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Eli Stein was the first to appreciate the interplay among representation theory, classical Fourier analysis, and partial differential equations, and to perceive the fundamental insights in each field arising from that interplay. How did Stein’s scope and originality contribute to numerical analysis?

Today, 16 September is International Red Panda Day! Red pandas (Ailurus fulgens) are also called lesser pandas, or red bear-cats. Red pandas are named for the reddish-brown fur that is found on the upper parts of their body. Their legs usually have a darker or black fur, and their faces are round with light fur that shows tear markings. They also have long, bushy tails with six orange rings. Red pandas are good climbers, and often try to flee from danger by climbing rocks or trees to get away from their predators. When not climbing, red pandas have a waddling gait due to having anatomically shorter front legs than hind legs. Red pandas are found in bamboo forests from central Nepal eastward along the Himalayas through Bhutan, India, and Myanmar into China. Despite being found in a relatively broad region, they are endangered and suffer from habitat loss, population isolation, and human interference in the wild.

Red pandas are the sole living representative of its subfamily classification “Ailurinae” and are a part of the broad superfamily Musteloidea. Despite what their name would suggest, red pandas are more closely related to other musteloids – including skunks, raccoons, and weasels – than they are to giant pandas. However, like giant pandas, red pandas are carnivores and their diet specializes in bamboo. About 90% of a red panda’s annual diet comes from the leaves of bamboo trees, though red pandas also eat eggs, birds, insects, and fruit (and, apparently, sushi).

“As biologists our great aim is to find order in all the diversity and complexity of the living world. This is something we all strive for: it is what gives us a feeling of fulfilment and satisfaction. We seek the rules that underlie living phenomena to make ignorance and confusion turn into clarity and order.”

But sometimes there is no order. John Tyler Bonner explores how randomness plays an important part in the process of evolution.

The penultimate episode in our Blue Planet II series takes us to the coast, where land and sea collide. In this episode, we meet creatures who alternate between these two very different domains, and learn how they adapt to survive in this ever-changing environment. What are some of the most notable aspects of this bridge between two worlds?

Tide pools on rocky shores provide a refuge to many marine organisms, including those that prefer continuous submersion. As tides recede along these coasts, rock depressions and crevices remain filled with water and samples of ocean creatures.

Fur seals and sea lions (Carnivora: Otariidae) evolved in the North Pacific and later dispersed throughout the Southern Hemisphere. However, the timing and number of dispersals into the Southern Hemisphere remains poorly understood. Research indicates that the distribution of these mammals is tightly linked to sea surface temperature and productivity, and suggests that otariids may be vulnerable to future anthropogenic climate change.

Newly-weaned Southern elephant seal (Mirounga leonine) pups must strike a balance between conserving energy during their post-weaning fast and simultaneously developing diving abilities to become independent. Research suggests that temperamental weather, such as increased westerly winds and erratic storms, can have a detrimental impact on the pups’ cardiorespiratory activity.

The common octopus (Octopus vulgaris) has one of the richest motor repertoires of all animals, enabling them to complete a range of complex tasks, such as using their siphon to emit a jet of water to deter intruders, or to remove sand from a shell to make it easier to carry. They also use their arms to open large clams, and have been known to remove the lids of their aquariums to escape!

Mussels are the most important aquaculture species in Europe (based on live weight). Blue mussels (Mytilus) are usually considered a robust species, resistant to disease. Since 2010, however, abnormal mortality events have occurred in farmed blue mussels in France, with scientists hypothesizing that water-borne pathogenic bacteria are being passed from wild blue mussel parents to their larvae, especially under hatchery conditions.

Rock crabs, green crabs, and grapsid crabs live in rock pools, which may be subject to periods of low oxygen. When oxygen is low, they can increase the water flow over their gills to get more oxygen.

The Atlantic puffin (Fratercula arctica) is a migratory seabird, and research suggests that they visit a range of overwintering destinations, resulting in a range of migratory routes, with different energy expenditures. However, it appears that puffins tend to stick to the same timings and locations for major movements.

King Penguins dive during day and night-time. During daytime, they reach depths of between 100 m and 300 m in 1–4 minutes, and at these depths light levels fall to within the nocturnal range. Therefore, the birds are, from a sensory perspective, nocturnal foragers at all times: either they forage at night at relatively shallow depths (30–40 m) or they forage during the day at night-time light levels at greater depths.

There are four basic research principles:

Basic research is curiosity driven.

Basic research employs reductionist models.

Basic research searches for universal principles.

Basic research relies on simplifications and idealization.

Do these rules still apply? Ivory tower academia has long weathered accusations of remaining out of touch, pedantic, and weighed down by esoteric practices. Old models of research, conducted in dusty, solitary libraries, have difficulty translating to the fast-paced technological models and the rapid growth of the internet.

The new era of research requires new models; the future will require collaboration over solitude and the integration of innovation with time-worn methods. Two guiding theories are the ABC and SED models. ABC (‘Applied and Basic Combined’) promotes the ability to produce both models of research in order to created high-impact research. The SED principle (‘Science Engineering and Design’) further blends methods of science, engineering, and design to create invigorating new discoveries. Old practices are infused with new life, and proves the integration of information is much like the time-worn truth: the whole is greater than the sum of its parts.

“Theory without practice cannot survive and dies just as quickly it lives. He who loves practice without theory is like the sailor who boards a ship without a rudder and compass and never knows where he may cast.” 

- Leonardo da Vinci