George Habash, a militant and former secretary-general of the Popular Front for the Liberation of Palestine, once characterized terrorism as a "thinking man's game." Using mathematics, researchers at Stanford University's Center for International Security and Cooperation (CISAC) have made fighting terrorism a thinking man's game as well.

CISAC affiliate Lawrence M. Wein of the Graduate School of Business and CISAC Science Fellow Jonathan Farley are both applying mathematical models to homeland security problems, such as preventing a nuclear detonation in a major U.S. city and determining whether terrorist cells have likely been disrupted.

Wein, who teaches operations classes about different business processes used to deliver goods and services, has focused his research on bioterrorism and border issues. He has performed, he says, the first mathematical analyses of hypothetical botulism poisoning, anthrax outbreaks and smallpox infections.

"One overriding theme of my work is that all these homeland security problems are operations problems," said Wein, the Paul E. Holden Professor of Management Science. "Just as McDonald's needs to get hamburgers out in a rapid and defect-free manner, so too does the government have to get vaccines and antibiotics out and test the borders for nuclear weapons or terrorists in a rapid and defect-free manner."

In collaboration with Stephen Flynn of the Council on Foreign Relations, a nonpartisan research center, Wein recently has conducted research to improve security at U.S. borders and ports. Port security has received significant attention recently owing to the furor over Dubai Ports World's bid to manage six terminals at major U.S. harbors. The aim of Wein and Flynn's work is to prevent terrorists from bringing into the country a nuclear weaponbe it an atomic bomb or a so-called "dirty bomb," or conventional explosive packed with radioactive waste.

"Of all the problems I've studied, this is the most important because the worst-case terrorist scenario is a nuclear weapon going off in a major U.S. city and also it is the one the government has dropped the ball on the most," Wein said. "They have done a very poor job."

Instead of using the existing approach, where U.S. Customs actively inspects a minority of containers based on information from a specialized tracking system designed to identify suspicious containers, Wein and Flynn have recommended the government use a multi-layer, passive screening system for every container entering the country. Under their system, Customs would photograph a shipping container's exterior, screen for radioactive material and collect gamma-ray images of the container's contents. If terrorists shielded a bomb with a heavy metal such as lead to hide it from radiation detectors, gamma-ray imaging would allow inspectors to see the shielding and flag the container for inspection. Wein and Flynn believe this whole process would cost about $7 per container.

"Right now about maybe 6 percent of the containers are deemed suspicious and they will go through some testing and the other 94 percent of the containers just waltz right into the country without an inspector laying an eye on them," Wein said. "What we're proposing to do is 100 percent passive testing."

Wein's earlier work addressed a different threat: bioterrorism. In 2005, Wein revealed the nation's milk supply was vulnerable--a terrorist could potentially poison 100,000 gallons of milk by sneaking a few grams of botulinum into a milk tanker. Although the government and dairy industry have collaborated to intensify the heat pasteurization formula for milk, Wein is still pushing for additional botulinum testing, which he says would cost less than 1 percent of the cost of milk.

Wein also has used math to study smallpox outbreaks, the U.S. fingerprint identification system and U.S.-Mexico border security issues. Wein's congressional testimony on the fingerprint identification system in 2004 led to a switch from a two-finger system to a 10-finger system. His 2003 research on anthrax attacks resulted in a Washington, D.C., pilot program to use the U.S. Postal Service to distribute antibiotics throughout the capital after an outbreak. Seattle is now testing a similar program.

"In Washington, D.C., now, if there is a large-scale anthrax attack, postal workers will be the first to get their Cipro and, on a voluntary basis, they will go door-to-door distributing antibiotics," Wein said.

He said the common thread throughout his research is queuing theory, or the mathematical study of waiting lines, but he also draws upon mathematical epidemiology for his smallpox studies; air dispersion models for the anthrax model; supply chain management for the milk study; probability theory for the fingerprint identification system; and models for nuclear transport and detection for his work with containers.

From tainted lactose to lattice structures

While Wein is working on improving the government's counterterrorism systems, Jonathan Farley is working to figure out when terrorist organizations have been effectively disrupted. His mathematical model is designed to help law enforcement decide how to act once they have captured or killed a terrorist or a number of terrorists in a cell.

A professor at the University of the West Indies who will chair the Department of Mathematics and Computer Science there next year, Farley is on a one-year science fellowship at CISAC. In 2003, he co-founded Phoenix Mathematical Systems Modeling Inc., a company that develops mathematical solutions to homeland security problems.

He is using lattice theory--a branch of mathematics that deals with ordered sets--to determine the probability a terrorist cell has been disrupted once some of its members have been captured or killed.

"Law enforcement has to make decisions about what resources they should allocate to target different cells," Farley said. "The model should provide them with a more rational basis for allocating their scarce resources. ... It will inform you when you're making decisions about how much time and effort and how much money you're going to spend going after a particular cell."

While at Stanford, Farley hopes to unearth the perfect structure, mathematically speaking, for a terrorist cell--or in other words, a cell structure that is most resistant to the loss of members.

"If it's possible to determine the structure of an ideal terrorist cell, you can focus on a much smaller number of possibilities, because it makes more sense to assume the adversary is going to be smart rather than stupid," Farley said.

Farley has suggested it is possible Al-Qaida and other terrorist organizations already may have figured out the perfect structure for a terror cell by trial and error.

"I don't expect Osama bin Laden to be reading lattice theory in his caves in Afghanistan," said Farley. "But if it follows from the mathematics, perhaps heuristically, the terrorists will have come to the same conclusion--that this is the best way to structure a terrorist cell."

Although Farley acknowledges his model is not a panacea for terrorism, he hopes it will help reduce guesswork that might be involved in pursuing terrorists.

"It's not that I think mathematics can solve all of these problems," Farley said. "Because it can't. But it's better to use rational means to make decisions rather than guesswork."

John B. Stafford is a science-writing intern at Stanford News Service.

When India spectacularly burst into the headlines via its nuclear explosions in May 1998, then US president Bill Clinton had openly vented his fury before aides in the White House. "We are going to come down on those guys like a ton of bricks," he had remarked. Clinton's "volcanic fit" found its echo in the White House statement that expressed "distress" and "displeasure", culminating in Washington imposing a slew of sanctions against India.

These images from the past, culled out from Engaging India, then deputy secretary of state Strobe Talbott's book, appear incredible now. Especially as India readies itself to accord a warm reception to US President George W. Bush next week. The entente, the product of laboriously conducted diplomacy as much as geopolitical shifts that yoked the two together as 'natural allies', is now taking deep root. Sure, there will be protest rallies, strident voices will rail against Bush's hegemonic designs, Prime Minister Manmohan Singh will be cautioned against any tight clinch with Bush. Yet even these voices arise from the awareness that there's a growing relationship between the US and India, realized through knots of strategic partnership and cooperation in every conceivable field - from economy and nuclear technology to education, space and agriculture.

Bush's visit next week prompted Karl Inderfurth, who was assistant secretary of state for South Asia in the Clinton administration, to say, "All of this represents a refreshing degree of continuity in US foreign policy, based on a recognition by the last two American presidents that India is a country that will be a key player in the 21st century." Similarly, Robert Hathaway, of the Woodrow Wilson Center for International Scholars, is impressed that "two successive Indian governments representing different political views and parties... both came to the same conclusion that it is in India's interest to forge a better relationship with the US."

From imposing sanctions against India to laying out a blueprint for nuclear cooperation, both New Delhi and Washington have come a long way in an inordinately short time. Ironically, it was Clinton who provided the impetus for this transformation. Talbott says the former president, after coming to terms with the Pokhran II realities, found it "downright distasteful and counterproductive" to impose sanctions against a country he was trying to improve relations with. Consequently, Talbott, Inderfurth and senior director in the National Security Council Bruce Riedal were entrusted with the task of pulling out Indo-US relations from the abyss in which it had been languishing from the beginnings of the Cold War era.What followed was a dialog between foreign minister Jaswant Singh and Talbott, both seeking to convey to each other the security and strategic interests of their respective countries.

The dialog started yielding dividends immediately, even during the Kargil conflict. Clinton's confrontation of then Pakistani prime minister Nawaz Sharif at their July 4, 1999, meeting in Washington took trust patterns between the US and India to a new level. "Throughout this period, we kept the Indian government informed of what we were doing to try to ease the crisis," recalls Inderfurth, who played a key role in the dialog with Sharif. "All of this turned into an important confidence-builder in our new relationship with India."

"The July 4 meeting was the turning point," agrees Michael Krepon of the Henry L. Stimson Center in Washington. "It demonstrated that US engagement in the India-Pakistan imbroglio would not be detrimental to New Delhi's interests, and it shifted the Clinton administration's focus from proliferation to engagement." The trust was manifest in Clinton's spectacularly successful visit to India in March 2000. An enabling factor in the budding Indo-US romance, says former ambassador Richard Celeste, was the now-forgotten Y2K factor. "The crisis introduced India's enormously talented manpower to our business leaders. Today, the 24/7 bond between companies in the US and service providers in India is the stuff of books and myth-making."

The budding romance acquired a new meaning with the advent of Bush in the White House. His most perspicacious decision was to appoint confidant Robert D. Blackwill as ambassador to India. Blackwill appealed to the popular imagination; his unequivocal pronouncements against Pakistan for fomenting terrorism in India further bolstered the trust between New Delhi and Washington. More importantly, he sought to impart a new heft to the relationship by putting his formidable weight behind the "Next Steps in Strategic Partnership", which envisaged cooperation between the two countries in civil nuclear energy, hi-tech trade, space and dual technology. "If Clinton was the pioneer of the new relationship, Bush is its architect," says Teresita Schaffer of the Center for Strategic and International Studies in Washington.

The impulse for the new relationship is linked to the question: why has India started to matter to the US? Inderfurth cites three reasons: India will become the world's most populous nation, it may well have the world's fastest growing economy by 2020, and it is the world's largest democracy. Krepon adds one more to the list: intellectual capital. "The world expects India to do more heavy lifting," he says.

Ultimately, a relationship in international affairs hinges on convergence of interests. Ashley Tellis of the Carnegie Endowment for International Peace, who's now advising under secretary of state R. Nicholas Burns, listed a string of "common interests" at a congressional hearing last year. These included:

preventing Asia from being dominated by any single power that has the capacity to crowd out others and which may use aggressive assertion of national self-interest to threaten American presence, American alliances, and American ties with the states of the region; eliminating the threat posed by state sponsors of terrorism; protecting the global commons, especially the sea lanes of communications, through which flow not only goods and services critical to the global economy but also undesirable commerce such as drug trafficking, people smuggling and weapons of mass destruction technologies.

So, isn't China the "single power" that Tellis thinks could threaten American interests in Asia? He denied this assumption to Congress, but many feel China is indeed the factor behind Washington's attempts to assist India in becoming a major world power.As author Sunil Khilnani, of the Johns Hopkins School of Advanced International Studies, says, "Many current inhabitants of the Pentagon see an India allied to the US as a potential bulwark to a China whose ambitions are still difficult to read." Washington's long-term view is that since China will not support the US war on terror, it's a threat against which the US needs a counterweight. "Japan has proven it does not have the emotional and intellectual muscle to face China. Hence, India should play that role," explains Rafiq Dossani of Stanford University.

The Bush regime's keenness on India also springs from the disaster his other foreign policy initiatives have been. "Bush would like to leave at least one foreign policy achievement as his legacy. He'd like to claim that he 'delivered' India to the US, just as Nixon could earlier claim the same about China," says Khilnani.

These reasons apart, the relationship has gathered great momentum from business-to-business links over the last decade. Says Anatol Lieven of the New America Foundation in Washington, "India's abandoning of its social democratic economic model, derived from the Nehru period, in favor of globalization and free market economics has made it much more attractive to investment and ideologically sympathetic to the US." Indeed, the more the two countries deepen their economic interdependence, the more each will have a stake in the other. And this economic interdependence can deepen, says Stephen P. Cohen of the Brookings Institution, through the removal of obstacles to US investments. "Infrastructure, (inadequate) liberalization, and education are three real obstacles. These (improvement in the three areas) will make it easy to implement the strategic relationship."

That India matters to the US is no longer a promise of the future. At a recent conference, former state department official Walter Andersen pointed out two US decisions that underscored India's enhanced importance. First, the four-country tsunami relief efforts involving the navies of the US, Japan, Australia and India. Two, the Bush administration's efforts to exempt a nuclear-capable India from exports restrictions on nuclear and dual use technology.

The blossoming ties have enabled significant partnerships in the international arena too. India has supported the war on terror in Afghanistan; its navy protected high-value US cargoes through the Straits of Malacca; more recently, India voted with the US at the International Atomic Energy Agency to declare Iran in "non-compliance" with the nuclear Non-Proliferation Treaty.

All this doesn't mean the US and India will automatically collaborate on every problem dogging them. "Nobody expects a perfect alignment ever, but increasing alignment is something we hope will come naturally," says Schaffer. Partly this alignment can be brought about through changes in the conduct of foreign policy. For instance, the US, Hathaway admits, needs to recognize that India expects to be treated on a basis of equality. Similarly, Khilnani contends, a section of Indian political elites need to shed its instinctive anti-Americanism. "This does not mean renouncing a critical position, or an independent assessment of our own interests. It means engaging more deeply and confidently, and picking battles more selectively and prudently," he says.

Obviously, like any two countries, there will be disagreements. "Indeed, there have been over the past few years on a number of issues, including the war in Iraq," says Inderfurth. But, he adds optimistically, "the fact that this has not disrupted the upward trajectory of our relationship is a good sign and a promising one for future relations."

Pre-emption used to be the watchword of Bush foreign policy. The world's sole superpower would not hesitate to wield force against an imminent threat to its security. The old doctrines of the Cold War era -- of containment and deterrence of a potential enemy -- were disdained as weakness.

Now, facing the most serious national security challenge since the end of the Cold War -- the nuclear weapons programs of Iran and North Korea -- the administration is reaching back to those oldies but goodies.

The determination of Iran and North Korea to develop nuclear weapons has so far been largely unchecked by this administration. The North Koreans, since breaking out of the freeze agreed to during the Clinton administration, have been steadily producing plutonium, and presumably warheads. The Iranians, after the election of hard-line President Mahmoud Ahmadinejad, reversed their deal to suspend uranium-enrichment activities, the crucial step toward nuclear weapons.

Diplomatic negotiations in both cases have produced little movement. But a military strike on their nuclear facilities is almost inconceivable. The danger of potentially horrendous retaliation and the sapping of American will and resources in Iraq have almost killed that option.

"As shaky as a policy of containment is, it is certainly preferable to confrontation, 'rollback,' or 'regime change' through military force,'' wrote conservative national security expert Thomas Donnelly in a recent analysis. "Containment is, in fact, regime change by tolerable means, and the solution to the problems of Iran and North Korea lie in an indirect approach.''

While we try to contain a nuclear Iran and North Korea, suggested Donnelly, we should surround Iran with movements for democratic change in Iraq and Afghanistan. North Korea, he believes, will be changed through Chinese influence.

Donnelly cautions that there may be circumstances when containment proves even more risky than intervention -- say if Iran tries to slip nuclear materials to Islamist terrorists. Iran is less stable than the Soviet Union, though it is worth remembering that the first 15 years of the Cold War brought us to the brink of nuclear war once and close to it several times.

For the administration, this is a stealth policy shift. That is no surprise. It flows directly from the mess in Iraq, a mistake the administration can never really acknowledge.

For those who once touted American global domination, it is still hard to face the reality that containment is impossible without allies and partners. By ourselves, we cannot press those regimes by cutting off their access to investment and advanced technology.

The administration is rightly moving to take Iran to the United Nations Security Council to seek a mandate to enforce the demands of the International Atomic Energy Agency. North Korea is undoubtedly watching this carefully.

China and Russia, who have veto power in the Security Council, are reluctantly going along. But they still resist any move to impose economic sanctions against Iran. Nor are the Europeans, Japanese and others who depend on oil and gas from Iran eager to halt their investment and trade.

Similarly in the case of North Korea, the Chinese and South Koreans are not prepared to cut the flow of economic aid and investment into the otherwise isolated North Korean state. This is less a case of economic interests than a fear that sanctions will escalate to greater confrontation, even war.

"The strategic challenge the Bush administration faced was to convince the rest of the world that Iran is more dangerous than the United States,'' says nuclear proliferation expert George Perkovich. "They finally did it -- and it took Ahmadinejad to do it,'' referring to the inflammatory rhetoric, including threats to "wipe Israel off the map,'' issued by the Iranian leader.

The administration made some headway down the same path with North Korea by engaging in direct talks with that regime this past fall, dispelling the image that the United States was unwilling to negotiate. But that progress has been undermined recently because hard-liners inside the Bush administration pulled the plug on such talks.

Managing an effective containment partnership will be a huge challenge. And there is still tremendous resistance inside the administration to engaging and negotiating -- and compromising -- with the enemy. But that was always a part of making containment succeed, even at the height of the Cold War.

Containment is no silver bullet. It is merely, as Donnelly puts it, "the least bad alternative, but not by a lot, and not under all circumstances.'' And right now, it is the only game in town.

In the old popular song about the rout by Americans at New Orleans during the War of 1812, the British "ran so fast the hounds couldn't catch 'em." Even allowing for patriotic hyperbole, it can hardly be argued that the British extricated themselves with a great deal of dignity, particularly given that another battle in the same war inspired the American national anthem.

The impact of that defeat on the British national psyche is now obscure, but nearly two centuries later, as the Americans and their British allies seek to extricate themselves from Iraq, the story of how a superpower looks for a dignified way out of a messy and often unpopular foreign conflict has become a historical genre of sorts. As the pressure to leave Iraq increases, that genre is receiving new and urgent attention.

And in the shadow of the bleak and often horrific news emerging from Iraq nearly every day, historians and political experts are finding at least a wan hope in those imperfect historical analogies. Even in the absence of a sudden and dramatic shift on the battlefield toward a definitive victory, there may still be a slight opening, as narrow as the eye of a needle, for the United States to slip through and leave Iraq in the near future in a way that will not be remembered as a national embarrassment.

Most of the recent parallels do not seem to offer much encouragement for a confounded superpower that wants to save face as it cuts its losses and returns home. Among them are the wrenching French pullout from Algeria, the ill-fated French and American adventures in Vietnam, the Soviet humiliation in Afghanistan and the disastrous American interventions in Beirut and Somalia.

Still, there are a few stories of inconclusive wars that left the United States in a more dignified position, including the continuing American presence in South Korea and the NATO peacekeeping mission in Bosnia. But even those stand in stark contrast to the happier legacy of total victory during World War II.

The highly qualified optimism of these experts about what may still happen in Iraq - let's call it something just this side of hopelessness - has been born of many factors, including greatly reduced expectations of what might constitute not-defeat there. The United States already appears willing to settle - as if it were in a relationship that had gone sour but cannot quite be resolved by a walk out the door, punctuated with a satisfying slam.

Alongside the dampening of hopes, there has also been a fair amount of historical revisionism regarding the darker tales of conflicts past: a considered sense that if the superpowers had made different decisions, things could have turned out more palatably, and that they still might in Iraq.

Maybe not surprisingly, Vietnam is the focus of some of the most interesting revisionism, including some of it immediately relevant to Iraq, where the intensive effort to train Iraqi security forces to defend their own country closely mirrors the "Vietnamization" program in South Vietnam. If Congress had not voted to kill the financing for South Vietnam and its armed forces in 1975, argues Melvin R. Laird in a heavily read article in the current issue of Foreign Affairs, Saigon might never have fallen.

"Congress snatched defeat from the jaws of victory by cutting off funding for our ally in 1975," wrote Mr. Laird, who was President Nixon's defense secretary from 1969 to 1973, when the United States pulled its hundreds of thousands of troops out of Vietnam.

In an interview, Mr. Laird conceded that the American departure from Vietnam was not a pretty sight. "Hell, the pictures of them getting in those helicopters were not good pictures," he said, referring to the chaotic evacuation of the American embassy two years after Vietnamization was complete, and a year after Nixon resigned. But on the basis of his what-if about Vietnam, Mr. Laird does not believe that all is lost in Iraq.

"There is a dignified way out, and I think that's the Iraqization of the forces over there," Mr. Laird said, "and I think we're on the right track on that."

Many analysts have disputed the core of that contention, saying that large swaths of the Iraqi security forces are so inept they may never be capable of defending their country against the insurgents without the American military backing them up. But Mr. Laird is not alone in his revisionist take and its potential application to Iraq.

William Stueck, a history professor at the University of Georgia who has written several books on Korea, calls himself a liberal but says he buys Mr. Laird's basic analysis of what went wrong with Vietnamization.

Korea reveals how easy it is to dismiss the effectiveness of local security forces prematurely, Mr. Stueck said. In 1951, Gen. Matthew Ridgeway felt deep frustration when Chinese offensives broke through parts of the line defended by poorly led South Korean troops.

But by the summer of 1952, with intensive training, the South Koreans were fighting more effectively, Mr. Stueck said. "Now, they needed backup" by Americans, he said. By 1972, he said, South Korean troops were responsible for 70 percent of the front line.

Of course, there are enormous differences between Iraq and Korea. Korean society was not riven by troublesome factions, as Iraq's is, and the United States was defending an existing government rather than trying to create one from scratch.

Another intriguing if imperfect lesson can be found in Algeria, said Matthew Connelly, a Columbia University historian. There, by March 1962, the French had pulled out after 130 years of occupation.

That long colonial occupation, and the million European settlers who lived there before the bloody exodus, are major differences with Iraq, Mr. Connelly noted. But there were also striking parallels: the insurgency, which styled its cause as an international jihad, broke down in civil war once the French pulled out; the French, for their part, said theirs was a fight to protect Western civilization against radical Islam.

Like President Bush in Iraq, President Charles de Gaulle probably thought he could settle Algeria in his favor by military means, Dr. Connelly said. In the short run, that turned out to be a grave miscalculation, as the occupation crumbled under the insurgency's viciousness.

Over the long run, though, history treated de Gaulle kindly for reversing course and agreeing to withdraw, Mr. Connelly said. "De Gaulle loses the war but he wins in the realm of history: he gave Algeria its independence," he said. "How you frame defeat, that can sometimes give you a victory."

The Americans in Beirut and the Soviets in Afghanistan are seen, even in the long view, as cases of superpowers paying the price of blundering into a political and social morass they did not understand.

For the Soviets, that mistake was compounded when America outfitted Afghan rebels with Stinger missiles capable of taking down helicopters, nullifying a key Soviet military superiority. "I don't think they had a fig leaf of any kind," said Henry Rowen, a fellow at the Institute for International Studies at Stanford who was assistant secretary of defense for international security affairs from 1989 to 1991. "They just left."

In Beirut, the Americans entered to protect what they considered a legitimate Christian-led government and ended up, much as in Iraq, in the middle of a multipronged civil conflict. In October 1983, a suicide attack killed 241 American servicemen at a Marines barracks, and four months after that, with Muslim militias advancing, President Ronald Reagan ordered the remaining marines withdrawn to ships off the coast, simply saying their mission had changed. The episode has been cited by Vice President Dick Cheney as an example of a withdrawal that encouraged Arab militants to think the United States is weak.

Today, even as expectations for Iraq keep slipping, some measure of victory can still be declared even in a less-than-perfect outcome, said Richard Betts, director of the Saltzman Institute of War and Peace Studies at Columbia. For example, he said, an Iraqi government that is authoritarian but not totalitarian might have to do.

The key point, he said, is that under those circumstances, the outcome "doesn't look like a disaster even if it doesn't look good."