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How mathematicians combat violence

Using math, data can help find 'tipping point' that makes difference with gangs.
ASU mathematician to support El Salvador center that bears his name.
March 15, 2016

Salvadoran university names center after ASU's Castillo-Chavez; his work models ways to quell violence

Upon first thought, the idea of math combating violent crime seems unlikely, at best. Can an algorithm be more effective than a SWAT team with a battering ram?

Yes. By mathematically modeling systems, pressure points can be identified and squeezed until the system changes or collapses. Instead of bludgeoning a problem into line, it’s like finding a carotid artery and pinching it until the opponent collapses.

That’s the idea behind the establishment of a mathematical modeling center at an El Salvador university named after Arizona State University professor Carlos Castillo-Chavez late last month.

This center will focus on researching the main problems of the country, particularly, in the short term, designing models for addressing violence and its prevention. The objective is to analyze data related to the issues of violence, insecurity and their derivatives.

Francisco Gavidia University has created the Center for Mathematical Modeling “Carlos Castillo-Chavez” in honor of the Mexican-American scientist at ASU. Dr. Castillo-ChavezDr. Castillo-Chavez is a University Regents’ Professor and Joaquin Bustoz Jr. Professor of mathematical biology in the School of Human Evolution and Social Change in the College of Liberal Arts and Sciences, distinguished sustainability scientist in the Julie Ann Wrigley Global Institute of Sustainability, and executive director of the Simon A. Levin Mathematical, Computational and Modeling Sciences Center. will support the center’s technical implementation and assist in the development of collaborative research with ASU and other institutions throughout Latin America.

Mathematics can’t solve the problem of violence per se, but mathematical models are key components of interdisciplinary efforts aimed at quantifying the impact of violence, Castillo-Chavez said.

Models can “help identify what are the key mechanisms that facilitate the spread of violence in communities and regions to the point that it may alter societal norms,” he said. “They can also help you identify the pressure points of the system; that is, what are the key nodes that, if modified, would have the most impact on the reduction of crime.”

“A key problem in El Salvador involves gangs. Can we model their dynamics? Recruitment? Progression? ... What would happen if we reduce recruitment — somehow make it harder? By 10 percent? By 20 percent? By 30 percent? At what point does it make a difference?”
— ASU mathematician Carlos Castillo-Chavez

The process is to ask questions, build scenarios in the form of experiments, define constraints and proceed to address the problem.

“A key problem in El Salvador involves gangs,” Castillo-Chavez said. “Can we model their dynamics? Recruitment? Progression? Until they become hard-core? What are the key pressure points? Recruitment? What would happen if we reduce recruitment — somehow make it harder? By 10 percent? By 20 percent? By 30 percent? At what point does it make a difference? What if recidivism is high? How do we reduce the levels of recidivism? Can we do it if individuals within the environment that they live in are dominated by gangs?”

What Castillo-Chavez is looking for is the “tipping point,” an idea explained by journalist Malcolm Gladwell in his 2000 book of the same name.

It’s “the idea that social problems behave like infectious agents,” Gladwell said in his original article on the topic in the New Yorker magazine in 1996. “This is the fundamental lesson of nonlinearity. When it comes to fighting epidemics, small changes — like bringing new infections down to thirty thousand from forty thousand — can have huge effects. And large changes — like reducing new infections to fifty thousand from a hundred thousand — can have small effects. It all depends on when and how the changes are made.”

Castillo-Chavez also wrote about applying epidemiology modeling to life and social sciences in a 2011 paper.

“The concept of threshold or tipping point, a mathematical expression that characterizes the conditions needed for the occurrence of a drastic transition between epidemiological states, is central to the study of the transmission dynamics and control of diseases,” he wrote. “Epidemiological thinking has transcended the realm of epidemiological modeling and in the process, it has found applications to the study of dynamic social process where contacts between individuals facilitate the build-up of communities that can suddenly (tipping point) take on a life of their own.”

The main idea is to use mathematics to model the processes that produce violence, and then use the model to figure out how to alter these processes by whatever interventions are appropriate to reduce violence, said Ed Kaplan, the main speaker at the center’s opening.

Kaplan is the William N. and Marie A. Beach Professor of Management Science at the Yale School of Management, professor of public health at the Yale School of Medicine, and professor of engineering in the Yale School of Engineering and Applied Science.

“Reducing gang violence largely reduces to reducing the population of gang members; fewer gang members, fewer people to commit violent crimes,” he said. “There are two basic ways to reduce the size of any population: increase the rate that people leave, or reduce the rate that people join.

“Increasing the rate that people leave is essentially the job of law enforcement — and the many arrests and incarcerations of Salvadoran gang members testify to this approach. But even more important is starving gangs of new members. Here the key ingredients are education and job opportunities.

“A mathematical model can help relate the impact of investments in such diversion programs as well as the impact of different levels of enforcement on the resulting gang population, and show what the most cost-effective interventions are.”

Top photo by Aleksandar Milosevic/

Scott Seckel

Reporter , ASU News


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ASU education, public affairs among big gains in US News rankings

@ASU is all over the list of #BestGradSchools in 2017 @USNewsEducation rankings
@ASUeducation is ranked 14 on list of #BestGradSchools by @USNewsEducation @ASU
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@Thunderbird among the #BestGradSchools on @USNewsEducation list @ASU
March 15, 2016

Law school, School of Art also rise in national review of graduate programs

Arizona State University’s education and public affairs graduate programs broke into the top 15 and joined the university’s law school and fine arts program in jumping to higher spots in the latest rankings by U.S. News & World Report, which were released Tuesday.

All four of those graduate schools ranked within the top 25 in the nation and were the top-ranked schools in Arizona.

“The model we have been working on for a New American University has always been focused on raising the quality of the programs we deliver,” said Mark S. Searle, executive vice president and university provost. “The results from the U.S. News & World Report rankings reflect one indicator that we are being recognized for our efforts.”

ASU’s Mary Lou Fulton Teacher’s College marked a non-stop rise in the rankings, from 35th to 14th, over the past six years, underscoring the variety of ways in which ASU is strengthening education in Arizona and the nation and outperforming schools such as UC Berkeley, Michigan State and NYU.

Dean Mari Koerner emphasized that some colleges of education focus on teacher preparation but don’t have faculty who conduct world-class research. Others produce PhDs who join the academy but don’t prepare educators to serve in K-12 schools.

“We are an extraordinary college because we are committed to both,” Koerner said. ”The most enduring testament to the knowledge we create, the programs we implement and the partnerships we foster are our extraordinary graduates who are embedded in communities and have a great impact on schools.”

The graduate programs within the School of Public Affairs, at the College of Public Service and Community Solutions, also elbowed into the top 15, rising three places to 13th in the nation, ahead of Columbia and Georgetown. Even better? Its city management programs are ranked fourth, higher than Harvard’s.

The school helps lead the Alliance for Innovation, a unique partnership with 400 city managers across the nation that allows the school to have a direct impact on how many U.S. cities are run. Students and faculty connect with city leadership from member communities for internships and other valuable learning experiences, as well as research.

“We have an impact on practice that goes far beyond the classroom and journals,” said Karen Mossberger, director of the School of Public Affairs, “through research that addresses challenges these communities are facing and through students who gain invaluable experience alongside some of the leading managers around the country.”

The Sandra Day O’Connor College of Law is now a top-25 law school, moving up a notch from 26 last year, especially noteworthy given the emphasis that the legal community places on rankings, and outranking UC Davis, Colorado and Ohio State University. Its legal writing program ranked No. 7 in the nation, topping schools such as Marquette and Temple.

“For a law school that has been operating for fewer than 50 years to be so highly ranked is truly amazing,” said Dean Douglas J. Sylvester. “It is a testament to the quality of our students, devotion of our alumni, and deep community support.” 

ASU Law continues to adapt legal education in response to a changing world and economy, including global engagement through a legal “Peace Corps” in its Rule of Law & Governance Program, and a community legal center incorporated into the Arizona Center for Law and Society in downtown Phoenix — the new home of ASU Law — that opens in August. The center will provide valuable experience and embody ASU’s commitment to the downtown community.

The ASU School of Art, in the Herberger Institute for Design and the Arts, rose into the top 20, up two spots from last year’s No. 22 and from No. 30 in 2012, and its printmaking programs rank fifth in the country. The Herberger Institute’s overall ranking topped schools such as the University of Chicago and Cornell.

The Herberger Institute maintains that artists must be embedded in their communities and dedicate their creative energy and talent to building, reimagining and sustaining our world, Dean Steven J. Tepper explained. He said design and the arts must be socially relevant and never viewed as extras or grace notes. The perspective is shared by renowned choreographer and MacArthur Fellow Liz Lerman, who recently joined the Institute’s faculty and described her work across campuses and the community as “equal commitment to concert and community.” “That is,” Lerman said, “spending time in different disciplines, which is just a thrill.”

The U.S. News rankings showed that ASU remains the best for business in the state, with the full-time MBA at the W. P. Carey School of business ranking 35th in the nation, with highly ranked specialty programs. Students looking for international business find a No. 3 program with the Thunderbird School of Global Management. The Supply Chain and Logistics program is heralded as fourth in the country. Both of these specialty programs beat out Stanford and the University of Pennsylvania (Wharton).

The College of Nursing and Health Innovation remains in the top 30 in the country.

Individual programs within the College of Health Solutions are ranked as top-notch, each rising in the rankings: ASU is ninth for its doctorate in audiology, up from 17th, and 17th for its master’s in speech-language pathology, up from 21st.

For more information about applying to ASU’s graduate programs, visit the graduate admissions website.