^{\mu\nu}$ have vanishing Poisson brackets with all
primary constraints, no term containing Lagrange multipliers has
appeared in Eq. (\ref{7}). Therefore, consistency of 12 primary
constraints $\Phi_i^{\mu\nu}$ give 12 second level constraints
$\chi_i^{\mu\nu}$. consistency of $\chi_i^{\mu\nu}$ will be
investigated afterward.

For $\Omega_{\mu\lambda\nu}$ we have
\begin{eqnarray}\label{5}
\{\Omega_{\mu\lambda\nu},H_T\}&=&g_{\lambda\rho}\left (\
\xi^\rho_{\mu\nu}
-\frac{1}{2}(\xi^\sigma_{\mu\sigma}\delta^\rho_\nu
+\xi^\sigma_{\nu\sigma}\delta^\rho_\mu)\right )\ -\frac{1}{2}
(g_{\lambda\mu,i}
\delta^i_\nu+g_{\lambda\nu,i}\delta^i_\mu-g_{\mu\nu,i}\delta^i_\lambda)\nonumber\\
&-&\frac{1}{2}(U_{\lambda\mu}\delta^0_\nu+U_{\lambda\nu}\delta^0_\mu-U_{\mu\nu}\delta^0_\lambda).
\end{eqnarray}
The last term above includes Lagrange multipliers $U_{\mu \nu}$.
For $\mu=i$, $\nu=j$ and $\lambda=k$ this term vanishes and the
consistency of constraints $\Omega_{ikj}$ lead to the following second
level constraints:
\begin{eqnarray}\label{8}
\Theta_{ikj}=g_{k\rho}\left (\
\xi^\rho_{ij}-\frac{1}{2}(\xi^\sigma_{i\sigma}\delta^\rho_j
+\xi^\sigma_{j\sigma}\delta^\rho_i)\right )\
-\frac{1}{2}(g_{ki,j}+g_{kj,i}-g_{ij,k}).
\end{eqnarray}
The constraints $\Theta_{ikj}$ are in fact the same as
$\Psi_{ikj}$ given in Eq. (\ref{13}). We should investigate the
consistency of $\Theta_{ikj}$'s in the next level of consistency.
Let come back to Eq. (\ref{5}). The Lagrange multipliers
$U_{\alpha\beta}$ have appeared in the last term due to Poisson
brackets $\{\Omega_{\mu\lambda\nu}, \phi^{\alpha\beta}\}$ with one
of indices $\mu$ or $\lambda$ or $\nu$ considered as zero. This is
a ($12 \times 6$) rectangular matrix of rank 6. So it is possible
to divide $\Omega_{\mu\lambda\nu}$'s with at least one zero index
into two 6-member sets, as follows:
 \begin{eqnarray}\label{s1}
  \Omega^{(1)}=\left\{ \begin{array}{l} B_1\equiv \Omega_{001}\\ B_2\equiv
 \Omega_{002}\\ B_{11}\equiv \frac{1}{2}\Omega_{011}+\Omega_{101} \\ B_{22}\equiv
 \frac{1}{2}\Omega_{022}+\Omega_{202}\\ B_{12}\equiv
 \frac{1}{2}(\Omega_{012}+\Omega_{021})+\Omega_{102}\\ B'_{12}=\Omega_{012}-\Omega_{021}
 \end{array} \right. \hspace{1cm}
 \Omega^{(2)}=\left\{ \begin{array}{l} C_0\equiv \Omega_{000}\\ C_1\equiv
 \Omega_{010}\\ C_2\equiv \Omega_{020} \\ C_{11}\equiv \Omega_{011}-\frac{1}{2}\Omega_{101}\\
 C_{22}\equiv \Omega_{022}-\frac{1}{2}\Omega_{202}\\ C_{12}\equiv
 \frac{1}{2}(\Omega_{021}-\Omega_{012}-2\Omega_{102}) \end{array} \right.
 \end{eqnarray}
The constraints of the set $\Omega^{(1)}$ commute (i.e. has
vanishing Poisson brackets) with $\phi_{\alpha\beta}$'s and the
other set, $\Omega^{(2)}$ constitute a second class system with
$\phi^{\alpha\beta}$'s, so that the $6 \times 6$ matrix
$\{\Omega^{(2)}, \phi \}$ is nonsingular. We can redefine the
Lagrange multipliers $V_{\mu\lambda\nu}$ corresponding to the
division of the constraints $\Omega^{\mu\lambda\nu}$ into the
sets $\Omega^{ikj}$, $\Omega^{(1)}$ and $\Omega^{(2)}$, such that
 \begin{equation} \sum V_{\mu\lambda\nu}\Omega^{\mu\lambda\nu} = \sum
 V_{ikj}\Omega^{ikj} + \sum V_{(1)}\Omega^{(1)} + \sum
 V_{(2)}\Omega^{(2)}. \label{s20} \end{equation}
This gives
 \begin{eqnarray}\label{s2}
V_{(1)}=\left\{ \begin{array}{l} V^1_{(1)}\equiv V^{001}\\
V^2_{(1)}\equiv V^{002}\\ V^{11}_{(1)}\equiv
\frac{2}{5}(2V^{101}+V^{011}) \\ V^{22}_{(1)}\equiv
\frac{2}{5}(2V^{202}+V^{022})\\ V^{12}_{(1)}\equiv
 V^{012}+V^{021}\\ V'^{12}_{(1)}=V^{012}-\frac{1}{2}V^{102}
 \end{array} \right. \hspace{1cm}
 V_{(2)}=\left\{ \begin{array}{l} V^0_{(2)}\equiv V^{000}\\
V^1_{(2)}\equiv V^{010}\\V^2_{(2)}=V^{020}\\ V^{11}_{(2)}\equiv
\frac{2}{5}(2V^{011}-V^{101}) \\ V^{22}_{(2)}\equiv
\frac{2}{5}(2V^{022}-V^{202})\\ V^{12}_{(2)}\equiv
 V^{012}+V^{021}-V^{102}\end{array}. \right.
 \end{eqnarray}
 If we consider at this point the consistency of
$\phi^{\mu\nu}$'s, we get
\begin{eqnarray}\label{6}
\{\phi^{\mu\nu},H_T\}&=&-\frac{1}{4}m^2g_{\alpha\beta}g^{-1/2}
(\Pi_0^{\alpha\mu}\Pi_0^{\beta\nu}-3\Pi_0^{\alpha\beta}\Pi_0^{\mu\nu})
+\frac{1}{16}m^2g^{-1/2}g^{\mu\nu}\mathcal{G}_{\alpha\sigma\beta\lambda}
\Pi_0^{\alpha\beta}\Pi_0^{\sigma\lambda}\nonumber\\
&-&2m^2\Pi_0^{\mu\nu}-\sqrt{g}g^{\mu\nu}(\Lambda-3m^2)+\frac{1}{2}A^{\alpha\mu\beta}\left
(\ \xi^\nu_{\alpha\beta}
-\frac{1}{2}(\xi^\sigma_{\alpha\sigma}\delta^\nu_\beta+\xi^\sigma_{\beta\sigma}\delta^\nu_\alpha)\right )\
\nonumber\\
&-&\frac{1}{2}(A^{i\mu\nu}-\frac{1}{2}A^{\mu
i\nu})_{,i}+\frac{1}{2}(V^{0\mu\nu}-\frac{1}{2}V^{\mu 0
\nu})+\mu\longleftrightarrow\nu.
\end{eqnarray}
It can be seen easily that the last term in Eq. (\ref{6}) contains
Lagrange multipliers $V_{(2)}$ corresponding to the constraints in the
set $\Omega^{(2)}$ which have nonvanishing Poisson brackets with
$\phi^{\mu\nu}$'s. In this way the set of constraints
\begin{eqnarray}\label{17}
\phi \leftrightarrow \Omega^{(2)}
\end{eqnarray}
constitute a one-level 12-member family of second class
constraints which is constructed of two cross-conjugate chains
that determine 12 Lagrange multipliers $U_{\alpha\beta}$ and
$V_{(2)}$. In this description, we have used the language of ref.
\cite{refLoranshirzad} in classifying the families of constraints.
We just remind here that a family of constraints are determined as
a set of constraints which are resulted as the consistency of a
limited subset of primary constraints and make a close algebra of
Poisson brackets among themselves, and with the canonical Hamiltonian.
  Consistency of the set $\Omega^{(1)}$ gives 6 other constraints of
the next level as follows:
 \begin{equation} \Psi^{(1)}=\left\{ \begin{array}{l} D_{11}\equiv \frac{1}{2}
 \Psi_{011}+\Psi_{101}\\ D_{22}\equiv \frac{1}{2}
 \Psi_{022}+\Psi_{202}\\ D_{12}\equiv
 \frac{1}{2}(\Psi_{012}+\Psi_{021})+\Psi_{102}
 \end{array} \right. \hspace{1cm}\Psi^{(2)}=\left\{ \begin{array}{l}
  D_j\equiv  \Psi_{0j0}~~~~~j=1,2
 \\ D'_{12}=\Psi_{012}-\Psi_{021}
 \end{array} \right. \label{s11} \end{equation}
where $\Psi_{\alpha\lambda\beta}$ are Lagrangian constraints given in
Eq. (\ref{13}). We should continue to investigate consistency of
the above constraints in the next level. This will make the
meaning of the classification given in Eq. (\ref{s11}) more clear.
As can be seen, second level constraints $\Theta_{ikj}$,
$\Psi^{(1)}$, and $\Psi^{(2)}$ are 12 out of 18 Lagrangian
constraints (\ref{13}). The remaining 6 Lagrangian constraints
correspond to expressions (\ref{13}) including Lagrange
multipliers $U_{\mu\nu}$. In fact the equations of motion of
$g_{\mu\nu}$ gives $\dot{g}_{\mu\nu}=U_{\mu\nu}$. Putting this
into Eq. (\ref{5}) gives the corresponding Lagrangian constraints
(\ref{13}) for the cases which include time derivatives of the
metric.

Now we proceed to the next level by considering the consistency of
$\chi_i^{\mu\nu}$'s, $\Theta_{ikj}$'s and the sets $\Psi^{(1)}$
and $\Psi^{(2)}$. For $\Theta_{ikj}$'s we find
\begin{eqnarray}\label{10}
\{\Theta_{ikj},H_T\}=&&\frac{m^2}{4}[g_{k0}(\mathcal{G}_{\alpha
i\beta j}+\mathcal{G}_{\alpha j\beta
i})-\frac{1}{2}(g_{ki}(\mathcal{G}_{\alpha j\beta
0}+\mathcal{G}_{\alpha 0\beta j})\nonumber\\
+&&g_{kj}(\mathcal{G}_{\alpha i\beta 0}+\mathcal{G}_{\alpha 0\beta
i}))]\Pi_0^{\alpha\beta}
-g_{k0}(\xi^l_{ij,l}-\xi^\lambda_{i\sigma}\xi^\sigma_{j\lambda}
+\frac{1}{2}\xi^\lambda_{i\lambda}\xi^\sigma_{j\sigma})\nonumber\\
+&&\frac{1}{2}(g_{ki}(\xi^l_{j0,l}-\xi^\lambda_{j\sigma}\xi^\sigma_{0\lambda}
+\frac{1}{2}\xi^\lambda_{j\lambda}\xi^\sigma_{0\sigma})
+g_{kj}(\xi^l_{i0,l}-\xi^\lambda_{i\sigma}\xi^\sigma_{0\lambda}
+\frac{1}{2}\xi^\lambda_{i\lambda}\xi^\sigma_{0\sigma})) \nonumber\\
+&&4m^2(g_{k0}g_{ij}-\frac{1}{2}(g_{ki}g_{0j}+g_{kj}g_{0i}))\nonumber\\
+&&(\xi^\lambda_{ij}-\frac{1}{2}(\xi^\sigma_{j\sigma}\delta^\lambda_i
+\xi^\sigma_{i\sigma}\delta^\lambda_j))U_{k\lambda}-\frac{1}{2}(U_{kj,i}+U_{ki,j}-U_{ij,k})\nonumber\\
+&&g_{kl}\lambda^l_{ij}-\frac{1}{2}(g_{ki}\lambda^l_{jl}+g_{kj}\lambda^l_{il}).
\end{eqnarray}
Since $U_{\mu\nu}$ are determined previously, the Eq. (\ref{10})
should be considered as equations to find $\lambda^l_{mn}$. It is
easy to check that the matrix of coefficients of $\lambda^l_{mn}$'s
, i.e. $\{\Theta_{ikj}, \Phi_l^{mn}\}$, is nonsingular and
these Lagrange multipliers can be determined completely.\\
Consistency of constraints in the set $\Psi^{(2)}$ gives
 \begin{eqnarray}\label{D1}
 \{D_j, H_T\}&=&\frac{1}{8}m^2g^{-1/2}(g_{00}(\mathcal G_{0\mu
 j\nu}+\mathcal G_{j\mu 0\nu})-2g_{0j}\mathcal G_{0\mu 0\nu})
 \Pi_0^{\mu\nu}\nonumber\\&-&\frac{1}{2}\left (\
 g_{00}(\xi^i_{0j,i}-\xi^\lambda_{0\sigma}\xi^\sigma_{j\lambda}+
 \frac{1}{2}\xi^\sigma_{0\sigma}\xi^\lambda_{j\lambda})
 -2g_{0j}(\xi^i_{00,i}-\xi^\lambda_{0\sigma}\xi^\sigma_{0\lambda}
 +\frac{1}{2}\xi^\sigma_{0\sigma}\xi^\lambda_{0\lambda})\right )\
 \nonumber\\&-&\frac{1}{2}(g_{00}\lambda^i_{ji}+g_{0j}\lambda^i_{0i}
 -2g_{0i}\lambda^i_{0j}),~~~~~~~j=1,2
\end{eqnarray}
\begin{eqnarray}\label{D3}
\{D'_{12}, H_T\}&=&\frac{1}{8}m^2g^{-1/2}g_{10}(\mathcal G_{0\mu
2\nu}+\mathcal G_{2\mu 0\nu}) \Pi_0^{\mu\nu}-\frac{1}{2}
g_{10}(\xi^i_{02,i}-\xi^\lambda_{0\sigma}\xi^\sigma_{2\lambda}+
\frac{1}{2}\xi^\sigma_{0\sigma}\xi^\lambda_{2\lambda})\nonumber\\
&-&\frac{1}{2}(g_{10}\lambda^i_{2i}+g_{20}\lambda^i_{1i}-2g_{1i}
\lambda^i_{02})-1\longleftrightarrow
2
\end{eqnarray}
Since Lagrange multipliers $\lambda^i_{jk}$ are already
determined, Eqs. (\ref{D1})-(\ref{D3}) are three equations for
seven unknowns $V^1_{(1)}$, $V^2_{(1)}$, $V'^{12}_{(1)}$, and
$\lambda^i_{j0}$'s. Therefore, we should keep these equations in
mind and wait for finding four other equations which should be
solved together with (\ref{D1}) and (\ref{D3}) to find the above
unknowns. Anyhow, the consistency of $D_1$, $D_2$ and $D'_{12}$ do
not go further. Hence, we have a 6 member family of second class
constraints as
\begin{equation} \begin{array}{lll}\label{fc}
 B_{1}\hspace{1cm}&B_{2}\hspace{1cm}&B'_{12} \\
 \downarrow\hspace{1cm}&\downarrow\hspace{1cm}&\downarrow\\
 D_{1}\hspace{1cm}&D_{2}\hspace{1cm}&D'_{12}
 \end{array} \end{equation}
Consistency of $\chi_i^{\mu\nu}$'s leads the
following expression vanish:
\begin{eqnarray}\label{9}
\{\chi_i^{\mu\nu},H_T\}&=&(\Pi_0^{\lambda\mu}(\xi_{\lambda 0}^\nu
-
\xi^\sigma_{\lambda\sigma}\delta^\nu_0))_{,i}-\frac{1}{2}(g_{\lambda
0} A^{\mu\lambda\nu}-g_{\lambda\sigma}
A^{\sigma\lambda\mu}\delta_0^\nu)_{,i}\nonumber \;\;\;\;\;\;\;\;\;\;\;\;\;\;  \\
&-&\frac{1}{4}m^2g^{-1/2}((\mathcal{G}_{\alpha\lambda\beta i} +
\mathcal{G}_{\alpha
i\beta\lambda})\delta_0^\nu-\frac{1}{2}(\mathcal{G}_{\alpha\lambda\beta
0} + \mathcal{G}_{\alpha
0\beta\lambda})\delta_i^\nu)\Pi_0^{\lambda\mu}\Pi_0^{\alpha\beta}\nonumber\\
&-&4m^2(g_{\lambda i}\delta_0^\nu-\frac{1}{2}g_{\lambda 0}
\delta_i^\nu
)\Pi_0^{\lambda\mu}+(\Pi_0^{\sigma\lambda}\xi^\nu_{\sigma
0}+\Pi_0^{\sigma\nu}\xi^\lambda_{\sigma 0})\xi^\mu_{\lambda i}\nonumber\\
&-&\frac{1}{2}(\Pi_0^{\alpha\beta}\xi^\nu_{\beta
i}\delta^\mu_0+\Pi_0^{\alpha\mu}\xi^\nu_{0i})\xi^\rho_{\alpha\rho}
-\frac{1}{2}(\Pi_0^{\alpha\beta}\xi^\mu_{\alpha
0}
+\Pi_0^{\alpha\mu}\xi^\beta_{\alpha 0})\xi^\rho_{\beta\rho}\delta^\nu_i\nonumber\\
&+&(\xi^j_{\alpha
i,j}-\xi^\rho_{\alpha\sigma}\xi^\sigma_{i\rho}+\frac{1}{2}\xi^\rho_{\alpha\rho}
\xi^\sigma_{i\sigma})\Pi_0^{\alpha\mu}\delta^\nu_0\nonumber\\
&-&\frac{1}{4}(\Pi_0^{\sigma\alpha}\xi^\lambda_{\alpha\lambda}\delta_0^\mu
 +\Pi_0^{\sigma\mu}\xi^\lambda_{0\lambda})\xi^\rho_{\sigma\rho}\delta^\nu_i
 -\frac{1}{2}(\xi^j_{\lambda
 0,j}-\xi^\rho_{\lambda\sigma}\xi^\sigma_{0\rho}+\frac{1}{2}
 \xi^\rho_{\lambda\rho}\xi^\sigma_{0\sigma})\Pi_0^{\lambda\mu}\delta^\nu_i\nonumber\\
 &-&g_{\rho 0}(\xi^\nu_{\lambda i}-\frac{1}{2}\xi_{\lambda\sigma}^\sigma
 \delta^\nu_i)A^{\lambda\rho\mu}+g_{\rho\alpha}(A^{\alpha\rho\lambda}
 \xi^\nu_{\lambda i}\delta_0^\mu+A^{\alpha\rho\mu}\xi^\nu_{0i}\nonumber\\
 &-&\frac{1}{2}(A^{\alpha\rho\lambda}\xi^\sigma_{\lambda\sigma}\delta^\mu_0
 +A^{\alpha\rho\mu}\xi^\sigma_{0\sigma})\delta^\nu_i)
 -\Pi_0^{\sigma\mu}(\lambda^j_{\sigma i}\delta^\nu_j-\frac{1}{2}\lambda^j_{\sigma
 j}\delta^\nu_i)\nonumber\\&+&\frac{1}{2}(A^{\mu\sigma\nu}U_{i\sigma}
 -A^{\rho\sigma\mu}U_{\sigma\rho}\delta^\nu_i)+\frac{1}{2}(g_{\sigma
 i}V^{\mu\sigma\nu}-g_{\sigma\rho}V^{\rho\sigma\mu}\delta^\nu_i)+\mu\leftrightarrow\nu.
 \end{eqnarray}
Let us first consider 6 equations concerning the cases $\mu=j$ and
$\nu=k$ in Eq. (\ref{9}). It can be seen that the $6\times6$
matrix of coefficients of Lagrange multipliers $V^{ikj}$ is
nonsingular. Moreover, the corresponding equations do not include
the yet undetermined Lagrange multipliers $\lambda_{0j}^i$ and
$\lambda_{00}^i$. They include, however, the Lagrange multipliers
$U_{\mu\nu}$, $V_{(2)}$ and $\lambda^i_{lm}$ which are determined
previously. Therefore, the Eq. (\ref{9}) for the cases considered
can be used to determine 6 Lagrange multiplier $V^{ikj}$.
Nonsingularity of the ($6\times 6$) sub-matrix $\{\chi_i^{jk},
\Omega_{lmn}\}$
has an interesting meaning in the terminology of ref.
\cite{refLoranshirzad} on classifying the constraint families. To
this end, the set of constraints
\begin{eqnarray}\label{18}
\Omega_{ikj}\nwarrow\nearrow\Phi_i^{jk}\nonumber
\\\Theta_{ikj}\swarrow\searrow\chi_i^{jk},
\end{eqnarray}
constitute a family of 24-member, 2-level and cross-conjugate
second class system in which the consistency of constraints of the
first row give the constraints of the second row, while the
constraints at the end of any chain have nonvanishing Poisson
brackets with the constraints at the top of the other chain. We
can check that $\{\Omega_{ikj}, \Theta_{mln}\}$ as well as
$\{\Phi_i^{jk}, \chi_l^{mn}\}$ vanish.

Let us come back to Eq. (\ref{9}) and consider the case
($\mu=i,\nu=0$) or ($\mu=0,\nu=i$). We have four equations in this
case again for seven unknowns $V^1_{(1)}$, $V^2_{(1)}$,
$V'^{12}_{(1)}$ and $\lambda^i_{j0}$'s. These equations are in
fact, 4 equations which we were expecting, after Eq. (\ref{D3}).
Hence, we have 7 independent equations for 7 unknowns. In this way
the constraints $\chi_i^{0j}$ and their parents $\Phi_i^{0j}$
constitute an 8-member, 2-level family of second class constraints
shown as
 \begin{eqnarray}\label{19}
 \Phi_i^{0j}\nonumber\\ \downarrow \\ \chi_i^{0j}. \nonumber
 \end{eqnarray}

The only remaining case in Eq.(\ref{9}) is $\mu=\nu=0$. No term
containing $\lambda_{00}^i$ appears in Eq.(\ref{9}). This
corresponds to two constraints $\chi_i^{00}$ for which the term
including Lagrange multipliers $\lambda_i^{00}$ vanishes.
Consistency of $\chi_i^{00}$ lead to third level constraints
$\Sigma_i^{00}$ as
\begin{eqnarray}
\Sigma_i^{00}&=&-2(\Pi_0^{\lambda 0}\xi_{\lambda j}^j
)_{,i}-((g_{\lambda 0} A^{0\lambda 0}-g_{\lambda\sigma}
A^{\sigma\lambda 0}))_{,i}-8m^2g_{\lambda i} \Pi_0^{\lambda
0}+2(\Pi_0^{\sigma\lambda}\xi^0_{\sigma 0}+\Pi_0^{\sigma
0}\xi^\lambda_{\sigma 0})\xi^0_{\lambda
i}\nonumber\\&-&\frac{1}{2}m^2g^{-1/2}(\mathcal{G}_{\alpha\lambda\beta
i} + \mathcal{G}_{\alpha i\beta\lambda})\Pi_0^{\lambda
0}\Pi_0^{\alpha\beta}+2(\xi^j_{\alpha
i,j}-\xi^\rho_{\alpha\sigma}\xi^\sigma_{i\rho}+\frac{1}{2}
\xi^\rho_{\alpha\rho}\xi^\sigma_{i\sigma})\Pi_0^{\alpha
0}\nonumber\\
&-&(\Pi_0^{\alpha\beta}\xi^0_{\beta i}+\Pi_0^{\alpha
0}\xi^0_{0i})\xi^\rho_{\alpha\rho}-2(g_{\rho 0}\xi^0_{\lambda
i}A^{\lambda\rho 0}-g_{\rho\alpha}(A^{\alpha\rho\lambda}
 \xi^0_{\lambda i}+A^{\alpha\rho 0}\xi^0_{0i}))\nonumber\\&+&A^{0\lambda
0}U_{i\lambda}
 +g_{\sigma
 i}V^{0\sigma 0}.
\end{eqnarray}
Direct calculation shows that $\{\Sigma^{00}_i,\Phi_j^{00}\}$ is a
nonsingular matrix. Therefore, consistency of $\Sigma^{00}_i$
determines two Lagrange multipliers $\lambda_i^{00}$ and shows
that the constraints $\Sigma_i^{00}$ as well as their parents in
the corresponding chain are second class. In this way we have
derived a 6-member family of second class constraints gathered
in three-level chains as
 \begin{eqnarray}\label{22}
 \begin{array}{c}  \Phi_i^{00} \\ \downarrow \\ \chi_i^{00}\\ \downarrow
  \\ \Sigma_i^{00}
 \end{array}\ \ .\end{eqnarray}

Hence, 12 second class constraints in families (\ref{17})
determine 12 Lagrange multipliers $U_{\alpha\beta}$ and $V_{(2)}$ at
first level of consistency; 38 second class constraints in
families (\ref{18}), (\ref{19}) and (\ref{22}) determine 19
Lagrange multipliers $\lambda_i^{jk}$, $\lambda_i^{0j}$,
$V^{ikj}$, $V_{(1)}^1$, $V_{(1)}^2$ and ${V'}_{(1)}^{12}$ at
second level of consistency; and 6 second class constraints in
family (\ref{22}) determine 2 Lagrange multipliers
$\lambda_i^{00}$ at third level of consistency. We have a total of
S=12+38+6=56 second class constraints which determine 12+19+2=33
Lagrange multipliers. There remain 36-33=3 undetermined Lagrange
multipliers which are $V_{(1)}^{11}$, $V_{(1)}^{22}$, and
$V_{(1)}^{12}$ corresponding to primary constraints $B_{11},
B_{22}$ and $B_{12}$ given in (\ref{s1}).\\
 Let us recall that consistency of primary constraints $B_{11},
 B_{22}$, and $B_{12}$ gave us the second level constraints $D_{11},
 D_{22}$ and $D_{12}$ as in (\ref{s11}). Straightforward
 calculations shows that the Poisson brackets of $D_{11}, D_{22}$,
 and $D_{12}$ with the total Hamiltonian vanishes. Therefore, we
 collect the following constraints:
 \begin{equation}\label{fc1}
 \begin{array}{lll}
 B_{11}\hspace{1cm}&B_{22}\hspace{1cm}&B_{12} \\
 \downarrow\hspace{1cm}&\downarrow\hspace{1cm}&\downarrow\\
 D_{11}\hspace{1cm}&D_{22}\hspace{1cm}&D_{12}
 \end{array}
  \end{equation}
as a 6-member, 2-level and first class family of constraints. So
the number of first class constraints in the form of family
(\ref{fc1}) is $F=6$.

For the number of dynamical variables, using the famous formula
\cite{refHenoux}
\begin{eqnarray}\label{23}
D=N-S-2F,
\end{eqnarray}
where $N$ is the number of initially introduced variables in phase
space, we have $D=84-56-2\times 6=16$. This is in Hamiltonian
formalism. In Lagrangian formalism, we have half of this number as
dynamical variables. By dynamical variables, we mean those
variables which obey differential equations containing
accelerations. Taking a look on the complete action (\ref{4})
shows that the auxiliary variables $A^{\alpha\lambda\beta}$ are
not within these variables. Therefore, Eq.(\ref{23}) says that
after eliminating the redundant variables by using the constraints
and gauge fixing conditions, we have 8 dynamical equations for
$g_{\mu\nu}$'s and $\xi^\lambda_{\mu\nu}$'s. As we mentioned
before, the total number of variables $g_{\mu\nu}$ and
$\xi^\lambda_{\mu\nu}$ is 4 times greater than the number of
principle variable $g_{\mu\nu}$. Therefore, we conclude that the
number of dynamical variables is 8/4=2 out of six $g_{\mu\nu}$.

Notice that throughout our calculations concerning the constraint
structure of the NMG model we have kept the cosmological constant
term up to end. Hence, it is easy to find the constraint
structure of the model without cosmological model just by putting
$\Lambda=0$.\\
It should be noted that although the main structure of the
constraints and the number of degrees of freedom is the same, the
cosmological constant has a serious effect on the form of constrains
[see eq.(\ref{6})] as well as the final Hamiltonian, after
imposing the derived forms of Lagrange multipliers in the total
Hamiltonian (\ref{24}). Therefore, it can be expected that the
dynamics of the remaining physical degrees of freedom in the
reduced phase space is affected deeply by the presence of the
cosmological constant. Specially, particular solutions of the
equations of motion appear when $\Lambda\neq 0$ which are
forbidden in the absence of cosmological constant. However, our
purpose in this paper is not investigating the properties of
particular solutions, which stand beyond studying the constraint
structure of the system, although it could be interesting in turn.
\section{Concluding Remarks}
 In this paper we studied the Hamiltonian structure of new
 massive gravity model. This is a complicated model in 3d gravity
 that contains higher order derivatives as well as higher than
 quadratic terms. We used some form of the Palatini formalism in
 which combinations of Christoffel symbols, i.e., the variables
 $\xi^\lambda_{\mu\nu}$, are used as independent variables while
 their relation with derivatives of the metric is imposed as
 additional conditions in the Lagrangian using the auxiliary
 variables $A^{\alpha\lambda\beta}$.\\
  As is expected, the system is highly constrained with 36 primary
  and 26 secondary constraints, where 56 of them are second class
  and 6 are first class. This classification makes the system suitable to be
  studied more carefully in the context of constrained systems.
  For example, one may be interested in finding the generator of
  gauge transformations in terms of first class constraints and study more carefully the gauge
  symmetries of the system. Moreover, if one decides to fix the
  gauges, one needs to know carefully which gauge fixing conditions
  should be imposed. As is well-known \cite{refLoranshirzad} and \cite{refshirzad},
  for this proposes it is necessary to know the constraint
  structure of the system.\\
   We showed, finally in phase space there remain 16 physical
   variables. This means that there are 8 dynamical Lagrangian variables
   composed of the metric and Christoffel symbols. If one
   eliminates the Christoffel symbols, there remain 2
   dynamical degrees of freedom out of 6 components of the metric.
   This conclusion is in agreement with the result
   that the NMG model constitute 2 gravitons
   under linearization of the equations of motion.\\

 {\bf Acknowledgments: } the authors thank M. Alishahiha for his
useful comments and bringing their attention to NMG model.\\
\textbf{Note added}.-When completing our paper we observed reference
   \cite{refBlagojevic2} in which the total number of 2 degrees of
   freedom is derived in another approach.\vspace{0.5cm}

redpajama_set_name: RedPajamaArXiv


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