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."