Monday, June 14, 2010

KNIGHTIAN UNCERTAINTY

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The global economic crisis of the last two years has stemmed, in part, from the inability of financial institutions to effectively judge the riskiness of their investments. For this reason, the crisis has cast new attention on an idea about risk from decades past: “Knightian uncertainty.”

Frank Knight was an idiosyncratic economist who formalized a distinction between risk and uncertainty in his 1921 book, Risk, Uncertainty, and Profit. As Knight saw it, an ever-changing world brings new opportunities for businesses to make profits, but also means we have imperfect knowledge of future events. Therefore, according to Knight, risk applies to situations where we do not know the outcome of a given situation, but can accurately measure the odds. Uncertainty, on the other hand, applies to situations where we cannot know all the information we need in order to set accurate odds in the first place.

“There is a fundamental distinction between the reward for taking a known risk and that for assuming a risk whose value itself is not known,” Knight wrote. A known risk is “easily converted into an effective certainty,” while “true uncertainty,” as Knight called it, is “not susceptible to measurement.” An airline might forecast that the risk of an accident involving one of its planes is exactly one per 20 million takeoffs. But the economic outlook for airlines 30 years from now involves so many unknown factors as to be incalculable.

Some economists have argued that this distinction is overblown. In the real business world, this objection goes, all events are so complex that forecasting is always a matter of grappling with “true uncertainty,” not risk; past data used to forecast risk may not reflect current conditions, anyway. In this view, “risk” would be best applied to a highly controlled environment, like a pure game of chance in a casino, and “uncertainty” would apply to nearly everything else.

Even so, Knight’s distinction about risk and uncertainty may still help us analyze the recent behavior of, say, financial firms and other investors. Investment banks that in recent years regarded their own apparently precise risk assessments as trustworthy may have thought they were operating in conditions of Knightian risk, where they could judge the odds of future outcomes. Once the banks recognized those assessments were inadequate, however, they understood that they were operating in conditions of Knightian uncertainty — and may have held back from making trades or providing capital, further slowing the economy as a result.

Ricardo Caballero, chair of MIT’s Department of Economics and the Ford International Professor of Economics, Macroeconomics, and International Finance, is among those who have recently invoked Knightian uncertainty to explain the behavior of investors in times of financial panic. As Caballero stated in a lecture at the International Monetary Fund’s research conference last November: When investors realize that their assumptions about risk are no longer valid and that conditions of Knightian uncertainty apply, markets can witness “destructive flights to quality” in which participants rid their portfolios of everything but the safest of investments, such as U.S. Treasury bonds.

One solution offered by Caballero to stem these moments of panic is government-issued investment insurance for large financial institutions. In this sense, the existence of Knightian uncertainty is not just a quasi-philosophical dispute; the subjective perception of Knightian uncertainty among businesses is a pressing practical problem.

MIT

MORE IS LESS

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The architect Mies van der Rohe is famous for promoting the slogan “less is more.” But if Venkat Chandrasekaran, a graduate student in the Department of Electrical Engineering and Computer Science, had a slogan for his own work, it might be “more is less.”

Science, engineering and other quantitative disciplines are largely concerned with uncovering the mathematical relationships between data points — such as energies of molecules, measurements of temperature or gene activity, or stock prices. In most cases, adding more data points just makes the math more complicated. But sometimes it makes it simpler. And for many types of calculations, if there are additional data points that will make them simpler, Chandrasekaran’s techniques will find them.

To see how adding data points can mean simpler calculations, suppose that you’re trying to understand the relationships between a bunch of stocks in the same industry sector — say, Apple, Gateway, Dell, Hewlett-Packard and other computer manufacturers. On the one hand, an increase in Apple’s share price could mean a decrease in, say, Dell’s, because Apple and Dell compete for a limited pool of computer buyers’ dollars; on the other hand, if large institutional investors are bullish about computer stocks in general, an increase in Apple’s stock could indicate an increase in Dell’s as well.

It might be possible to build a complicated mathematical model that, on the basis of considerations like the companies’ price-to-earnings ratios, trade volumes and revenues determines whether an increase in Apple’s share price will cause an increase or decrease in Dell’s — and Gateway’s, and Hewlett-Packard’s, and so on. But it might also turn out that a single extra variable — say, the average price of all the companies’ stock — provides a good indication of general trends in the sector. Since the new variable accounts for institutional investors’ enthusiasm or skittishness, the relationships between the individual stocks no longer have to. The overall calculation becomes much simpler.

In this case, Chandrasekaran’s techniques would tell you only that adding another variable — the average stock price — simplifies the overall calculation. They wouldn’t tell you why. And indeed, the extra variable could turn out to be something more complicated than an average. It might factor in the price-to-earnings ratios of some companies, the revenues of others, the share prices of still others, and so on. A savvy analyst might be able to deduce that this new, more complex variable represents the trading strategies of a bunch of large hedge funds that concentrate on the computer industry. But then again, it could be that no one has any idea what the new variable refers to.

“There’s this temptation that I even had initially, that you can sort of discover hidden variables,” says Chandrasekaran. “And that’s true: You can discover hidden variables. But it’s not going to be easy to attribute meaning to these hidden variables.” For most purposes, however, that may not matter. “From the mathematical point of view, just putting these things in helps you simplify,” Chandrasekaran says. If the added variable helps you predict Dell’s share price from Apple’s, does it really matter what it refers to — or whether it refers to anything at all?

At the most recent Symposium on System Identification, hosted by the International Federation of Automatic Control, Chandrasekaran and MIT Professors of Electrical Engineering Alan Willsky and Pablo Parrilo described their approach to finding hidden variables that simplify calculations.

Generally, computer science is concerned with questions of computational complexity: Given a particular algorithm, you want to know whether a computer can execute it quickly, slowly or never. So computer science provides some standard methods for calculating the complexity of mathematical models.

If you have an equation that describes the complexity of a mathematical model, you want to find its minimum values: where the complexity is lowest, the model is simplest, and thus easiest to work with. If you imagine the graph of the equation as a complex surface with lots of peaks and troughs, you want to find the bottom of the deepest trough.

But that in itself can be a prohibitively complex process. Computer scientists have developed a host of methods for analyzing such equations and finding solutions that are probably near the bottom of a trough in a particular region of the graph. For certain types of problems, however, the techniques developed by Chandrasekaran and his colleagues are mathematically guaranteed to find the bottom of the graph’s lowest trough.

According to Ben Recht, an assistant professor in the University of Wisconsin’s computer sciences department, “There are a lot of people who would be surprised if you told them that you could solve this particular hidden-variable problem using [Chandrasekaran’s] methods.” He adds, however, that “it’s not a general-purpose tool, even for these hidden-variable problems.” Chandrasekaran agrees. In fact, he prefers to describe his methods as “tricks” rather than “techniques,” because it might require some mathematical insight to determine how to apply them in any particular case.

Still, Recht says, “he’s shown that in a relatively large set of cases, you can actually use this. And it’s a first step to explore the space of what sorts of problems can be solved using this technology.”

(Photo: Christine Daniloff)

MIT

MEDITATION REDUCES THE EMOTIONAL IMPACT OF PAIN

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People who meditate regularly find pain less unpleasant because their brains anticipate the pain less, a new study has found.

Scientists from The University of Manchester recruited individuals into the study who had a diverse range of experience with meditation, spanning anything from months to decades. It was only the more advanced meditators whose anticipation and experience of pain differed from non-meditators.

The type of meditation practised also varied across individuals, but all included ‘mindfulness meditation’ practices, such as those that form the basis of Mindfulness-Based Cognitive Therapy (MBCT), recommended for recurrent depression by the National Institute for Health and Clinical Excellence (NICE) in 2004.

“Meditation is becoming increasingly popular as a way to treat chronic illness such as the pain caused by arthritis,” said Dr Christopher Brown, who conducted the research. “Recently, a mental health charity called for meditation to be routinely available on the NHS to treat depression, which occurs in up to 50% of people with chronic pain. However, scientists have only just started to look into how meditation might reduce the emotional impact of pain.”

The study, to be published in the journal Pain, found that particular areas of the brain were less active as meditators anticipated pain, as induced by a laser device. Those with longer meditation experience (up to 35 years) showed the least anticipation of the laser pain.

Dr Brown, who is based in Manchester’s School of Translational Medicine, found that people who meditate also showed unusual activity during anticipation of pain in part of the prefrontal cortex, a brain region known to be involved in controlling attention and thought processes when potential threats are perceived.

He said: "The results of the study confirm how we suspected meditation might affect the brain. Meditation trains the brain to be more present-focused and therefore to spend less time anticipating future negative events. This may be why meditation is effective at reducing the recurrence of depression, which makes chronic pain considerably worse.”

Dr Brown said the findings should encourage further research into how the brain is changed by meditation practice. He said: “Although we found that meditators anticipate pain less and find pain less unpleasant, it’s not clear precisely how meditation changes brain function over time to produce these effects.

“However, the importance of developing new treatments for chronic pain is clear: 40% of people who suffer from chronic pain report inadequate management of their pain problem.”

In the UK, more than 10 million adults consult their GP each year with arthritis and related conditions. The estimated annual direct cost of these conditions to health and social services is £5.7 billion.

Study co-author Professor Anthony Jones said: “One might argue that if a therapy works, then why should we care how it works? But it may be surprising to learn that the mechanisms of action of many current therapies are largely unknown, a fact that hinders the development of new treatments. Understanding how meditation works would help improve this method of treatment and help in the development of new therapies.

“There may also be some types of patient with chronic pain who benefit more from meditation-based therapies than others. If we can find out the mechanism of action of meditation for reducing pain, we may be able to screen patients in the future for deficiencies in that mechanism, allowing us to target the treatment to those people.”

University of Manchester

FLOW IN EARTH'S MANTLE MOVES MOUNTAINS

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Mountains and volcanoes in the Mediterranean rise due to pressure from mantle below, according to a new theory published in Nature.

If tectonic plate collisions cause volcanic eruptions, as every fifth grader knows, why do some volcanoes erupt far from a plate boundary?

A study in Nature suggests that volcanoes and mountains in the Mediterranean can grow from the pressure of the semi-liquid mantle pushing on Earth's crust from below.

"The rise and subsidence of different points of the earth is not restricted to the exact locations of the plate boundary. You can get tectonic activity away from a plate boundary," said study co-author Thorsten Becker of the University of Southern California.

The study connects mantle flow to uplift and volcanism in "mobile belts": crustal fragments floating between continental plates.

The model should be able to predict uplift and likely volcanic hotspots in other mobile belts, such as the North American Cordillera (including the Rocky Mountains and Sierra Nevada) and the Himalayas.

"We have a tool to be able to answer these questions," Becker said.

Scientists previously had suggested a connection between mantle upwelling and volcanism, Becker said. The Nature study is the first to propose the connection in mobile belts.

Becker and collaborator Claudio Faccenna of the University of Rome believe that small-scale convection in the mantle is partly responsible for shaping mobile belts.

Mantle that sinks at the plate boundary flows back up farther away, pushing on the crust and causing uplift and crustal motions detectable by global positioning system, the authors found.

The slow but inexorable motions can move mountains – both gradually and through earthquakes or eruptions.

The study identified two mountain ranges raised almost entirely by mantle flow, according to the authors: the southern Meseta Central plateau in Spain and the Massif Central in France.

Becker and Faccenna inferred mantle flow from interpreting seismic mantle tomography, which provides a picture of the deep earth just like a CAT scan, using seismic waves instead of X-rays.

Assuming that the speed of the waves depends mainly on the temperature of crust and mantle (waves travel slower through warmer matter), the authors used temperature differences to model the direction of mantle convection.

Regions of upward flow, as predicted by the model, mostly coincided with uplift or volcanic activity away from plate boundaries.

"Mantle circulation … appears more important than previously thought, and generates vigorous upwellings even far from the subduction zone," the authors wrote.

(Photo: USC)

University of Southern California

FIRST PAPER 'DIPSTICK' TEST FOR DETERMINING BLOOD TYPE

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Scientists are reporting development of the first "dipstick" test for instantly determining a person's blood type at a cost of just a few pennies. Their study on the test, which involves placing a drop of blood on a specially treated paper strip, appears in ACS' semi-monthly journal Analytical Chemistry, where the authors say it could be a boon to health care in developing countries. The test also could be useful in veterinary medicine, for typing animals' blood in the field, they note.

Gil Garnier and colleagues explain that determining a patient's blood type is critical for successful blood transfusions, which save millions of lives each year worldwide. There are four main blood types: A, B, AB, and O. Use of the wrong blood type in a patient can be fatal. Current methods for determining blood type require the use of sophisticated instruments that are not available in many poor parts of the world. An inexpensive portable test could solve that problem.

The scientists describe development of prototype paper test strips impregnated with antibodies to the antigens on red blood cells that determine blood type. In lab tests using blood samples from human volunteers, the scientists showed that a drop of blood placed on the strip caused a color change that indicated blood type. The results were as accurate as conventional blood typing. "The paper diagnostics manufacturing cost is a few pennies per test and can promote health in developing countries," the report notes.

(Photo: iStock)

ACS Publications

CHOCOLATE MILK IS A 'NATURAL' FOR POST-EXERCISE RECOVERY

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One of the best post-exercise recovery drinks could already be in your refrigerator, according to new research presented at the American College of Sports Medicine conference. In a series of four studies, researchers found that chocolate milk offered a recovery advantage to help repair and rebuild muscles, compared to specially designed carbohydrate sports drinks.

Experts agree that the two-hour window after exercise is an important, yet often neglected, part of a fitness routine. After strenuous exercise, this post-workout recovery period is critical for active people at all fitness levels – to help make the most of a workout and stay in top shape for the next workout.

The new research suggests that drinking fat free chocolate milk after exercise can help the body retain, replenish and rebuild muscle to help your body recover. Drinking lowfat chocolate milk after a strenuous workout could even help prep muscles to perform better in a subsequent bout of exercise. Specifically, the researchers found a chocolate milk advantage for:

* Building Muscle – Post-exercise muscle biopsies in eight moderately trained male runners showed that after drinking 16 ounces of fat free chocolate milk, the runners had enhanced skeletal muscle protein synthesis – a sign that muscles were better able to repair and rebuild – compared to when they drank a carbohydrate only sports beverage with the same amount of calories. The researchers suggest that "athletes can consider fat-free chocolate milk as an economic nutritional alternative to other sports nutrition beverages to support post-endurance exercise skeletal muscle repair."

* Replenishing Muscle "Fuel" – Replacing muscle fuel (glycogen) after exercise is essential to an athlete's future performance and muscle recovery. Researchers found that drinking 16 ounces of fat free chocolate milk with its mix of carbohydrates and protein (compared to a carbohydrate-only sports drink with the same amount of calories) led to greater concentration of glycogen in muscles at 30 and 60 minutes post exercise.

* Maintaining Lean Muscle – Athletes risk muscle breakdown following exercise when the body's demands are at their peak. Researchers found that drinking fat free chocolate milk after exercise helped decrease markers of muscle breakdown compared to drinking a carbohydrate sports drink.

* Subsequent Exercise Performance – Ten trained men and women cyclists rode for an hour and a half, followed by 10 minutes of intervals. They rested for four hours and were provided with one of three drinks immediately and two hours into recovery: lowfat chocolate milk, a carbohydrate drink with the same amount of calories or a control drink. When the cyclists then performed a subsequent 40 kilometer ride, their trial time was significantly shorter after drinking the chocolate milk compared to the carbohydrate drink and the control drink.

Chocolate milk's combination of carbohydrates and high-quality protein first made researchers take notice of a potential exercise benefit. The combination of carbs and protein already in chocolate milk matched the ratio found to be most beneficial for recovery. In fact, studies suggest that chocolate milk has the right mix of carbs and protein to help refuel exhausted muscles, and the protein in milk helps build lean muscle. This new research adds to a growing body of evidence suggesting milk can be just as effective as some commercial sports drinks in helping athletes refuel and recover.

Milk also provides fluids for rehydration and electrolytes, including potassium, calcium and magnesium lost in sweat, that both recreational exercisers and elite athletes need to replace after strenuous activity. Plus, chocolate milk is naturally nutrient-rich with the advantage of additional nutrients not found in most traditional sports drinks. Penny-for-penny, no other post-exercise drink contains the full range of vitamins and minerals found in chocolate milk.

Weber Shandwick

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