Alan Veliz-Cuba, University of Dayton

You can probably think of a time when you’ve used math to solve an everyday problem, such as calculating a tip at a restaurant or determining the square footage of a room. But what role does math play in solving complex problems such as curing a disease?

In my job as an applied mathematician, I use mathematical tools to study and solve complex problems in biology. I have worked on problems involving gene and neural networks such as interactions between cells and decision-making. To do this, I create descriptions of a real-world situation in mathematical language. The act of turning a situation into a mathematical representation is called modeling.

Translating real situations into mathematical terms

If you ever solved an arithmetic problem about the speed of trains or cost of groceries, that’s an example of mathematical modeling. But for more difficult questions, even just writing the real-world scenario as a math problem can be complicated. This process requires a lot of creativity and understanding of the problem at hand and is often the result of applied mathematicians working with scientists in other disciplines.

As an example, we could represent a game of Sudoku as a mathematical model. In Sudoku, the player fills empty boxes in a puzzle with numbers between 1 and 9 subject to some rules, such as no repeated numbers in any row or column.

The puzzle begins with some prefilled boxes, and the goal is to figure out which numbers go in the rest of the boxes.

Imagine that a variable, say x, represents the number that goes in one of those empty boxes. We can guarantee that x is between 1 and 9 by saying that x solves the equation (x-1)(x-2) … (x-9)=0. This equation is true only when one of the factors on the left side is zero. Each of the factors on the left side is zero only when x is a number between 1 and 9; for example, (x-1)=0 when x=1. This equation encodes a fact about our game of Sudoku, and we can encode the other features of the game similarly. The resulting model of Sudoku will be a set of equations with 81 variables, one for each box in the puzzle.

Another situation we might model is the concentration of a drug, say aspirin, in a person’s bloodstream. In this case, we would be interested in how the concentration changes as we ingest aspirin and the body metabolizes it. Just like with Sudoku, one can create a set of equations that describe how the concentration of aspirin evolves over time and how additional ingestion affects the dynamics of this medication. In contrast to Sudoku, however, the variables that represent concentrations are not static but rather change over time.

But the act of modeling is not always so straightforward. How would we model diseases such as cancer? Is it enough to model the size and shape of a tumor, or do we need to model every single blood vessel inside the tumor? Every single cell? Every single chemical in each cell? There is much that is unknown about cancer, so how can we model such unknown features? Is it even possible?

Applied mathematicians have to find a balance between models that are realistic enough to be useful and simple enough to be implemented. Building these models may take several years, but in collaboration with experimental scientists, the act of trying to find a model often provides novel insight into the real-world problem.

Mathematical models help find real solutions

After writing a mathematical problem to represent a situation, the second step in the modeling process is to solve the problem.

For Sudoku, we need to solve a collection of equations with 81 variables. For the aspirin example, we need to solve an equation that describes the rate of change of concentrations. This is where all the math that has been and is still being invented comes into play. Areas of pure math such as algebra, analysis, combinatorics and many others can be used – in some cases combined – to solve the complex math problems arising from applications of math to the real world.

The third step of the modeling process consists of translating the mathematical solution into the solution to the applied problem. In the case of Sudoku, the solution to the equations tells us which number should go in each box to solve the puzzle. In the case of aspirin, the solution would be a set of curves that tell us the aspirin concentration in the digestive system and bloodstream. This is how applied mathematics works.

When creating a model isn’t enough

Or is it? While this three-step process is the ideal process of applied math, reality is more complicated. Once I reach the second step where I want the solution of the math problem, very often, if not most of the time, it turns out that no one knows how to solve the math problem in the model. In some cases, the math to study the problem doesn’t even exist.

For example, it is difficult to analyze models of cancer because the interactions between genes, proteins and chemicals are not as straightforward as the relationships between boxes in a game of Sudoku. The main difficulty is that these interactions are “nonlinear,” meaning that the effect of two inputs is not simply the sum of the individual effects. To address this, I have been working on novel ways to study nonlinear systems, such as Boolean network theory and polynomial algebra. With this and traditional approaches, my colleagues and I have studied questions in areas such as
decision-making,
gene networks,
cellular differentiation and
limb regeneration.

When approaching unsolved applied math problems, the distinction between applied and pure mathematics often vanishes. Areas that were considered at one time too abstract have been exactly what is needed for modern problems. This highlights the importance of math for all of us; current areas of pure mathematics can become the applied mathematics of tomorrow and be the tools needed for complex, real-world problems.

Alan Veliz-Cuba, Associate Professor of Mathematics, University of Dayton

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Jonathan D. Quick, Duke University and Eszter Rimanyi, Duke University

In 2023, 42 state attorneys general sued Meta to remove Instagram features that Meta’s own studies had shown – and independent research had confirmed – are harmful to teenage girls.

The same year, a report from the nonprofit Sandy Hook Promise found gun manufacturers were targeting the youth market with eye-catching ads and product placements in video games.

And in the run-up to the Paris Olympics, a leading international health journal urged the International Olympic Committee to end its relationship with Coca-Cola because of the increased obesity, diabetes, heart disease and high blood pressure associated with sugary drinks.

Social media, guns, sugar: These are all examples of what we call “market-driven epidemics.”

When people think of epidemics, they might think they’re caused only by viruses or other germs. But as public health experts, we know that’s just part of the story. Commerce can cause epidemics, too. That’s why our team coined the phrase in a recent study because you can’t solve a problem without naming it.

Market-driven epidemics follow a familiar script. First, companies start selling an appealing, often addictive product. As more and more people start using it, the health harms become clearer. Yet even as evidence of damage grows and deaths pile up, sales continue to rise as companies resist efforts by health authorities, consumer groups and others to control them.

We see this pattern with many products today, including social media platforms, firearms, sugar-sweetened beverages, ultra-processed foods, opioids, nicotine products, infant formula and alcohol. Collectively, their harm contributes to more than 1 million deaths in the U.S. each year.

How to fight a commercial epidemic

In our study, we asked two critical questions: Is it possible to combat such epidemics by changing the consumption patterns of millions of people? And if so, what does it take?

We found the answers by looking at decades of efforts to reduce unhealthy consumption of three products: cigarettes, sugar and prescription opioids.

In each case, Americans kept consuming more and more of these products, even in the face of growing health concerns, until a tipping point was reached. That was followed by steady declines in consumption.

The immediate cause for each tipping point varied considerably. For cigarettes, it was the trusted, authoritative voice of the U.S. Surgeon General unequivocally declaring in 1964 that smoking causes cancer.

In the case of sugar, one of the key moments was a high-profile 1999 petition titled “America: Drowning In Sugar” submitted by the Center for Science in the Public Interest and supported by 72 leading public health organizations and experts. The petition urged the Food and Drug Administration to require food labels to disclose the number of added sugars and their percentage of the daily recommended intake.

Once enacted, this policy helped consumers make healthier food choices, while also highlighting just how full of sugar many items on the market were.

And for prescription opioids, in 2011, the U.S. Centers for Disease Control and Prevention declared an opioid epidemic, signaling to doctors that they were overprescribing, and to the drug industry that it was acting irresponsibly.

In each case, success came after years of persistent efforts by scientists, public health officials and advocates to sway public opinion, often against the deliberate efforts of corporations to undermine them.

The 1964 report on smoking came after a decade of confusion that the industry had sown to distract the public from the scientific consensus about the harms of tobacco. The report offered conclusive authority that changed the narrative. Smoking went from being viewed as a widely accepted social custom to a deadly habit almost overnight. Today, just 1 in 9 American adults smoke, down from nearly half of all adults in 1954.

The push in 1999 by public health leaders connected the dots between rising obesity rates and sugar-laden foods and drinks. People began scrutinizing their diets, especially their sugar intake. As result, annual sugar consumption has since dropped by more than 15 pounds per person, erasing half of the amount of sugar Americans added to their diets between 1950 and 2000.

And the CDC report on opioids effectively communicated to doctors that they couldn’t just rely on patients to avoid misuse of the highly addictive drugs, underscoring their responsibility to help control the epidemic by reducing prescriptions of opioids such as OxyContin. Since the report, opioid prescription has been reduced by 60% – more in line with actual medical need.

Learning from the past

While there are no easy solutions for today’s market-based epidemics, we can learn from history about steps that can be effective in reducing the consumption of harmful products.

Changing attitudes on smoking show that an authoritative governmental voice can still be immensely useful to combat corporate resistance and the spread of corporate mis- and disinformation.

It can be effective to provide clear guidance about products and alternatives, as public health leaders did in telling consumers to cut consumption of sugar-sweetened beverages.

And from opioids, we can learn that applying pressure to those who make decisions about consumption, who are not always the consumers themselves, can be immensely powerful in bending patterns of use.

Despite the progress made in these three cases, the U.S. continues to face ongoing and emerging epidemics of unhealthy products. For example, while smoking has dramatically declined, the shift to vaping and other nicotine delivery products is creating new challenges, especially among teenagers.

Meanwhile, gun deaths keep rising, and firearms are now the leading killer of children under 18, and the gun industry remains committed to opposing public health measures to reduce gun violence.

And ultra-processed foods now account for nearly 60% of the average American’s diet, yet as new evidence confirms their harms, the food industry defends them.

But our research shows that these problems can be solved – that it is in fact possible to change millions of Americans’ behavior. This is very good news. It means sound evidence and public health action can turn the tide on some of the world’s biggest health challenges, potentially saving millions of lives and billions of dollars in health-care costs.

Jonathan D. Quick, Adjunct Professor of Global Health, Duke Global Health Institute, Duke University and Eszter Rimanyi, Chronic disease and addiction epidemiologist, Duke University

This article is republished from The Conversation under a Creative Commons license. Read the original article.

Jillian Hubertz, Purdue University

Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to curiouskidsus@theconversation.com.

I like to listen to music all the time. Are there any negative aspects to this? – Hussein, age 17, Iraq

Music surrounds us. It can be a companion throughout the day – listening on the way to school or work, checking out a favorite artist with friends, hearing it live at concerts and sporting events, enjoying or enduring it in stores and restaurants, and then listening again in the evening to unwind.

As meaningful and uplifting as music can be, it might also help you while studying, working on school projects and doing homework. As a clinical assistant professor of audiology, I can tell you the research shows that music can increase your focus and even motivate you.

This connection depends somewhat on the individual. Some people need silence while doing homework. Human brains are limited in their ability to multitask, and some people are better at doing two things at once compared with others. The style of music, the activity you’re doing and the effort it takes to complete the work also matter.

Some types of music work better than others

Numerous studies have discovered how music can affect study and work habits:

1. Listening to instrumental or familiar music in the background competes less with a study assignment than music with lyrics or unfamiliar music. Instrumental music also seems to interfere less with reading comprehension and assignments requiring verbal and visual memory than does music with lyrics.

2. One study showed soft, fast music had a positive impact on learning, but loud and fast, loud and slow, and soft and slow hindered learning.

3. Upbeat music with a higher tempo may help when you’re doing something requiring movement or motivation, such as exercising or cleaning your room.

4. The more difficult your task is – for instance, memorizing material, problem-solving or learning something new – the more likely the music is distracting and people often need to turn it off.

But before listening to your favorite sounds while studying, don’t miss an important detail: the volume.

The damage begins early

Whether listening through speakers, headphones or earbuds, too high a volume can damage your hearing. It’s known as noise-induced hearing loss, and it happens more often than you might think – those high-volume sounds can destroy tiny, delicate hair-like structures in the inner ear that help you hear.

Inner-ear damage can occur from a single exposure to an extremely loud sound or from repeated exposure to loud sounds over months or years. While some parts of the ear can repair themselves, the inner ear cannot fix itself.

Close to 1 in 5 Americans ages 12 to 19 – about 17% – demonstrate signs of noise-induced hearing changes in one or both ears, which could eventually lead to hearing loss.

Volume, time, distance

How dangerous a sound is to your hearing depends on three things: the volume of the sound, the length of time you listen, and how close you are to the sound.

Sounds are measured in decibels, or dB, and the dBA scale reflects how the human ear hears sound.

Typically, sounds at or below 70 decibels are safe for listening. Conversations generally register at about 60 dBA, city traffic at about 80 dBA.

Sounds that may be harmful include lawn mowers, at roughly 95 dBA, rock concerts, at around 120 dBA, and fireworks, at about 140 dBA.

The World Health Organization suggests a sound allowance for weekly exposure, based on loudness. For example, you could listen to a 75 dBA sound for 40 hours per week. But listen to something at 89 dBA and that time allowance is drastically reduced, to about an hour and a half.

Signs you’ve been exposed to a dangerously loud sound include muffled hearing, ringing in the ears and difficulty having a conversation from 3 feet (1 meter) away.

Although your hearing generally returns to normal after such an experience, there is a cost. This temporary shift in hearing could lead to permanent harm to inner-ear structures and ultimately damage your hearing.

How to stay safe

Technology not available even a few years ago can now alert you of a risky listening environment. A sound-level meter app measures the sound around you to determine whether it’s too loud. So can some smartwatches.

If listening through speakers, the sound-level app can warn you if your tunes are creeping toward too loud. When wearing headphones or earbuds, keep it at or below 60% of the volume allowed by your device. One rule of thumb: If someone else can hear the sound emanating from your headphones or earbuds when they are an arm’s length away from you, the volume is too loud.

Use high-quality, noise-canceling headphones or earbuds to hear the audio at a safer, lower level. Some headphones also have volume limitations.

Use hearing protection, such as disposable earplugs or earmuffs, when you’re around loud sounds, such as concerts, fireworks or a lawn mower.

You can also simply decrease listening time. Taking breaks lets you avoid overexposure.

Follow these tips and you should be able to enjoy your favorite music, games and conversations for decades to come. Pay attention to what music helps your concentration rather than distracts you, and your schoolwork might benefit, too.

Hello, curious kids! Do you have a question you’d like an expert to answer? Ask an adult to send your question to CuriousKidsUS@theconversation.com. Please tell us your name, age and the city where you live.

And since curiosity has no age limit – adults, let us know what you’re wondering, too. We won’t be able to answer every question, but we will do our best.

Jillian Hubertz, Clinical Assistant Professor in Speech, Language, and Hearing Sciences, Purdue University

This article is republished from The Conversation under a Creative Commons license. Read the original article.