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English \ Politics \ Presentation at the Culture and Education Roundtable Ukraine in Washington 2012 Conference December 1, 2012 by Marta Farion
Presentation at the Culture and Education Roundtable Ukraine in Washington 2012 Conference December 1, 2012 by Marta Farion
Culture and education are at the center of shaping Ukraine's national identity and recently have been the targets of conflicts and confrontations in Ukrainian society. These two areas are fundamental to Ukraine's nation-building process as they represent the values, the customs, and the accumulated knowledge reflected through the nation's history.
I have been involved with Ukraine since the beginnings of perestroika – the thaw during the days of Mikhail Gorbachev. I observed the historic role played by the grassroots pro-democracy movement, Rukh early in the independence process, witnessed some of the negotiations, and had the opportunity to "live in the moment" of Ukraine's declaration of independence on August 24, 1991, before the formal dissolution of the Soviet Union, when on December 25, Soviet President Gorbachev handed over power to Russian President Yeltsin, and the red Soviet flag in front of the Kremlin was lowered and replaced with the three-colored flag of the Russian Federation.
In neighboring Ukraine, the intellectuals who led the revolt in Ukraine at that time showed great courage. They did not know how the conflicts in Moscow would be resolved, but they recognized that moment as pivotal in the nation's history and chose to risk a vote for independence.
However, the real heroes were the people of Ukraine. In January 1991, millions formed a human chain through the country to voice their support for independence; on December 1, 82% of eligible voters came to the polls and chose independence by an overwhelming majority of more than 90%. The proposal for the December 1 national referendum to confirm the Parliament's August 24 declaration of independence came from two politically opposing camps, from majority leader Oleksandr Moroz and opposition leader Ihor Yukhnovsky, as they proposed the referendum together.
The people were united as citizens of Ukraine. These events demonstrated that regardless of political, religious, ethnic affiliation, or geographic location, the people of Ukraine identified themselves as citizens of their country, who chose and demanded to be free in their own land. When considering the issue of Ukrainian identity now, the importance of these events and the prevailing sense of nationhood with common rights and aspirations should not be overlooked.
Ukraine's position at the time was progressive and inclusive. Ukraine chose citizenship, and not ethnicity, as the basis upon which to define Ukrainian identity. Although the leaders of the new Ukraine belonged to various political parties, they were united on this critical principle of citizenship, which was included in Ukraine's Constitution with foresight toward unification of the nation. That key phrase in the Constitution states, "All citizens of the former USSR permanently residing within the territory of Ukraine at the moment of declaration of independence of Ukraine (24 August 1991), are citizens of Ukraine". This was the position that formed the basis of Ukraine's independence in 1991 in anticipation of building a democratic society for all of its citizens.
This fact is important to remember in view of the political maneuvering now taking place to destabilize society by promoting ethnic and linguistic divisions and calling into question the idea of citizenship and identity. In turn, good words alone will not sustain the vision of unity and loyalty. Economic security and protection for all citizens under rule of law, a nation governed by the principles of a respected Constitution, these elements will build national pride and identity and will provide legitimacy for the country's government.
Furthermore, to understand more fully the issues of culture and identity, reference needs to be made to events that are embedded in the nation's memory bank. Ukraine in the 20th century was a country that most appropriately has been named "Bloodlands" by historian and author Timothy Snyder and this fact also cannot be overlooked.
Ukraine still bears the scars of the Soviet occupation, of the repressions and the Gulag, and the deep scars of the politically motivated Great Famine of 1933, known as the Holodomor, which translates as massive death by starvation. Millions of Ukrainians died during the two-year Soviet-made famine. As historian and Holodomor scholar James Mace perceptively stated – Ukraine is a post-genocide society – a society that is still struggling with the consequences of these traumas. There is hardly a family in Ukraine that has not been victimized by these events. Therefore, it should not be a surprise that the population tends to be mistrustful of government and cynical about claims of the powerful to work for the people. It is a population still vulnerable to fear, suspicion, and loss of faith. In many ways, the nation wants to embrace reconciliation and forgiveness, but many factors prevent such closure.
Yet despite the traumas of the 20th century, in little more than 20 years, Ukraine has moved well beyond its recent totalitarian past. Six presidential elections and numerous Parliamentary elections have taken place and even though there were serious questions of violations during some of them, the one element that remained constant was that the population of Ukraine always came out to vote. Ukraine's citizens want democracy. And while we would like to see democracy develop at a faster pace, the process of transformation is moving forward, and the process cannot be turned back.
However, while the citizens support the democratic process, there are reasons for the recent pushback to democracy among the power elite. In a country where the current economic elite believe in a political and legal system of "by the few and for the few," complete political control is essential to maintain the status quo. Combine this impulse with old habits, a totalitarian mindset that is hard to break and the evolution to an open and progressive society is being stifled.
I recall an "anecdote" from the days when the Anti-Ballistic Missile Treaty was signed between the United States and the Soviet Union in 1972. During the lengthy and secretive negotiations, President Nixon, Chancellor Willy Brandt, and General Secretary of the Communist Party Leonid Brezhnev met to discuss their various interests. At one point Nixon said, "You think it is easy for me? Every day I look outside the window of the White House and I see people protesting again my policies, they carry signs against me, they shout "Down with Nixon! Down with Nixon! But, I cannot do anything… because that is democracy." Willy Brandt also complained and said, "It is so difficult to be chancellor. Every day outside my office I look out and people carry banners against me and chant 'Down with Brandt!', but there is nothing I can do… because that is democracy." Then Brezhnev said, "Gentlemen, I understand – every day I look out the window of the Kremlin and I see people yelling "Down with Nixon! Down with America! Down with Brandt! and there is nothing I can do."
So indeed old habits are hard to break. There is a struggle taking place between those who still cling to centralized control, and the younger generation that never experienced the closed doors of the Iron Curtain and understands that the future belongs to those with knowledge, innovation, and a fair share at competitiveness.
The current backsliding in democracy and rule of law in Ukraine is of great concern. Furthermore, corruption is so pervasive that it affects every aspect of life and provokes political and economic instability in the entire region.
Recent attacks on culture and education has become pervasive with a focus on disruptions and manipulation for ideological and political purposes that cause social and political unrest. Culture, religion, education, media, and language have been the direct targets.
Examples of this campaign include a focus on the pressure for unification of the Ukrainian Orthodox Church with the Russian Orthodox Church Moscow Patriarchate, the illegally passed Law on Language, the rewriting of history textbooks and central control of education promoted by the Minister of Education, politically motivated harassment of non-conforming media, massive financing of Russian language and cultural activities, and illegal changes to the Constitution and national security breaches that other speakers will address.
During the past two years, educational institutions have become political targets. Financing of culture and education is selective and often based on political loyalties and lack of political submissiveness is punished.
Duplicity and a continuous gap between declaratory statements and implementation have become the norm. Such a policy led to loss of credibility both at home and in the international arena. The Ministry of Education proposed a law based on central control of universities that has become a topic of scorn and ridicule in the international academic community, and yet, in Ukraine, less than a handful of university rectors openly opposed it. Others, who privately express disapproval with the current policies, are haunted openly by the fear of losing their positions and funding. Such a system prevents serious academic work, innovative research, and blocks the country's economic growth and competitive position.
A change in leadership in the Ministry of Education is essential. National education cannot be left to the mercy of conforming to the worldview of one minister or a president. Serious changes need to be made now. This is not an issue that affects only schools, universities and research institutions; this is an economic and security issue as well, one that will affect future generations for years.
This presentation cannot bypass the mention of the grave threat to democracy related to the criminalization of politics, the pattern of selective prosecutions, harassment and imprisonment of political opponents and their families and associates, and control over the media.
Regardless of these dangerous patterns, there is no denying that the past 20 years have seen the formation of a civil society. There are encouraging signs in the engagement of the private community and philanthropy. Many non-governmental organizations and foundations have been established. Certain universities pioneered innovative programs, transparency in admissions and degree completion, and they are demanding necessary reforms. As a positive sign, Ukraine's prime minister established a Committee to Propose a New Law on Higher Education, headed by the Rector of the well-respected Kyiv-Polytechnic Institute with experts in the field from National University of Kyiv Mohyla Academy and other leading academics.
Other positive signs include social media that is creating new conditions. Technology and innovation is breaking down monopolies on information and control over ideologies and censorship. The internet is a tool that civil society can use to engage and protect itself. Surveys by Internet World Statistics indicate that in 2000, there were 200,000 internet users in Ukraine, or .04% of Ukraine's population. By 2010, there were 15,300,000 internet users or 33.7% of the population. The numbers keep growing exponentially and now the number is even greater. Such numbers bode well for the growth of civil society. Ukraine is strong in the field of Information Technology and in the 21st century, the country can play a leading world role in this sector.
Surveys in Ukraine demonstrate that regardless of political sympathies, ethnic background or geographic location, people seek a better life for their children and grandchildren, freedom from the fear of political persecution, fair and equal opportunities and a system of education that will provide competitive employment, and a quality of life enjoyed by their European peers.
Therefore the people of Ukraine understand that there is something wrong when individuals who have direct control over education and culture, including financing, are the same ones who send their own children to study abroad in the West. This is an unacceptable double standard and the people of Ukraine know it.
As I close, I must state that the Government of Ukraine needs to release Yulia Tymoshenko, Yuri Lutsenko and all political prisoners. And if I could nominate a candidate for the position of Minister of Education of Ukraine, it would be a person who has in mind the best interests of his or her own country, not a neighboring country, an individual who cares about young people and their potential, not just the interests of a select few, a person who is proud and not ashamed to be a citizen of Ukraine and is happy and eager to speak the nation's language, Ukrainian. It would be a person who respects the Russian language, and the languages and cultures of all the citizens of Ukraine, including the language and culture of the Tatar people who are also Ukrainian citizens, without denigrating the Ukrainian language, as is being currently done. The new minister will be someone who will not hesitate to collaborate with the best educators in the world, whether they are in the East or in the West, a uniter, not a divider, and someone who respects the dignity of all the citizens of Ukraine. The new minister will be one that will conform Ukraine's educational system to international norms so that Ukraine's students can later enter foreign universities for study, rather than returning to Soviet norms of secondary education that were incompatible with those of Europe and North America. The parents and children of Ukraine deserve no less.
And, the rest of the world deserves no less, as well. It is in the interest of Europe, the United States, the people of Ukraine, and the people of the region to support a stable democracy in Ukraine, to avoid conflict in the region and to avoid a return to repressive authoritarianism with control and power in the hands of an elite, self-chosen few.
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"IN THE BAR OF A TOKYO HOTEL": Tennessee Williams Comes to Alphabet City!
On the night I saw a preview of Tennessee Williams' "In the Bar of a Tokyo Hotel", The 292 Theater seated only sixteen people. There were ten chairs in the "back row", and six plump red cushions making up the "front row"– perfect for sitting lotus style. To say that the Theater's faithful production of the play, running through March 31, is an "intimate experience" is a major understatement. This production is so up-close-and- personal that it even lets you see right into the eyes of all the characters. And, let it be said that these eyes speak volumes! You have the wild, "too far gone" eyes of Mark (Charles Schick), an American artist who is losing his grip on reality at full speed ahead. You have the restless, hungry, and often wickedly manipulative eyes of his sexually frustrated wife Miriam (Regina Bartkoff), who is preoccupied with plotting her escape from her unhinged husband without losing his financial support. And, you also have the eyes of the character known only as "Bar-Man" (Brandon Lim), who watches all the unfolding drama from behind the bar. Limited by his servile status in the overly structured Japanese society of the time, this character is severely restricted in what he can say, even when he's having his crotched grabbed by Miriam or having drinks spilled all over the stage by the tremulous Mark. Like Bar-Man, the audience gets a magnified, almost voyeuristic view of all the highly emotional goings-on.
"In the Bar of a Tokyo Hotel", which premiered in 1969, is one of Williams' lesser-known and lesser-produced works. Today, however, it is looked upon as one of the author's more underappreciated as well as most personal pieces. Fans of the playwright will also soon realize that many of the elements of Williams' more well-known, more popular plays are here. At one point, the major female character offers an oh-so-stylized monologue about her fear of aging and the potential loss of her beauty ("I'm fully aware, of course, that there's no magical trick to defend me indefinitely from the hideous product of calendars, clocks, watches…") which may remind you of the troubled Blanche Dubois of "A Streetcar Named Desire". But vanity is only one of Williams' trademark themes. There's also… desire (including sexual desires, as well as the desire for a higher social status), loneliness, and a good range of human neuroses– cumulating with full-on madness. This being from Tennessee Williams, many audience members will expect a larger than-life, passionate female character, and we have it here with Miriam — played with gusto by Ms. Bartkoff. The actor's portrayal of the desperate housewife is dripping with vinegar… but her Miriam is often so funny that our feelings towards the character become as complex as Miriam herself. We even feel a bit sorry for the woman who's clearly not suited for the confines of traditional marriage– much less a marriage to a husband who started out as a "shy, gifted man" and is now talking to his paintings and embarrassing both himself and his wife in public. As Mark, Charles Schick (who co-directed the play with Bartkoff), establishes an almost otherworldly presence as a tortured soul who has gone, shall we say, way beyond the accepted quirkiness that we often expect from artists. In their less showy roles, Brandon Lim and Wayne Henry are perfectly cast as Bar-Man and Leonard (Mark's friend and art dealer) respectively. Both are given their moments to compete with their tempestuous co-stars– often when the audience least expects it!
To say that the Set Designer (Master Michael Quinn) makes the most of Theater 292's small stage is, once again, making a huge understatement. The highly stylized set is elaborate and colorful, with the stage entirely bathed in red light. In addition, some creative directorial touches really boost "In the Bar of a Tokyo Hotel" as well. In the play's program, actor and Co-Director Regina Bartkoff recalls when she met Tennessee Williams himself when he visited a Lower East Side eatery where she was waitressing. It's good to see that over 30 years later, Williams is visiting New York City again.
"In the Bar of a Tokyo Hotel" is now playing at 292 Theater, 292 East 3rd Street between Aves C and D, New York City. Visit www.292Theater.com for more information.
Previous FRANCE JOLI COMES TO NEW YORK!
Next BLACK BRIEFS: DVD REVIEW

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What Are Ranger Horses, Really?
What Are Ranger Horses, Really? Feb 26, 2020 14:18:14 GMT -5
Post by yosefu on Feb 26, 2020 14:18:14 GMT -5
When you think about it, it is pretty interesting. Their flexibility in tasks and many versatile commands are interesting enough on its own, but there is also this telepathic bond between their owners and themselves.
That being said, is it actually them talking or just the rangers reading too much into it? The quotes of the second Tug put it in the gray area, I think.
There's also the case of replacing the horses. The way they are named the same as the previous horse and have the old horse renamed struck me as pretty weird at first, because it felt like all these horses were in a hive mind or something. Do you think it could be written that way to close up a plot hole or was it intended to be like that from the beginning?
What Are Ranger Horses, Really? Feb 26, 2020 14:42:31 GMT -5 Arkøs, Sebias, and 2 more like this
Post by booklover on Feb 26, 2020 14:42:31 GMT -5
They are certainly more intelligent than normal horses. As for them talking, I think early on it was 'his eyes seemed to say', or things like that (can't think of any exact quotes), but in later books it just had them speaking, maybe just something John Flanagan changes, or maybe because Will (and us readers as well, I suppose) was used to it, and by then they knew each other so well by then, which could explain how Ranger horses know what their riders are thinking, it's just their intelligence. Alternatively, it could be a fantasy element, since even though the later books don't show it as much, RA is a fantasy series (though apart from the horses there's only really the kalkara, wargals, and barrow-wights). I don't think even the Rangers know for sure. But it seems they can't always do it when they want to, as in Oakleaf Bearers, Tug tried to warn Halt that they were on Will's trail, but Halt didn't understand. That could be because Tug wasn't Halt's horse, but the fact they need those trained warnings suggests that there's more to it. They can't just talk whenever they want, and there are limits to what they can say.
As for what the second Tug 'said', either it is really telepathic, or there's a small possibility that at some point, he'd have communicated with Tug/Bellerophon. It isn't too unlikely that at some point they'd have had a chance to communicate, if Will ever visited Bob, given it's not too far away from Redmont. I know that John Flanagan didn't plan for the replacing horses, as it says just before The Wolf that he wrote it in reply to an email from a fan, who said that their working life couldn't be much more than 17 years. I'm not so sure about the 'hive mind' thing, but Ranger horses definitely seem to tease each other (like Rangers do), such as when Tug commented on Blaze (? I think it was) carrying a bag of bones (referring to Gilan, I believe). It could be just to add a bit of humour, or it could be a fantasy element. It's hard to tell, really.
I agree about the most of what you say, but now that you mention it, Tug not being able to warn Halt feels kind of inconsistent because Will rode on a retired ranger horse on "The Wolf" and was able to hear him. Maybe it is because it doesn't have an owner? I have no idea, honestly.
What Are Ranger Horses, Really? Mar 3, 2020 9:15:24 GMT -5 yosefu likes this
Post by Arkøs on Mar 3, 2020 9:15:24 GMT -5
When I first read the title I thought you would be asking breed lol
Great evaluation booklover
What Are Ranger Horses, Really? Mar 5, 2020 12:10:30 GMT -5
Post by Robsan on Mar 5, 2020 12:10:30 GMT -5
Interesting! I've never thought about that before but your answer sounds logic.
What Are Ranger Horses, Really? Mar 5, 2020 14:35:12 GMT -5 yosefu likes this
Post by Deleted on Mar 5, 2020 14:35:12 GMT -5
insert quote here Posted by yosefu
Mmm, maybe each horse and rider has a slightly different way of warning, and since the retired horses can be rode by other peolpe, and every rider is diferent, thus giving (cannot think of horse name) a more general way of warning.
(this is not canon, I am just guessing)
Last Edit: Mar 5, 2020 14:39:00 GMT -5 by Deleted
What Are Ranger Horses, Really? Mar 13, 2020 12:00:09 GMT -5 Robsan and yosefu like this
Post by booklover on Mar 13, 2020 12:00:09 GMT -5
www.wattpad.com/848878466-collection-of-ranger%27s-apprentice-theories-the-not/page/3
I found this, and it includes a theory about the Ranger horses. There are other interesting ones on there as well.
What Are Ranger Horses, Really? Mar 15, 2020 20:50:33 GMT -5
What an interesting topic... To be honest, I was wondering the same thing myself.
What Are Ranger Horses, Really? Mar 19, 2020 21:18:04 GMT -5 yosefu likes this
Post by elkifasi on Mar 19, 2020 21:18:04 GMT -5
What puzzles me more than Halt not being able to understand Tug is the scene where, after they'd found Will and were going down the mountain again, Tug was rumbling and the Abelard started doing it too. Halt remarked something along the lines of 'Great, now you've got my horse doing it too' but both horses were actually trying to warn their riders of impending danger, as they found out.
namelock
New to the site
Post by namelock on Mar 21, 2020 18:35:15 GMT -5
What if the rangers never knew their horses would do that when afaid, and so didn't understand the signal?
"Did you even aim for that?!"
"You know, actually, I believe I did."
What Are Ranger Horses, Really? Mar 23, 2020 9:31:44 GMT -5
Post by Arkøs on Mar 23, 2020 9:31:44 GMT -5
It was most likely that they were distracted by banter and dint interpret the signal correctly
What Are Ranger Horses, Really? Apr 3, 2020 21:37:58 GMT -5
or maybe, they just miss interpreted the signal...
Never the less, they're still great horses, even if they are misunderstood..
Post by booklover on Apr 4, 2020 11:27:53 GMT -5
What I wonder is (this is while watching the (virtual) Grand National) how the Ranger horses would compare to modern horses, specifically racing. It's whether superior training and breeding, plus being specialised, means that the best modern horses will have an edge over Ranger horses, despite Ranger horses being, well, Ranger horses. And Bob's training does seem extremely effective. I'm not certain if exact statistics for Ranger horse's speed, especially as they never seem to go absolutely full out. And I don't know enough about horses, anyway.
Post by namelock on Apr 4, 2020 11:51:20 GMT -5
I thought in the Ruins of gorlan that Bob said as fast as the racehorses, but they could run longer. Maybe im getting things mixed up.
What Are Ranger Horses, Really? Apr 6, 2020 8:57:59 GMT -5
Post by Arkøs on Apr 6, 2020 8:57:59 GMT -5
Yeah, he said that they could run the same speed as a battlehorse but the key was they could go longer.
tbh though I am not sure. Race horses are trained bread for literally one purpose, to race.
So lets say a ranger horse could match a race horse.
As stupid as it sounds, leg length would be the key. And ranger horses were mentioned to be on the smaller side, while race horses are know to be on the larger side.


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Sequart News
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» ON GRANT MORRISON WORKS
The Anatomy of Zur-en-Arrh: Understanding Grant Morrison's Batman
Curing the Postmodern Blues: Reading Grant Morrison and Chris Weston's The Filth in the 21st Century
Grant Morrison: The Early Years
Our Sentence is Up: Seeing Grant Morrison's The Invisibles
» ON WARREN ELLIS WORKS
Warren Ellis: The Captured Ghosts Interviews
Voyage in Noise: Warren Ellis and the Demise of Western Civilization
Shot in the Face: A Savage Journey to the Heart of Transmetropolitan
Keeping the World Strange: A Planetary Guide
» ON SCI-FI FRANCHISES
Somewhere Beyond the Heavens: Exploring Battlestar Galactica
The Cyberpunk Nexus: Exploring the Blade Runner Universe
A More Civilized Age: Exploring the Star Wars Expanded Universe
Bright Eyes, Ape City: Examining the Planet of the Apes Mythos
A Galaxy Far, Far Away: Exploring Star Wars Comics
A Long Time Ago: Exploring the Star Wars Cinematic Universe
The Sacred Scrolls: Comics on the Planet of the Apes
New Life and New Civilizations: Exploring Star Trek Comics
The Weirdest Sci-Fi Comic Ever Made: Understanding Jack Kirby's 2001: A Space Odyssey
» ON TV AND MOVIES
Time is a Flat Circle: Examining True Detective, Season One
Moving Panels: Translating Comics to Film
Gotham City 14 Miles: 14 Essays on Why the 1960s Batman TV Series Matters
Mutant Cinema: The X-Men Trilogy from Comics to Screen
Improving the Foundations: Batman Begins from Comics to Screen
» ON OTHER SUBJECTS
Musings on Monsters: Observations on the World of Classic Horror
From Bayou to Abyss: Examining John Constantine, Hellblazer
The Mignolaverse: Hellboy and the Comics Art of Mike Mignola
Moving Target: The History and Evolution of Green Arrow
Humans and Paragons: Essays on Super-Hero Justice
The Best There is at What He Does: Examining Chris Claremont's X-Men
The British Invasion: Alan Moore, Neil Gaiman, Grant Morrison, and the Invention of the Modern Comic Book Writer
Classics on Infinite Earths: The Justice League and DC Crossover Canon
The Future of Comics, the Future of Men: Matt Fraction's Casanova
When Manga Came to America: Super-Hero Revisionism in Mai, the Psychic Girl
The Devil is in the Details: Examining Matt Murdock and Daredevil
Minutes to Midnight: Twelve Essays on Watchmen
Teenagers from the Future: Essays on the Legion of Super-Heroes
» SINGLES
Blind Dates and Broken Hearts: The Tragic Loves of Matthew Murdock
Everything and a Mini-Series for the Kitchen Sink: Understanding Infinite Crisis
Revisionism, Radical Experimentation, and Dystopia in Keith Giffen's Legion of Super-Heroes
And the Universe so Big: Understanding Batman: The Killing Joke
» FORTHCOMING
Meet the Magus: Magic in the Work of Alan Moore
This Lightning, This Madness: Understanding Alan Moore's Miracleman, Book One
Judge Dredd Anthology
Why Do We Fall?: Examining Christopher Nolan's The Dark Knight Trilogy
Neil Gaiman: Dream Dangerously
She Makes Comics
Diagram for Delinquents
The Image Revolution
Comics in Focus: Chris Claremont's X-Men
Warren Ellis: Captured Ghosts
Grant Morrison: Talking with Gods
THE CONTINUITY PAGES
The Tao of Alan Moore and Grant Morrison
by Bobby Campbell | in Articles | Thu, 18 January 2018
I have something of a fascination for the recurring manufactured drama between comic/occult/visionary writers Alan Moore & Grant Morrison. Often times billed as an epic magickal war, w/ thematic shades of Aleister Crowley vs. William Butler Yeats coloring the contextual landscape, this imaginary battle persists through ideaspace, converging into a mythic hypercontextual metanarrative.
There are plenty of blow by blow accounts that establish the conflict from each side's point of view, each of which demonstrates the kind of selective attention and confirmation bias that one would expect from any such dust-up. For my own part I not only don't care who is "right," I disbelieve in any such animal, at least in this particular conflict. This is all a nonsensical Hulk vs. Superman argument for the Vertigo set after all, with impossibly low stakes all around, which is all the more reason to have some fun with it, so here's some fuel for the campfire :)))
My all time favorite writer is Robert Anton Wilson, the iconoclastic, psychedelic, futurist, occultist, agnostic-mystic, who seems in many ways to have prefigured the likes of Moore & Morrison. Both AM & GM have professed admiration for RAW, and I tend to see their conflict in terms of each wanting to occupy the same role as the successor to Pope Bob's illuminating, cosmic triggering, tale of the tribe. The Merlinesque sage. Though I doubt it's actually that specific, and both AM & GM have surpassed RAW in fame & fortune anyways, but I certainly do think that both are trying to fill the same niche, preach to the same choir, and have misgivings about whether or not the town is big enough for the both of them.
I used to think that this was some sort of unfortunate state of affairs, the world's 2 greatest magi, who should have so much common ground, engaged in petty dispute. Their egoless cosmic wisdom deployed in service of"well, he started it!" Though I've come to see this antagonism as a perfectly natural consequence of a metaphysical duality. They seem to me to be two sides of the same coin, a janus head locked in a discordian entanglement, the diametrically opposed Hodge & Podge of the Erisians' Sacred Chao.
Their duality is explicitly evident even in just the plain fact of their contrasting visages, the mythically shaggy Alan Moore and the gleamingly shorn Grant Morrison. Though perhaps their oddly iterative surnames are the more obvious tell? I suppose now is as good a time as any to mention that the word "Magis" is a Latin word that means "more." Though this interconnection goes well beyond mere superficial coincidence, and seems to permeate their creative personas and great works.
On the one hand we have the principled and incorruptibly working class Alan Moore, who has been unable to get Hollywood to stop turning his stories into movies, no matter how much venom he spits their way, and on the other hand, we have the stylish and glamorous pop art star Grant Morrison, who despite his great enthusiasm and full cooperation, has yet to see a mainstream adaptation of his work hit the big screen.
It's perfect yin/yang imagery: Alan Moore sitting in his hometown of Northampton UK, with an active disdain for the corporate entertainment industry, yet unable to escape its harsh spotlight. Meanwhile, Grant Morrison, cruising around the hollywood hills in extravagant sports cars, actively developing mass media content, relegated to creating his masterpieces in relative obscurity. (Though I do certainly hope and expect GM's ideas will have their time in the sun, and by the looks of his new SyfyTV series Happy! that time may yet be upon us.)
Moore seems furious at corporate media for their exploitative and manipulative business practices, rightfully so, whereas Morrison seems giddy w/ his opportunity to exploit and manipulate the global reach of corporate brands to broadcast his idiosyncratic ideas, also rightfully so.
Morrison for his part seems somewhat aware and encouraging of the view that he and Moore are a dichotomous pair, as evidenced by his description of their contrasting approaches to the superhero genre in his book Supergods, comparing Moore's approach to that of a missionary and his own to that of an anthropologist. Though this is a critical comparison that naturally favors his own style, there is an element of truth to how each writer has handled the unreality of the genre.
Moore's superhero work was deconstructive in nature, bursting the bubble of these adolescent power fantasies by bringing real world logic to these imaginary worlds. Moore's approach was to make the superhero genre more like the real world, where absolute power corrupts absolutely, and the concept of heroism is ambiguous at best. Moore brought superheroes to their logical conclusion, and having brought them to their end, saw little use for them moving forward.
Morrison's work is a contrary reaction to this take on superheroism, which embraces a more idealistic perspective, and attempts to bring the wondrous surreality of these fictional universes into our own. Instead of making the Superheroes more like us, Morrison wants to make us more like the Superheroes, crafting aspirational and provocative stories meant to transform the reader into self actualized super beings.
I see these as perfectly compatible perspectives, Moore's art imitating life & Morrison's life imitating art, functioning as a virtuous feedback loop, as Stan Lee would say, "excelsior!"
And just to complete the bizarro circuit, Alan Moore recognizes no such kinship with Grant Morrison, and seems quite irritated to be brought up in the same breath as him at all. GM seems perfectly willing to acknowledge and praise the genius of AM's work, and to admit to some degree of fault in his provocation of Moore. Whereas Moore refuses to acknowledge GM's work might be possessed of mere competence, and expresses righteous fury at the indignity of being dragged into any of this ridiculous nonsense. (Sorry, Alan!)
These contrasting observations seem nearly inexhaustible, and you'd be hard pressed to find a significant character trait in one that isn't antithetically expressed in the other, we Discordians must stick apart, after all, and these two have it down to a science. Though there is a kind of agree-to-disagree beauty to this odd couple, where each seems to strive to express that which is beyond individual expression, to become transparent to a light that is bigger than themselves, and perhaps this effect is best achieved through combined effort, unintentional as it may be. I know my mind is a much better place for having read from both of these oeuvres, and for that, I thank them both very very much :)))
Also, and of course, the synthesis of AM's thesis & GM's antithesis would be the bald headed & bearded Warren Ellis.
As the saying goes,
the wise read
Grant Morrison in good times,
Warren Ellis in bad times,
and Alan Moore in old age.
Tagged Alan Moore, Grant Morrison, Supergods (Grant Morrison book). Bookmark the permalink.
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In Classical Lit today, we looked at Book 18 in The Iliad, specifically the shield of Achilles. A centerpiece of the story, the extended description of the piece of armor (called an ekphrasis) may seem at first glance out of place. Here we are, in the middle of a poem about rage, death, and war, and the bard gives us 130 lines of peace and prosperity.
reaping the ripe grain, swinging their whetted scythes.
supplying grain to the binders, endless bundles.
stood tall in silence, rejoicing in his heart.
Before we discussed the possible meaning(s) of the shield, students were put in groups and had an opportunity to try their hand at drawing the shield itself. The only stipulation was that they had to work strictly from the text -- no Internet searches for "shield of Achilles image."
An excerpt from A Companion to the Iliad, which has a handy diagram and describes and analyzes each part of the shield in turn.
An article called "The Shield of Achilles in the Iliad" by Oliver Taplin, in which he discusses the state of the question (in 1980, at least!), and then offers several possible interpretations, defending one.
An article called "Reading the Shield of Achilles: Terror, Anger, Delight" by Stephen Scully, responding in part to Taplin's article.
We approached our discussion via the articles above for several reasons. First, to model academic discussion at the highest level, seeing how two scholars have different interpretations and carry on their discussion in writing. And second, to demonstrate a strategy for finding sources in research -- find a good secondary source and look at the footnotes!
Drawing by a student, including Greek text from Book I.


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Home >> Waltraud "Traudy" (Jaeger) McElhinney
Waltraud "Traudy" (Jaeger) McElhinney
McElhinney, Waltraud "Traudy" (Jaeger), of West Roxbury, MA, died peacefully on November 5, 2022 after a brief illness. She was 80. Steadfast wife of Philip J. McElhinney of West Roxbury. Devoted mother to Kara J. Stoecker and her husband Falko of Hamburg, Germany. Doting grandmother of Emma and Eleanor. Also survived by many beloved nieces, nephews, cousins and other extended family members.
Born on January 7, 1942 in Kiel, Germany to the late Irma Jaeger and Werner Kielgast, she was raised from a young age by the late Emma and Johannes Baasch in Kronshagen. After earning a certificate in Retail Marketing in Kiel and managing a chocolate shop in Flensburg, Traudy's sense of adventure led her to emigrate to the US in 1966 and spend two years employed as an au pair in Stamford, CT. After short stints as a bookkeeper in Stamford and San Francisco, she made her way to Boston where she spent over ten years working as an accounts manager and payroll officer at Grahm Junior College, the Combined Insurance Company of America, and several other institutions. Traudy and Phil married in 1981. She had always enjoyed caring for and working with children, and after the birth of her daughter she began her second career as a pre-school teacher. Traudy graduated from Wheelock College in 1995 with an Associate's Degree in Early Childhood Education. After over ten years as a teacher at the Village Preschool in Roslindale, she began her third career as a dining room server at Fox Hill Village in Westwood, a job which she truly loved and which she continued to do until her retirement in 2017. Traudy was a lifelong cat lover and also enjoyed socializing and simply being with people. She was generous to those in need and regularly gave to several charities.
Visiting hours at 9:30am on Monday, November 14th at Gormley Funeral Home, 2055 Centre St. West Roxbury. Funeral Mass to follow at 11:30am at Holy Name Church in West Roxbury. Relatives and friends are kindly invited to attend. In lieu of flowers, donations can be made in Traudy's name to St. Jude Children's Research Hospital or to Beth Israel Deaconess Medical Center.
Gormley Funeral Service
2055 Centre Street
West Roxbury, MA 02132
http://www.gormleyfuneral.com


This year has been a hard fought battle to protect and increase workers' benefits under the New York State Workers Compensation System.
Employers and their Insurance companies had been using this " attachment" criterion to prevent injured workers from receiving monetary benefits for their continued disability sometimes characterized as indemnity benefits.
The second major event occurred when attempts to restrict the amount of monetary benefits permitted by what is called schedules. What is left is the existing law. The attempted restrictions unless modified or altered by the Workers' Compensation Board, will primarily remain unchanged. As stated a schedule is a determination that permanent injuries to body parts not subject to classification as a permanent partial disability will continue to be given an evaluation on the overall degree of disability with determined and established as a monetary award. This award will be granted for the overall scheduled disability for that body pars involved. This means a set schedule will be found for the amount of disability payable at one time less indemnity payments made leaving open medical benefits for the life of the worker without any reduction of the established schedules as found in the statute.
The attacks on workers benefits has been forestalled at this time by the efforts of many pro-worker advocates and organizations who all deserve praise for their effort and accomplishments.


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Home / Insurance / The Court of Appeal says compound cream for pain is allowed
The Court of Appeal says compound cream for pain is allowed
An appeals court in Louisiana on Wednesday denied an appeal by a shellfish processing company over a decision that it had to pay for compound cream to treat a worker suffering from pain and found that there was no evidence to show that the cream did not was appropriate.
Bayou Shrimp Processors Inc. and its employee compensation insurer, Bridgefield Employers Insurance Co., appealed against the decision of a State Compensation Judge who approved a current drug for Shelly Delahoussaye and found that it was "permitted without specific restrictions" under state medical guidelines. treatment, according to documents in Bayou Shrimp Processors, Inc. and Bridgefield Employers Insurance Company v. Shelly Delahoussaye, filed with the Louisiana Third Circuit Court of Appeals, in Lake Charles.
Miss. Delahoussaye was "seriously" injured in 201
6 after being run over and towed under a forklift, according to documents describing injuries to several body parts, all of which required surgery, according to documents.
In 2019, Ms. Delahoussaye's treatment treated painkillers, submitted a formal request for approval of a "Neuro Compound Cream", which he testified was in line with treatment options for pain and has "led to improvements in opiate-free function." A claimant denied the claim. Later that year, a medical director approved the therapy and stated that the cream was in line with the state's medical guidelines.
On appeal, a workers' compensation judge ruled earlier this year that the employer "did not meet its burden of proof through clear and convincing evidence" to overturn the medical director's decision.
The State Board of Appeal upheld the decision and wrote that it found "no manifest error" in the judge's decision "that the petitioners did not support their position with clear and convincing evidence necessary to overturn the medical director's decision."


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You are here: Home » Blog » Latest News » Workers likely to face problems with final salary pension schemes
Workers likely to face problems with final salary pension schemes
November 17, 2017 Latest Newsadmin
A number of leading associations are warning that members of final salary pension schemes could face problems in the future.
Amongst those issuing warnings is the powerful pensions body, the Pension and Lifetime Savings Association (PLSA), which has said that around three million workers with final salary pension schemes have just a 50:50 chance of getting a full pay out.
According to the PLSA, increasing life expectancy, low interest rates and weaker investment returns have seen the total deficit for final salary pension schemes grow to more than £400 billion.
It said that "while most schemes will be able to reach a sustainable funding position by drawing on their resources and the financial strength of their sponsoring employer, this won't be the case for all schemes."
Meanwhile, the Financial Conduct Authority (FCA) has issued warnings to those looking to transfer generous final salary pensions in later life.
It has uncovered a series of failings in the advice provided to savers, which included cases where savers were at risk of moving pensions to scam schemes.
The FCA said that among the 88 transfers it had reviewed, 47 per cent of recommendations were suitable, but 17 per cent were unsuitable and in 36 per cent of cases they were neither suitable or unsuitable.
When it came to the investment products or funds that savers were recommended to transfer to, it also found that 35 per cent were suitable, but 24 per cent were not and in 40 per cent of cases it was once again unclear whether they were truly suitable.
It is calling on those looking to transfer final salary schemes to look for experienced independent advice, pointing out that savers should check that financial advisers have the necessary skills to handle pension transfers or are using a reputable specialist transfer firm to avoid their money being mismanaged.
LINK: PLSA Report on Defined Benefit Pensions
← More than 15 million people still have no private pension in the UK, according to the FCA	Millennials warned to plan ahead as intergenerational wealth gap widens →
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A.C. Leonard, 82, a former Dumas resident, passed away on Saturday, January 15, 2011. Graveside Services are scheduled for 2:00 P.M. on Tuesday, January 18, 2011 at Dumas Cemetery. Rev. Jay McGaughy, pastor of Temple Baptist Church in Dumas will be officiating. Arrangements are by Morrison Funeral Directors.
A.C. was born on August 15, 1928 in Goodlett, Texas to Sol and Ora Lenoard. He married Reba Boswell on September 3, 1948 in Dumas. She preceded him in death on July 4, 2004. A.C. was a hard worker. He was employed at the smelter plant in Dumas for 25 years. He moved to Plainview in 1972, and was a resident there for 38 years. He worked for Occidental & Zip Fertilizer until his retirement.
A.C. loved to ride motorcycles. One of his greatest joys was riding at the Canadian River with his son-in-laws and grandkids. He loved the outdoors, camping out and fishing with his family. They were his life, and he was a very dedicated husband, father and grandfather. He was a quiet man, but when he spoke, everyone listened. He was a Christian, and a member of Seth Ward Baptist Church in Plainview.
Survivors include: two daughters, Barbara Henry and husband Farrell of Dumas and Cathy Myers and husband David of Plainview; one sister, Valine Ballard of Dumas; and numerous other family members.
The family will be at 1707 Lewis in Dumas.


HI ALL: I HAVE A LOT OF A4 PAGES TO STUDY, I HAVE THE SPANISH BOOK WHERE ONLY SPEAK ABOUT THE BLIP PAGE, BUT I ASK IF IS IT POSSIBLE PHOTOREAD PAGE BY PAGE USING A SOFT VIEW,ONLY LOOKING THE PAGE WITH OUT OF FOCUS.
IS IT A GOOD WAY TO ACTIVE IF I BEGIN READING THE TEXT AND I MARK THE MOST IMPORTANT PARTS AND AT LAST I MAKE THE MIND MAP. IT�S TOO DIFICULT FOR ME OPEN THE BOOK AND TO LOOK IT IN ANY PAGE WITHOUT I HAVE A WAY.
IS IT POSSIBLE TO ACTIVE IN 48 HOURS?
Imaginary X technique is the way to go for single pages and computer screens.
Yes you can activate 48 hours later. 20 minutes incubation is the minimum there is no set maximum.
1-BEGIN TO MAKE THE MENTAL MAP OF THAT BOOK.
� 2 - IN TIME OF MAKING A MENTAL MAP MARK THE BOOK.
� 3-BEGIN TO MAKE THE MENTAL MAP OF ANOTHER BOOK THAT I PHOTOREAD BEFORE.
B -SOMETIMES WHEN I PHOTOREAD I RELAX MYSELF SO MUCH THAT IT COULD BE SLEEPING. IS THAT GOOD OR NOT? THANK YOU.
Hi Marisaf; i would wait at least 20 minutes but you can wait 4 hours, 8 hours even 24 hours. You want to allow time for the mind to process the book you photoread.So i would suggest that you do not mindmap immediately after photoreading a book. Do something else completely unrelated to the book Go for a walk, ride a bike something completely unrelated to the book for you allow your mind time to process the information you photoread.
As for being relaxed to the point of being asleep you notice that Paul Scheele talks about the relaxed but alert state. That says it all. You want to be relaxed but not too relaxed.
I AM NEW IN THIS AND ME I HAVE TO SURRENDER AN EXAM ON TUESDAYS. I DO NOT KNOW HOW PHOTOREADING CAN HELP ME.
SO I ASK IF IS IT BENEFICIAL FOR ME THAT FIRST I READ AND MARK THE TEXT, MAKE THE MIND MAP AND LATER I PHOTOREAD ALL THIS MATERIAL, EVEN THE MIND MAP. THEN I GIVE IT THE NECESSARY TIME TO ACTIVATE. WHILE I PHOTOREAD AS THE ACTIVATION I LISTEN MOZART�S MUSIC.
THEN WHEN I DO NOT HURRY I ATTEMPT PHOTOREAD LIKE PAUL SENDS. THANKS FOR THE PATIENCE.
Marisa; this is not the time to be learning Photoreading. Just use your regular study habits for now and concentrate on studying and preparing for your examinations.
school for example learn Photoreading on a book that has nothing to do with school then later in future when you have mastered Photoreading then use Photoreading with school books now is not the time to be learning Photoreading.Marisa please do not use big letters when typing on the computer.It is very difficult on the eyes to read the computer when all the letters are big. Good luck on your examinations.
Marisa; ahorita no es la tiempo para aprender Photoreading. Marisa usted tienes muchas libros en esta tiempo no es buen tiempo para aprender Photoreading. Estudio & preparar por tu examen con la metodo usted es acostumbrado. En la futuro aprender Photoreading con libros sin escuela libros no relacion con la escula Mariza es mejor aprender Photoreading sin no tension. Por favor no usar grande letra en la computadora es muy dificil con la ojos para leer la computadora. Buena surte con tu examen.
is it convenient to practice "transcendental meditation" by example, before and then I photoread?
Not necessry. If you happen to do it normally there is no reason not to PhotoRead afterwards.


Direct To Travel – Travel Agency, Online Travel, Cruises, Air, Getaways, Hotels, etc. – Direct To Travel – Travel Agency, Online Travel, Cruises, Air, Getaways, Hotels, etc.
Direct To Travel – Travel Agency, Online Travel, Cruises, Air, Getaways, Hotels, etc.


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Q: import org.testng.annotations.*; Can not be resolved I have successfully installed TestNG and confirmed in eclipse (4.9.0) as well. But while creating a basic class without main class i am getting error at the annotation @Test. Even after importing the test annotations package and the error is present on package as well. and error states it can not be resolved.
enter image description here

A: If you are using maven project change scope test and add scope compile-
<!-- https://mvnrepository.com/artifact/org.testng/testng -->
        <dependency>
            <groupId>org.testng</groupId>
            <artifactId> testng </artifactId>
            <version>6.14.3</version>
            <scope>compile</scope>  //replace test to compile
        </dependency>

A: In eclipse you need to add testng library to your project after installation. Right click on project --> build path --> Add Libraries --> TestNG library,  then it will work

A: Remove the module-info.java class from the project and try again.

A: Download TestNg jar and add it to build path. It will resolve your issue.
Url: https://mvnrepository.com/artifact/org.testng/testng

A: change JavaSE version to JavaSE-1.8

A: Test annotations work only inside the main class. If you are trying to call Test annotations inside an extended class (a class that extends another class) then your test annotations will not work in this case.
In other words, @Test annotations should be inside the parent class, not the child class.

A: Changing JavaSE version to JavaSE-1.8 works

redpajama_set_name: RedPajamaStackExchange


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Business Resources / Maryland Small Business / Maryland Startups / Research and Technology
TEDCO startup support continues to shine
By Samantha Foley /
Maryland's TEDCO, a support resource for startup technology and life sciences companies, recently announced the results of an independent study outlining the organization's impacts within the state. The study was directed by the University of Baltimore's Jacob France Institute and found that TEDCO helped support the state's startup community through sustaining 10,433 Maryland jobs and providing more than $2.3 billion in statewide economic impact this year.
The study shows TEDCO has helped create solid and continuous economic and fiscal outcomes for Maryland. When looking at the impact of job creation over the past few years, the companies supported by TEDCO saw an increase of almost 3,000 jobs, expanding from 7,746 in 2018 to 10,433 in 2021. The jobs supported by the companies under the TEDCO umbrella have earned a total of $885 million in labor income and created estimated state and local government revenues of more than $100 million, including an estimated $57 million in state of Maryland revenues alone. The overall economic influence of these companies on the state has also seen an increase from $1.6 billion in 2018 to $2.3 billion in 2021.
The previous study in 2018 predicted that by the year 2023, TEDCO's economic impact would increase to $2.4B and would bolster a total of 11,812 jobs. The organization is set to achieve these goals ahead of schedule by nearly two years.
Read TEDCO's original announcement and the full report here.


Clinicians are slow to embrace new findings from research. Two new studies cast more doubt on the standard guidelines for screening mammography. Overdiagnosis is a problem, and we have no data on woman over age 75. It's frustrating for doctors who have to decide whether to stick to existing guidelines until new ones are issued based on new evidence or to use their own judgment about individual patients.
A chiropractic organization has warned that using mobile phones for texting could cause hyperkyphosis and shorten your life, and that poor posture is as big a health risk as obesity. They are wrong about these and a lot of the other claims on their website. They don't even mention the real danger of texting: accidents that occur when people pay more attention to their phone than to traffic.
Homeopathy is nonsense. A new report from Australia confirms what we already knew: the evidence shows it does not work. There is no rational justification for further investment in this pre-scientific and disproved notion.
The drug Tamiflu is recommended for prevention and treatment of influenza and is stockpiled for use in a pandemic. Unpublished research has now been added to the dataset, but it hasn't changed what we already knew. The benefits of Tamiflu are limited, but it may have a role in selected patients and in preventing the spread of influenza.
Teething necklaces made of amber beads continue to be popular. The alleged mechanisms of action range from the hilarious ("activates the solar plexus and root chakra") to the just barely plausible. There is no evidence that they work and no reason to think they might work. And necklaces are hazardous to young children: they could cause strangulation.


This week in yoga we have inspiring articles and videos on love and yoga, tips and techniques for your asana practice, yoga for tea lovers, beautiful bookstores, yoga poses for a good side body stretch, and more!
We're also giving away lifetime access passes to Kino MacGregor's Yoga Practice Kit! Contest ends tomorrow, so check out the details below and join now if you haven't yet!


Okay, so this may be a silly question to ask, right? But have you really thought about what our design process really is? Most people think Interior Designers or Decorators live a glamorous life fluffing pillows and picking out beautiful fabrics for window treatments and furniture. Although that is a fun part of my job, I can tell you it's not as glamorous as you may think. If I were to give those of us in the industry a different title it would be "Problem Solver." Yep, that pretty much sums it up… THE END!
Okay, so I'll go into a little more detail than that. We not only solve your decorating dilemmas, but we solve all the little problems that come along to designing and pulling together a room. And let me tell you, problems do arrive, in EVERY project. If you have a designer that tells you your project will be free of problems and/or challenges, find another one. They are not being honest with you. Problems, or opportunities in disguise, will happen and this is the very reason why you want to hire an Interior Designer. We keep the project moving forward and many times can head problems off before it even reaches you, the client, saving you both time and money. When you don't have an Interior Designer it's like going into court without a Lawyer. Okay, so maybe it's not that dramatic, but it's an easy way to understand it.
Every design firm will do things a little different, but each firm does have a step-by-step process for each project that they take their client through. I will explain what Blooming Daisy Interior Design does and hopefully shed some light on what we do when we are working on your project.
Each consultation lasts about 2 hours.
This is where we outline the scope of work for the entire project, as well as our estimated design fees. This document takes some time to put together as we research and pull information together to try and give you the best possible estimate for the fee as well as the timeline for your project. Once the fee proposal and Letter of Agreement is signed and the retainer fee paid, we move to the next step of the project.
This is where we come back to your home and start the design process. We take measurements and photos of each room that's part of the project. Discuss with you what items, if any, will be staying and going. If trades/contractors are needed they will also show up on this day to gather information in order to provide a written estimate outlining their scope of work and cost of labor and/or materials. These estimates will be provided to you in the Presentation Meeting.
This part is probably my favorite part. This is where the creative design process happens. We take the time to plan out your project. This will include sketches, drawing up a floor plan that's to-scale, elevations, renderings if needed, and color schemes. We source all materials, including fixtures, furnishings, fabrics, and flooring to make sure everything flows together and is functional. We work closely with our vendors in providing you with the best quality of products that will fit into your unique design. The budget will also be developed during this step.
This is where we present to you the custom design plan. This will include drawings, floor plan, mood boards, color scheme, fabric samples, furniture selection and budget breakdown including estimated costs for any work by the trades. If any revisions need to be made it needs to be discussed during this meeting. The cost of the furniture and/or materials will be due at this time, so that items can be ordered. A follow-up presentation may be needed if revisions are requested.
This step is a big reason why hiring a designer is so attractive. In this step we create all purchase orders, track orders, assess lead times, note any back-orders or discontinued items that may affect the time line, and decide if a replacement items should be ordered. We work with fabricators to make sure window treatments and furniture are made to our specifications. We make sure that our projected time-line is adhered to by all vendors and trades.
This is sometimes needed on large projects, or when revisions had to be made and/or change orders were requested by client. We want to make sure we are on track with the budget and timeline.
When items are received at the warehouse they are inspected and stored for the big install day. Claims and reorders are made for any items that arrive damaged, and yes this does happen. As your Design team we take care of these pesky little details that you don't have time to deal with. When all the items have arrived, we will install all items on the same day instead of several different days. However, if custom window treatments are ordered they will be installed prior to the final reveal. This is something that as the Designer we have to coordinate and pull together, not to mention being on-site to insure a satisfied outcome.
This is a fun step, where everything comes together and the vision becomes a reality. And this is the part you were waiting for… fluffing the pillows, lol. However, there is a lot that goes into this one day. Coordinating with the warehouse to have items delivered and moving items in, placing them according to the floor plan, and styling. On this day we are in jeans and hair is up in pony tail. It's an all hands-on deck working day. After everything is in place a thorough cleaning is done. A Starbucks Refresher is definitely in order at the end of this day.
This is very exciting for us as we show our clients the finished space. We will go through every item and show its functionality and benefits. Accent pieces may be used to give the space a "finished" look and can be purchased by client if desired. We discuss any care instructions and warranties (if any), and allow the client to point out any concerns they may have. We will coordinate with any trades people involved to cure any deficiencies within 14 days. Often times this is not needed, but we want to make sure our clients are happy with their new space.
We will schedule a professional photographer to take pictures of the finished space. This may be done on the same day as the project reveal, but may need to be scheduled on a different day due to availability.
Step 12 – ENJOY YOUR NEW PACE!
For the client this step is the most gratifying. To be able to walk into your home and have the space completely done. It gives you a sense of calm, and relaxation knowing that you will love coming home, again and again.
As you can see Interior Design is not for the faint of heart, especially if you own your own business. It's a lot of hard work, and most projects take a minimum of 6-8 weeks, and that's if everything goes perfect. Some projects, depending on the scope of work can take several months. We also have marketing and accounting that for the sake of time, was not mentioned. Despite all the hard work, it's also one of the most gratifying jobs when you've created a space that your client absolutely loves. Just knowing they will be able to enjoy that space for years to come is a wonderful feeling.
Contact Blooming Daisy Interior Design to book your consultation today. Let us help you create a space you love coming home to again and again, because your home matters.
My NY decorative arts studio has been workong with interior designers for the past 18 years, and you should add "magician"to your job description.
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Description Koli National Park lies in North Karelia, eastern Finland, on the western shore of Lake Pielinen. Established in 1991, the national park is 3000 hectares in size. The purpose in conserving this area is to ensure the preservation of Koli's heritage landscape and the forests of the Koli highlands as well as maintaining the plant communities created in the past by swidden cultivation.


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redpajama_set_name: RedPajamaGithub


text:
In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications in many areas of Science and became a useful tool for physicists dealing, for instance, with optimization problems, with data analysis, with the solution of linear integral equations, etc. The existence of such applications alone should attract the interest of students and researchers in the Moore-Penrose pseudoinverse and in related subjects, like the singular values decomposition theorem for matrices. In this note we present a tutorial review of the theory of the Moore-Penrose pseudoinverse. We present the first definitions and some motivations and, after obtaining some basic results, we center our discussion on the Spectral Theorem and present an algorithmically simple expression for the computation of the Moore-Penrose pseudoinverse of a given matrix. We do not claim originality of the results. We rather intend to present a complete and self-contained tutorial review, useful for those more devoted to applications, for those more theoretically oriented and for those who already have some working knowledge of the subject.
The Moore-Penrose Pseudoinverse. A Tutorial Review of the Theory
J. C. A. Barata111e-mail: and M. S. Hussein222e-mail:
Instituto de Física, Universidade de São Paulo, C.P. 66318, 05314-970 São Paulo, SP, Brazil
1 Introduction, Motivation and Notation
In this paper we present a self-contained review of some of the basic results on the so-called Moore-Penrose pseudoinverse of matrices, a concept that generalizes the usual notion of inverse of a square matrix, but that is also applicable to singular square matrices or even to non-square matrices. This notion is particularly useful in dealing with certain linear least squares problems, as we shall discuss in Section 6, i.e., problems where one searches for an optimal approximation for solutions of linear equations like Ax=y, where A is a given m×n matrix, y is a given column vector with m components and the unknown x, a column vector with n components, is the searched solution. In many situations, a solution is non-existing or non-unique, but one asks for a vector x such that the norm of the difference Ax−y is the smallest possible (in terms of least squares).
Let us be a little more specific. Let A∈Mat(C,m,n) (the set of all complex m×n matrices) and y∈Cm be given and consider the problem of finding x∈Cn satisfying the linear equation
Ax=y. (1)
If m=n and A has an inverse, the (unique) solution is, evidently, x=A−1y. In other cases the solution may not exist or may not be unique. We can, however, consider the alternative problem of finding the set of all vectors x′∈Cn such that the Euclidean norm ∥Ax′−y∥ reaches its least possible value. This set is called the minimizing set of the linear problem (1). Such vectors x′∈Cn would be the best approximants for the solution of (1) in terms of the Euclidean norm, i.e., in terms of "least squares". As we will show in Theorem 6.1, the Moore-Penrose pseudoinverse provides this set of vectors x′ that minimize ∥Ax′−y∥: it is the set
where A+∈Mat(C,n,m) denotes the Moore-Penrose pseudoinverse of A. An important question for applications is to find a general and algorithmically simple way to compute A+. The most common approach uses the singular values decomposition and is described in Appendix B. Using the Spectral Theorem and Tikhonov's regularization method we show that A+ can be computed by the algorithmically simpler formula
A+=s∑b=1βb≠01βb⎛⎜ ⎜⎝s∏l=1l≠b(βb−βl)−1⎞⎟ ⎟⎠⎡⎢ ⎢⎣s∏l=1l≠b(A∗A−βl1n)⎤⎥ ⎥⎦A∗, (3)
where A∗ denotes the adjoint matrix of A and βk, k=1,…,s, are the distinct eigenvalues of A∗A (the so-called singular values of A). See Theorem 5.1 for a more detailed statement. One of the aims of this paper is to present a proof of (3) by combining the spectral theorem with the a regularization procedure due to Tikhonov [4, 5] .
Some applications of the Moore-Penrose pseudoinverse
Problems involving the determination of the minimizing set of (1) are always present when the number of unknowns exceeds the number of values provided by measurements. Such situations occur in many areas of Applied Mathematics, Physics and Engineering, ranging from imaging methods, like MRI (magnetic resonance imaging) [8, 9, 10] , fMRI (functional MRI) [12, 11] , PET (positron emission tomography) [16, 17] and MSI (magnetic source imaging) [13, 14, 15] , to seismic inversion problems [18, 19] .
The Moore-Penrose pseudoinverse and/or the singular values decomposition (SVD) of matrices (discussed in Appendix B) are also employed in data analysis, as in the treatment of electroencephalographic source localization [24] and in the so-called Principal Component Analysis (PCA). Applications of this last method to astronomical data analysis can be found in [21, 20, 22, 23] and applications to gene expression analysis can be found in [25, 26] . Image compression algorithms using SVD are known at least since [27] and digital image restoration using the Moore-Penrose pseudoinverse have been studied in [28, 29] .
Problems involving the determination of the minimizing set of (1) also occur, for instance, in certain numerical algorithms for finding solutions of linear Fredholm integral equations of the first kind:
∫bak(x,y)u(y)dy=f(x),
where −∞<a<b<∞ and where k and f are given functions. See Section 4 for a further discussion of this issue. For an introductory account on integral equations, rich in examples and historical remarks, see [30] .
Even this short list of applications should convince a student of Physics or Applied Mathematics of the relevance of the Moore-Penrose pseudoinverse and related subjects and our main objective is to provide a self-contained introduction to the required theory.
In Section 2 we present the definition of the Moore-Penrose pseudoinverse and obtain its basic properties. In Section 3 we further develop the theory of the Moore-Penrose pseudoinverses. In Section 4 we describe Tikhonov's regularization method for the computation of Moore-Penrose pseudoinverses and present a first proof of existence. Section 5 collects the previous results and derives expression (3), based on the Spectral Theorem, for the computation of Moore-Penrose pseudoinverses. This expression is algorithmically simpler than the usual method based on the singular values decomposition (described in Appendix B). In Section 6 we show the relevance of the Moore-Penrose pseudoinverse for the solution of linear least squares problems, its main motivation. In Appendix A we present a self-contained review of the results on Linear Algebra and Hilbert space theory, not all of them elementary, that we need in the main part of this paper. In Appendix B we approach the existence problem of the Moore-Penrose pseudoinverse by using the usual singular values decomposition method.
Notation and preliminary definitions
In the following we fix the notation utilized throughout the paper. We denote Cn the vector space of all n-tuples of complex numbers: Cn:={(z1⋮zn), with zk∈C for % all k=1,…,n}. We denote the usual scalar product in Cn by ⟨⋅,⋅⟩C or simply by ⟨⋅,⋅⟩, where for z=(z1⋮zn)∈Cn and w=(w1⋮wn)∈Cn, we have
⟨z,w⟩C≡⟨z,w⟩:=n∑k=1¯¯¯¯¯zkwk.
Note that this scalar product is linear in the second argument and anti-linear in the first, in accordance with the convention adopted in Physics. Two vectors u and v∈Cn are said to be orthogonal according to the scalar product ⟨⋅,⋅⟩ if ⟨u,v⟩=0. If W⊂Cn is a subspace of Cn we denote by W⊥ the subspace of Cn composed by all vectors orthogonal to all vectors of W. The usual norm of a vector z∈Cn will be denoted by ∥z∥C or simply by ∥z∥ and is defined by ∥z∥C≡∥z∥=√⟨z,x⟩. It is well known that Cn is a Hilbert space with respect to the usual scalar product.
The set of all complex m×n matrices (m rows and n columns) will be denoted by Mat(C,m,n). The set of all square n×n matrices with complex entries will be denoted by Mat(C,n).
The identity matrix will be denoted by 1. Given A∈Mat(C,m,n) we denote by AT element of Mat(C,n,m) whose matrix elements are (AT)ij=Aji for all i∈{1,…,n}, j∈{1,…,m}. The matrix AT is said to be the transpose of A. It is evident that (AT)T=A and that (AB)T=BTAT for all A∈Mat(C,m,n) and B∈Mat(C,n,p).
If A∈Mat(C,m,n), then its adjoint A∗∈Mat(C,n,m) is defined as the matrix whose matrix elements (A∗)ij are given by ¯¯¯¯¯¯¯Aji for all 0≤i≤n and 0≤j≤m.
Given a set α1,…,αn of complex numbers we denote by diag(α1,…,αn)∈Mat(C,n) the diagonal matrix whose k-th diagonal entry is αk:
The spectrum of a square matrix A∈Mat(C,n) coincides with the set of its eigenvalues (see the definitions in Appendix A) and will be denoted by σ(A).
We denote by 0a,b∈Mat(C,a,b) the a×b whose matrix elements are all zero. We denote by 1l∈Mat(C,l) the l×l identity matrix. If no danger of confusion is present, we will simplify the notation and write 0 and 1 instead of 0a,b and 1l, respectively. We will also employ the following definitions: for m,n∈N, let Im,m+n∈Mat(C,m,m+n) and Jm+n,n∈Mat(C,m+n,n) be given by
Im,m+n:=(1m0m,n) and Jm+n,n:=(1n0m,n). (4)
The corresponding transpose matrices are
(Im,m+n)T:=(1m0n,m)=Jm+n,m and (Jm+n,n)T:=(1n0n,m)=In,m+n. (5)
The following useful identities will be used bellow:
Im,m+n(Im,m+n)T = Im,m+nJm+n,m=1m, (6)
(Jm+n,n)TJm+n,n = In,m+nJm+n,n=1n, (7)
For each A∈Mat(C,m,n) we can associate a square matrix A′∈Mat(C,m+n) given by
A′:=(Im,m+n)TA(Jm+n,n)T=Jm+n,mAIn,m+n=(A0m,m0n,n0n,m). (8)
As one easily checks, we get from (6)–(7) the useful relation
A=Im,m+nA′Jm+n,n. (9)
The canonical basis of vectors in Cn is
e1=⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝100⋮0⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠,e2=⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝010⋮0⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠,…,en=⎛⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜⎝00⋮01⎞⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟⎠, (10)
Let x1,…,xn be vectors, represented in the canonical basis as
xa=⎛⎜ ⎜⎝xa1⋮xan⎞⎟ ⎟⎠.
We will denote by [[x1,…,xn]] the n×n constructed in such a way that its a-th column is the vector xa, that means,
It is obvious that 1=[[e1,…,en]]. With this notation we write
for any B∈Mat(C,m,n), as one easily checks. Moreover, if D is a diagonal matrix D=diag(d1,…,dn), then
[[x1,…,xn]]D=[[d1x1,…,dnxn]]. (13)
If v1,…,vk are elements of a complex vector space V, we denote by [v1,…,vk] the subspace generated v1,…,vk, i.e., the collection of all linear combinations of the v1,…,vk: [v1,…,vk]:={α1v1+⋯+αkvk,α1,…,αk∈C}.
More definitions and general results can be found in Appendix A.
2 The Moore-Penrose Pseudoinverse. Definition and First Properties
In this section we define the notion of a Moore-Penrose pseudoinverse and study its uniqueness. The question of the existence of the Moore-Penrose pseudoinverse of a given matrix is analyzed in other sections.
Generalized inverses, or pseudoinverses
Let m,n∈N and let A∈Mat(C,m,n) be a m×n matrix (not necessarily a square matrix). A matrix B∈Mat(C,n,m) is said to be a generalized inverse, or a pseudoinverse, of A if it satisfies the following conditions:
ABA=A,
BAB=B.
If A∈Mat(C,n) is a non-singular square matrix, its inverse A−1 satisfies trivially the defining properties of the generalized inverse above. We will prove later that every matrix A∈Mat(C,m,n) has at least one generalized inverse, namely, the Moore-Penrose pseudoinverse. The general definition above is not enough to guarantee uniqueness of the generalized inverse of any matrix A∈Mat(C,m,n).
The definition above is too wide to be useful and it is convenient to narrow it in order to deal with certain specific problems. In what follows we will discuss the specific case of the Moore-Penrose pseudoinverse and its application to optimization of linear least squares problems.
Defining the Moore-Penrose pseudoinverse
Let m,n∈N and let A∈Mat(C,m,n). A matrix A+∈Mat(C,n,m) is said to be a Moore-Penrose pseudoinverse of A if it satisfies the following conditions:
AA+A=A,
A+AA+=A+,
AA+∈Mat(C,m) and A+A∈Mat(C,n) are self-adjoint.
It is easy to see again that if A∈Mat(C,n) is non-singular, then its inverse satisfies all defining properties of a Moore-Penrose pseudoinverse.
The notion of Moore-Penrose pseudoinverse was introduced by E. H. Moore [1] in 1920 and rediscovered by R. Penrose [2, 3] in 1955. The Moore-Penrose pseudoinverse is a useful concept in dealing with optimization problems, as the determination of a "least squares" solution of linear systems. We will treat such problems later (see Theorem 6.1), after dealing with the question of uniqueness and existence of the Moore-Penrose pseudoinverse.
The uniqueness of the Moore-Penrose pseudoinverse
We will first show the uniqueness of the Moore-Penrose pseudoinverse of a given matrix A∈Mat(C,m,n), assuming its existence.
Let A+∈Mat(C,n,m) be a Moore-Penrose pseudoinverse A∈Mat(C,m,n) and let B∈Mat(C,n,m) be another Moore-Penrose pseudoinverse of A, i.e., such that ABA=A, BAB=B with AB and BA self-adjoint. Let M1:=AB−AA+=A(B−A+)∈Mat(C,m). By the hypothesis, M1 is self-adjoint (since it is the difference of two self-adjoint matrices) and (M1)2=(AB−AA+)A(B−A+)=(ABA−AA+A)(B−A+)=(A−A)(B−A+)=0. Since M1 is self-adjoint, the fact that (M1)2=0 implies that M1=0, since for all x∈Cm one has ∥M1x∥2=⟨M1x,M1x⟩=⟨x,(M1)2x⟩=0, implying M1=0. This showed that AB=AA+. Following the same steps we can prove that BA=A+A (consider the self-adjoint matrix M2:=BA−A+A∈Mat(C,n) and proceed as above). Now, all this implies that A+=A+AA+=A+(AA+)=A+AB=(A+A)B=BAB=B, thus establishing uniqueness.
As we already commented, if A∈Mat(C,n) is a non-singular square matrix, its inverse A−1 trivially satisfies the defining conditions of the Moore-Penrose pseudoinverse and, therefore, we have in this case A+=A−1 as the unique Moore-Penrose pseudoinverse of A. It is also evident from the definition that for 0mn, the m×n identically zero matrix, one has (0mn)+=0nm.
Existence of the Moore-Penrose pseudoinverse
We will present two proofs of the existence of the Moore-Penrose pseudoinverse A+ for an arbitrary matrix A∈Mat(C,m,n). Both proofs produce algorithms for the explicit computation of A+. The first one will be presented in Section 4 (Theorems 4.3 and 5.1) and will follow from results presented below. Expressions (39) and (40) furnish explicit expressions for the computation of A+ in terms of A, A∗ and the eigenvalues of AA∗ or A∗A (i.e., the singular values of A).
The second existence proof will be presented in Appendix B and relies on the singular values decomposition presented in Theorem A.16. For this proof, the preliminary results presented below are not required. This second proof is the one more frequently found in the literature, but we believe that expressions (39) and (40) provide an algorithmically simpler way for the determination of the Moore-Penrose pseudoinverse of a given matrix.
Computing the Moore-Penrose pseudoinverse in some special cases
If A∈Mat(C,m,1), A=(a1⋮am), a non-zero column vector, then one can easily verify that A+=1∥A∥2A∗=1∥A∥2(¯¯¯¯¯a1,…,¯¯¯¯¯¯am), where ∥A∥=√|a1|2+⋯+|am|2. In particular, if z∈C, then (z)+={0,z=01z,z≠0, by taking z as an element of Mat(C,1,1).
This can be further generalized. If A∈Mat(C,m,n) and (AA∗)−1 exists, then
A+=A∗(AA∗)−1, (14)
because we can readly verify that the r.h.s. satisfies the defining conditions of A+. Analogously, if (A∗A)−1 exists, one has
A+=(A∗A)−1A∗. (15)
For instance, for A=(20i0i1) one can check that AA∗ is invertible, but A∗A is not, and we have A+=A∗(AA∗)−1=19(4−2i1−5i−i4). Similarly, for A=(120i03), AA∗ is singular, but A∗A is invertible and we have A+=(A∗A)−1A∗=110(102i−60−i3).
The relations (14)–(15) are significant because they will provide an important hint to find the Moore-Penrose pseudoinverse of a general matrix, as we will discuss later. In Proposition 3.2 we will show that one has in general A+=A∗(AA∗)+=(A∗A)+A∗ and in Theorem 4.3 we will discuss what can be done in the cases when A∗A or A∗A are not invertible.
3 Further Properties of the Moore-Penrose Pseudoinverse
The following properties of the Moore-Penrose pseudoinverse follow immediately from its definition and from uniqueness. The proofs are elementary and left to the reader: for any A∈Mat(C,m,n) one has
(A+)+=A,
(A+)T=(AT)+, ¯¯¯¯¯¯¯A+=(¯¯¯¯A)+ and, consequently (A+)∗=(A∗)+,
(zA)+=z−1A+ for all z∈C, z≠0.
It is however important to remark that for A∈Mat(C,m,n) and B∈Mat(C,n,p), the Moore-Penrose pseudoinverse (AB)+ is not always equals to B+A+, in contrast to what happens with the usual inverse in the case m=n=p. A relevant exception will be found in Proposition 3.2.
The next proposition lists some important properties that will be used below.
Proposition 3.1
The Moore–Penrose pseudoinverse satisfies the following relations:
A+ = A+(A+)∗A∗, (16)
A = AA∗(A+)∗, (17)
A∗ = A∗AA+, (18)
A+ = A∗(A+)∗A+, (19)
A = (A+)∗A∗A, (20)
A∗ = A+AA∗, (21)
valid for all A∈Mat(C,m,n).
For us, the most relevant of the relations above is relation (18), since we will make use of it in the proof of Proposition 6.1 we when deal with optimization of least squares problems.
Proof of Proposition 3.1. Since AA+ is self-adjoint, one has AA+=(AA+)∗=(A+)∗A∗. Multiplying to the left by A+, we get A+=A+(A+)∗A∗, proving (16). Replacing A→A+ and using the fact that A=(A+)+, one gets from (16) A=AA∗(A+)∗, which is relation (17). Replacing A→A∗ and using the fact that (A∗)+=(A+)∗, we get from (17) that A∗=A∗AA+, which is relation (18).
Relations (19)–(21) can be obtained analogously from the fact that A+A is also self-adjoint, but they follow more easily by replacing A→A∗ in (16)–(18) and by taking the adjoint of the resulting expressions.
From Proposition 3.1 other interesting results can be obtained, some of which are listed in the following proposition:
For all A∈Mat(C,m,n) one has
(AA∗)+=(A∗)+A+. (22)
From this we get
A+=A∗(AA∗)+=(A∗A)+A∗, (23)
also valid for all A∈Mat(C,m,n).
Expression (23) generalizes (14)–(15) and can be employed to compute A+ provided (AA∗)+ or (A∗A)+ were previously known.
Proof of Proposition 3.2. Let B=(A∗)+A+. One has
AA∗(???)=AA∗(A+)∗A∗(???)=AA∗(A+)∗A+AA∗=(AA∗)B(AA∗),
where we use that (A∗)+=(A+)∗. One also has
B=(A∗)+A+(???)=(A+)∗A+AA+(???)=(A+)∗A+AA∗(A+)∗A+=B(AA∗)B.
Notice that
(AA∗)B=(AA∗(A+)∗)A+(???)=AA+
which is self-adjoint, by definition. Analogously,
B(AA∗)=(A+)∗(A+AA∗)(???)=(A∗)+A∗,
which is also self-adjoint. The facts exposed in the lines above prove that B is the Moore-Penrose pseudoinverse of AA∗, establishing (22). Replacing A→A∗ in (22), one also gets
(A∗A)+=A+(A∗)+. (24)
Notice now that
A∗(AA∗)+(???)=A∗(A∗)+A+(???)=A+
(A∗A)+A∗(???)=A+(A∗)+A∗(???)=A+,
establishing (23).
The kernel and the range of a matrix and the Moore-Penrose pseudoinverse
The kernel and the range (or image) of a matrix A∈Mat(C,m,n) are defined by Ker(A):={u∈Cn|Au=0} and Ran(A):={Au,u∈Cn}, respectively. It is evident that Ker(A) is a linear subspace of Cn and that Ran(A) is a linear subspace of Cm.
The following proposition will be used below, but is interesting by itself.
Let A∈Mat(C,m,n) and let us define P1:=1n−A+A∈Mat(C,n) and P2:=1m−AA+∈Mat(C,n). Then, the following claims are valid:
P1 and P2 are orthogonal projectors, that means, they satisfy (Pk)2=Pk and P∗k=Pk, k=1,2.
Ker(A)=Ran(P1), Ran(A)=Ker(P2), Ker(A+)=Ran(P2) and Ran(A+)=Ker(P1).
Ran(A)=Ker(A+)⊥ and Ran(A+)=Ker(A)⊥.
Ker(A)⊕Ran(A+)=Cn and Ker(A+)⊕Ran(A)=Cm, both being direct sums of orthogonal subspaces.
Proof. Since AA+ and A+A are self-adjoint, so are P1 and P2. One also has (P1)2=1−2A+A+A+AA+A=1−2A+A+A+A=1−A+A=P1 and analogously for P2. This proved item 1.
Let x∈Ker(A). Since Ran(P1) is a closed linear subspace of of Cn, the "Best Approximant Theorem", Theorem A.1, and the Orthogonal Decomposition Theorem, Theorem A.3, guarantee the existence of a unique z0∈Ran(P1) such that ∥x−z0∥=min{∥x−z∥,z∈Ran(P1)}. Moreover, x−z0 is orthogonal to Ran(P1). Hence, there exists at least one y0∈Cm such that x−P1y0 is orthogonal to every element of the form P1y, i.e., ⟨x−P1y0,P1y⟩=0 for all y∈Cm, what implies ⟨P1(x−P1y0),y⟩=0 for all y∈Cm what, in turn, implies P1(x−P1y0)=0. This, however, says that P1x=P1y0. Since x∈Ker(A), one has P1x=x (by the definition of P1). We therefore proved that if x∈Ker(A) then x∈Ran(P1), establishing that Ker(A)⊂Ran(P1). On the other hand, the fact that AP1=A(1−A+A)=A−A=0 implies Ran(P1)⊂Ker(A), establishing that Ran(P1)=Ker(A).
If z∈Ker(P1), then z=A+Az, proving that z∈Ran(A+). This established that Ker(P1)⊂Ran(A+). On the other hand, if u∈Ran(A+) then there exists v∈Cm such that u=A+v. Therefore, , proving that u∈Ker(P1) and that Ran(A+)⊂Ker(P1). This established that Ker(P1)=Ran(A+).
P2 is obtained from P1 by the substitution A→A+ (recalling that (A+)+=A). Hence, the results above imply that Ran(P2)=Ker(A+) and that Ker(P2)=Ran(A). This proves item 2.
If M∈Mat(C,p) (with p∈N, arbitrary) is self-adjoint, that ⟨y,Mx⟩=⟨My,x⟩ for all x,y∈Cp. This relation makes evident that Ker(M)=Ran(M)⊥. Therefore, item 3 follows from item 2 by taking M=P1 and M=P2. Item 4 is evident from item 3.
4 Tikhonov's Regularization and Existence Theorem for the Moore-Penrose Pseudoinverse
In (14) and (15) we saw that if (AA∗)−1 exists, then A+=A∗(AA∗)−1 an that if (A∗A)−1 exists, then A+=(A∗A)−1A∗. If those inverses do not exist, there is an alternative procedure to obtain A+. We know from Proposition A.4 that even if (AA∗)−1 does not exist, the matrix AA∗+μ1 will be invertible for all non-vanishing μ∈C with |μ| small enough. Hence, we could conjecture that the expressions A∗(AA∗+μ1)−1 and (A∗A+μ1)−1A∗ are well-defined for μ≠0 and |μ| small enough and converge to A+ when the limit μ→0 is taken. As will now show, this conjecture is correct.
The provisional replacement of the singular matrices AA∗ or A∗A by the non-singular ones AA∗+μ1 or A∗A+μ1 (with μ≠0 and |μ| "small") is a regularization procedure known as Tikhonov's regularization. This procedure was introduced by Tikhonov in [4] (see also [5] and, for historical remarks, [30] ) in his search for uniform approximations for the solutions of Fredholm's equation of the first kind
∫bak(x,y)u(y)dy=f(x), (25)
where −∞<a<b<∞ and where k and f are given functions satisfying adequate smoothness conditions. In operator form, (25) becomes Ku=f and K is well known to be a compact operator (see, e.g., [6] ) if k is a continuous function. By using the method of finite differences or by using expansions in terms of orthogonal functions, the inverse problem (25) can be replaced by an approximating inverse matrix problem Ax=y, like (1). By applying A∗ to the left, one gets A∗Ax=A∗y. Since the inverse of A∗A may not exist, one first considers a solution xμ of the regularized equation (A∗A+μ1)xμ=A∗y, with some adequate μ∈C, and asks whether the limit lim|μ|→0(A∗A+μ1)−1A∗y can be taken. As we will see, the limit exists and is given precisely by A+y. In Tikhonov's case, the regularized equation (A∗A+μ1)xμ=A∗y can be obtained from a related Fredholm's equation of the second kind, namely K∗Kuμ+μuμ=K∗f, for which the existence of solutions, i.e., the existence of the inverse (K∗K+μ1)−1, is granted by Fredholm's Alternative Theorem (see, e.g., [6] ) for all μ in the resolvent set of K∗K and, therefore, for all μ>0 (since K∗K is a positive compact operator)333Tikhonov's argument in [4] is actually more complicated, since he does not consider the regularized equation (K∗K+μ1)uμ=K∗f, but a more general version where the identity operator 1 is replaced by a Sturm-Liouville operator.. It is then a technical matter to show that the limit limμ→0μ>0uμ exists and provides a uniform approximation to a solution of (25).
Tikhonov, however, does not point to the relation of his ideas to the theory of the Moore-Penrose inverse. This will be described in what follows. Our first result, presented in the next two lemmas, establishes that the limits limμ→0A∗(AA∗+μ1m)−1 and limμ→0(A∗A+μ1n)−1A∗, described above, indeed exist and are equal.
Lemma 4.1
Let A∈Mat(C,m,n) and let μ∈C be such that AA∗+μ1m and A∗A+μ1n are non-singular (that means μ∉σ(AA∗)∪σ(A∗A), a finite set). Then, A∗(AA∗+μ1m)−1=(A∗A+μ1n)−1A∗.
Recall that, by Proposition A.7, σ(AA∗) and σ(A∗A) differ at most by the element 0.
Proof of Lemma 4.1. Let Bμ:=A∗(AA∗+μ1m)−1 and Cμ:=(A∗A+μ1n)−1A∗. We have
Therefore, (A∗A+μ1n)Bμ=A∗, what implies Bμ=(A∗A+μ1n)−1A∗=Cμ.
For all A∈Mat(C,m,n) the limits limμ→0A∗(AA∗+μ1m)−1 and limμ→0(A∗A+μ1n)−1A∗ exist and are equal (by Lemma 4.1), defining an element of Mat(C,n,m).
Proof. Notice first that A is an identically zero matrix iff AA∗ or A∗A are zero matrices. In fact, if, for instance, A∗A=0, then for any vector x one has 0=⟨x,A∗Ax⟩=⟨Ax,Ax⟩=∥Ax∥2, proving that A=0. Hence we will assume that AA∗ and A∗A are non-zero matrices.
The matrix AA∗∈Mat(C,m) is evidently self-adjoint. Let α1,…,αr be its distinct eigenvalues. By the Spectral Theorem for self-adjoint matrices, (see Theorems A.9 and A.13) we may write
AA∗=r∑a=1αaEa, (26)
where Ea are the spectral projectors of AA∗ and satisfy EaEb=δabEa, E∗a=Ea and ∑ra=1Ea=1m. Therefore,
AA∗+μ1m=r∑a=1(αa+μ)Ea
and, hence, for μ∉{α1,…,αr}, one has, by (50),
There are now two cases to be considered: 1. zero is not an eigenvalue of AA∗ and 2. zero is eigenvalue of AA∗.
In case 1, it is clear from (27) that the limit limμ→0A∗(AA∗+μ1m)−1 exists and
limμ→0A∗(AA∗+μ1m)−1=r∑a=11αaA∗Ea. (28)
In case 2, let us have, say, α1=0. The corresponding spectral projector E1 projects on the kernel of AA∗: Ker(AA


Songwriting is about getting the demon out of me. It's like being possessed. You try to go to sleep, but the song won't let you. So you have to get up and make it into something, and then you're allowed to sleep. It's always in the middle of the bloody night, or when you're half awake or tired, when your critical faculties are switched off. So letting go is what the whole game is.
Fearless" is living in spite of those things that scare you to death.
The only reason that we don't open our hearts and minds to other people is that they trigger confusion in us that we don't feel brave enough or sane enough to deal with. To the degree that we look clearly and compassionately at ourselves, we feel confident and fearless about looking into someone else's eyes.
Acknowledging fear is not a cause for depression or discouragement. Because we possess such fear, we also are potentially entitled to experience fearlessness. True fearlessness is not the reduction of fear; but going beyond fear.


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Penland in North Carolina is accepting applications for it's core fellowship program. Deadline is soon... October 15th! More info here.
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