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Dear Bob, While drinking beer yesterday several ideas came about our maximization problem and the question of root selection. You have probably solved the problem by now, but here are a few points anyhow. First, as you know, the solution is a simple saddle point of [equation], gotten by setting both partials to zero. The problem is how to select between the 3 roots which sometimes occur. I have thought a little about why the “magic” multipliers (Lagrange) work to express constraints, and will try to briefly give you the picture: If we have a function f(xi) to be maximized subject to constraints gj(xi) = cj,[?...

The rusty patched bumble bee, a prized but vanishing pollinator once familiar to much of North America, was listed on Tuesday as an endangered species, becoming the first wild bee in the continental United States to gain such federal protection. One of several species facing sharp declines, the bumble bee known to scientists as Bombus affinis has plunged nearly 90 percent in abundance and distribution since the late 1990s, according to the U....

The bold dream of synthetic biology is a world in which all living things can be reliably engineered in ways that help everyone and everything. In this dream, we can use genetics to program living organisms: “if condition A is met, then do action B.” To give a near-term example, bacteria might produce a medicinal protein only in the presence of indicators of a particular disease. Why use living systems and not a vat of chemicals?...

All around us, we see people battling for the benefit of those like themselves—women clamoring for abortion rights in Poland; Black Lives Matter protesters fighting to end police brutality against people of color in the U.S.; LGBT people calling for marriage equality worldwide. But what makes these people care so much about these issues, and not about others connected to their group? One possible answer is painfully obvious: we speak up when our fellow group members suffer....

Editor’s Note: This story was first published in 2016 and was updated after the 2017 Las Vegas shooting. It is being resurfaced following a mass shooting that occurred on February 14, 2018, at Marjory Stoneman Douglas High School in Parkland, Florida. America has experienced yet another mass shooting, this time at the Mandalay Bay Resort and Casino on the strip in Las Vegas, Nevada. It is reportedly the deadliest mass shooting in U....

A jaw-dropping picture of the planet Saturn was recently released by NASA’s Cassini probe orbiting the ringed giant. The black-and-white photo shows the gas giant tilted, with its iconic rings draping striking shadows against the planet’s atmosphere. A faint dot in the top middle of the image, which you might be forgiven for thinking was a speck on your monitor, is actually Saturn’s moon Mimas. The moon, at 246 miles (396 kilometers) across, is dwarfed by its much larger parent....

The following essay is reprinted with permission from The Conversation, an online publication covering the latest research. In case you missed it, last week the World Heritage Centre of UNESCO revealed its draft decision to list the Great Barrier Reef as “in danger” — a decision that appeared to shock the Australian government. In an opinion piece published yesterday in The Australian newspaper, Environment Minister Sussan Ley acknowledged climate change is the biggest threat to the Great Barrier Reef, and that it “has been through a few rough years”....

The harmful effects of ultraviolet (UV) light on the skin apparently do not scare off teenagers, who are flocking to indoor tanning salons. Among non-Hispanic white high-school students, about 29 percent of girls and about 7 percent of boys admit to indulging in frequent trips to tanning salons. Now medical researchers are taking state governments to task for lax or nonexistent regulations surrounding teenage indoor tanning. “This is no longer just a prom phenomenon—kids are using tanning beds frequently,” says Alan Geller, a public health researcher of Harvard University School of Public Health and co-author of a new study of tanning regulations....

LANSING, Mich.—After more than a decade of research, a team of scientists has found that by releasing one pollutant into the environment, we might help capture another. Findings from one of the National Science Foundation’s longest-running studies show that adding nitrogen to soil prompts northern hardwood forests to absorb more heat-trapping carbon dioxide. As the atmosphere’s most abundant element, nitrogen plays a significant role in ecosystems, and one to which scientists and policymakers are paying greater attention....

Key concepts Adsorption Activated carbon Physics Chemistry Water filter Introduction Do you filter your tap water before drinking? Maybe at home you have a water filter on your faucet, in the fridge or use special pitchers that have a filter in them. You have probably heard commercials that claim these filters make your drinking water cleaner and safer. But have you ever wondered what, exactly, these filters do and if the water is really cleaner in the end?...

When newly graduated environmental lawyer Keilly Witman joined U.S. EPA in 2007, she was handed one of its toughest jobs. She had to convince supermarkets that their leaky air conditioning and refrigeration systems needed to be fixed or they would substantially warm the Earth’s atmosphere. When it comes to making refrigeration more efficient and less harmful to the climate, U.S. supermarkets have been a long-slumbering giant. There are at least 38,000 of them....

By Amanda MascarelliOil has been here. It has blasted this tiny barrier island on the southeastern edge of Louisiana, turning the entire rim of wetland vegetation yellow and the surrounding soil black. The flagging marsh grass stems are tinged dull brown, as if they’ve been dipped in turpentine. As for the animals living in the water below– well, it is hard to know their story.Kim de Mutsert, a postdoctoral coastal ecologist from Louisiana State University (LSU) in Baton Rouge, is here on a blistering July day to find out....

Advances in agricultural technology—including, but not limited to, the genetic modification of food crops—have made fields more productive than ever. Farmers grow more crops and feed more people using less land. They are able to use fewer pesticides and to reduce the amount of tilling that leads to erosion. And within the next two years, agritech com­panies plan to introduce advanced crops that are designed to survive heat waves and droughts, resilient characteristics that will become increasingly important in a world marked by a changing climate....

Gray blotches poke up from the murky depths of Lake Michigan in an image on maritime archaeologist Tamara Thomsen’s computer screen. These are the remains of the SS Wisconsin, an steel-hulled steamer that sank in 1929 off Kenosha, Wis., after a storm engulfed the vessel during a routine passage between Chicago and Milwaukee. The shipwreck of the SS Wisconsin is one of hundreds believed to be lurking in Lake Michigan’s depths (which reach a maximum of 923 feet), says Thomsen, who works with the Wisconsin Historical Society’s Maritime Preservation and Archaeology Program....

Enormous volcanoes vomited lava over the ancient Earth much more often than geologists had suspected. Eruptions as big as the biggest previously known ones happened at least 10 times in the past 3 billion years, an analysis of the geological record shows. Such eruptions are linked with some of the most profound changes in Earth’s history. These include the biggest mass extinction, which happened 252 million years ago when volcanoes blanketed Siberia with molten rock and poisonous gases....

On his first trip to the Solomon Islands in 2010 Tyrone Lavery heard rumors about a strange rodent on Vangunu Island. The giant rat, according to locals, lived in the rainforest canopy and could crack open coconuts with its teeth. Vangunu is situated some 1,000 miles northwest of Australia, at the western end of the 900-plus-island archipelago. The “vika,” as the creature is known, was apparently once familiar enough that it featured in Vangunu children’s songs and nursery rhymes....

Mike started drinking at age 14. At his very first party, he recalls, “I probably had 10 beers.” He partied for seven years while playing high school and college football, and the consequences of his drinking resemble a “Just Say No” campaign: blackouts, arrests, academic problems, emergency room visits, driving suspensions and mandatory treatment programs. About 10 percent of eighth graders, 18 percent of 10th graders and 24 percent of high school seniors binge on alcohol....

Shelley Latin’s odyssey with chronic pain and opioids began innocuously enough in June 2011, when she awoke with a stomachache. It took a year for the cause to be correctly diagnosed—a bacterial infection in her gut—and arrested with antibiotics, but by then the pain had taken on a life of its own, no longer linked to the infection. “I couldn’t drive, or walk, or sit. I could only lie in bed on my back,” she recalls....

“Know thyself” has been the guiding principle of many philosophers. Perhaps the first evolutionary step toward that goal is to realize that a “self” exists, distinct from others. For this, a mirror can be a great help. Humans can recognize their own reflection before the age of two. Chimpanzees and dolphins share the ability. Now elephants are known to be members of the club. Joshua Plotnik, a graduate student at Emory University, and his colleagues bolted a giant plastic mirror inside the elephant enclosure at the Bronx Zoo and watched three Asian elephants progress from curiously sniffing and feeling around and behind the mirror, to eating in front of it, to inspecting their own mouths, to playing peekaboo....

A leading group of international climate scientists is warning that “large-scale strategies” are needed immediately to reduce greenhouse gas emissions and avert “catastrophic circumstances” that threaten every part of the world. In a paper published yesterday in the journal Science, 21 researchers from 14 countries said climate change is already damaging the planet more than scientists had projected, endangering everything from food supply to the existence of island nations. Heat waves are intensifying in North America and Europe....