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Q: Counting k-tuples constrained to contain all elements The elements for the k-tuples are: $\{1,2,\ ...\ ,n\}$. I know the total amount of tuples is $n^k$, but I fail to find a simple way to count the part of them containing all elements.
In mathematica I made this function, which does the thing (to be able to verify):
count[n_, k_] := Sum[Fold[{#[[1]] - #2, #[[2]] Binomial[#[[1]], #2]} &,
{n, 1}, Tally[i][[All, 2]]][[2]]/Times @@ (i!) k!, {i, IntegerPartitions[k, {n}]}]

It's not inefficient, however it's no way near the simple stuff my teacher wants. Does a simple formula even exist?

A: Basically you are looking for the number of surjective (onto) functions from a set of size $k$ to a set of size $n$--in your case, the set of size $n$ is $\{1, 2,...,n\}$.
This can be determined with the Principle of Inclusion and Exclusion.
For a function (or equivalently a $k$-tuple) define events: $A_1$: 1 is not used in the $k$-tuple; $A_2$: 2 is not used in the tuple, etc.
Then $A_1\cup A_2\cup \cdots \cup A_n$ is the event that at least one number is not used in the tuple.  The size of this set can be counted by inclusion/exclusion.  Then you want the size of the complementary set (since you want every number to be used in the tuple.  But as you noted, you already know the size of the parent set, namely $n^k$.

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Skeleton role for ex-England front rower
Former England international Neil McCarthy has swapped rugby for skeleton after taking over as Performance Pathway Manager within the GB set up.
The ex-Bath, Gloucester, Bedford and Bristol front rower won three caps for England and was a member of the 1999 Rugby World Cup squad that also featured the likes of Jonny Wilkinson, Martin Johnson and Lawrence Dallaglio.
Since a knee injury forced his retirement as a player in 2002, McCarthy has forged a successful career in talent development, heading up the Leicester Tigers and then Gloucester academies from 2008 onwards.
But he has now taken on an entirely new sport after joining the BBSA to plot the pathway to more Olympic medals for one of the country's most successful winter pursuits.
"I'm really excited about getting involved with GB Skeleton. When you look at their journey from Olympic inception to where it is now - especially without an ice track in the UK - it's mind boggling," said McCarthy.
"This is a consistent medal winning programme. It's remarkable the work that's been done and, of course, there is going to be pressure within the sport to continue that success.
My role is not to come and change that - it's to try and improve it and challenge it so that we can consistently produce athletes for the performance end of the system.
"Yes, I was also a rugby coach but my role was that I headed up academies. That encompassed the full pathway in professional sport. I'm obviously not going to be doing any skeleton coaching so my role here is to manage the talent and development aspects of the performance pathway. It's about identifying talent and then developing it all the way through to the top end. The programme has been unbelievably successful as a system and now it's about small tweaks to keep moving forward."
The difference in the two sports may seem significant at first but McCarthy insists there are plenty of similarities when it comes to talent development. That's true of the both the skills required to succeed as an athlete and the platforms you need to put in place as a pathway to bring out the very best in those aiming for the ultimate glory.
"It's a shift from professional sport to Olympic sport but the dynamics of performance don't change. In respect of the environment and all the dynamics around that, there is not a huge amount of difference," added McCarthy, who insists the idea of working in a sport such as skeleton had long been on his radar.
On the face of it, you see that one is a team sport and the other is an individual sport, but there's a high degree of teamship in skeleton. The journey these athletes go on from novice to podium would be pretty lonely if there wasn't a team aspect to it. But the dynamics around talent development are always individualised anyway so that aspect is imminently applicable and transferable.
"The parallels are also actually striking in terms of the physical development. In rugby, you spend a lot of time working on developing horizontal force, whether that is a tackle, a clean out in contact situations or scrummaging. It's the same as the start in skeleton - you produce force bent over.
"Career-wise, I was heading towards this kind of role. Outside of the coaching, providing support and helping challenge an athlete on their journey is what I've done for the last ten or 15 years.
"Whilst I worked in professional rugby, a lot of my research interests sat outside of that in terms of performance pathways and sporting academies in general. I've always had aspirations to look towards Olympic sport and when this role came along, I saw it as a great opportunity. This is a natural progression in terms of expanding that knowledge and challenging myself in a different environment."
McCarthy will be responsible for delivering the strategic development for the Talent programme within GB Skeleton, a programme which gave the likes of reigning Olympic Champion Lizzy Yarnold her start in the sport.
His appointment is a major boost for the programme as the building blocks for the Beijing 2022 Winter Olympics start to be set in place and Head of Performance, Danny Holdcroft, has no doubt that McCarthy will add significant value to the team.
"We're delighted to have Neil on board and have immediately been impressed with what he has brought to the role," said Holdcroft.
"Neil brings a huge amount of cross-over experience from his time at the Leicester and Gloucester academies and he has a strong track record of supporting athlete transition from talent to performance."
James Howard will be working closely with McCarthy and the existing Talent coaching staff, led by Mark Wood, after starting the summer in a new role with the programme having swapped sliding for coaching. Howard joined GB Skeleton in 2011 via the same recruitment process as the nine new hopefuls and went on to compete for his country on more than 25 occasions.
The 28-year-old made his debut in 2013 and competed across the Europa Cup, North American Cup and Intercontinental Cup circuits over a three-year period but will now turn his attentions to helping produce the next generation of international sliders.

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Blog | Grace on the Margins
Honorary degree violated Jesuit mission, some Fordham University faculty members say
by Jamie Manson
New York — For most Catholics, Lent is a time for the repentance from sins, and Holy Week in particular is a period of reflection on the suffering of Jesus.
At Fordham University in New York, this Lenten season has been a time for faculty members to reflect on the suffering of torture victims and to call university administrators to offer contrition for a decision they made a few years ago.
In 2012, Fordham University's board of trustees selected John O. Brennan to offer the commencement address and to receive an honorary degree from the university.
The decision quickly became a cause of concern among a group of faculty members and students. At the time, Brennan was assistant to the president for homeland security and counterterrorism, and from 1980 to 2005, he served in various positions in the CIA.
Two graduating seniors launched a petition charging that by choosing Brennan, "Fordham University is implicitly endorsing the 'War on Terror,' the use of rendition, the CIA's heinous drone campaign, and the subversion of the rule of law in America, including the assassination of its own citizens."
Though the petition polarized faculty and students on campus, Fordham's administration moved forward with bestowing the honorary degree on Brennan in May 2012. In January 2013, President Barack Obama appointed Brennan as the director of the CIA.
Brennan, who received a bachelor's degree in political science from Fordham in 1977, was furthered feted by the university in September 2014, when Fordham's president, Jesuit Fr. Joseph McShane, gave him the Brien McMahon Award for Distinguished Public Service. By then, the controversy surrounding Brennan had mostly settled.
But just three months later, in December 2014, the Senate Intelligence Committee issued a damning report on the CIA's program of detaining and interrogating terrorism suspects in the years since Sept. 11, 2001. The report detailed some of the grim techniques the CIA used to torture prisoners, including waterboarding, death threats, sleep deprivation and rectal feedings.
The report, and Brennan's subsequent defense of some of the CIA's tactics, reawakened concerns about the honors Fordham had conferred on Brennan. Professor Orlando Rodriguez, chair of Fordham's sociology department, reached out to some of the faculty to explore a meaningful response to university administrators.
Rodriguez is no stranger to the horrors of terrorism or to the struggle for peace. He and his wife, Phyllis, lost their son in the attacks on the World Trade Center. Together, they wrote an open letter, "Not In Our Son's Name," calling on President George W. Bush not to resort to a military retaliation against Afghanistan. (Their story is told in the new documentary "In Our Son's Name.")
Rodriguez and six other faculty members formed Fordham Faculty Against Torture (FFAT) and, in early February, created an online petition calling the university "to exercise its moral leadership and reaffirm its guiding principles by" taking three actions: revoking the honorary degree awarded to Brennan; "promoting reflection within the Fordham community on how our university can better live up to the values espoused in its mission statement"; and "initiating a public dialogue on how, in the wake of the human rights violations committed by our government, we can advance the cause of restorative justice."
Within a week, the petition garnered 200 signatures, the first 100 of which were from faculty.
Jeanne Flavin, a professor of sociology at Fordham and one of the seven organizing faculty members of FFAT, said she sees the petition as an opportunity for the university to examine its shared responsibility to its mission.
"The honorary degree is one of the highest honors the university can bestow," Flavin said, "and yet, in 2012, that degree was given over faculty and student protests."
According to the university's mission statement, as a Jesuit university, "Fordham is committed to research and education that assist in the alleviation of poverty, the promotion of justice, the protection of human rights and respect for the environment."
"We are calling to revoke a degree that never should have been awarded, but we also want this to be a period of reflection and dialogue," Flavin said. "As a community, we should be asking ourselves: Who are we? What does it mean to say that we are champions of human rights and social justice?"
Before the petition went online, the seven faculty members met with McShane in late January. According to a letter posted on Fordham Against Torture's Tumblr, McShane asked the faculty to refrain from moving forward with the petition and offered to invite Brennan back to campus for further conversation. The faculty members respectfully declined.
"We realized that if we invited Brennan to campus in advance of any kind protest, it would be another celebration of him," said David Myers, a professor of history at Fordham and one of the seven organizing members of FFAT. "It didn't reflect the reality of the situation to have him come without the controversy already being there. And the only way for the controversy to be there was for the petition to go forward."
The faculty members began to create events around campus that would promote discussion of the destructive effects of torture and the struggle for human rights. The themes of the Lenten season offered fertile symbolic ground.
Their first event was an Ash Wednesday service. Sister of St. Joseph Elizabeth Johnson, a professor of theology at Fordham, offered a Gospel reflection on Jesus as a victim of torture based her previously written essay "You Did It to Me."
"As the church meditates on the passion of Jesus during Lent, the torture of prisoners by U.S.-approved methods ('coercive interrogation') should not be far from our minds. It is still being done in our name, to enhance national security. Apart from the debate over whether torture is 'effective' or not, Christ's words, amplified by his own graphic suffering, mandate an end to this reprehensible brutality: 'You did it to me,' " Johnson said, invoking Matthew 25:39-40.
The liturgy galvanized enough student interest in the controversy that the organizing faculty members decided to change their group's name to Fordham Against Torture (FAT) to signify the inclusion of students and alumni in the movement.
Louie Dean Valencia-García, a fifth-year doctoral student in history, said he hopes his involvement will leave a legacy of student action in social justice issues.
"If we give an honorary degree to someone who is complicit in torture, then the question is, what is it that Fordham honors? What does that say about our mission statement and, more importantly, about our values?" Valencia-García said. "I want to be associated with Fordham. It's a great place with a wonderful community. I think it will be a better community if we are thinking more broadly about those values as they are stated in the mission statement."
For Rachel Dougherty, a senior at Fordham College's Rose Hill campus, FAT is inspiring not only because of the justice it seeks, but because of the way it has united students and professors.
"In my four years of student organizing at Fordham, this is the first time I've seen a real commitment to students and faculty organizing together," Dougherty said. "I am excited to see faculty leading the charge because it shows a true investment in Fordham University. It's incredible for us to evaluate Fordham's fulfillment -- or lack thereof -- of its own mission and work together to hold our university accountable, because this truly affirms that the university is a space for all of us, together."
Last week, members of FAT organized a teach-in on torture, human rights, and restorative justice in which members of the Fordham faculty offered unique perspectives on torture based on their own areas of expertise. Barry Rosenfeld, a professor of psychology whose work has been dedicated to treating victims of torture, offered a seminar on its psychological and social impact.
The teach-in was held March 24, a date that has significance for both global human rights and the Catholic church. March 24 is the United Nations' International Day for the Right to the Truth Concerning Gross Human Rights Violations and for the Dignity of Victims; the U.N. decided on March 24 because it is the anniversary of the assassination of Archbishop Oscar Romero.
The significance of the day was not lost of Professor Héctor Lindo-Fuentes. Born in El Salvador, Lindo-Fuentes, who is a professor of history and Latin American studies, spoke about the legacy of Romero's denunciation of human rights violations, his defense of the principles promoting human dignity, and his opposition to all forms of violence.
The teach-in's final presentation was offered by Jeannine Hill Fletcher, a professor of theology, who reflected on the ways in which Catholic identity and sacramentality relate to torture.
"Our piety sometimes allows us to forget that the incarnation of the divine resides in the body of an incarcerated victim of torture," Hill Fletcher said, "that the focal point of our worshipping community is a crucifix, on which hangs a dead or dying victim of torture.
"For me, as a theologian," she continued, "revoking [Brennan's] degree would be a statement about our Catholic identity, as one that affirms the sacramental presence in all human beings and which stands up against the humiliation and torture, seeing our responsibility in the sins of our nation and seeking ways that the violated order might be repaired."
Since the teach-in, the number of signatures on the petition has grown to over 420, including 140 faculty members. Other signers include current students and alumni. FAT has not set a date for when they will present McShane and Fordham's board of trustees with the petition.
Though the Fordham University administration has not formally responded to FAT's creation of the petition or the teach-in, on Sunday, Bob Howe, Fordham's senior director of communications, provided the following statement to NCR:
"The Fordham University Board of Trustees stands behind its decision to award John Brennan an honorary degree. The University, and the Board, condemns torture and extrajudicial imprisonment in the strongest possible terms. That said, as a public servant, Mr. Brennan answers to elected officials, including the president of the United States, who are the originators of such policies and who are legally responsible for their creation and implementation.
"President Obama has said he has 'full confidence' in Mr. Brennan, and has reminded reporters that it was Mr. Brennan who called for an inspector general's report. To revoke Mr. Brennan's degree merely because it is within the University's power to do so, as opposed to honors accorded to the elected officials who created and upheld the policies, is both unfair and ineffectual."
Myers said convincing the university to revoke the degree was a long shot. Instead, he sets his hopes on the educational potential of a moment like this.
"We want to make people aware that awarding these degrees is not just something for the week it happens," he said. "Down the road, the degree recipient puts it on his or her resume, can claim approval from a place like Fordham."
That said, Myers said he is proud of the air of civility that has run throughout the process so far. "We have tried to handle the situation like academics," he said. "We've had very good relations with the university, and Father McShane, who is a good and decent man, has been gracious in talking with us about this."
As a historian, he also is acutely aware that, embedded in this controversy, is an important lesson on being on the right side of history.
Brennan, Myers said, "has been actively involved in a policy that overall will bring nothing but shame to this country in the long run."
"If we can say that Father McShane, along with the university, puts into place a dialogue emphasizing rights and responsibilities as Fordham University," Myers added, "and if he seeks to find some way to redress the balance of awarding one degree to Brennan by recognizing someone who has opposed this criminality, then we have done something."
[Jamie L. Manson is NCR books editor. She received her Master of Divinity degree from Yale Divinity School, where she studied Catholic theology and sexual ethics. Her email address is jmanson@ncronline.org.]
Editor's note: We can send you an email alert every time Jamie Manson's column, "Grace on the Margins," is posted to NCRonline.org. Go to this page and follow directions: Email alert sign-up.
Justice | Honorary degree violated Jesuit mission, some Fordham University faculty members say
Encyclical-themed week brings prominent cardinals to US
Fordham University's president rejects call to revoke honorary degree
'Laudato Si'' represents a new 'Rerum Novarum,' says Cardinal Rodríguez at Fordham
Prosecution or pardon of torturers?
Campus Notebook: Aquinas scales back; Midnight Runs; Schneck steps down


I had a great sunrise surprise this morning ,along with the deer in the yard,there were some great sun rays through the morning fog.
Thank you for the great compliment Audrey I'm glad you enjoyed it.
Thanks for the great comment Paul,I'm glad you enjoyed it.
Thanks for the great comment Gracious,and welcome to the L/F.
Thanks for the great comment Rumia,I'm glad you enjoyed it.
I don't know where you live, but it looks like one of Andersen's fairytales, this photo...it inspires a great sense of peace to the viewer!
Thanks for the great comment Larry,I'm glad you enjoyed it.
Thanks for the great comment Gary,that is a one in a million shot for sure.
Man!!! What a great photo! This is the kind of photo I would expect to see in National Geographic. Congratulations.
Alber,I'm sorry I missed your question earlier,this is my back yard in Maine,USA.
Thanks for the great comments Alber,Kathy,and Kelly,I'm glad you enjoyed it.
I haven't been on for quite a while, and stopped by last night to have a look at what everyone's been up to. So glad I did, Absolutely outstanding! What a perfect shot, you couldn't ask for anything better with the lighting. Way to go!
Unbelievably beautifull scenery and shot.Make you feel like you are in a paradise. Could you please write where this photo is taken?
Thanks for the comment Mary,I'm glad you enjoyed it. I loke to catch those sun rays on a foggy morning,especially when there are some critters there too.
This is a beautiful picture. Worth making a wallpaper.
Thanks for the comment Indieshell,I'm glad you enjoyed it.
Thanks for the comment Talsi,I'm glad you enjoyed it.
Thanks for the comment Shawna,I'm glad you enjoyed it.
Thanks for the comment the compliment Joyce,I'm glad you enjoyed it. I hope you stop by long enough to upload some of your great photos.
Thanks for the comment Tammy,I'm glad you enjoyed it.
Thanks for the comments Alandra, Alan,and Karen,I'm glad you enjoyed it.
Gorgeous image. It has so many beautiful elements. One of your best.
what more could a person ask for, right!! What a wonderful photo op. gorgeous sight.


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Auction alert: Rare Sneider 8 gauge hammerless sxs…
June 16, 2016 by Gregg
8 gauge Sneider Baltimore SxS Hammerless Shotgun
I've always been fascinated by 8 gauges. Back in the 19th and in the early 20th century, high-quality eights like the one you see here were used by sportsman to pass shoot ducks, geese & swans. Parker, L.C. Smith & Lefever all made eights. So did smaller American makers like Sneider.
This 8g Sneider was made in the 1880s. When this SxS was built, it was one of the finest hammerless shotguns being made in America — and one of the most innovative.
Charles Edward Sneider learned his trade in Europe and by 1859 he was in Baltimore working for Thomas Poultney & David B. Trimble. By 1865, Sneider was on his own, working in Baltimore from a shop on 66 S Sharp St. In 1874 his sons — Charles Lewis & Charles William — were working with him. Charles William filed the patent that created this shotgun in 1880.
This patent cocked on the fall of the barrels and the locks used coiled springs, which were thought to be more reliable than leaf springs. Sneider built several grades of shotguns on this patent. The upper grades (like the one shown here), locked up with a sliding bolt which engaged a bite in the rear barrel lump and top extension. They also featured compensating hinge pin which could be adjusted for wear and a unique sliding barrel stop which kept the barrels from wearing on the hinge pin when the gun was opened.
Front cover of an original Clark & Sneider catalog
This Sneider is on Gunbroker.com now and the auction ends 6/26/2016 9:00 PM.
Sneider Highgrade 8 GA. SxS: barrel rib marked "Sneider's Patent Baltimore MD" Sneider was America's first true sidelock shotgun. 36″ fine damascus barrels. Nice shinny bore with very small area of light pitting. No dings dents or bulges in barrels. Gun locks up tight and solid. Receiver and trigger guard are beautifully engraved. Dog head on trigger guard. Marsh scene with water foul on side plates. Gun is serial numbered 610 on trigger guard and water table. Small chip at toe of butt plate only – not wood. Chip at end of right side of forearm. Weight 13lbs 14.1 oz. LOP 13 5/8″ & 12 5/8″. DAC 2 1/4″. DAH 3 5/8″
Page from Original Clark & Sneider catalog
DOUBLE BARREL SHOTGUNS8 gauge, American, Baltimore, double barrel, eight gauge, shotgun, Side by Side, sneider, SxS
« Auction alert: SxS Webley & Scott Model 700 12 gauge, 28″…
Auction alert: 20 gauge Beretta BL-4 O/U, 28″ barrels… »
Odd, but still decent: a 16g Fox Sterlingworth
July 15, 2019 July 14, 2019 by Gregg
This isn't what I had hoped it would be, but it's still a nice gun. It looks like it would awesome for grouse, woodcock, and quail.
This week's 5 doubles you don't want to miss …
July 14, 2019 by Gregg
Great guns -- from this incredible W & C Scott Premier and an awesome Parker to a killer Fox A grade and two more hard-to-find side by sides. See all 5 guns now.
Auction alert: 16g L.C. Smith Field Grade, 28″ bbls…
Vintage, but not too vintage. You may be able to get a deal on this great looking L.C. Smith 16. Check it out now.


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GEF's response to COVID-19
Photo: Alex Yuzhakov/Shutterstock
The coronavirus pandemic has forced us all to confront how environmental degradation bringing wildlife and people too close together endangers economies and societies alike. In a document prepared for the 58th GEF Council, the Global Environment Facility Secretariat outlines its planned response to COVID-19. Read it here.
The coronavirus pandemic that has shuttered most of the world in 2020 has its roots in the environmental degradation that the Global Environment Facility and its partners are working to stop. It is increasingly clear that to manage this crisis and avert future ones, we need to understand the root cause of zoonotic diseases – namely, a collision between human systems and natural systems.
Recognizing the urgency of this moment, and the high stakes for governments and businesses who are starting to think through economic recovery plans, the GEF Secretariat has outlined a set of steps for the immediate, medium, and longer term to help address the present situation and reduce the probability of new environmental crises emerging in the foreseeable future. The response spans measures to address wildlife trading, deforestation, urban sprawl, and other pressures on ecosystems that are bringing wild animals and humans in dangerous proximity.
The response also includes efforts to support a green economic recovery consistent with sustainable and nature-based development. These steps focus on the acceleration of needed transformations to economic and social systems to reduce their conflict with nature – building on efforts already underway by the GEF-funded Good Growth Partnership and the GEF Impact Programs on Food Systems, Land Use and Restoration; Sustainable Cities; and Sustainable Forest Management.
The planned steps include:
Immediate actions
Increased focus on efforts to deal with the wildlife trade and consumption challenges. Through the Global Wildlife Program, the largest global effort to date to tackle wildlife trafficking, the GEF has been working with the World Bank and many other partners to help countries in Africa and Asia invest in innovative solutions. However, important gaps remain. Furthermore, the demand side of the equation needs to be placed in sharper focus to handle unchecked consumption of bushmeat and wildlife products.
Conduct analysis on the future risks linked to emerging infectious diseases along with their root causes, including their connection with deforestation and ecosystem fragmentation. A group of experts is being formed to identify priority near-term actions, to explore how projects could be fitted with campaigns on public awareness and behavior change, and to gather and disseminate information on the ecological and local economic consequences of pandemics. The experts group will also support the development of a white paper on future risks linked to emerging infectious diseases and to critical aspects of environmental degradation such as deforestation and habitat fragmentation.
Identify risks in projects and programs that may seriously compromise past gains and future outcomes. The GEF is already engaging with implementing agencies to explore how important operations, such as those performed by rangers and other essential personnel in the target protected areas, could be sustained during this difficult period.
Medium-term actions
Develop an internal blueprint on how to deploy ongoing and upcoming projects that can help lay the foundation for a green recovery. This blueprint will integrate the risks and opportunities linked to COVID-19 in the current funding cycle and include an examination of how the crisis is affecting strategic platforms of engagement on themes such as food security, cities, mining and mercury, and the circular economy. The blueprint will also encompass the GEF program on adaptation funded by the Least Developed Countries Fund and Special Climate Change Fund, and delve into other areas such as infectious healthcare waste.
Longer-term actions
Further promote systems change thinking in the strategies to guide GEF's upcoming 8th Replenishment cycle. The replenishment discussion provides an opportunity to explore the lasting solution to COVID-19 and other such diseases, which is to accelerate transformational change to the human systems, be they energy, cities, food, and production and consumption, so that a balance between natural systems and human systems be restored within planetary boundaries.
Read the Council document for more information.
COVID-19 updates from the GEF partnership


With the help of friends, I've been working on a logo for the Living with Loss project. We are still fine-tuning it, but the general idea is a tree, blown in the wind, with leaves falling. The tree's roots are also visible, representing how being rooted in love and faith (for those who embrace faith) enables us to keep standing even through the winds of life.
But the important part is the leaves dropping, being blown off, and we stand there as a tree denuded of its green growth.
The focus of the picture is on ourselves, the bereaved, and our life in the here and now – our life with loss – as that's the focus of my Living with Loss projects.
Our loved one(s) are missing.
I miss my children when I wake up in the morning. I miss my daughter's morning calls, the "hello mum" while she sat in her kitchen in her own home, coffee and cigarette in hand. I miss what was, and I miss what might have been.
I talk with other bereaved people and hear what they are missing. The companionship of a lifelong partner. The empty nest of a bereaved parent. The friendship of a brother or sister.
They say that some of those who lose a limb experience phantom sensations, as though the limb is still intact. We bereaved have those feelings too.
I visited friends recently and was shown what appeared at first glance to be a beautiful picture of a full and complete family. Three generations, all ages, sizes and shapes, different personalities. It was easy to forget, looking at that picture of so many happy faces, that a central figure was missing – the mother/grandmother, taken by cancer some years back.
Who isn't living with loss? Who isn't missing someone?
One way of handling those profound feelings of loss is to try to distract yourself, and that sometimes works. Another way is to make them a part of your day. Just writing about Catherine for a moment made me feel a bit better. And just now I looked up at my big picture of Pax and see him smiling. I remember the feel of the fabric of the dungarees he's wearing, and that sensation roots me back into that time, so long ago, when he was here.
Back to the tree of the logo. A tree is full of history, each ring inside is another layer of its story. Those stories and memories are part of us, to be treasured.


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Rangitahi Bridge To Open in the New Year
The eponymously named Rangitahi Bridge, linking the peninsula to mainland Raglan is to open next year, with a karakia by local iwi. The bridge now only needs to complete the asphalt surface and the installation of pou designed by Kawharu Greensil, and this huge milestone will be ready to use to conduct people to the Rangitahi project.
Rangitahi Marketing and Communications Manager, Sophie Peacocke says, "It means the Raglan community and beyond will be able to access the peninsula, including people who have purchased land there, which is pretty exicting for the project. The landowners will be able to begin building their homes."
The distinctive 'pou' which will be installed at each corner of the bridge represent turuturu, the pegs used to string the cloak across during the weaving process, and the zig zag pattern on the bridge represents the cloak, and signifies the two pieces of land coming together.
The bridge is two lanes, with pedestrian and cycle access. The footpath on the northern side is 2.5m wide, and acts as shared spaces to link to the walking tracks around the peninsula. There is also a narrow footpath on the southern side of the bridge, just 1.5 metres wide, so there is safe access on both sides. "We wanted to enourage people to get out walking or cycling rather than using their cars, especially on the weekend; they can walk or cycle into town," she says.
Work started at the beginning of November to upgrade Opotoru Road and connect it to the bridge, and this will continue through summer, and is expected to be completed in six months. "With the constrution of the subdivision, earthworks, roading and landscaping, we are now into our second construction season, due to delays mostly to do with wet weather."
The Rangitahi Project aims to provide land for those wanting to join Raglan's laid-back seaside community, to build their own dreams, and to create a life that promises beauty and simplicity, so for more information on Rangitahi peninsula development, Ragland properties for sale and Waikato property please go to https://rangitahi.co.nz .


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text:
Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials
M. K. Nishijima, R. C. Koehler, P. D. Hurn, S. M. Eleff, S. Norris, W. E. Jacobus, R. J. Traystman
We tested the hypotheses that after complete cerebral ischemia, first, rate of recovery of ATP, phosphocreatine (PCr), and intracellular pH (pH(i)) varies with ischemic duration and second, rate of metabolic recovery is a more sensitive predictor of consequent electrophysiological deficit than steady-state metabolic recovery. With the use of transient intracranial hypertension in anesthetized dogs, ischemic duration was set for either 3, 12, or 30 min, which depressed somatosensory-evoked potential (SEP) recovery amplitude by 30, 59, and 88%, respectively. In contrast, ATP, PCr, and pH(i), measured by 31P magnetic resonance spectroscopy, fully recovered. When ischemic duration was increased from 3 to 12 min, mean recovery time of ATP (6 min) remained rapid but that of pH(i) (12-28 min) was prolonged. After 30 min of ischemia, pH(i) recovery was not slowed further (25 min) but that of ATP was now markedly prolonged (36 min). PCr recovery time increased progressively with ischemic duration (5, 11, and 21 min, respectively) and correlated best with SEP recovery (r = 0.74). We conclude that the brain's ability to rapidly normalize pH is a sensitive predictor of electrophysiological recovery after short ischemia but that ATP regeneration becomes important with prolonged ischemia. PCr recovery rate was the best overall predictor, probably because it depends on both pH(i) and the ratio of ATP to ADP by the creatine kinase reaction.
American Journal of Physiology - Heart and Circulatory Physiology
bicarbonate ion
cerebral oxygen consumption
somatosensory evoked potential
Dive into the research topics of 'Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials'. Together they form a unique fingerprint.
Phosphocreatine Medicine & Life Sciences 100%
Evoked Potentials Medicine & Life Sciences 79%
Adenosine Triphosphate Medicine & Life Sciences 63%
ATP Synthetase Complexes Medicine & Life Sciences 22%
Intracranial Hypertension Medicine & Life Sciences 14%
Creatine Kinase Medicine & Life Sciences 12%
Brain Ischemia Medicine & Life Sciences 11%
Nishijima, M. K., Koehler, R. C., Hurn, P. D., Eleff, S. M., Norris, S., Jacobus, W. E., & Traystman, R. J. (1989). Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials. American Journal of Physiology - Heart and Circulatory Physiology, 257(6), 26/6.
Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials. / Nishijima, M. K.; Koehler, R. C.; Hurn, P. D.; Eleff, S. M.; Norris, S.; Jacobus, W. E.; Traystman, R. J.
In: American Journal of Physiology - Heart and Circulatory Physiology, Vol. 257, No. 6, 1989, p. 26/6.
Nishijima, MK, Koehler, RC, Hurn, PD, Eleff, SM, Norris, S, Jacobus, WE & Traystman, RJ 1989, 'Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials', American Journal of Physiology - Heart and Circulatory Physiology, vol. 257, no. 6, pp. 26/6.
Nishijima MK, Koehler RC, Hurn PD, Eleff SM, Norris S, Jacobus WE et al. Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials. American Journal of Physiology - Heart and Circulatory Physiology. 1989;257(6):26/6.
Nishijima, M. K. ; Koehler, R. C. ; Hurn, P. D. ; Eleff, S. M. ; Norris, S. ; Jacobus, W. E. ; Traystman, R. J. / Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials. In: American Journal of Physiology - Heart and Circulatory Physiology. 1989 ; Vol. 257, No. 6. pp. 26/6.
@article{ee6d594041034eb2bfba11565707e581,
title = "Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials",
abstract = "We tested the hypotheses that after complete cerebral ischemia, first, rate of recovery of ATP, phosphocreatine (PCr), and intracellular pH (pH(i)) varies with ischemic duration and second, rate of metabolic recovery is a more sensitive predictor of consequent electrophysiological deficit than steady-state metabolic recovery. With the use of transient intracranial hypertension in anesthetized dogs, ischemic duration was set for either 3, 12, or 30 min, which depressed somatosensory-evoked potential (SEP) recovery amplitude by 30, 59, and 88%, respectively. In contrast, ATP, PCr, and pH(i), measured by 31P magnetic resonance spectroscopy, fully recovered. When ischemic duration was increased from 3 to 12 min, mean recovery time of ATP (6 min) remained rapid but that of pH(i) (12-28 min) was prolonged. After 30 min of ischemia, pH(i) recovery was not slowed further (25 min) but that of ATP was now markedly prolonged (36 min). PCr recovery time increased progressively with ischemic duration (5, 11, and 21 min, respectively) and correlated best with SEP recovery (r = 0.74). We conclude that the brain's ability to rapidly normalize pH is a sensitive predictor of electrophysiological recovery after short ischemia but that ATP regeneration becomes important with prolonged ischemia. PCr recovery rate was the best overall predictor, probably because it depends on both pH(i) and the ratio of ATP to ADP by the creatine kinase reaction.",
keywords = "adenosine triphosphate, bicarbonate ion, cerebral blood flow, cerebral oxygen consumption, dogs, magnetic resonance spectroscopy, somatosensory evoked potential",
author = "Nishijima, {M. K.} and Koehler, {R. C.} and Hurn, {P. D.} and Eleff, {S. M.} and S. Norris and Jacobus, {W. E.} and Traystman, {R. J.}",
pages = "26/6",
journal = "American Journal of Physiology",
T1 - Postischemic recovery rate of cerebral ATP, phosphocreatine, pH, and evoked potentials
AU - Nishijima, M. K.
AU - Koehler, R. C.
AU - Hurn, P. D.
AU - Eleff, S. M.
AU - Norris, S.
AU - Jacobus, W. E.
AU - Traystman, R. J.
N2 - We tested the hypotheses that after complete cerebral ischemia, first, rate of recovery of ATP, phosphocreatine (PCr), and intracellular pH (pH(i)) varies with ischemic duration and second, rate of metabolic recovery is a more sensitive predictor of consequent electrophysiological deficit than steady-state metabolic recovery. With the use of transient intracranial hypertension in anesthetized dogs, ischemic duration was set for either 3, 12, or 30 min, which depressed somatosensory-evoked potential (SEP) recovery amplitude by 30, 59, and 88%, respectively. In contrast, ATP, PCr, and pH(i), measured by 31P magnetic resonance spectroscopy, fully recovered. When ischemic duration was increased from 3 to 12 min, mean recovery time of ATP (6 min) remained rapid but that of pH(i) (12-28 min) was prolonged. After 30 min of ischemia, pH(i) recovery was not slowed further (25 min) but that of ATP was now markedly prolonged (36 min). PCr recovery time increased progressively with ischemic duration (5, 11, and 21 min, respectively) and correlated best with SEP recovery (r = 0.74). We conclude that the brain's ability to rapidly normalize pH is a sensitive predictor of electrophysiological recovery after short ischemia but that ATP regeneration becomes important with prolonged ischemia. PCr recovery rate was the best overall predictor, probably because it depends on both pH(i) and the ratio of ATP to ADP by the creatine kinase reaction.
AB - We tested the hypotheses that after complete cerebral ischemia, first, rate of recovery of ATP, phosphocreatine (PCr), and intracellular pH (pH(i)) varies with ischemic duration and second, rate of metabolic recovery is a more sensitive predictor of consequent electrophysiological deficit than steady-state metabolic recovery. With the use of transient intracranial hypertension in anesthetized dogs, ischemic duration was set for either 3, 12, or 30 min, which depressed somatosensory-evoked potential (SEP) recovery amplitude by 30, 59, and 88%, respectively. In contrast, ATP, PCr, and pH(i), measured by 31P magnetic resonance spectroscopy, fully recovered. When ischemic duration was increased from 3 to 12 min, mean recovery time of ATP (6 min) remained rapid but that of pH(i) (12-28 min) was prolonged. After 30 min of ischemia, pH(i) recovery was not slowed further (25 min) but that of ATP was now markedly prolonged (36 min). PCr recovery time increased progressively with ischemic duration (5, 11, and 21 min, respectively) and correlated best with SEP recovery (r = 0.74). We conclude that the brain's ability to rapidly normalize pH is a sensitive predictor of electrophysiological recovery after short ischemia but that ATP regeneration becomes important with prolonged ischemia. PCr recovery rate was the best overall predictor, probably because it depends on both pH(i) and the ratio of ATP to ADP by the creatine kinase reaction.
KW - adenosine triphosphate
KW - bicarbonate ion
KW - cerebral blood flow
KW - cerebral oxygen consumption
KW - dogs
KW - magnetic resonance spectroscopy
KW - somatosensory evoked potential
SP - 26/6
JO - American Journal of Physiology
JF - American Journal of Physiology


After reading Bernard Lunn's piece about Xing and LinkedIn I found another interesting article of his about Google's recent reaction towards a Microsoft Yahoo merger ("it is not good for the Internet"). "What pussies" a friend mine said (sorry;-).
But so far I thought Yahoo's most valuable asset is Yahoo Finance. Of course, they also have, Yahoo Mail. And together with Microsoft that makes 56% market share for the mail market (so they say). And it is kind of a hard question, what conveys more information about you, your web surfing habits or your email exchanges.
Anyway, now comes the other scary number that Bernard Lunn brought up, that email represents 49% of web page impressions! That makes 27% market share of all internet impressions. Wow.
Here is the article: 49% & 56%: Are These What Have Brin Worried?
* Email is 49% of Impressions. Portals and Search Engines is 10% by contrast. This is some free data from Nielsen-Netratings. click on Top Site Genres.
* 56% is Microsoft and Yahoo combined market share of webmail. Gmail is down at 7%. This data is via Fred Wilson's back of envelope calculations.
Yes both data sets can have a pretty wide margin of error, but even discounting that, this would be cause for worry.
Sure, in the early adopter world we live in, Gmail rocks and who would be seen dead with AOL or Hotmail? But that 50% market share for Microhoo is what you will see in the real world.
Hotmail has lagged terribly. Most people who used it would not return, I cannot imagine who would switch (an AOL user maybe) and most people already have email. So it is a lost cause. One major reason it lagged IMHO was Microsoft fear of cannibalizing Outlook. So they won't offer the features that users want that both Google and Yahoo have been rushing to fill. Yahoo is reputed to have the most "Outlook-like" interface and that matters massively to people making the switch.
Microsoft will probably do the smart thing and let the Yahoo team run with email. Hotmail will die as a separate brand, eventually.
The real battle of course remains around search within email and thus monetization. Google is better at relevant ads in Gmail because they have a better search engine. But if Microhoo gets its act together in search, they have the bigger content/audience to monetize. Technically improving search is not that hard. Microsoft have all the R&D money they need and, more importantly, every search start-up looking to exit to them. If you really can improve search you have one fat valuation offer coming down the pike!
Here is the really interesting bit. Improving ad relevance within email does not require any searching behavior change. That is worth repeating. Say after me, "if we have 56% of 49% we have something like 25% of ad impressions and all we need to do is serve relevant ads". Come on developers, you can fix that, right? Page rank is not relevant. Getting people to switch from Google to another search engine is not required.
However email is not just fodder for search it is the key to ad relevance, via the social graph. As Fred Wilson puts it, email is "the biggest social graph".
Yes, the graph, who is connected to whom, that is indeed valuable. But the content of the mail is also, hmm, private and personal?! Everyone surfs the web, but does everyone publish there? Out in the open? Hardly. Only a minority publishes anything. But every working citizen has an email account and will write job related and private emails. Do people write everything they think in emails. Unlikely, but who would be comfortable if their mailbox would leak to the public:).
Another point, each mail has at least two parties involved. So with 10% market share of mail boxes you might actually cover twice as much percentage wise of the email universe. That doesn't help for serving ads, but, it helps building intelligence about what is going on out there and optimizing the algos. Again, it is a hard question what is more important, knowing what people search and surf on the web, or what they write in their personal email. With 56% email market share, Microhoo might actually know about maybe something like 70-80% of all mails?!
But then, who ever is in second place might just go to the NSA for a flat copy of it all in exchange for potentially better technology to snoop through it all:o).


GnuCash - User - Foreign currency accounts and transactions.
Foreign currency accounts and transactions.
for $45 and in the split balanced it with Expenses:Books.
the world can this balance?
or the value from the Price Editor?
account and GBP0.00 in another?
How in the world can the accounts balance when I forget to E-E-R?
Re: Foreign currency accounts and transactions.
> or the value from the Price Editor?
happen properly in all cases.
> account and GBP0.00 in another?
> How in the world can the accounts balance when I forget to E-E-R?
moment. However it's not balancing in terms of changes-in-capital.
But GnuCash doesn't check that now.
those accounts no longer exist.
>> or the value from the Price Editor?
> happen properly in all cases.
I'll do a few more in the same place and see what happens.
>> How in the world can the accounts balance when I forget to E-E-R?
> moment. However it's not balancing in terms of changes-in-capital.
> But GnuCash doesn't check that now.
> those accounts no longer exist.
currency I have in my desk, right?
>>> or the value from the Price Editor?
>> happen properly in all cases.
> I'll do a few more in the same place and see what happens.
>>> How in the world can the accounts balance when I forget to E-E-R?
>> moment. However it's not balancing in terms of changes-in-capital.
>> But GnuCash doesn't check that now.
each transaction, it shows up as GBP0.00 in the expense account!
pre-loaded.) Is this a reportable bug?
>>>> or the value from the Price Editor?
>>> happen properly in all cases.
>> I'll do a few more in the same place and see what happens.
>>>> How in the world can the accounts balance when I forget to E-E-R?
>>> moment. However it's not balancing in terms of changes-in-capital.
>>> But GnuCash doesn't check that now.
> each transaction, it shows up as GBP0.00 in the expense account!
> pre-loaded.) Is this a reportable bug?
are bugs where this does not happen properly in all cases".
>>>>> or the value from the Price Editor?
>>>> happen properly in all cases.
>>> I'll do a few more in the same place and see what happens.
so far. Any advice would be very welcome.
> so far. Any advice would be very welcome.
exchange rate of that transaction.
have an exchange rate entered at the time the transaction is created.
in, because the transaction has no meaning without the exchange rate.
rate AND the actual value in the register at the same time!
> rate AND the actual value in the register at the same time!
billed in GBP (which is also my main currency).
reconcilable with my statement, and Expenses:Books will be correct.
this approach seems straightforward. Is it wrong?
>> each transaction, it shows up as GBP0.00 in the expense account!
>> pre-loaded.) Is this a reportable bug?
> are bugs where this does not happen properly in all cases".
with a 0.00 value in the Expenses tree?
> billed in GBP (which is also my main currency).
> be their correct values.
> reconcilable with my statement, and Expenses:Books will be correct.
> this approach seems straightforward. Is it wrong?
it doesn't work when you're actually buying the currency.
handle as a "negative expense": eg.
card bill will eventually be.
>> billed in GBP (which is also my main currency).
>> be their correct values.
>> reconcilable with my statement, and Expenses:Books will be correct.
>> this approach seems straightforward. Is it wrong?
> This approach would certainly work when you're buying goods..
That's the only thing I meant! So it's OK for that?
> But it doesn't work when you're actually buying the currency.
know I'll have to handle it "the complicated way".
function of the "Price Editor"?
>> This approach would certainly work when you're buying goods..
> That's the only thing I meant! So it's OK for that?
> function of the "Price Editor"?
you that, then current value of the holding.
price) and gain/loss (sale price) of that foreign currency.
> you that, then current value of the holding.
> price) and gain/loss (sale price) of that foreign currency.
liabilities to be revalued --- right?
> I hope this clears up your confusion.
Yes, I think so! Thanks again.
>> you that, then current value of the holding.
> (e.g. Assets:Cash:Euros or Assets:Investments:YoyodyneShares).
>> price) and gain/loss (sale price) of that foreign currency.
> liabilities to be revalued --- right?
will not change what appears in your registers.
>> I hope this clears up your confusion.
> Yes, I think so! Thanks again.
Great! Maybe someone else will learn from it, too.
>> liabilities to be revalued --- right?
> will not change what appears in your registers.
That's what I meant. All clear now, thanks!
in the Income accounts to match it?
#3--they don't exist except in concept.
> >> How in the world can the accounts balance when I forget to E-E-R?
> > moment. However it's not balancing in terms of changes-in-capital.
> > But GnuCash doesn't check that now.
> in the Income accounts to match it?


text:
Q: Can two different sets of semiprimes share the same sum? Given:

*

*A semiprime number is defined as the product of two primes

*$a$, $b$, $c$, $d$, $e$ and $f$ are all distinct semiprimes
Can a proof be constructed showing that the following equation cannot be satisfied:
$$a + b = c + d$$
Moreover, can this be expanded to sums of more than two semiprimes, for example:
$$a + b + c = d + e + f$$

A: Both equations can be satisfied.
$$
4 + 21 = 10 + 15
$$
and
$$
9 + 10 + 21 = 4 + 14 + 22
$$
Hence no such proof is possible.