How to Use mathematical modelling for social studies

A researcher at The University of Texas at Arlington has used mathematical modeling to demonstrate that negative peer pressures can spread in a high-risk setting, influencing students’ decisions to drop out of school.

“This study postulates that social behavior can spread interpersonally through social interactions and influences, just as infectious diseases can,” said Christopher Kribs, UTA professor of Mathematics and Curriculum & Instruction. Kribs is also an expert in mathematical epidemiology with research supported by the National Science Foundation.

The study showed that students who are failing at two or more subjects are at risk for dropping out, largely due to their increased interactions with other failing students.

“Positive parenting is clearly very important for students but the study discovered that there is a point where negative peer influences overcome positive parental influences,” Kribs said.

“We feel there is a real opportunity to intervene at the school level to reduce dropout rates by controlling negative influences,” he added.

The study looked at 125 students at a struggling high school in Chicago. The researchers surveyed the students on whether they were failing in core subjects such as mathematics, English, science and social sciences, the degree of parental involvement in their life and the number of failing and dropout friends of each student during the last year.

The mathematical model they developed defined students as being in one of two environments: a non-risky environment, where they are passing all core subjects or failing one and considered vulnerable; or a risky environment, where they are failing two or more core subjects and could drop out.

The data suggests that as the degree of parental involvement in a vulnerable student’s life increases, the number of their failing friends decreases.

If the student is already failing two core courses and in the risky zone, the effectiveness of parental involvement changes: the number of their failing friends initially decreases, but then increases again. This may occur if students become more rebellious to a sudden increase in parental involvement at the same time they are receiving negative peer pressure from other failing students.

“Parental guidance is a significant factor only when students are under a low level of negative social influence at school,” Kribs said. “If negative social influence increases beyond a critical value, the impact of parental influence becomes negligible. To manage dropout levels, we need to manage social influences at school.”

The paper concludes that making sure that vulnerable and failing students are not only mixing with other failing and dropout students could achieve a sustained reduction in dropout rates.

Jianzhong Su, UTA mathematics chair, emphasized the importance of this project within the strategic theme of data-driven discovery within UTA’s Strategic Plan 2020: Bold Solutions, Global Impact.

“Dr. Kribs’ work shows the relevance of mathematical studies to real-life social issues and demonstrates the importance of cross-disciplinary studies on social problems,” Su said. “The next step would be to roll the model out with larger groups of students to further demonstrate its accuracy and efficacy to education policymakers to make a real difference.”

Story Source:

Materials provided by University of Texas at Arlington. Note: Content may be edited for style and length.

Journal Reference:

  1. Bechir Amdouni, Marlio Paredes, Christopher Kribs, Anuj Mubayi. Why do students quit school? Implications from a dynamical modelling study. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2017; 473 (2197): 20160204 DOI: 10.1098/rspa.2016.0204

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Minimum age of criminal responsibility

The minimum age of criminal responsibility continues to divide opinion

A proposal to let Philippine criminal courts try nine-year-olds has drawn sharp criticism. But in 35 American states, children of any age can be convicted and sentenced

COMMON law has long held that committing a crime requires both a prohibited act and a “mens rea”, or “guilty mind”—the criminal knowing that the act was wrong. There is no global consensus regarding the youngest age at which a child can be deemed to have such intent, and thus can be tried and convicted of a criminal offence. Ten years ago the United Nations Committee on the Rights of the Child recommended an “absolute minimum” age of 12 for criminal responsibility, and urged countries “to continue to increase it to a higher age level”. The Philippines appears poised to move in the opposite direction: lawmakers there have proposed reducing the cut-off from 15 years old to nine. The bill has prompted sharp criticism both at home and abroad, and legislators are still arguing over its text.

Not long ago the Philippines earned a reputation for a relatively progressive stance on this issue. It introduced its current minimum age of criminal responsibility (MACR) in 2006, making it one of just 19 countries whose MACR is 15 or older. However, Rodrigo Duterte, the president, has adopted a harsh “tough-on-crime” agenda. The bill’s supporters say it would stop adult criminals from recruiting children under the age of criminal responsibility for drug-trafficking. Human-rights advocates counter that there is no evidence that this would reduce crime. Instead, says Leo Ratledge of Child Rights International Network, a British charity, it would punish victims of exploitation rather than those who exploit them.

The other members of the MACR-above-14 club are an incongruous bunch. Predictably, they include places like Norway and Sweden, which take a generally liberal approach to criminal justice. However, the top of the table is occupied by less developed countries that happen to have revised their juvenile-justice laws in recent years: in Timor-Leste and Mozambique, the MACR is now 16. Although most European states sit comfortably above the UN recommendation, there are notable exceptions. Scotland can hand out criminal records to eight-year-olds, though legislation is being mooted that will raise the minimum age limit to 12. In the rest of Britain, ten-year-olds can be tried for a crime. This British colonial legacy is reflected in the relatively low MACRs seen in South Africa, Australia and New Zealand. Similarly, Nigeria, India, Pakistan and Bangladesh are among the 21 countries that set a MACR of seven, the lowest national age globally.

In some cases the law is not clear-cut. The MACR in Comoros is based on puberty. It can differ by sex (as in Iran) or type of offence (Malaysia), while Poland and France entrust the issue to judges’ discretion. Nonetheless, even a vague minimum of “puberty” provides more protection than simply having no MACR at all. Just a handful of countries have no national MACR. The most striking is the United States. Although America sets a threshold of 11 years old for federal offences, the overwhelming share of crimes are policed at the state level. And 35 out of the 50 states have not set a MACR, putting them in a club with Cuba, Malaysia (exclusively for terrorism) and Sudan (for drug offences).

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How to devise the perfect recommendation algorithm

Winner takes all: If you liked that, you will love this

How to devise the perfect recommendation algorithm

Recommendations must be neither too familiar nor too novel

AT LAST YEAR’S consumer-electronics show in Las Vegas, Reed Hastings, the CEO of Netflix, set out an ambitious goal for serving his customers: “One day we hope to get so good at suggestions that we’re able to show you exactly the right film or TV show for your mood when you turn on Netflix.”

Winner takes allMore in this special report:

But what is exactly the right show? Mr Hastings’s company has been a pioneer in the science of recommendation algorithms, dating back to its days as a humble DVD-by-mail company. Netflix’s thinly sliced classifications of films and TV shows, and its equally finely graded assessments of customers’ viewing preferences, established the standard for product suggestions.

Still, algorithms take some of the adventure and serendipity out of hunting for new entertainment, and rarely nudge a customer towards anything way off his radar. This is a challenge for independent producers of music, literature or film, who already find it extremely difficult to get noticed amidst so much choice. Recommendation software can make the problem worse.

Suggestion algorithms can exploit what customers are known to like by pushing similar fare, or they can encourage them to explore things they might be less familiar with. Typical algorithms tend to exploit known preferences more than encourage exploration. When a customer buys a book, for instance, Amazon will recommend books on similar subjects that previous shoppers have also bought. Netflix will suggest a show based on the choices of other people with similar viewing histories.

Some recommendations are fairly crude, as when an online store repeatedly offers more of something the consumer has already bought and is unlikely to want more of, like an umbrella. Others are more adventurous, encouraging the customer to try something new. But if they go too far, they risk putting him off. “It’s more predictable to use similar recommendations over and over to get the engagement,” says Robert Kyncl, chief business officer of YouTube. “But the pay-off is much greater when you introduce something that is a bit of an odd choice and it works.”

Spotify, a music-streaming service, offers a different model with its Discover Weekly playlist, which it produces for more than 100m customers. It analyses billions of users’ playlists to find songs that others with similar interests have liked. These tracks are combined into a playlist of 30 songs (perhaps including some familiar as well as new ones) delivered each Monday.

The company says the service is used by tens of millions of listeners and gives a significant boost to thousands of performers each week. By limiting the list to a couple of hours-worth of listening, and by setting an expiration date each week, Spotify creates a sense of scarcity to keep listeners engaged.

Music lends itself well to this treatment. Streaming services have catalogues of around 30m songs each, compared with mere thousands of film and TV titles. And songs, unlike films, are short enough for a poor recommendation not to matter much. Spotify’s experience shows that algorithms can occasionally nudge people away from hits and expand their horizons.

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Plea to America’s Business Leaders

Dear America’s Business Leaders:

I am writing you today because it will soon become clear that you’re going to need to do a job that you’ve never thought of doing before: saving the country from a leader with a truly distorted view of how the world works and the role America should play in it.

There is no Republican Party today to restrain President Trump’s worst instincts. Save for a few courageous senators, the G.O.P. has melted into spinelessness. The mainstream media can expose misbehavior, but can’t veto legislation. The Democrats control no levers of power. And Jared Kushner couldn’t even stop the Steve Bannon-led White House from issuing a Holocaust Remembrance Day decree that deliberately omitted any reference to Jews.

The only group whom Trump has some respect for, who can get access to him and who can maybe counter the malign ideological instincts of Bannon & Company are the likes of Bill Gates, Tim Cook, Jeff Immelt, Mark Zuckerberg, Eric Schmidt, Jamie Dimon, Mike Bloomberg, Elon Musk, Indra Nooyi, Ginni Rometty, Dennis Muilenburg and Doug McMillon.

Sure, if Trump executes on his promises for deregulation, infrastructure and tax reform, your companies will enjoy a quick sugar high. But if you listen to what Trump and Bannon are saying, their vision of America and the world is unlike anything you business leaders have encountered before.

They are playing with, and happy to dispense with, big systems — like Nafta, the World Trade Organization and the European Union — that drive so much of the global economy. They believe things that are provably wrong — that the majority of job loss in America is from Mexicans and Chinese, when in fact it’s from microchips and computers, i.e., improved productivity.

Yes, some things are true even if Trump believes them: Islam does have problems with gender and religious pluralism, and integration in Western societies. Ignoring that is reckless.

But some things are true even if liberals believe them: that America has integrated Muslims better than any European country, because we are a melting pot. And making Muslims part of our community at home and our alliances abroad — rather than treating them as permanent aliens — has made us safer since 9/11. Ignoring that is dangerous.

And while we’re talking dangerous, why are there record numbers of migrants flooding out of sub-Saharan Africa, the Mideast and Central America, trying to get into Europe and America? Two big reasons are droughts and population explosions. And what do Trump and Bannon propose? Ignoring climate change and halting U.S. government help with family planning in the developing world.

Nothing is connected in their world. Everything is just a box to check or wall to build.

The Washington Post on Monday quoted Bannon as saying that he and Jeff Sessions were at the center of Trump’s “pro-America movement” that was “poorly understood by cosmopolitan elites in the media. … What we are witnessing now is the birth of a new political order, and the more frantic a handful of media elites become, the more powerful that new political order becomes itself.”

When someone tells you he is giving birth to a “new political order” in America, be afraid. Yes, the acceleration in technology and globalization has particularly benefited higher-skilled knowledge workers in the West and lower-skilled rising middle classes in Asia. And, yes, it did squeeze middle-skilled workers in the West, who were more vulnerable to outsourcing, algorithms and automation. More needs to be done to help them.

If Trump is simply out to negotiate better trade deals for America and get our allies to share the burdens of defending the free world more equitably, God bless him. That can be a win for our workers.

But I fear that Bannon is manipulating Trump into a more messianic mission — that his “new political order” is not just about jobs, but culture, an attempt to recreate an America of the 1950s: a country dominated by white Christians, not “cosmopolitans”; where no one spoke Spanish at the grocery store; where America’s biggest C.E.O.s weren’t named Satya or Sundar; where every worker could have a high-wage middle-skilled job; and where trade walls and the slow pace of automation meant you didn’t have to be a lifelong learner.

If that’s where Trump is going, it will take us to a dark place. The way we lift American workers is not by building higher walls, but rather stronger communities — where business, philanthropies, the local school system and local government forge adaptive coalitions to enable every worker to engage in lifelong learning and every company to access global markets and every town to attract the smart risk-takers who start companies.

That is exactly what is happening in America’s best communities, and the job of government is to scale it, and the job of big business is to defend it. So don’t be fooled by a Trump sugar high; your businesses will thrive only if America is the country that prepares itself and its workers to live in a world without walls, not one that goes around erecting them.

This is the “new political order” we need and that you must defend. You ignore this mission at your — and our — peril.

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