Bicycles, networks, and biological homeostasis

The linked article is for SIAM News, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While this article contains equations, I wrote it to be understandable even if you gloss over the math.

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Balancing Homeostasis and Health

For SIAM News:

Human beings are not bicycles. However, mechanistic metaphors for the human body abound. For instance, we compare athletes to finely-tuned machines and look for equations that are derived from mechanics to describe biological processes — even when the relationship is no better than an analogy.

However, the concept of homeostasis clearly exemplifies the breakdown of mechanistic models when one applies them to the human body. Homeostasis is the process by which an organism maintains a stable output regardless of input (within reasonable limits). The most familiar example is human body temperature, which stays within a remarkably small range of values regardless of whether one is sitting in a cold room or walking outside on a hot day.

“In a bicycle, you know what each part is for,” Michael Reed, a mathematician at Duke University, said. “We are not machines with fixed parts; we are a large pile of cooperating cells. The question is, how does this pile of cooperating cells accomplish various tasks?”

[ Read the rest at SIAM News ]

Ecological stability far from equilibrium

toxic algae on Lake Erie, as seen by the Landsat 8 satellite

The linked article is for SIAM News, the magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While this article contains equations, I wrote it to be understandable even if you gloss over the math.

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

Ecological Transients and the Ghost of Equilibrium Past

For SIAM News:

The sight and smell of eutrophication—in the form of a layer of stinking green algae on a lake or pond—is likely familiar to many readers. The result is detrimental, even toxic, to other species that rely on the water, ranging from tiny animals to birds and even humans. For example, eutrophication on Lake Erie affects millions (see Figure 1). But the real culprit is actually the substance that feeds the algae: excess phosphorous that is produced by human activities like fertilizer runoff and leaky septic systems.

To manage eutrophication, one must know whether the affected body of water resides in a eutrophic stable state, or if its state is a long transient. The second case mimics stability because it can last a long time but is sustained by another source of phosphorous in the lakebed sediments. According to Tessa Francis, an ecologist at the University of Washington Puget Sound Institute, the wrong management choice has major consequences in terms of costs and trade-offs.

“You’re investing all of this social, political, and economic capital into management, but you’re getting no results from it,” Francis said. “If you gave the system a bigger smack by adding an alternative management strategy to tackle the phosphorus pool at the bottom of the lake, that would be more likely to get your lake back to the state you want. This is just one consequence of long transients in terms of how they affect management decisions.”

[Read the rest at SIAM NEWS]

The math behind leopard spots and chemical waves

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This article is a little different from the fare you’re used to getting from me: it’s for SIAM News, which is the glossy magazine for members of the Society for Industrial and Applied Mathematics (SIAM). The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. While the article contains equations, I wrote it to be understandable even if you skip over the math.

Leopard Spots, Frog Eggs, and the Spectrum of Nonlinear Diffusion Processes

For SIAM News:

Stripes, spots, or a mix of both appear on the skin of many animals — from tigers to beetles to whale sharks. These patterns are typically unique to individual creatures, and biologists often use them for identification. While distinct patterns may seem random, they obey certain rules that suggest a common underlying description. Striping and spotting occur in many unrelated species, implying that both evolutionary advantages and simple biochemical mechanisms drive such patterns.

As Björn Sandstede of Brown University noted during his invited address at the 2018 SIAM Annual Meeting, held in Portland, Ore., this July, similar patterns appear in certain chemical reactions and granular material under vibration. Nonlinear reactions and diffusion describe biological and non-biological patterns, producing stable concentrations in this space.

Alan Turing—best known for his work in computer science and cryptography—first made the mathematical connection between nonlinear diffusion processes and animal stripes in the 1950s. Many researchers have applied the resulting model to demonstrate how various species get their spots and describe nonlinear waves in chemical reactions.

[Read the rest at SIAM News]

Swarming in time, synchronizing in space

[ This blog is dedicated to tracking my most recent publications. Subscribe to the feed to keep up with all the science stories I write! ]

This article is a little different from the fare you’re used to getting from me: it’s for SIAM News, which is the glossy magazine for members of the Society for Industrial and Applied Mathematics. The audience for this magazine, in other words, is professional mathematicians and related researchers working in a wide variety of fields. In this case, I covered research by mathematicians looking at a type of system that occurs in biology and materials science. While the article contains equations, I wrote it to be understandable if you skim that part.

Self-organization in Space and Time

For SIAM News:

Self-organization is an important topic across scientific disciplines. Be it the spontaneous flocking of birds or dramatic phase transitions like superconductivity in materials, collective behavior without underlying intelligence occurs everywhere.

Many of these behaviors involve synchronization, or self-organization in time, such as activation in heart cells or the simultaneous blinking of certain firefly species. Others are aggregations, or self-organization in space, like swarming insects, flocking birds, or the alignment of electron spins in magnetic material.

Despite their conceptual similarity, self-organization in space and time have largely been treated separately. “I was curious about whether the two fields had been wedded, and it turns out they hadn’t, at least not fully,” Kevin O’Keeffe, a postdoctoral researcher at the Massachusetts Institute of Technology, said. “I knew all these tricks and mathematical tools from synchronization, and I was looking to cross-fertilize them into the swarming world.”

[Read the rest at SIAM News]