I gave a talk at MSR New England, to a fairly eclectic audience, so the talk isn't too technical (although it has technical flourishes:).
Random Graph Models in Kidney Exchange - Theoretical Developments and Practical Challenges (the movie), presented at MSR New England, July 25, 2012. The video runs an hour and a half, including the questions at the end.
It gives a quick history of kidney exchange developments, leading up to my recent work on random graphs with Itai Ashlagi, David Gamarnik (who was in the audience) and Mike Rees (who was probably doing a transplant while I spoke). And it ends with some discussion of repugnance--motivated by the laws against buying and selling organs for transplant.
Microsoft has come a long way towards mastering the art of presenting the video and the slides at the same time...you can't see where I'm pointing with the laser pointer or with my hand (since that goes off camera), and when I backtrack on the slides you can seldom see it in the video, but the slides are presented in a way that's mostly well synchronized with the talk (until near the end), and the cameraman doesn't have to choose between the slides and the speaker. (I don't think you can hear the questions though, I'm wearing a microphone, but there wasn't one for the audience members.) (I wrote the above paragraph after viewing on a large screen: when I viewed the same video on my laptop, and then again on an iPad I had a very different, much less satisfactory experience, and couldn't see the slides at all...:(
Friday, July 27, 2012
Thursday, July 26, 2012
Altruistic kidney donors help many, in Science News
Rachel Ehrenberg in Science News reports on long kidney chains: Altruistic kidney donors help many.
"Many people needing kidney transplants have a willing donor, but they can’t take the kidney because it’s not compatible with their blood type or immune system. Paired exchanges, where incompatible donor/recipient pairs swap kidneys with another incompatible pair, is one trick for getting kidneys into hard-to-match patients. Another trick is a donor chain: A person gives a kidney to a clearinghouse or kidney exchange, which can set off a chain of donations.
"Within the kidney transplant community, there’s been an ongoing debate over whether long chains ultimately mean more transplants. “The mathematical question was, are we really transplanting more people?” says Alvin Roth, an expert in game theory and market design at Harvard. “The answer is yes, a lot more.”
...
"It turns out to not be an easy problem. It’s very hard computationally,” says MIT’s Itai Ashlagi, who conducted the analysis along with Roth, MIT’s David Gamarnik, and Michael Rees, a transplant surgeon at the University of Toledo and medical director of the Alliance for Paired Donation, which arranged the first non-simultaneous chain of 10 kidney transplants."
The story also quotes a dissenting voice from Dorry Segev at Johns Hopkins...
**********
Here's the paper:
Ashlagi, Itai, David Gamarnik, Michael A. Rees and Alvin E. Roth, "The Need for (long) Chains in Kidney Exchange," working paper, May 2012.
"Many people needing kidney transplants have a willing donor, but they can’t take the kidney because it’s not compatible with their blood type or immune system. Paired exchanges, where incompatible donor/recipient pairs swap kidneys with another incompatible pair, is one trick for getting kidneys into hard-to-match patients. Another trick is a donor chain: A person gives a kidney to a clearinghouse or kidney exchange, which can set off a chain of donations.
"Within the kidney transplant community, there’s been an ongoing debate over whether long chains ultimately mean more transplants. “The mathematical question was, are we really transplanting more people?” says Alvin Roth, an expert in game theory and market design at Harvard. “The answer is yes, a lot more.”
...
"It turns out to not be an easy problem. It’s very hard computationally,” says MIT’s Itai Ashlagi, who conducted the analysis along with Roth, MIT’s David Gamarnik, and Michael Rees, a transplant surgeon at the University of Toledo and medical director of the Alliance for Paired Donation, which arranged the first non-simultaneous chain of 10 kidney transplants."
The story also quotes a dissenting voice from Dorry Segev at Johns Hopkins...
**********
Here's the paper:
Ashlagi, Itai, David Gamarnik, Michael A. Rees and Alvin E. Roth, "The Need for (long) Chains in Kidney Exchange," working paper, May 2012.
Wednesday, July 25, 2012
More on circumcision in Germany
Further developments on the ruling of a German court earlier this summer, banning circumcision.
"German lawmakers have passed a cross-party motion to protect religious circumcision, after a regional court ruled it amounted to bodily harm.
The resolution urges the government to draw up a bill allowing the circumcision of boys.
Germany's main political parties - together with Jewish and Muslim groups - have criticised the ruling by the Cologne court in June.
Chancellor Angela Merkel said it risked making Germany a "laughing stock".
The Cologne ruling involved a doctor who carried out a circumcision on a four-year-old that led to medical complications.
The doctor involved in the case was acquitted and the ruling was not binding. However, critics feared it could set a precedent for other German courts.
Germany's Medical Association told doctors after the ruling not to perform circumcisions.
'Tolerant country' The motion approved on Thursday in the lower house of parliament says the government should "present a draft law in the autumn... that guarantees that the circumcision of boys, carried out with medical expertise and without unnecessary pain, is permitted".
"Jewish and Muslim religious life must continue to be possible in Germany. Circumcision has a central religious significance for Jews and Muslims," it added.
The new law would overrule the decision by the Cologne court.
Ahead of the vote, Foreign Minister Guido Westerwelle said the proposed motion showed that Germany was a "tolerant and cosmopolitan country".
European Jewish and Muslim groups earlier also joined forces to defend circumcision.
An unusual joint statement was signed by leaders of groups including the Rabbinical Centre of Europe, the European Jewish Parliament, the European Jewish Association, Germany's Turkish-Islamic Union for Religious Affairs and the Islamic Centre Brussels.
"We consider this to be an affront [to] our basic religious and human rights," it said.
The BBC's Stephen Evans in Berlin says opinion in Germany about the issue has been mixed, though slightly more Germans were in favour of the ban.
He says that many readers' comments on newspaper websites have indicated anger that this generation of Germans seems to be being constricted in its actions because of the Holocaust."
Angela Merkel intervenes over court ban on circumcision of young boys--Spokesman says right to circumcision must be restored as a matter of urgency, after Cologne court's ruling against practice
"Angela Merkel's spokesman has promised Germany's Jewish and Muslim communities they will be free to carry out circumcision on young boys, despite a court ban that has raised concerns about religious freedom.
"The government said it would find a way around a ban imposed by a court in Cologne in June as a matter of urgency.
"For everyone in the government it is absolutely clear that we want to have Jewish and Muslim religious life in Germany," said Merkel's spokesman, Steffen Seibert.
*********
Ynet covers the story this way: Chancellor told party members she did not want Germany to be 'only country in which Jews cannot practice their rites'
************
July 19: German MPs vote to protect religious circumcision
"German lawmakers have passed a cross-party motion to protect religious circumcision, after a regional court ruled it amounted to bodily harm.
"German lawmakers have passed a cross-party motion to protect religious circumcision, after a regional court ruled it amounted to bodily harm.
The resolution urges the government to draw up a bill allowing the circumcision of boys.
Germany's main political parties - together with Jewish and Muslim groups - have criticised the ruling by the Cologne court in June.
Chancellor Angela Merkel said it risked making Germany a "laughing stock".
The Cologne ruling involved a doctor who carried out a circumcision on a four-year-old that led to medical complications.
The doctor involved in the case was acquitted and the ruling was not binding. However, critics feared it could set a precedent for other German courts.
Germany's Medical Association told doctors after the ruling not to perform circumcisions.
'Tolerant country' The motion approved on Thursday in the lower house of parliament says the government should "present a draft law in the autumn... that guarantees that the circumcision of boys, carried out with medical expertise and without unnecessary pain, is permitted".
"Jewish and Muslim religious life must continue to be possible in Germany. Circumcision has a central religious significance for Jews and Muslims," it added.
The new law would overrule the decision by the Cologne court.
Ahead of the vote, Foreign Minister Guido Westerwelle said the proposed motion showed that Germany was a "tolerant and cosmopolitan country".
European Jewish and Muslim groups earlier also joined forces to defend circumcision.
An unusual joint statement was signed by leaders of groups including the Rabbinical Centre of Europe, the European Jewish Parliament, the European Jewish Association, Germany's Turkish-Islamic Union for Religious Affairs and the Islamic Centre Brussels.
"We consider this to be an affront [to] our basic religious and human rights," it said.
The BBC's Stephen Evans in Berlin says opinion in Germany about the issue has been mixed, though slightly more Germans were in favour of the ban.
He says that many readers' comments on newspaper websites have indicated anger that this generation of Germans seems to be being constricted in its actions because of the Holocaust."
Angela Merkel intervenes over court ban on circumcision of young boys--Spokesman says right to circumcision must be restored as a matter of urgency, after Cologne court's ruling against practice
"Angela Merkel's spokesman has promised Germany's Jewish and Muslim communities they will be free to carry out circumcision on young boys, despite a court ban that has raised concerns about religious freedom.
"The government said it would find a way around a ban imposed by a court in Cologne in June as a matter of urgency.
"For everyone in the government it is absolutely clear that we want to have Jewish and Muslim religious life in Germany," said Merkel's spokesman, Steffen Seibert.
*********
Ynet covers the story this way: Chancellor told party members she did not want Germany to be 'only country in which Jews cannot practice their rites'
************
July 19: German MPs vote to protect religious circumcision
"German lawmakers have passed a cross-party motion to protect religious circumcision, after a regional court ruled it amounted to bodily harm.
The resolution urges the government to draw up a bill allowing the circumcision of boys.
Germany's main political parties - together with Jewish and Muslim groups - have criticised the ruling by the Cologne court in June.
Chancellor Angela Merkel said it risked making Germany a "laughing stock".
The Cologne ruling involved a doctor who carried out a circumcision on a four-year-old that led to medical complications.
The doctor involved in the case was acquitted and the ruling was not binding. However, critics feared it could set a precedent for other German courts.
Germany's Medical Association told doctors after the ruling not to perform circumcisions.
...
The motion approved on Thursday in the lower house of parliament says the government should "present a draft law in the autumn... that guarantees that the circumcision of boys, carried out with medical expertise and without unnecessary pain, is permitted".
"Jewish and Muslim religious life must continue to be possible in Germany. Circumcision has a central religious significance for Jews and Muslims," it added.
The new law would overrule the decision by the Cologne court.
Ahead of the vote, Foreign Minister Guido Westerwelle said the proposed motion showed that Germany was a "tolerant and cosmopolitan country".
...
The BBC's Stephen Evans in Berlin says opinion in Germany about the issue has been mixed, though slightly more Germans were in favour of the ban.
He says that many readers' comments on newspaper websites have indicated anger that this generation of Germans seems to be being constricted in its actions because of the Holocaust.
Tuesday, July 24, 2012
Incentives and privacy
A new paper by three computer scientists and an economist reports on some connections between privacy and incentive compatibility.
MECHANISM DESIGN IN LARGE GAMES: INCENTIVES AND PRIVACY
by
MICHAEL KEARNS, MALLESH M. PAI, AARON ROTH and JONATHAN ULLMAN
July 18, 2012
ABSTRACT
We study the design of mechanisms satisfying two desiderata— incentive compatibility and privacy. The first, requires that each agent should be incentivized to report her private information truthfully. The second, privacy, requires the mechanism not reveal ‘much’ about any agent’s type to other agents. We propose a notion of privacy we call Joint Differential Privacy. It is a variant of Differential Privacy, a robust notion of privacy used in the Theoretical Computer Science literature. We show by construction that such mechanisms, i.e. ones which are both incentive compatible and jointly differentially private exist when the game is ‘large’, i.e. there are a large number of players, and any player’s action affects any other’s payoff by at most a small amount. Our mechanism adds carefully selected noise to no-regret algorithms similar to those studied in Foster-Vohra [FV97] and Hart-Mas-Colell [HMC00]. It therefore implements an approximate correlated equilibrium of the full information game induced by players’ reports.
*********
As I understand it, adding appropriate randomness to regret learning algorithms doesn’t harm their long term equilibration properties, and gives them good privacy properties, which together give them good incentive properties.
Monday, July 23, 2012
Parag Pathak wins Presidential Early Career Award for Scientists and Engineers
It was announced in Washington today that Parag Pathak (who is in Istanbul giving the Shapley Lecture at the World Congress of the Game Theory Society) is one of the winners of the Presidential Early Career Awards for Scientists and Engineers: President Obama Honors Outstanding Early-Career Scientists
"President Obama today named 96 researchers as recipients of the Presidential Early Career Awards for Scientists and Engineers, the highest honor bestowed by the United States Government on science and engineering professionals in the early stages of their independent research careers."
I've had lots of occasions to blog about Parag and his work...
"President Obama today named 96 researchers as recipients of the Presidential Early Career Awards for Scientists and Engineers, the highest honor bestowed by the United States Government on science and engineering professionals in the early stages of their independent research careers."
I've had lots of occasions to blog about Parag and his work...
Should there be one kidney exchange or many, and which ones, and when?
The July issue of the Nephrology Times carries a story from the recent American Transplant Congress meetings, at which reports were given by the main kidney exchange networks and transplant centers: In National Paired Donation Pilot, Most Match Offers Declined
Ruthanne Hanto reported on the progress of the Organ Procurement and Transplantation Network (OPTN) Kidney Paired Donation (KPD) Pilot Program run by UNOS.
"The pilot has made about 240 matches since its first run on Oct. 27, 2010, but about 220 of the offers were declined, and only 19 of the matches led to transplantation."
The pilot program hopes to add bridge donors--donors who temporarily end a chain and donate later--at some future time.
In the meantime, the story covers an ongoing debate about whether having multiple kidney exchange networks is a good thing. There's general agreement that, run well, a larger network creates a thicker market which would produce more transplants. And the support of the OPTN, which deals with the nation's deceased donors, gives the pilot program enormous convening power, since they already have working relations with every transplant center in the country.
Nevertheless, the other programs have been vastly more successful in producing transplants, both for patients in general and for the most highly sensitized patients who now make up the majority of those in kidney exchange networks. (It's hard to come by exact numbers, but we're talking two orders of magnitude--the pilot program so far accounts for about 1% of the kidney exchange transplants to date.) So the story quotes both Ruthanne Hanto and Stanford surgeon Marc Melcher as saying that, for the moment, it would be premature to try to close any of the successful networks down, not least because they are where the innovation is taking place.
(Melcher: “I think at some point most people agree that we need to have a national program. I think really the question is when, and when have we really learned enough about the right way to go.")
The story also quotes Hopkins surgeon Dorry Segev who reaches the opposite conclusion, and would apparently be glad to close down the independent networks: "There's a tremendous amount of competition among the various KPD providers in this country, and this competition is actually hurting the chances for those hardest-to-match patients.”
*******************
My recent papers which have some bearing on this controversy, in the sense that they are about best practices pioneered in practice by other exchange networks (namely nonsimultaneous chains), are these:
Ruthanne Hanto reported on the progress of the Organ Procurement and Transplantation Network (OPTN) Kidney Paired Donation (KPD) Pilot Program run by UNOS.
"The pilot has made about 240 matches since its first run on Oct. 27, 2010, but about 220 of the offers were declined, and only 19 of the matches led to transplantation."
The pilot program hopes to add bridge donors--donors who temporarily end a chain and donate later--at some future time.
In the meantime, the story covers an ongoing debate about whether having multiple kidney exchange networks is a good thing. There's general agreement that, run well, a larger network creates a thicker market which would produce more transplants. And the support of the OPTN, which deals with the nation's deceased donors, gives the pilot program enormous convening power, since they already have working relations with every transplant center in the country.
Nevertheless, the other programs have been vastly more successful in producing transplants, both for patients in general and for the most highly sensitized patients who now make up the majority of those in kidney exchange networks. (It's hard to come by exact numbers, but we're talking two orders of magnitude--the pilot program so far accounts for about 1% of the kidney exchange transplants to date.) So the story quotes both Ruthanne Hanto and Stanford surgeon Marc Melcher as saying that, for the moment, it would be premature to try to close any of the successful networks down, not least because they are where the innovation is taking place.
(Melcher: “I think at some point most people agree that we need to have a national program. I think really the question is when, and when have we really learned enough about the right way to go.")
The story also quotes Hopkins surgeon Dorry Segev who reaches the opposite conclusion, and would apparently be glad to close down the independent networks: "There's a tremendous amount of competition among the various KPD providers in this country, and this competition is actually hurting the chances for those hardest-to-match patients.”
*******************
My recent papers which have some bearing on this controversy, in the sense that they are about best practices pioneered in practice by other exchange networks (namely nonsimultaneous chains), are these:
- Ashlagi, Itai, Duncan S. Gilchrist, Alvin E. Roth, and Michael A. Rees, ; ''Nonsimultaneous Chains and Dominos in Kidney Paired Donation -- Revisited,'' American Journal of Transplantation, 11, 5, May 2011, 984-994.
- Ashlagi, Itai, Duncan S. Gilchrist, Alvin E. Roth, and Michael A. Rees, "NEAD Chains in Transplantation," American Journal of Transplantation, December 2011, 11:2780-2781.
- Ashlagi, Itai and Alvin E. Roth, "Individual rationality and participation in large scale, multi-hospital kidney exchange," working paper, January 2011.
- C. Bradley Wallis; Kannan P. Samy; Alvin E. Roth; and Michael A. Rees, "Kidney paired donation," Nephrology Dialysis Transplantation 2011, doi:10.1093/ndt/gfr155
- Ashlagi, Itai and Alvin E. Roth, "New challenges in multi-hospital kidney exchange," American Economic Review papers and proceedings, May 2012, 102,3, 354-59.
- Rees, Michael A., Mark A. Schnitzler, Edward Zavala, James A. Cutler, Alvin E. Roth, F. Dennis Irwin, Stephen W. Crawford,and Alan B. Leichtman, “Call to Develop a Standard Acquisition Charge Model for Kidney Paired Donation,” American Journal of Transplantation, 2012, 12, 6 (June), 1392-1397.
- Ashlagi, Itai, David Gamarnik, Michael A. Rees and Alvin E. Roth, "The Need for (long) Chains in Kidney Exchange," working paper, May 2012.
Sunday, July 22, 2012
Don't get sick in July...the market for new medical residents
An experienced nurse reflects on the influx of inexperienced new doctors each July in the U.S.: Don't get sick in July
And in England, Thousands of junior doctors have concerns over patient safety: GMC
"One in seven said they had felt forced to cope with clinical problems beyond their competence or experience, according to a survey carried out by the General Medical Council, with a small proportion saying this happened on “a daily basis”.
And in England, Thousands of junior doctors have concerns over patient safety: GMC
"One in seven said they had felt forced to cope with clinical problems beyond their competence or experience, according to a survey carried out by the General Medical Council, with a small proportion saying this happened on “a daily basis”.
Saturday, July 21, 2012
Hermit Crab Vacancy Chains
From Scientific American:
On a Tiny Caribbean Island, Hermit Crabs Form Sophisticated Social Networks [Video]
In 2009, Lewis and Rotjan surveyed the entire hermit crab population on Carrie Bow Cay. Many crabs were living in shells that were a tight fit or had one too many holes. As they grow, hermit crabs must move into larger shells, so they are always on the lookout for a more spacious dwelling. And an undamaged shell is preferable to a broken one, even if the shells are the same size. Knowing this, the researchers decided to dramatically change the available hermit crab real estate on Carrie Bow Cay. They placed 20 beautifully intact shells that were a little too big for most hermit crabs at various spots around the island and watched what happened.
When a lone crab encountered one of the beautiful new shells, it immediately inspected the shelter with its legs and antennae and scooted out of its current home to try on the new shelter for size. If the new shell was a good fit, the crab claimed it. Classic hermit crab behavior. But if the new shell was too big, the crab did not scuttle away disappointed—instead, it stood by its discovery for anywhere between 15 minutes and 8 hours, waiting. This was unusual. Eventually other crabs showed up, each one trying on the shell. If the shell was also too big for the newcomers, they hung around too, sometimes forming groups as large as 20. The crabs did not gather in a random arrangement, however. Rather, they clamped onto one another in a conga line stretching from the largest to smallest animal—a behavior the biologists dubbed "piggybacking."
Only one thing could break up the chain of crabs: a Goldilocks hermit crab for whom the shell introduced by Lewis and Rotjan was just right. As soon as such a crab claimed its new home, all the crabs in queue swiftly exchanged shells in sequence. The largest crab at the front of the line seized the Goldilocks crab's abandoned shell. The second largest crab stole into the first's old shell. And so on.
When a lone crab encountered one of the beautiful new shells, it immediately inspected the shelter with its legs and antennae and scooted out of its current home to try on the new shelter for size. If the new shell was a good fit, the crab claimed it. Classic hermit crab behavior. But if the new shell was too big, the crab did not scuttle away disappointed—instead, it stood by its discovery for anywhere between 15 minutes and 8 hours, waiting. This was unusual. Eventually other crabs showed up, each one trying on the shell. If the shell was also too big for the newcomers, they hung around too, sometimes forming groups as large as 20. The crabs did not gather in a random arrangement, however. Rather, they clamped onto one another in a conga line stretching from the largest to smallest animal—a behavior the biologists dubbed "piggybacking."
Only one thing could break up the chain of crabs: a Goldilocks hermit crab for whom the shell introduced by Lewis and Rotjan was just right. As soon as such a crab claimed its new home, all the crabs in queue swiftly exchanged shells in sequence. The largest crab at the front of the line seized the Goldilocks crab's abandoned shell. The second largest crab stole into the first's old shell. And so on.
No one had ever documented such well-orchestrated shell swapping before, but similar behavior was not unknown. In 1986, Ivan Chase of Stony Brook University made the first observations of hermit crabs exchanging shells in a "vacancy chain"—a term originally coined by social scientists to describe the ways that people trade coveted resources like apartments and jobs. When one person leaves, another moves in. Since then, several researchers—including Lewis and Rotjan—have studied the behavior in different hermit crab species. Some preliminary evidence suggests that other animals use vacancy chains too, including clown fish, lobsters, octopuses and some birds. As Chase explains in the June issue of Scientific American, vacancy chains are an excellent way to distribute resources: Unlike more typical competition, a single vacancy chain benefits everyone involved—each individual gets an upgrade. So it makes sense that hermit crabs and other animals have evolved sophisticated social behaviors to make the most of vacancy chains.
The orderly vacancy chain that Lewis and Rotjan observed is called a synchronous vacancy chain, which is different from an asynchronous vacancy chain in which a lone crab encounters a shell, claims it and leaves behind its old home, which is later seized by a different crab that never interacts with the first animal. As the above video makes clear, however, synchronous vacancy chains are not always civilized affairs. Sometimes crabs fight each other for the best shell or gather in violent groups. And the exchanges often happen extremely quickly. Lewis and Rotjan had to slow down the footage just to see what was happening and it is still difficult to make out: three hermit crabs crowd a large green shell; the largest claims the green shell and the other two swiftly trade up. Lewis thinks the chain would have been more orderly if the crabs were not disturbed by two biologists filming them.
The orderly vacancy chain that Lewis and Rotjan observed is called a synchronous vacancy chain, which is different from an asynchronous vacancy chain in which a lone crab encounters a shell, claims it and leaves behind its old home, which is later seized by a different crab that never interacts with the first animal. As the above video makes clear, however, synchronous vacancy chains are not always civilized affairs. Sometimes crabs fight each other for the best shell or gather in violent groups. And the exchanges often happen extremely quickly. Lewis and Rotjan had to slow down the footage just to see what was happening and it is still difficult to make out: three hermit crabs crowd a large green shell; the largest claims the green shell and the other two swiftly trade up. Lewis thinks the chain would have been more orderly if the crabs were not disturbed by two biologists filming them.
Sara Lewis and Randi Rotjan
HT: Benjamin Kay
**************
Update: here's another video https://www.facebook.com/video.php?v=844190408934712 (HT: Yingua He)
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And on YouTube (HT Joshua Gans)
Friday, July 20, 2012
Chain of lives: kidney exchange in Forbes
Itai Ashlagi and David Gamarnik in Forbes: Kidney Transplants: How To Extend A Chain of Life
"What is the best way to use the kidney of an altruistic donor so that the greatest number of patients get transplants?
"To answer this question, we gathered data from a kidney exchange clearinghouse. Included was detailed information about patients’ blood and tissue types, which told us how hard it would be to find matches for them. We analyzed the data using the tool of graph theory, an approach used in mathematics and computer science to understand relationships among pairs of objects. This tool is used to find the largest number of matches achievable in each exchange program. Working with us were two pioneers of kidney exchange, Michael Rees, a transplant surgeon at the University of Toledo, and Alvin Roth, an economics professor at Harvard Business School.
"We found that long chains and long cycles of donations are essential to helping the greatest number of patients. This is especially true for patients whose blood or tissue types make them difficult to match. The percentage of hard to match patients in kidney exchange programs is very high since easy to match patients can often find a donor without the aid of the exchange program (even when enrolling the program they can be matched quickly while hard to match patients accumulate over time). But lengthy chains will benefit hard to match patients while not harming easy to match patients who are in kidney exchange programs, we found."
Here's the paper reporting the results in detail:
Ashlagi, Itai, David Gamarnik, Michael A. Rees and Alvin E. Roth, "The Need for (long) Chains in Kidney Exchange"
"What is the best way to use the kidney of an altruistic donor so that the greatest number of patients get transplants?
"To answer this question, we gathered data from a kidney exchange clearinghouse. Included was detailed information about patients’ blood and tissue types, which told us how hard it would be to find matches for them. We analyzed the data using the tool of graph theory, an approach used in mathematics and computer science to understand relationships among pairs of objects. This tool is used to find the largest number of matches achievable in each exchange program. Working with us were two pioneers of kidney exchange, Michael Rees, a transplant surgeon at the University of Toledo, and Alvin Roth, an economics professor at Harvard Business School.
"We found that long chains and long cycles of donations are essential to helping the greatest number of patients. This is especially true for patients whose blood or tissue types make them difficult to match. The percentage of hard to match patients in kidney exchange programs is very high since easy to match patients can often find a donor without the aid of the exchange program (even when enrolling the program they can be matched quickly while hard to match patients accumulate over time). But lengthy chains will benefit hard to match patients while not harming easy to match patients who are in kidney exchange programs, we found."
Here's the paper reporting the results in detail:
Ashlagi, Itai, David Gamarnik, Michael A. Rees and Alvin E. Roth, "The Need for (long) Chains in Kidney Exchange"
Thursday, July 19, 2012
Matching in Europe
Estelle Cantillon draws my attention to the new website of the network of European researchers in matching and market design, with concentration on school choice and labor markets:
Matching in Practice--European network for research on matching practices in education and early labour markets
Their membership list is a Who's Who of European researchers in the area:
Matching in Practice--European network for research on matching practices in education and early labour markets
Their membership list is a Who's Who of European researchers in the area:
Jorge Alcalde-Unzu | Department of Economics, Public University of Navarra, Spain |
Rebecca Allen | Department of Quantitative Social Science, Institute of Education University of London, UK |
Haris Aziz | Department of Computer Science, TU Munchen, Germany |
Sophie Bade | Research Unit Martin Hellwig, Max Planck Institue for Research on Collective Goods, Germany |
Péter Biro | Institute of Economics, Hungarian Academy of Sciences, Hungary |
Francis Bloch | Department of Economics, Ecole Polytechnique, France |
Simon Burgess | Department of Economics, University of Bristol, UK |
Caterina Calsamiglia | Departament d’Economia i Història Econòmica. Universitat Autònoma de Barcelona. Spain |
Emilio Calvano | Innocenzo Gasparini Institute for Economic Research, Università Commerciale Luigi Bocconi, Italy |
Andrea Canidio | Central European University,Hungary |
Estelle Cantillon | ECARES, Université Libre de Bruxelles, Belgium |
Katarina Cechlarova | Institute of Mathematics, Univerzita Pavla Jozefa Šafárika, Slovakia |
Melvyn Coles | Department of Economics, University of Essex, UK |
Nadja Dwenger | Research Unit: Public Economics, Max-Planck-Institut for Tax Law and Public Finance, Germany |
Jan Eeckhout | Department of Economics, Universitat Pompeu Fabra, Spain |
Aytek Erdil | Faculty of Economics, University of Cambridge, UK |
Tamas Fleiner | Department of Operations Research, Eötvös Loránd University, Hungary |
Alfred Galichon | Economics Department, Ecole Polytechnique, France |
Thomas Gall | Department of Economics, University of Bonn, Germany |
Guillaume Haeringer | Departament d'Economia i d'Historia Economica, Universitat Autonoma de Barcelona,Spain |
Yinghua He | Toulouse School of Economics, France |
Maria Humlum | Aarhus University, Denmark |
Elena Inarra | Faculty of Economics, University of the Basque Country, Spain |
Rob Irving | School of Computing Science, University of Glasgow, UK |
John Kennes
| Department of Economics, University of Copenhagen, Denmark |
Sofya Kiselgof |
Higher School of Economics, Russia
|
Bettina Klaus | Faculty of Business and Economics (HEC), University of Lausanne, Switzerland |
Flip Klijn | Institute for Economic Analysis, Universitat Autònoma de Barcelona, Spain |
Laszlo Koczy | Institute of Economics, Hungarian Academy of Sciences, Hungary |
Dorothea Kuebler | Research Unit: Market Behavior, WZB, Germany |
Alexey Kushnir | Institute for Empirical Research in Economics, University of Zurich, Switzerland |
Patrick Legros | ECARES, Université Libre de Bruxelles, Belgium |
François Maniquet | Département des sciences économiques, Université Catholique de Louvain, Belgium |
David Manlove | School of Computing Science, University of Glasgow, UK |
Jordi Masso | Departament d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona,Spain |
Ana Mauleon | Department of Economics, Facultés Universitaires Saint-Louis, Belgium |
Luca Merlino | ECARES, Universitè Libre de Bruxelles, Belgium |
Antonio Miralles | Department of Economics, Universitat Autònoma de Barcelona, Spain |
Elena Molis | Center for Research in Economics, Facultés Universitaires Saint-Louis, Belgium |
Daniel Monte | Simon Fraser University, Canada |
Kurino Morimitsu | Department of Economics, Maastricht University, Netherlands |
Heinrich Nax | Oxford, UK |
Alexandru Nichifor | Department of Economics, Maastricht University, Netherlands |
Antonio Nicolo | Department of Economics , University of Padua, Italy |
Gregg O'Malley | School of Computing Science, University of Glasgow, UK |
Joana Pais | Research Unit on Complexity and Economics, Universidade Técnica de Lisboa, Portugal |
Katarzyna Paluch | Institute of Computer Science, University of Wroclaw, Poland |
Agnes Pinter | Department of Economic Analysis, Universidad Autónoma de Madrid, Spain |
Salmai Qari | Research Unit: Public Economics, Max-Planck-Institut for Tax Law and Public Finance, Germany |
Eve Ramaekers | Center for Operations Research and Econometrics, Université Catholique de Louvain, Belgium |
Antonio Romero | Departamento de Economía, Universidad Carlos III de Madrid, Spain |
Ildiko Schlotter | Department of Computer Science, Budapest University of Technology and Economics, Hungary |
Olivier Tercieux | Centre national de la recherche scientifique, Paris School of Economics, France |
Norovsambuu Tumennasan | Aarhus University, Denmark |
Rune Veijlin | Aarhus University, Denmark |
Alexander Westkamp | Department of Economic Theory II, University of Bonn, Germany |
Labels:
job market,
market designers,
matching,
school choice
Wednesday, July 18, 2012
The Federal Law Clerk Hiring Plan is pretty much over
...and acknowledged to be over.
In October 2011 I wrote this post:
Stanford Law School has issued a memo to the legal community, dated July 17, 2012 (reporting on a June 29 letter to the Judicial Conference), saying that they will now freely communicate, before the dates allowed under the plan, with judges who do not stick to the hiring plan. The reason? Every other law school is doing it, and so it makes sense to do it openly...
Here are my papers on that market...
In October 2011 I wrote this post:
Another year of the judicial clerkship market: maybe the last one under the current system?
Stanford Law School has issued a memo to the legal community, dated July 17, 2012 (reporting on a June 29 letter to the Judicial Conference), saying that they will now freely communicate, before the dates allowed under the plan, with judges who do not stick to the hiring plan. The reason? Every other law school is doing it, and so it makes sense to do it openly...
Here are my papers on that market...
- Avery, Christopher, Christine Jolls, Richard A. Posner, and Alvin E. Roth, "The Market for Federal Judicial Law Clerks" University of Chicago Law Review, 68, 3, Summer, 2001, 793-902.(online at SSRN)
- Haruvy, Ernan, Alvin E. Roth, and M. Utku Unver, “The Dynamics of Law Clerk Matching: An Experimental and Computational Investigation of Proposals for Reform of the Market,” Journal of Economic Dynamics and Control, 30, 3 , March 2006, Pages 457-486.
- Avery, Christopher, Jolls, Christine, Posner, Richard A. and Roth, Alvin E., "The New Market for Federal Judicial Law Clerks" . University of Chicago Law Review, 74, Spring 2007, 447-486.
Match-Up 2012 in Budapest, July 19-20
MATCH-UP 2012: the Second International Workshop on Matching Under Preferences
Here's the conference program: Match-Up 2012, and here are the proceedings.
Tuesday, July 17, 2012
Getting into Harvard the hard way, by transferring
College admissions consists of lots of parts: early, regular, waiting lists, z-lists, transfers... It doesn't appear that transfers are a big part of Harvard's admissions strategy.
The Real 1%: Harvard Admits 15 Transfer Students...from a pool of 1,448 applicants.
"Mascolo said that the College, still within memory of its two-year moratorium on all transfer admissions, will probably accept a similarly tiny number of transfer students again next year."
The Real 1%: Harvard Admits 15 Transfer Students...from a pool of 1,448 applicants.
"Mascolo said that the College, still within memory of its two-year moratorium on all transfer admissions, will probably accept a similarly tiny number of transfer students again next year."
Monday, July 16, 2012
Centralized application systems: more consolidation
One of the ways the internet is changing job markets has to do with making it easier to transmit job market materials. (This becomes even more important as the internet makes it easier for job candidates to apply to a larger number of jobs.) Competing services have sprung up to serve this need, and as the market matures we are starting to see some consolidation.
In the humanities, Interfolio seems to be consolidating its position, with a recent endorsement from the Modern Language Association, which will integrate the service with its Job Information List:
Dossier and Search-Management Services Available through the JIL
"Job seekers will be able to apply for positions directly from advertisements in the JIL by creating a free Interfolio account
...
"All departments that place ads in the 2012–13 JIL will be able to use Interfolio’s suite of online search-management tools, called ByCommittee. ByCommittee provides a single secure Web interface for departments to manage search-committee memberships for multiple searches and to receive candidate applications, dossiers, and other materials."
...
"Letter writers receive requests for letters directly from a candidate’s Interfolio account and submit their letters to Interfolio’s centralized dossier service."
********
In Economics, some preliminary discussions have taken place about the possibility of a similar kind of integration between the job listing service Job Openings for Economists (JOE) and the application-materials aggregator Econjobmarket.org. but it remains for at least another year to see whether these discussions will be fruitful.
********
Previous related posts:
Academic letters of reference;
In the humanities, Interfolio seems to be consolidating its position, with a recent endorsement from the Modern Language Association, which will integrate the service with its Job Information List:
Dossier and Search-Management Services Available through the JIL
"Job seekers will be able to apply for positions directly from advertisements in the JIL by creating a free Interfolio account
...
"All departments that place ads in the 2012–13 JIL will be able to use Interfolio’s suite of online search-management tools, called ByCommittee. ByCommittee provides a single secure Web interface for departments to manage search-committee memberships for multiple searches and to receive candidate applications, dossiers, and other materials."
...
"Letter writers receive requests for letters directly from a candidate’s Interfolio account and submit their letters to Interfolio’s centralized dossier service."
********
In Economics, some preliminary discussions have taken place about the possibility of a similar kind of integration between the job listing service Job Openings for Economists (JOE) and the application-materials aggregator Econjobmarket.org. but it remains for at least another year to see whether these discussions will be fruitful.
********
Previous related posts:
Academic letters of reference;
Sunday, July 15, 2012
The university (Stanford) as a marketplace of ideas and innovation
Writing in the New Yorker, Ken Auletta thinks about what makes Stanford the heart of silicon valley, and whether this is an entirely good thing... Get Rich U.: There are no walls between Stanford and Silicon Valley. Should there be?
"Innovation comes from myriad sources, including the bastions of East Coast learning, but Stanford has established itself as the intellectual nexus of the information economy.
...
If the Ivy League was the breeding ground for the élites of the American Century, Stanford is the farm system for Silicon Valley. When looking for engineers, Schmidt said, Google starts at Stanford. Five per cent of Google employees are Stanford graduates. The president of Stanford, John L. Hennessy, is a director of Google; he is also a director of Cisco Systems and a successful former entrepreneur. Stanford’s Office of Technology Licensing has licensed eight thousand campus-inspired inventions, and has generated $1.3 billion in royalties for the university. Stanford’s public-relations arm proclaims that five thousand companies “trace their origins to Stanford ideas or to Stanford faculty and students.” They include Hewlett-Packard, Yahoo, Cisco Systems, Sun Microsystems, eBay, Netflix, Electronic Arts, Intuit, Fairchild Semiconductor, Agilent Technologies, Silicon Graphics, LinkedIn, and E*Trade.
...
"But Stanford’s entrepreneurial culture has also turned it into a place where many faculty and students have a gold-rush mentality and where the distinction between faculty and student may blur as, together, they seek both invention and fortune. Corporate and government funding may warp research priorities. A quarter of all undergraduates and more than fifty per cent of graduate students are engineering majors. At Harvard, the figures are four and ten per cent; at Yale, they’re five and eight per cent. Some ask whether Stanford has struck the right balance between commerce and learning, between the acquisition of skills to make it and intellectual discovery for its own sake."
"Innovation comes from myriad sources, including the bastions of East Coast learning, but Stanford has established itself as the intellectual nexus of the information economy.
...
If the Ivy League was the breeding ground for the élites of the American Century, Stanford is the farm system for Silicon Valley. When looking for engineers, Schmidt said, Google starts at Stanford. Five per cent of Google employees are Stanford graduates. The president of Stanford, John L. Hennessy, is a director of Google; he is also a director of Cisco Systems and a successful former entrepreneur. Stanford’s Office of Technology Licensing has licensed eight thousand campus-inspired inventions, and has generated $1.3 billion in royalties for the university. Stanford’s public-relations arm proclaims that five thousand companies “trace their origins to Stanford ideas or to Stanford faculty and students.” They include Hewlett-Packard, Yahoo, Cisco Systems, Sun Microsystems, eBay, Netflix, Electronic Arts, Intuit, Fairchild Semiconductor, Agilent Technologies, Silicon Graphics, LinkedIn, and E*Trade.
...
"But Stanford’s entrepreneurial culture has also turned it into a place where many faculty and students have a gold-rush mentality and where the distinction between faculty and student may blur as, together, they seek both invention and fortune. Corporate and government funding may warp research priorities. A quarter of all undergraduates and more than fifty per cent of graduate students are engineering majors. At Harvard, the figures are four and ten per cent; at Yale, they’re five and eight per cent. Some ask whether Stanford has struck the right balance between commerce and learning, between the acquisition of skills to make it and intellectual discovery for its own sake."
Saturday, July 14, 2012
Kidney broker sentenced to prison in New Jersey
Kidney Broker Sentenced To Prison As Donor Recalls Doubts
"In the first criminal organ-trafficking case in the U.S., Quick took the witness stand at the sentencing of Levy Izhak Rosenbaum, a Brooklyn, New York, man who pleaded guilty to brokering black-market sales of human kidneys to three Americans. After hearing Quick’s account of how Rosenbaum paid him $25,000 for a kidney, U.S. District Judge Anne Thompson sentenced Rosenbaum to 2 1/2 years in prison.
"In the first criminal organ-trafficking case in the U.S., Quick took the witness stand at the sentencing of Levy Izhak Rosenbaum, a Brooklyn, New York, man who pleaded guilty to brokering black-market sales of human kidneys to three Americans. After hearing Quick’s account of how Rosenbaum paid him $25,000 for a kidney, U.S. District Judge Anne Thompson sentenced Rosenbaum to 2 1/2 years in prison.
“It’s a kind of trading in human misery,” Thompson said of the black-market kidney trade. Rosenbaum “charged a fee” for kidneys while using “a complicated web of transactions” to finance his trade, she said. “He corrupted himself.”
See earlier posts on this case here, and yesterday's story about a conviction in Japan here.
Labels:
black market,
compensation for donors,
crime,
kidneys,
transplantation
Friday, July 13, 2012
Jail for Japanese kidney buyer
Kidney-buying doc's jail term upheld
"Presiding Judge Shoji Ogawa said the two defendants had damaged public trust in the organ transplant system, noting Horiuchi procured a kidney solely through financial means
...
"The 1997 Organ Transplantation Law bans all trade in organs, while the ethical guidelines of the Japan Society for Transplantation only permit live organ donation between family members to prevent illegal harvesting. The Japan Organ Transplant Network is the only entity permitted to act as an intermediary for organ transplants.
"Presiding Judge Shoji Ogawa said the two defendants had damaged public trust in the organ transplant system, noting Horiuchi procured a kidney solely through financial means
...
"The 1997 Organ Transplantation Law bans all trade in organs, while the ethical guidelines of the Japan Society for Transplantation only permit live organ donation between family members to prevent illegal harvesting. The Japan Organ Transplant Network is the only entity permitted to act as an intermediary for organ transplants.
"The law also forbids anyone from either requesting or promising payment for organs and from receiving commissions for mediating illegal transplants, to ensure a level playing field for potential recipients and to encourage voluntary donations from healthy citizens.
"The doctor allegedly tried to sidestep the law by technically adopting the donor "
Thursday, July 12, 2012
The political economy of organ transplantation in the U.S.
Ricky Vohra has an interesting post called $’s and Kidneys in which he notices that surgeons may have a financial interest in opposing a monetary market for kidneys, and provides some interesting background links.
The following paper discusses the roles and relationships of the Department of Health and Human Services, the Organ Procurement and Transplant Network (OPTN), the Organ Procurement Organizations (OPOs) and the United Network for Organ Sharing (UNOS), as determined by the National Organ Transplant Act of 1984 and its subsequent interpretations. Its focus is the debate over the different waiting times to receive a deceased donor organ in different regions of the country, resulting from the regional (as opposed to national) allocation of organs, based on how many deceased donors are in each region (and not on how many patients):
THE PUBLIC ADMINSTRATION OF ORGAN ALLOCATION: MAINTAINING THE PUBLIC – PRIVATE PARTNERSHIP by Stosberg and Gimbel
***********
And here's a news story about Tampa General Hospital's active transplant programs. It details some of the revenues:
"The revenues a transplant program can generate are also significant. For example, the average estimated hospital admission fee nationwide for a heart transplant patient in 2011 was $634,300, according to the United Network of Organ Sharing. The nonprofit network helps the federal government manage the nation’s organ transplant system.
The average hospital admission fee for a single lung transplant in 2011 was $302,900, the network estimates. Other average estimates from the network: A liver transplant was $316,900; a pancreas was $108,900; and a kidney transplant was $91,200."
The following paper discusses the roles and relationships of the Department of Health and Human Services, the Organ Procurement and Transplant Network (OPTN), the Organ Procurement Organizations (OPOs) and the United Network for Organ Sharing (UNOS), as determined by the National Organ Transplant Act of 1984 and its subsequent interpretations. Its focus is the debate over the different waiting times to receive a deceased donor organ in different regions of the country, resulting from the regional (as opposed to national) allocation of organs, based on how many deceased donors are in each region (and not on how many patients):
THE PUBLIC ADMINSTRATION OF ORGAN ALLOCATION: MAINTAINING THE PUBLIC – PRIVATE PARTNERSHIP by Stosberg and Gimbel
***********
And here's a news story about Tampa General Hospital's active transplant programs. It details some of the revenues:
"The revenues a transplant program can generate are also significant. For example, the average estimated hospital admission fee nationwide for a heart transplant patient in 2011 was $634,300, according to the United Network of Organ Sharing. The nonprofit network helps the federal government manage the nation’s organ transplant system.
The average hospital admission fee for a single lung transplant in 2011 was $302,900, the network estimates. Other average estimates from the network: A liver transplant was $316,900; a pancreas was $108,900; and a kidney transplant was $91,200."
Labels:
compensation for donors,
law,
politics,
transplantation
Wednesday, July 11, 2012
Report on Denver School Choice--first year
A Denver organization, A+ Denver, reports on the first year of Denver's new school choice system, which seems to have gone well.
Evaluation of Denver’s SchoolChoice Process for the 2011-12 School Year
Prepared for the SchoolChoice Transparency Committee at A+ Denver
by Mary Klute, U. of Colorado, Denver
and
Assessment of Assignment Tool
by Dr. Gary Kochenberger, U. of Colorado, Denver
See also Diving deep into SchoolChoice by Robert Reichardt
"The new choice process consolidated over 60 different processes into one. A computer program was used to assign students to schools based on student preferences, number of available seats, and school preferences (e.g. siblings, residents, or auditions for Denver School of the Arts). A second round is open now through August 31, 2012 for students who are not happy with their current assignment or did not enter the first round.
Denver school choice is an IIPSC project, see my earlier blog posts.
Evaluation of Denver’s SchoolChoice Process for the 2011-12 School Year
Prepared for the SchoolChoice Transparency Committee at A+ Denver
by Mary Klute, U. of Colorado, Denver
and
Assessment of Assignment Tool
by Dr. Gary Kochenberger, U. of Colorado, Denver
See also Diving deep into SchoolChoice by Robert Reichardt
"The new choice process consolidated over 60 different processes into one. A computer program was used to assign students to schools based on student preferences, number of available seats, and school preferences (e.g. siblings, residents, or auditions for Denver School of the Arts). A second round is open now through August 31, 2012 for students who are not happy with their current assignment or did not enter the first round.
"A Transparency Committee of DPS administrators and principals along with community stakeholders was selected by A+ Denver to receive and interpret an evaluation report on thecomputer program used to make the assignments and a second on the information created by the choice process. A+ Denver also provides spreadsheets of choice data by school.
...
"The choice process worked. DPS was able to collect over 20,000 hand-written choice requests and implement a complex computer program to assign students to schools.
"There are huge differences in demand for schools. The differences are largest in high schools: Denver School of Science and Technology, Stapleton, had 8.2 first choice requests per available seat compared to Denver Online High School which had .01 first choice requests per seat. This is a difference of 82,000%."
Denver school choice is an IIPSC project, see my earlier blog posts.
Tuesday, July 10, 2012
Living donors' stories
Narrative Inquiry in Bioethics (2, 1, Spring 2012) is devoted to a Narrative Symposium: Living Organ Donation
"As Elisa Gordon notes, the collection of stories represent the experiences of liver and kidney donors; donors whose organ was successfully and unsuccessfully transplanted into a recipient; related and unrelated donors; and donors who had overwhelmingly positive experiences, mixed experiences, and negative experiences. In these stories we read about a wide variety of motives for donation and concerns with the donation experience. We hope that the collection of personal narratives and commentaries by Drs. Dianne LaPointe Rudow and Paul Root Wolpe will lead to a better understanding of the current living donation process as well as improvements in that process for future donors."
"As Elisa Gordon notes, the collection of stories represent the experiences of liver and kidney donors; donors whose organ was successfully and unsuccessfully transplanted into a recipient; related and unrelated donors; and donors who had overwhelmingly positive experiences, mixed experiences, and negative experiences. In these stories we read about a wide variety of motives for donation and concerns with the donation experience. We hope that the collection of personal narratives and commentaries by Drs. Dianne LaPointe Rudow and Paul Root Wolpe will lead to a better understanding of the current living donation process as well as improvements in that process for future donors."
Living Organ Donors’ Stories: (Unmet) Expectations about Informed Consent, Outcomes, and Care
pp. 1-6 | DOI: 10.1353/nib.2012.0001Living Organ Donation
pp. 7-37 | DOI: 10.1353/nib.2012.0002
Laura Altobelli,
Sherri Bauman,
Janice Flynn, Andy Heath, Joseph Jacobs, Tim Joos, Amy K.
Lewensten, Donna L. Luebke,
Sarah A.
McDaniel, Donald Olenick,
Laurie E Post,
Vicky Young
An Altruistic Living Donor’s Story
pp. 7-10 | DOI: 10.1353/nib.2012.0018
The Essence of Giving—A Transplant Story
pp. 14-17 | DOI: 10.1353/nib.2012.0012
A Life For A Life: My Gift To My Dad
pp. 21-24 | DOI: 10.1353/nib.2012.0017
Lessons Learned: The Realities of Living Organ Donation
pp. 24-26 | DOI: 10.1353/nib.2012.0007
Sarah’s List Exchange Experience
pp. 26-29 | DOI: 10.1353/nib.2012.0009
Personal Narratives: Living Organ Donation (Web Only Content)
Getting Our Child Off Dialysis
p. E1 | DOI: 10.1353/nib.2012.0019
A Living Donor’s Journey
pp. E2-E6 | DOI: 10.1353/nib.2012.0020
Living Donors are People Too
pp. E9-E11 | DOI: 10.1353/nib.2012.0022
Gifts and Obligations: The Living Donor as Storyteller
pp. 39-44 | DOI: 10.1353/nib.2012.0003
The Gift of Life—Walking by Faith
pp. E11-E14 | DOI: 10.1353/nib.2012.0023
Journey of an Altruistic, Non–designated Living Donor
pp. E14-E16 | DOI: 10.1353/nib.2012.0024
Experiences of the Live Organ Donor: Lessons Learned Pave the Future
pp. 45-54 | DOI: 10.1353/nib.2012.0004
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