"The United States is the most powerful since the Roman Empire," stated Stephen Walt, the Belfer Professor of International Affairs and academic dean of the John F. Kennedy School, Harvard University, delivering the 2005 Robert G. Wesson Lecture in International Relations Theory and Practice, at the Freeman Spogli Institute on November 16, 2005. America's unmatched power is therefore of great interest and concern to leaders in most other parts of the world, from President Putin in Russia, to President Chirac in France, and President Musharraf in Pakistan. For Americans, however, the key issue is how others are now responding to U.S. power.

Speaking before an audience of Stanford faculty, students, and the broader community, Professor Walt examined three interwoven themes: why other states do not welcome U.S. power; what are the main strategies available to them for dealing with American power? and what should the United States do in response?

As an integral part of his analysis, Walt showed opinion polls demonstrating a striking gap between American views of U.S. primacy and other countries' perceptions of the current U.S. role. For example, although the 2002 Pew Global Attitudes Project found that 79 percent of U.S. citizens believe it is good that "American ideas and customs are spreading around the world," and 70 percent think that U.S. foreign policy takes the interests of other states into account either "a great deal" or "a fair amount," overwhelming majorities overseas say the United States considers the interest of others "not much" or "not at all." Similarly, a 2005 BBC survey of 21 countries found only five, India, the Philippines, Poland, South Africa, and South Korea, where a majority of people had "positive" attitudes toward the United States.

There are three major sources of anti-Americanism, Walt explained. First, our sheer power makes other nations nervous. Second, there is a perceived sense of hypocrisy between our words and our actions. The case of nuclear weapons provides a vivid example. We preach nonproliferation, yet accord new respect and policy cooperation with newly nuclear states, such as India. Third, how the United States behaves in the world-what we do-invites antipathy. This latter point is abundantly clear in global opinion polls: Even in regions where anti-Americanism seems most strident, nations and individuals report that they do not object to our values or to what we stand for but rather to what we do.

Other nations, Walt pointed out, can choose a strategy of accommodation to our power or a strategy of resistance. Commonly adopted strategies of accommodation include 'bandwagoning," or realigning foreign policies with U.S. wishes, such as Libya's abandonment of nuclear weapons; "regional balancing"-using U.S. power to balance regional threats; "bonding" to curry favor with the United States; and "penetration," a strategy aimed at infiltrating the American political system to influence foreign policy outcomes.

In contrast, countries that choose to resist American power pursue five strategies:

"balancing" our power, alone or in alliance with others; "asymmetric responses," such as terrorism, which try to exploit specific areas of U.S. vulnerability; "blackmail," like North Korea's efforts to extract concessions from its nuclear weapons program; "balking," or tacit non-cooperation; and "delegitimizing," or attempts to turn others against the legitimacy of our actions or policies.

In light of the growing antipathy to U.S. primacy in so many parts of the world, Walt proposed three major courses of action to produce a more favorable response to U.S. power. First, he urged that we reduce American's military footprint abroad-and especially our ground force deployments-and return to a more traditional policy of regional balancing in cooperation with other nations. This policy would make greater use of American air and naval power and limit American intervention to cases where vital U.S. interests are threatened. Second, we should work harder to defend our international legitimacy and rebuild the U.S. image abroad, through a sustained campaign of public diplomacy and by keeping key American institutions-such as higher education-available to foreign visitors. Third, he advocated a more nuanced approach to America's traditional support for Israel, one that balances our genuine support for Israel's existence with the urgent need to bring a lasting settlement to the Israeli-Palestinian conflict.

"The more the United States uses its power in an overwhelming and capricious manner," Professor Walt warned, "the more the rest of the world will resist us." Conversely, the more the United States recognizes and respects the interests of others, while using its power to defend its own interests, the more other nations will welcome U.S. power. "The task we face," he advised, "is to rebuild the trust, admiration, and legitimacy the United States once enjoyed, so the rest of the world can focus not on taming U.S. power but on reaping the benefits it can bring."

Co-author CESP senior fellow Harold A. Mooney details the dangerous impacts nitrogen-rich chemical fertilizers can have on the atmosphere and important watersheds. He asserts "the use of organic versus chemical fertilizers can play a role in reducing these adverse effects."

Organic farming has long been touted as an environmentally friendly alternative to conventional agriculture. A new study in the Proceedings of the National Academy of Sciences (PNAS) provides strong evidence to support that claim.

Writing in the March 6 online edition of PNAS, Stanford University graduate student Sasha B. Kramer and her colleagues found that fertilizing apple trees with synthetic chemicals produced more adverse environmental effects than feeding them with organic manure or alfalfa.

"The intensification of agricultural production over the past 60 years and the subsequent increase in global nitrogen inputs have resulted in substantial nitrogen pollution and ecological damage," Kramer and her colleagues write. "The primary source of nitrogen pollution comes from nitrogen-based agricultural fertilizers, whose use is forecasted to double or almost triple by 2050."

Nitrogen compounds from fertilizer can enter the atmosphere and contribute to global warming, adds Harold A. Mooney, the Paul S. Achilles Professor of Environmental Biology at Stanford and co-author of the study.

"Nitrogen compounds also enter our watersheds and have effects quite distant from the fields in which they are applied, as for example in contaminating water tables and causing biological dead zones at the mouths of major rivers," he says. "This study shows that the use of organic versus chemical fertilizers can play a role in reducing these adverse effects."

Nitrogen treatments

The PNAS study was conducted in an established apple orchard on a 4-acre site in the Yakima Valley of central Washington, one of the premiere apple-growing regions in the United States. Some trees used in the experiment had been raised with conventional synthetic fertilizers. Others were grown organically without pesticides, herbicides or artificial fertilization. A third group was raised by a method called integrated farming, which combines organic and conventional agricultural techniques.

"Conventional agriculture has made tremendous improvements in crop yield but at large costs to the environment," the authors write. "In response to environmental concerns, organic agriculture has become an increasingly popular option."

During the yearlong experiment, organically grown trees were fed either composted chicken manure or alfalfa meal, while conventionally raised plants were given calcium nitrate, a synthetic fertilizer widely used by commercial apple growers. Trees raised using the integrated system were given a blend of equal parts chicken manure and calcium nitrate.

Each tree was fertilized twice, in October and May, and given the same amount of nitrogen at both feedings no matter what the source-alfalfa, chicken manure, calcium nitrate or the manure/calcium nitrate blend.

Groundwater contamination

One goal of the PNAS experiment was to compare how much excess nitrogen leached into the soil using the four fertilizer treatments-one conventional, two organic (manure and alfalfa) and one integrated. When applied to the soil, nitrogen fertilizers release or break down into nitrates-chemical compounds that plants need to build proteins. However, excess nitrates can percolate through the soil and contaminate surface and groundwater supplies.

Besides having detrimental impacts on aquatic life, high nitrate levels in drinking water can cause serious illness in humans, particularly small children. According to the PNAS study, nearly one in 10 domestic wells in the United States sampled between 1993 and 2000 had nitrate concentrations that exceeded the Environmental Protection Agency's drinking water standards.

To measure nitrate levels during the experiment, water was collected in resin bags buried about 40 inches below the trees and then analyzed in the laboratory. The results were dramatic. "We measured nitrate leaching over an entire year and found that it was 4.4 to 5.6 times higher in the conventional treatment than in the two organic treatments, with the integrated treatment in between," says John B. Reganold, the Regents Professor of Soil Science at Washington State University and co-author of the study.

Nitrogen gas emissions

The research team also compared the amount of nitrogen gas that was released into the atmosphere by the four treatments. Air samples collected in the orchard after the fall and spring fertilizations revealed that organic and integrated soils emitted larger quantities of an environmentally benign gas called dinitrogen (N2) than soils treated with conventional synthetic fertilizer. One explanation for this disparity is that the organic and integrated soils contained active concentrations of denitrifying bacteria-naturally occurring microbes that convert excess nitrates in the soil into N2 gas. However, denitrifier microbial communities were much smaller and far less active and efficient in conventionally treated soils.

The research team also measured emissions of nitrous oxide (N2O)-a potent greenhouse gas that is 300 times more effective at heating the atmosphere than carbon dioxide gas, the leading cause of global warming. The results showed that nitrous oxide emissions were similar among the four treatments.

"We found that higher gas emissions from organic and integrated soils do not result in increased production of harmful nitrous oxide but rather enhanced emission of non-detrimental dinitrogen," Reganold says. "These results demonstrate that organic and integrated fertilization practices support more active and efficient denitrifier microbial communities, which may shift some of the potential nitrate leaching losses in the soil into harmless dinitrogen gas losses in the atmosphere."

Sustainable agriculture

Washington state produces more than half of the nation's apples. In 2004, the state crop was worth about $963 million, with organically grown apples representing between 5 and 10 percent of the total value. But the results of the PNAS study may apply to other high-value crops as well, according to the authors.

"This study is an important contribution to the debate surrounding the sustainability of organic agriculture, one of the most contentious topics in agricultural science worldwide," Reganold says. "Our findings not only score another beneficial point for organic agriculture but give credibility to the middle-ground approach of integrated farming, which uses both organic and conventional nitrogen fertilizers and other practices. It is this middle-ground approach that we may see more farmers adopting than even the rapidly growing organic approach."

Adds Mooney, "Organic farming cannot provide for all of our food needs, but it is certainly one important tool for use in our striving for sustainable agricultural systems. We need to explore and utilize all possible agricultural management techniques and technologies to reduce the very large global footprint of the needs to feed a population of over 6 billion people."

Other co-authors of the PNAS study are agroecologist Jerry D. Glover of the Land Institute in Salina, Kan., and Brendan J. M. Bohannan, associate professor of biological sciences at Stanford.

The study was funded by the U.S. Department of Agriculture, the National Science Foundation, the Land Institute and the Teresa Heinz Environmental Science and Policy Fellowship Program.

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.