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You too can do particle physics

Wednesday, October 31, 2007

This is just a heads-up for folks who are interested in particle physics and/or highly-distributed computing projects, like the well-known SETI@home.

You too can do particle physics
Public involvement in the Large Hadron Collider, a particle accelerator being built in Switzerland, has received a boost with the relaunch of the LHC@home project, which allows users to donate computer time for LHC computing projects.

Researchers hope the project will help them fine-tune the LHC to shed light on what dark matter is and why particles have mass.

More: here

As most readers undoubtedly know, there are quite a few distributed computing projects of this sort, in which anyone can participate. Examples include projects dealing with climate prediction, gravitational waves, protein folding, and Mersenne primes.

For more information, see the Wikipedia articles on distributed computing and the list of distributed computing projects.

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Peptide YY and appetite

Tuesday, October 30, 2007

Just about three months ago we came, briefly, across the peptide called PYY (peptide YY), which has been known, for a few years, to suppress appetite. It has also been known that obese people secrete less PYY than non-obese people. On the other hand, attempts to use PYY directly as a weight-loss drug have not met with much success.

About a year ago, research showed that consumption of protein boosts PYY levels, and in that case there was some benefit to experimental subjects in terms of reducing hunger and promoting weight loss. This would help explain the weight-loss experienced with high-protein diets. Here's a press release on that research:

Eating Protein Boosts Hormone That Staves Off Hunger (9/6/06)
The amount of a hunger-fighting hormone can be increased by eating a higher protein diet, researchers report in the September issue of the journal Cell Metabolism, published by Cell Press. The hormone, known as peptide YY (PYY), was earlier found by the researchers to reduce food intake by a third in both normal-weight and obese people when given by injection.

"We've now found that increasing the protein content of the diet augments the body's own PYY, helping to reduce hunger and aid weight loss," said Medical Research Council clinician scientist Rachel Batterham of University College London, who led the new study.

Scientists have known that high-protein content meals make people feel more full and reduce food intake, resulting in improvements in weight loss and weight loss maintenance. However, the mechanism responsible remained elusive.

In a study in normal-weight and obese people, the researchers now show that enhanced-protein meals stimulate greater release of PYY than either high-fat or high-carbohydrate meals and result in a greater reduction of hunger.

Here's another report on that research: Hello Protein, Goodbye Fat (sub. rqd.) And an earlier article on the PYY controversy: New Data on Appetite-Suppressing Peptide Challenge Critics (sub. rqd.)

Now there are additional findings from the same lab that developed the results of a year ago. The findings indicate that a cortical brain center associated with reward and pleasure (the orbital frontal cortex) responds to PYY:

Brain 'hunger pathways' pinpointed (10/15/07)
The brain circuitry that influences how much food a person will eat – whether they feel starving or full – has been revealed by a new imaging study. The results may help target new treatments against obesity, say researchers.

Rachel Batterham at University College London, UK, and her colleagues have previously shown that a hormone called peptide YY or PYY, which is released by the gut in proportion how many calories we eat, is a powerful appetite suppressant. Previous experiments show that treating normal and obese subjects with intravenous PYY decreases food intake by up to 30%.

Batterham's team used functional magnetic resonance imaging (fMRI) to investigate how PYY affects the brain.

So research findings to date certainly indicate that PYY has very interesting, and quite possibly useful effects. It could be very interesting to watch for further developments involving PYY.

More information:

Appetite 'control centres' found

Gluttons can blame overeating on the brain

Appetite hormone works in two brain areas

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Uniqueness of factorization

Saturday, October 27, 2007

Time for another installment of the series on algebraic number theory. Check here for previous articles.

In this installment we're going to look at an important property that some rings (such as ℤ) have, although most rings do not. But it is a useful and important property for proving many number theoretic results, which is why one bothers to consider it. We'll illustrate that soon.

But first we need a little terminology. In any ring, a unit is a ring element that has a multiplicative inverse which is also in the ring. For instance, in ℤ 1 and -1 are units, and they are the only units. Other rings of algebraic integers can have many units, and the set of units of the ring form an abelian group under multiplication. Determining this group of units, in fact, is one of the interesting computational issues in algebraic number theory.

Another important concept is that of a prime element of a ring. A little bit of care is required to define "prime" in a general ring, but essentially a prime element is one that has no factors other than itself and units. As far as divisibility and factors are concerned, units are essentially irrelevant, since they are invertible.

One of the most important properties that the integers have as a ring is unique factorization. That is, for any n∈ℤ, there is a unique way (apart from order and unit factors) to write n as a product of primes.

This fact can be proven using the order properties of ℤ, i. e. for every pair of distinct positive integers a, b, exactly one of a<b, a=b, or a>b is true. To begin with, this implies that for any pair of positive a,b∈ℤ, we can write a=qb+r with 0≤q and 0≤r<b. Reason: you can subtract b from a only a nonnegative but finite number of times (q) before the result is negative. This is because every number in the sequence a, a-b, a-2b, ... is strictly less than its predecessor, and if a is finite, there are only a finite number of distinct positive integers less than a. r is simply the last quantity before you have a negative number, and so 0≤r<b. The numbers q and r are uniquely determined by this procedure, and in fact there is a simple algorithm to find them, as we'll see in a moment.

For any positive integers a,b∈ℤ, we can define the greatest common divisor of the pair as the largest (positive) integer which divides both, written gcd(a,b), or simply (a,b). It may be, of course, that (a,b)=1, in which case we say a and b are relatively prime. As a matter of notation, if one number m divides another n, so that n=mq for some q∈ℤ, we write m|n. If this is not the case, then we write m∤n. (a,b) can be defined by the conditions that (a,b)|a, (a,b)|b, and if both c|a and c|b, then c|(a,b).

The Greek mathematician Euclid, known best for his geometry, was interested in number theory also. In addition to proving that there are infinitely many primes, he also gave a simple algrorithm for computing the greatest common divisior of two integers without explicitly factoring them – since factoring can be a relatively difficult process for large numbers. The algorithm is called, of course, the Euclidean algorithm.

To apply it, assume (without loss of generality) that a>b and write a=q1b+r1. Here, q1>0 and 0≤r1<b. Provided r1≠0 we can repeat the procedure and write b=q2r1+r2. We can repeat this procedure as long as the remainder rk isn't 0. If rk is the last nonzero remainder, then one notes that (a,b)|rk, because in fact (a,b) divides all such remainders in the process. But we also have rk-1=qk+1rk, hence rk|rk-1 and from rk-2=qkrk-1+rk, we find rk|rk-2 too. If we proceed back all the way we find rk|b and rk|a, hence rk|(a,b). Therefore rk=(a,b). In other words, (a,b) is the last nonzero remainder in this process.

But even nicer things are true. Go back to a=q1b+r1, so that r1=a-q1b. Similarly, r2= b-q2r1= b-q2(a-q1b)= Ma+Nb for some integers M and N (not necessarily positive). Proceding inductively, we have that (a,b)=Ma+Nb for some M,N∈ℤ. What this says is that a certain Diophantine equation can be solved for unknowns M and N if a, b (and hence (a,b)) are given. Note that if (a,b)>1, the equation d=Ma+Nb could not be solved if 1≤d<(a,b), because a solution would imply (a,b)|d.

We need one more fact about prime numbers. Suppose p is prime, and p|mn for some m,n∈ℤ. So by definition, mn=pq for some q∈ℤ. We claim that p must divide either m or n (perhaps both). For suppose that we don't have p|m, hence (p,m) can't be p. But p is prime, and (p,m)|p, so we must have (p,m)=1. Hence it is possible to write 1=Mp+Nm. Therefore n=n(Mp+Nm)=Mnp+Nmn=Mnp+Npq= p(Mn+Nq). In other words, p|n. This property possessed by primes in ℤ is not shared by "primes" in other rings of algebraic integers, as we shall soon see.

We now have all the facts we need to prove unique factorization in ℤ. The proof is done by supposing factorization isn't unique, and showing this leads to a contradiction. So suppose factorization isn't unique, and for some n there are two different factorizations of n (apart from units ±1). There cannot be any prime which occurs in one factorization but not the other, by the result of the preceding paragraph. Hence the same prime factors occur, but for at least one prime p we have n=Apr=Bps with 0<r<s, and (A,p)=(B,p)=1. Dividing through by pr reduces to the case where a prime occurs in one factorization but not the other, which is impossible. The contradiction proves the desired result.

It may seem "obvious" that factorization is unique, because we are so familiar with the fact this is true in ℤ that it is taken for granted. It may therefore be rather surprising that in many (in fact most) rings of algebraic integers, factorization is not unique. Unique factorization is actually a very special and rare occurrence, and a great deal of algebraic number theory is concerned with either trying to compensate for this "problem", or else trying to describe, in some sense, just how badly factorization fails to be unique.

In the next installment we'll explain why unique factorization is a useful property and look at some examples.

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A fear of pheromones

The following news item has me somewhat steamed:

Ban on Calif. Pesticide Spraying Lifted
The spraying of a pesticide to fight a crop-eating moth can resume after a judge said Friday he was satisfied with a government plan to address environmental and health concerns.

Earlier this month, Judge Robert O'Farrell issued a temporary injunction against the spraying on California's central coast amid concerns over the long-term health effects of CheckMate, which was first dropped in the area last month.

CheckMate is a pheromone spray developed specifically to keep the moth from mating without killing it.

The problem, of course, is that a pheromone is not a pesticide (such as DDT or any other). In common English usage the Latinate suffix "-cide" means killing something or someone. (E. g. "suicide", "genocide", "fratricide".) Pheromones do not kill, either moths or anything else (to the best of anyone's knowledge).

Why is this a problem? Because (in my opinion) it is irresponsible science journalism. And it has consequences. I happen to live in the affected area, and I know there is a lot of heated opposition to this spraying. But I think the opposition is misguided. People are up in arms because they have this general fear of the aerial spraying of strange "chemicals". And it is especially unhelpful for "journalists" and news agencies like the Associated Press, which ought to know better, to be putting out releases that misclassify pheromones as "pesticides".

To be sure, there might still be human or animal health issues associated with the spraying of pheromones. There are certainly some people who are sensitive or allergic to a lot of "chemicals". I do not know for sure whether there are such issues in this case, although it is claimed that "numerous state and federal agencies tested the product and all its ingredients and determined it was safe."

But I do know that the journalism in this case is seriously flawed, and is probably causing a lot of people to worry when they should not need to, simply by calling the pheromones "pesticides", when they are not that at all. Sometimes, not always, chemical sensitivities are psychosomatic. And this is much more likely if the chemicals involved are incorrectly called "pesticides".

Here's a press release from the US Department of Agriculture that says a bit more about the pheromone in question:

New Pheromone Sprayer Leads Amorous Moths Astray
For decades, apple and pear growers have "adorned" their orchards with hundreds of plastic dispensers that emit a chemical sex attractant, or pheromone, to disrupt codling moth mating. Now, thanks to Agricultural Research Service (ARS) studies in Wapato, Wash., growers could soon be spraying the pheromone instead.

Sadly, the Associated Press, even a few days later, was still putting out faulty journalism:

Gov. orders resumption of disputed apple moth pesticide spraying

Something the general population certainly doesn't need is more media confusion about scientific subjects from sources that demonstrate a lack of trustworthiness – and contribute to popular cynicism about journalism in general.

Update (1/18/08): This sort of journalistic malpractice continues: Calif. residents say moth spray dangerous
Residents of Monterey and Santa Cruz counties filed 330 formal complaints to the state related to the light brown apple moth insecticide spraying, and about 300 more complained to doctors or public interest groups, said a report by the California Alliance to stop the Spray, the Santa Cruz (Calif.) Sentinel reported Sunday.

And the same brief article also refers to the pheromone as a "pesticide". Does this sort of incompetence matter? Of course it does. It's quite likely that most of the complainers are reacting to journalistic reports of "pesticides" and "insecticides" rather than what was actually used. Sort of an inverse placebo effect. Misinform people that they've been sprayed with a "poison", and of course some will feel ill. Is it possible there was some real effect? Sure. Whatever substance is involved – including any number that are "organic" or "natural" yet allergenic – there are bound to be at least a few people who might have an adverse reaction. But this can only be greatly magnified by sloppy journalism.

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Our plant relatives

Humans aren't related merely to other animals – plants are kinfolk too. In fact, we share some genes with ancestors of both animals and plants, genes not found even in most modern plants.

Green Algae: The Nexus Of Plant-Animal Ancestry
Genes of a tiny, single-celled green alga called Chlamydomonas reinhardtii may contain scores more data about the common ancestry of plants and animals than the richest paleontological dig. This work is described in an article in Science.

A group of researchers, including Arthur Grossman of the Carnegie Institution, report on the results of a major effort to obtain the full library of genes, or the genome sequence, of Chamydomonas and to compare its ~15,000 genes to those of plants and animals, including humans. The research shows that this alga has maintained many genes that were lost during the evolution of land plants, has others that are associated with functions in humans, and has numerous genes of unknown function, but which are associated with critical metabolic processes.

In particular, cilia are important structures of some eukaryotic cells, are inherited from the common ancestor of plants and animals. Cilia are found in animal cells, analogous to flagella in Chamydomonas, but have no analogue in most plant cells.
Chlamydomonas, affectionately called Chlamy, is an alga of 10 micrometres in size that is present in soil and freshwater environments. It performs photosynthesis like plants, but it diverged evolutionarily from flowering land plants about 1 billion years ago. It is even more distantly related to animals (the split between animals and plants was ~1.6 billion years ago). Chlamy moves using two anterior, hair-like flagella that were lost by its cousins, the flowering land plants, after the evolutionary split of the two lineages. The flagella are equivalent to the cilia and centrioles in animal cells. Centrioles are structures involved in cell division; they form a spindle apparatus, which helps separate genetic material into two new cells during mitosis. Cilia are important to many animal functions.

More information:

The Chlamydomonas Genome Reveals the Evolution of Key Animal and Plant Functions (Sub. rqd.)

Study involving more than 100 scientists provides new insights on green algae

Scientists Sequence Genome of Soil-Dwelling Green Alga

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Readings: health and medicine, 20 October 2007

Saturday, October 20, 2007

The text following each item is quoted material, except for editorial comments, which are in color.

BubR1 Protein: A Key Regulator of Aging
Hoping to find a way to help people maintain their independence and quality of life as they grow older, Jan van Deursen, Ph.D., and a team of collaborators are investigating the relationship between common aging-associated diseases and the protein BubR1. He became interested in aging-related research after observing that mice deficient in the protein BubR1 age faster than normal mice. They say BubR1 deficient mice may hold the key to preventing or delaying disorders such as cataracts, muscle weakness and cardiovascular disease.

Aging and the Growth Hormone Crash: What Comes First?
"If pituitary hormones were released like water from a faucet into a bathtub, there'd be a constant slow filling of the tub in proportion to its size and whether or not the drain was open — you could solve that with high school physics," explains Dr. Veldhuis. "One of the complexities is that the pituitary squirts out a pulse of hormones at random times."

The pituitary gland, a pea-sized structure located at the base of the brain, regulates many key functions in the body. It secretes seven hormones in response to commands from the hypothalamus of the brain. Dr Veldhuis is interested in observing the pituitary response for its influence on aging. He is most interested in its secretion of the growth hormone (GH), which stimulates protein synthesis and cell division in cartilage and bone tissue. GH has a tendency to remove intra-abdominal fat, which is associated with diabetes and heart disease (metabolic syndrome).

Hormone dilemma, 5 years on
Five years ago this month, a landmark study dashed the belief that hormone treatment is the key to keeping women of a certain age sexy, healthy and young.

On the contrary, maintaining estrogen and progestin at abnormally high levels after menopause was shown to be risky for their hearts, brains, breasts and blood vessels.

The government study abruptly transformed the use of hormone therapy - and, in the ensuing years, has undermined the idea that women who don't get long-term treatment are doomed to decrepitude. ...

The landmark research remains bitterly controversial, its findings incredibly complex. In recent months, reanalyses of the data have found that while hormones raise heart risks for women long past menopause, they pose no such danger - and may have cardiac benefits - for recently menopausal women.

Critics of the study - known as the Women's Health Initiative - have argued for five years that it overstated the heart risks for younger women.

While the science is still evolving, hormones have been firmly reestablished in a limited role: to relieve the passing discomforts of dwindling estrogen.

And yet the risk of breast cancer from estrogen therapy has been reaffirmed in recent studies – under certain circumstances. But uncertainties still remain. See here, here, and here.

Can Fat Be Fit?
Two years ago Katherine M. Flegal, a re­search­er at the Centers for Disease Control and Prevention, did a new statistical analysis of national survey data on obesity and came to a startling conclusion: mildly overweight adults had a lower risk of dying than those at so-called healthy weights. ...

Stampfer cites the Flegal study as a prime example of the errors the critics make. The reason being overweight seemed to reduce mortality is because Flegal used the wrong comparison group, he says. The lean group in her study included smokers and people with chronic illnesses—both of whom have increased mortality risks, but not because they are slim. “When you get sick, you lose weight, and you die,” Stampfer says. Compared with those who are smokers or chronically ill, people who are overweight come out looking better than they should.

Eating Made Simple
Studies focusing on one nutrient in isolation have worked splendidly to explain symptoms caused by deficiencies of vitamins or minerals. But this approach is less useful for chronic conditions such as coronary heart disease and diabetes that are caused by the interaction of dietary, genetic, behavioral and social factors. If nutrition science seems puzzling, it is because researchers typically examine single nutrients detached from food itself, foods separate from diets, and risk factors apart from other behaviors. This kind of research is “reductive” in that it attributes health effects to the consumption of one nutrient or food when it is the overall dietary pattern that really counts most.

Cutting Cholesterol, an Uphill Battle
About 85 percent of the cholesterol in your blood is made in your body. The remaining 15 percent comes from food. But by reducing dietary sources of saturated fats and cholesterol and increasing consumption of cholesterol-fighting foods and drink, you can usually lower the amount of harmful cholesterol in your blood. My college roommate, for example, recently adopted a mostly vegetarian-and-fish diet, minus cheese but with occasional meat and chicken, and lowered her total cholesterol from 240 to 160 milligrams.

Deadly Inheritance, Desperate Trade-Off
Mrs. Platt is part of a study aimed at preventing pancreatic cancer in people who are at high risk for it, by finding precancerous growths and removing all or part of the pancreas to get rid of them. So far, about 20 people have had the preventive surgery at Johns Hopkins, and a small number of others have undergone it at other centers.

In essence, these patients are trading the risk of cancer for the reality of diabetes, and their willingness to do it is a measure of the fear and desperation that pancreatic cancer provokes.

“With pancreatic cancer you don’t have much opportunity to save lives, and we are, with this approach,” said Dr. Canto, the director of endoscopy at Johns Hopkins.

Electric fields have potential as a cancer treatment
Yoram Palti, of the Technion–Israel Institute of Technology in Haifa, and his colleagues have demonstrated another way to disrupt cell division: alternating electric fields with intensities of just 1–2 V/cm. The fields they use, with frequencies in the hundreds of kilohertz, were previously thought to do nothing significant to living cells other than heating them. But Palti and colleagues have conducted a small clinical trial showing that the fields have an effect in slowing the growth of tumors.

Science begins at home
Chemotherapy drugs, like most medicines, reach cells by slipping through narrow spaces in the walls of blood vessels that crisscross the body.

But all blood vessels are not alike.

The abnormal, leaky vessels that supply cancer cells have openings up to 100 times larger than those found in healthy vessels -- it's like comparing a soccer ball with a Goodyear blimp.

In a way, this biological quirk was the reverse of the problem he faced in seeking a molecular petroleum sieve.

Instead of creating a mesh, he wanted to bulk medicines up so their molecules wouldn't pass through the wall of normal blood vessels. At the same time, they needed to remain small enough to fit through pores of vessels feeding cancerous cells.

One anecdotal example of the difficulties of developing new and better drug therapies.

Mysteries of autoimmune diseases unravel
Scientists say immune disorders, which range from common diseases such as juvenile diabetes or lupus to some so unusual that many doctors have never heard of them, are among the most mysterious of ailments, genetically complex and so diverse that estimating their true prevalence is a guessing game. But with major advances in genetics and exponential growth of knowledge about the immune system, scientists say important discoveries are tantalizingly within reach. ...

Immune system disorders often cluster in families and within an individual, says Virginia Ladd, president of the American Autoimmune Related Diseases Association. "Once you have one, you have others. Some patients say if you live long enough, you can collect them."

Visualizing the Molecules that Cause Infectious Disease: Seeing with Supercomputers
CAMDL specializes in developing computer simulated models aimed at the discovery of new treatments for infectious diseases and cancer. It is one of few labs conducting advanced research in computational, medicinal, synthetic and combinatorial chemistry under one roof.

The laboratory houses supercomputing hardware and software used to process highly complex biological data, and develop comprehensive databases of three-dimensional molecules. Dr. Pang has adapted his imaging concepts from the small computer screen to a large wall screen where visitors are drawn into a three-dimensional, sub-microscopic world. Researchers can examine and study, in simulation, microsecond-scale proportions of proteins and enzymes associated with malaria, avian flu and severe acute respiratory syndrome (SARS). This ability has led to significant discoveries in the lab that Dr. Pang says will impact the prevalence and spread of infectious diseases.

Small-Scale Solutions
Chemists first invented lab-on-a-chip devices to analyze gases in the 1970s, but the effort to make practical microfluidics tools for biological studies has gained traction only in the past decade. One major advance, led by George Whitesides at Harvard University in the late 1990s, was to fabricate the chips from cheap, flexible rubber rather than the expensive, stiff silicon used to manufacture computer chips. In a method dubbed "soft" lithography, Whitesides and his colleagues started with the same photographic processes that computer-chip companies use to cast an integrated-circuit blueprint in a single wafer of silicon, but they poured rubber into the chip-making molds instead.

Vaccines and Their Promise Are Roaring Back
By the mid-1990s, however, innovation in vaccines had virtually come to a halt. Only a handful of companies even tried to develop new ones, compared with 25 in 1955.

But in a stunning reversal, innovators today are chasing dozens of vaccines, stimulated by some recent high-profile successes. ...

The allure of the silver bullet — of wiping out an entire class of related diseases with a single injection — remains a powerful symbol of technological advance.

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Rings and ideals

Wednesday, October 17, 2007

It's time to do some more algebraic number theory again. For a refresher on what's gone on so far, check here.

In the last installment, way back in June, I introduced rings of algebraic integers, which are the main object of study in algebraic number theory. A "ring" in abstract algebra is a very fundamental concept, first discussed in this article. And in this article the most elementary example of a ring – the rational integers (ℤ) – was discussed, along with the concept of modular arithmetic.

What we saw there was the construction, for any n∈ℤ, of a new ring (ℤ/nℤ), which has only finitely many elements. Modular arithmetic is a staple of elementary number theory (that is, the classical theory of numbers, which deals mainly with ℤ). It was introduced by Carl Friedrich Gauss over 200 years ago, in 1801.

Now we are going to see how that construction can be generalized in abstract ring theory, using the concept of "ideals". It will turn out that the set nℤ consisting of all integer multiples of any n∈ℤ is an example of an ideal, and the "quotient ring" ℤ/nℤ can be generalized for any abstract ring and any ideal of that ring. This construction occurs ubiquitously in the study of rings of algebraic integers, introduced in the last installment.

An ideal can be defined for an arbitrary ring R, but it's a little messy. If R isn't commutative, there can be ideals which are "right" ideals but not "left" ideals or vice versa, because the definition of an ideal involves multiplication. So we'll assume R is commutative and has a multiplicative identity element ("1") too. For such a ring R, consider a subset I⊆R. Then I is an ideal just in case:

  • I is closed under addition: a+b∈I for all a,b∈I.
  • I is closed under multiplication by any element of R:
    ar=ra∈I for all a∈I and r∈R.

These axioms imply that I is a subgroup of R under addition. The additive identity 0 is in I by the second axiom. The second axiom also means that additive inverses are in I because R has a multiplicative identity, and hence its additive inverse -1∈R, so -a∈I for all a∈I. Note that if I≠R, I isn't a full ring (so it isn't a subring of R), because if 1∈I we would have I=R, by the second axiom.

One of the motivations for this concept of ideals is that it makes possible the definition of another very important concept: quotient rings. If as above R is a ring and I is an ideal, the quotient ring, denoted by R/I, is defined as the set of distinct cosets of the form r+I for all r∈R, where r+I is defined for any r∈ R as the set {r+a | a∈I}. Not all cosets are distinct as r ranges over R. Two cosets r+I and r′+I are the same exactly when r-r′∈I. This is because we can write r+I = r′+(r-r′)+I = r′+I. (Because r+I = I if r∈I.)

Importantly, we can define a ring structure on the set of all cosets. Addition is simple: (r+I)+(r′+I) = (r+r′)+I. Multiplication is a little trickier: (r+I)(r′+I) = rr′+I, but this only works since it doesn't depend on the choice of representative of each coset. The problem is we can have r+I=r′′+I even though r≠r′&prime, if r-r′′∈I. But in that case, (r-r′′)r′∈I by the second axiom for ideals, so all is OK. Thus multiplication of cosets is well-defined and unambiguous.

Under these definitions of addition and multiplication R/I is a (commutative) ring with a multiplicative identity. The additive identity element is I, and the multiplicative identity is the coset 1+I.

The ideal structure of the rational integers ℤ provides some important examples. Let n∈ℤ. Then obviously the set nℤ = {nm | m∈ℤ} is an ideal, often written simply as (n). It is just all integral multiples of n. The quotient ring ℤ/nℤ=ℤ/(n) is known as the ring of integers modulo n, and it has n elements. It is familiar from elementary number theory, where one writes "equations" such as a≡b (mod n) just in case a-b is divisible by n, i. e. is a multiple of n, i. e. a-b∈(n). The study of such congruences, which is done all the time in number theory, is really just the study of the ring ℤ/nℤ.

A very important special case is when n is a prime p. Then it is a fact that ℤ/pℤ is a field -- a finite field of p elements, sometimes denoted by Fp. However, if n is not prime, then ℤ/nℤ isn't even an integral domain, because it has divisors of zero, i. e. nonzero elements whose product is 0. For instance, if n=st for s,t∈ℤ, but s,t≠±1, then as ideals (s)≠0 and (t)≠0, where 0=(0)=(n). Yet (s)(t)=0. We can in fact characterize prime numbers p as elements of ℤ such that ℤ/pℤ is a field.

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Are Women Being Scared Away From Math, Science, And Engineering Fields?

Tuesday, October 16, 2007

Are Women Being Scared Away From Math, Science, And Engineering Fields?
Have you ever felt outnumbered? Like there are just not that many people like you around? We’ve all felt outnumbered in one situation or another and walking into a situation in which you sense the possibility of being ostracized or isolated can be quite threatening.

One group that may experience this kind of threat is women who participate in math, science, and engineering (MSE) settings- settings in which the gender ratio is approximately 3 men to every 1 woman

I don't see how there could be much doubt that this is a problem.

However, the explanation may not be entirely that ostracism or isolation alone is threatening. Evolutionary psychology could provide another part of the explanation, because it seems likely that for most of the time humans have been evolving, it actually has been more dangerous for women to participate in groups where men far outnumber them. Sensitivity to sexual harassment is rather likely to be in the genes.

One has to wonder whether men would show the same degree of signs of discomfort in an experiment where groups in which women predominated were shown to the experimental subjects. It's not clear whether this was addressed in the research.

Similar considerations of evolutionary psychology could be a part of the explanation for this finding:

Female Anxiety: Females More Likely To Believe Negative Past Events Predict Future
A new study finds that young girls and women are more likely to believe that negative past events predict future events, compared to boys and men. And that, according to researchers, may help explain why females have more frequent and intense worries, perceive more risk, have greater intolerance for uncertainty, and experience higher rates of anxiety than males.

Nobel prize in chemistry

Friday, October 12, 2007

Nobel in Chemistry Honors Expert on Surface Encounters
A German scientist whose studies of chemical reactions on solid surfaces have affected fields as diverse as agriculture, manufacturing and climatology won the Nobel Prize in Chemistry yesterday.

Gerhard Ertl, an emeritus professor at the Fritz Haber Institute of the Max Planck Society in Berlin, received the $1.5 million prize for pioneering work in surface chemistry, a specialty that helps explain the processes in making fertilizer and computer chips, and sheds light on the activity inside the catalytic converter of a car and on the surface of ice crystals in the stratosphere.


Expert On Surface Chemical Reactions Wins 2007 Nobel Prize In Chemistry

Birthday Boy Gets a Nobel (Sub. rqd.)

Nobel Focus: Chemistry in 2D

Chemistry Nobel makes a great birthday gift

Catalysis researcher wins Nobel Prize

Surface chemistry awarded Nobel

Catalysis chemistry wins Nobel prize

German Ertl wins Nobel chemistry prize

The religious right has it wrong

Thursday, October 11, 2007

As usual.

Just about everyone except the RR knows this, of course. But here are some recent scientific findings that document the falsity of some common claims of the RR.

Children Of Lesbian Couples Are Doing Well, Study Finds
A study of families in the Netherlands indicates that children raised by lesbian couples “do not differ in well being or child adjustment compared with their counterparts in heterosexual-parent families.”

Doctor-aided Suicide: No Slippery Slope, Study Finds
Contrary to arguments by critics, a University of Utah-led study found that legalizing physician-assisted suicide in Oregon and the Netherlands did not result in a disproportionate number of deaths among the elderly, poor, women, minorities, uninsured, minors, chronically ill, less educated or psychiatric patients.

More: here, here

Legal Status Doesn't Deter Abortion
Women are just as likely to get an abortion in countries where it is outlawed as they are in countries where it is legal, according to research published Friday.

In a study examining abortion trends from 1995 to 2003, experts also found that abortion rates are virtually equal in rich and poor countries, and that half of all abortions worldwide are unsafe.

(So legality has no effect on the frequency of abortion; it only makes it safer.)

More: here, here, here

Nobel prize in physics

Tuesday, October 9, 2007

Disk technology takes Nobel Prize
French scientist Albert Fert and Peter Grunberg of Germany have won the 2007 Nobel Prize for physics.

They discovered the phenomenon of "giant magnetoresistance", in which weak magnetic changes give rise to big differences in electrical resistance.

The knowledge has allowed industry to develop sensitive reading tools to pull data off hard drives in computers, iPods and other digital devices.

It has made it possible to radically miniaturise hard disks in recent years.

Well, that's good timing. I just wrote about the field of disk technology here. That article isn't about giant magnetoresistance per se, but that part of physics is certainly an important part of the big picture.

Here are other reports on the news:

Nobel prize recognizes GMR pioneers
Giant magnetoresistance, or GMR, is the sudden change in electrical resistance that occurs when a material consisting of alternating ferromagnetic and non-magnetic metal layers is exposed to a sufficiently high magnetic field. In particular, the resistance becomes much lower if the magnetization in neighbouring layers is parallel and much higher if it is antiparallel. This change in resistance is due to "spin up" and "spin down" electrons scattering differently in the individual layers.

GMR has since been used to develop extremely small and sensitive read heads for magnetic hard-disk drives. These have allowed an individual data bit to be stored in a much smaller area on a disk, boosting the storage capacity greatly. The first commercial read heads based on GMR were launched by IBM in 1997 and GMR is now a standard technology found in nearly all computers worldwide and is also used in some digital cameras and MP3 players.


Discoverers Of Giant Magnetoresistance Used In Hard Drives Win 2007 Nobel Prize In Physics

Magnetic Effect Nets a Nobel (Sub. rqd.)

Effect that Revolutionized Hard Drives Nets a Nobel (Sub. rqd.)

The physics prize inside the iPod (Sub. rqd.)

Nobel Focus: Sensitive Magnetic Sandwich

Small is beautiful: Incredible shrinking memory drives new IT (also here)

2007 Nobel Prize in Physics

Hard-disk breakthrough wins Nobel Prize

Hard Drive Pioneers Win Nobel Prize

Physics of Hard Drives Wins Nobel

Physics Nobel Goes to German, Frenchman (AFP)

A Nobel Nod for 'Giant' Discovery

Hard Drive Pioneers Win Nobel Prize

Nobel research means you can read this

Hard disk pioneers win physics Nobel

Disk technology takes Nobel Prize

Nobel prize in physiology/medicine

Monday, October 8, 2007

It's Nobel season, so I'll take a bit of time to pass along the news as it comes out. Of course, you'll get the same basic information from whatever other news sources you pay attention to, but I'll try to point you to something that talks more about the underlying science than you'll get from the mass media. Here's a good place to start:

Capecchi, Smithies and Evans share the Nobel
Mario Capecchi of the University of Utah, Sir Martin Evans of Cardiff University in the UK and Oliver Smithies of University of North Carolina, Chapel Hill, will share this year's Nobel Prize in Physiology or Medicine for their work in gene manipulation that let to the development of knockout mice.


Gene Targeting Pioneers Win Nobel Prize For Discoveries In Embryonic Stem Cells And DNA Recombination

A Knockout Nobel (Sub. rqd.)

A Knockout Award in Medicine (Sub. rqd.)

Biologists claim Nobel prize with a knock-out (Sub. rqd.)

Stem cell pioneers scoop Nobel Prize

"Knockout mice" designers win Nobel Prize

Stem cell team wins 2007 Nobel for medicine

'Designer mice' work wins Nobel prize

Knockout mice earn U.S.-British trio Nobel Medicine Prize

Key gene work scoops Nobel Prize

3 Scientists Win Nobel Prize in Medicine

Star Cluster Bursts into Life

Friday, October 5, 2007

Star Cluster Bursts into Life in New Hubble Image
Thousands of sparkling young stars are nestled within the giant nebula NGC 3603. This stellar "jewel box" is one of the most massive young star clusters in the Milky Way Galaxy. NGC 3603 is a prominent star-forming region in the Carina spiral arm of the Milky Way, about 20,000 light-years away. This latest image from NASA's Hubble Space Telescope shows a young star cluster surrounded by a vast region of dust and gas. The image reveals stages in the life cycle of stars.

NGC 3603 – Click for 800×890 image

More information: here, here, here

Philosophia Naturalis #14 has been published

It's now up at Dynamics of Cats, and what a herd it is.

Thanks, Steinn.

Dwarf galaxies

Thursday, October 4, 2007

Smallest Galaxies Ever Seen Solve a Big Problem
Mauna Kea scientists may have solved a discrepancy between the number of extremely small, faint galaxies predicted to exist near the Milky Way and the number actually observed. In an attempt to resolve the “Missing Dwarf Galaxy” problem, two astronomers used the W. M. Keck Observatory to study a population of the darkest, most lightweight galaxies known, each containing 99% dark matter. The findings suggest the “Missing Dwarf Galaxy” problem is not as severe as previously thought, and may have been solved completely.

“It seems that very small, ultra-faint galaxies are far more plentiful than we thought,” said Dr. Marla Geha, co-author of the study and a Plaskett Research Fellow at the Herzberg Institute of Astrophysics in Canada. “If you asked me last year whether galaxies this small and this dark existed, I would have said no. I’m astonished that so many tiny, dark matter-dominated galaxies have now been discovered.”

I don't really have a lot to add to this, except to remark that this is probably a more significant result than may be immediately obvious. After all, so a lot of tiny, lightweight galaxies have been found in orbit around the Milky Way – so what?

The significance is that this observation goes a long way towards solving a problem with the hypothesis that the universe contains large amounts of "cold dark matter" – perhaps 4 times as much mass in the form of "dark matter" than there is in the form of more ordinary "baryonic" matter. There is already a huge amount of evidence for the existence of dark matter, as discussed here and here.

The problem is that simulations which have been done on the evolution of galaxies under the assumption of a ratio of 4:1 dark matter to baryonic matter predict the existence of many more small "dwarf" satellite galaxies around the Milky Way than are actually observed. Intuitively, one would expect many small galaxies, since if visible galaxies consist of stars made of baryonic matter inside blobs of dark matter, there ought to be a large range of sizes, from the smallest to the largest. Instead, what has been observed until now is far too few of the smallest sizes.

The solution suggested by the results here is that galaxies that formed inside the smallest blobs of dark matter have far fewer stars than would be expected, and hence they are intrinsically dim and hard to detect, so that most very small galaxies simply haven't been noticed.

But why would such galaxies have so few stars? This question remains to be answered, but a plausible hypothesis is that most of the gas of these galaxies, from which stars could form, may have been literally blown away by the intense light radiated by the first very large stars that formed in the Milky Way itself:
Based on the masses measured for the new dwarf galaxies, Drs. Simon and Geha concluded the fierce ultraviolet radiation given off by the first stars, which formed just a few hundred million years after the Big Bang, may have blown all of the hydrogen gas out of the dwarf galaxies forming at that time. The loss of gas prevented the galaxies from creating new stars, leaving them very faint, or in many cases completely dark. When this effect is included in theoretical models, the numbers of expected and observed dwarf galaxies agree.

“One of the implications of our results is that up to a few hundred completely dark galaxies really should exist in the Milky Way’s cosmic neighborhood,” said Dr. Geha. “If the Cold Dark Matter model is correct they have to be out there, and the next challenge for astronomers will be finding a way to detect their presence.”

Other reports on this research: here, here

Preprint of the research paper: The Kinematics of the Ultra-Faint Milky Way Satellites: Solving the Missing Satellite Problem

Preprint of a subsequent research paper describing how dark matter content of very faint dwarf galaxies might be confirmed: The Most Dark Matter Dominated Galaxies: Predicted Gamma-ray Signals from the Faintest Milky Way Dwarfs

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Digital storage technology

Wednesday, October 3, 2007

In 1983 personal computers (there were no laptop computers in those days) usually did not come with hard disks as standard equipment, but the disks could be bought as an add-on. I bought a 10 MB (megabyte) disk for about $200 back then.

In 1994 hard disks were standard equipment, but not too reliable. I had to buy a replacement disk for the computer I had then, when it was only a year old. The disk was 1000 MB = 1 GB (gigabyte), and still cost about $200. Today, for less than $200 one can buy a 500 GB disk, while larger disks (750 GB or 1000 GB = 1 TB (terabyte)) are available for about $300.

So there is nearly an improvement of 5 orders of magnitude in 24 years. Since 105 is about 216.6, that is 16.6 doublings in 24 years in disk capacity per dollar. Which is one doubling in about 1.5 years, or 18 months. And that's not even allowing for inflation – which would make the doubling time even less in terms of inflation-adjusted dollars. Since 1.61.5 is about 2, a doubling every 18 months (1.5 years), is roughly the same as an increase of 60% per year, while a doubling in 2 years is an increase of about 40% per year (since √2 ≅ 1.41).

Oddly enough, that's pretty close to what Moore's Law states for the doubling time for the number of transistors that can be fabricated in one integrated circuit chip. This number is usually figured to be between 18 and 24 months, but closer to the latter. (For Gordon Moore's latest thoughts on the "Law", see here, here, or here.)

However, I say "oddly", because the technology of hard disks is quite different, and largely independent of, the technology of semiconductor integrated circuits. This is important, because even Moore himself sees the end of his "Law" within 10 years, or maybe 15 years at most. If it lasted 10 more years, we would expect a factor of about 32 increase in the density of transistors on a chip. But that would imply the linear size of each transistor should decrease by a factor of 5 or 6. So the size of one transistor would have to shrink to just about 10 nm. That's only a few dozen silicon atoms, which implies big problems in quantum effects and fabrication difficulty of the chips.

The demise of Moore's Law presents the same problem for the density of digital storage that can be implemented in semiconductor chips. This includes "flash" memory, now used extensively in digital cameras, MP3 players, and similar gadgets.

The ultimate limits of data storage density using either silicon chips or magnetic media occur for the same reason – quantum effects that arise when the size of circuit elements or magnetic storage domains approach the size of a few dozen atoms, somewhere below 10 nm. But because of the difference in technology between silicon chips and the magnetic media used in hard disks, the limits need not be reached at the same time.

Data bits in magnetic media are not stored in silicon-based transistors, but in grains of magnetic material (originally iron oxide but more recently a cobalt-platinum alloy). With current technology it takes more than one grain to store a single bit – from 50 to 100 are actually required for acceptable reliability and absence of "noise". So without a change in technology, the only way to achieve higher density is through reduced grain size.

Unfortunately, grain sizes are already around 8 nm, and any further reduction with cobalt-platinum grains would not work, because the quantum effects in that material would permit the direction of magnetization to "flip" (i. e. reverse randomly) at room temperature.

What to do? Fortunately, serious problems are still a few years away, because one major change in technology is already going on – the switch from "horizontal" to "vertical" recording. Prior to the first shipment of disks using the latter technology in 2005, the 50 to 100 grains needed to store each bit were laid out horizontally (though not end-to-end) on the disk surface. But in 2005 disks employing "perpendicular recording" technology became commercially available from Toshiba. (See here.)

Perpendicular recording entails orienting the magnetic cell consisting of individual grains so that its long axis is perpendicular to the surface instead of parallel to it. The change was accomplished by redesigning the "head" that writes each bit by establishing a particular direction of magnetization. Successful implementation of perpendicular recording has not been either quick or easy, as the idea has been under investigation since the mid 70s.

The estimated maximum density of data on a disk using the older longitudinal recording technology is 100-200 gigabits per square inch, while the estimated maximum for perpendicular recording is 1000 gigabits (1 terabit) per square inch. So there is a potential increase in the maximum density by a factor of 5 to 10. But the full potential won't be realized immediately. The disk introduced by Toshiba in 2005 had a density of "only" 133 gigabits/in2. In 2006 Toshiba raised the density to 178.8 gigabits/in2 (see here).

Some experts estimate that it will be possible to keep improving densities with perpendicular recording at a rate of 50% per year. At that rate (which may be optimistic), the limit (1 terabit/in2) would be hit in 2010-2011. By comparison, the only real competitor at this time for practical, bulk, random-access, non-volatile, read/write digital data storage is silicon-based flash memory. As noted before, such technology has doubled in density about every 2 years, or 40% per year. Although flash memory is currently more expensive per bit than magnetic disk and has other disadvantages, as well as some advantages, the two types of memory are currently competitors. So there will be pressure on magnetic media to increase in density no less than 40% per year, and at that rate magnetic media would still reach its limits around 2011-2012.

Flash memory, on the other hand, might keep improving in density a little longer, until Moore's Law itself hits the wall somewhere around 2017. So there's a lot of pressure on magnetic media vendors to come up with new technology that is more than just incremental refinement, simply to stay in the race.

Is this possible or likely? Yes, as a matter of fact it is. But we'll save discussion of possible new technologies for magnetic media for another time, and also look at future data storage technologies that are silicon based, as well as other possible technologies – of which there are quite a few.


Industry divided over future of hard drives

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Philosophia Naturalis #14 is coming

Monday, October 1, 2007

After a slightly extended hiatus it will be back on Thursday, October 4 – a date to remember – at the Dynamics of Cats.

Although time is short, if you have a blog post you especially like that relates to the physical sciences or technology, submit it for the carnival – you won't want to miss this special day.

Besides that, it would be nice to see a little more interest in this carnival, so it will be worthwhile to continue. And if you have a blog that deals with some aspect of physical science or technology, please consider volunteering to host the carnival, so we can keep the ball rolling.

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