## söndag 27 februari 2011

### Atomic periodic table of shapes.

"We're trying to build a periodic table of shapes," says Tom Coates, a mathematician at Imperial College London.

Video at NS: Atoms in periodic table of shapes

A new dimension for mathematics – the Periodic Table of shapes
Mathematicians are creating their own version of the periodic table that will provide a vast directory of all the possible shapes in the universe across three, four and five dimensions, linking shapes together in the same way as the periodic table links groups of chemical elements. The three-year project, announced today, should provide a resource that mathematicians, physicists and other scientists can use for calculations and research in a range of areas, including computer vision, number theory, and theoretical physics. For some mental exercise, check out these animations ,2, 3, that have already been analyzed in the project.

"Most people are familiar with the idea of three-dimensional shapes, but for those who don't work in our field, it might be hard to get your head around the idea of shapes in four and five dimensions. However, understanding these kinds of shapes is really important for lots of aspects of science. If you are working in robotics, you might need to work out the equation for a five dimensional shape in order to figure out how to instruct a robot to look at an object and then move its arm to pick that object up. If you are a physicist, you might need to analyse the shapes of hidden dimensions in the universe in order to understand how sub-atomic particles work. We think the work that we're doing in our new project will ultimately help our colleagues in many different branches of science. In our project we are looking for the basic building blocks of shapes. You can think of these basic building blocks as 'atoms', and think of larger shapes as 'molecules.' The next challenge is to understand how properties of the larger shapes depend on the 'atoms' that they are made from. In other words, we want to build a theory of chemistry for shapes," added Dr Coates.

We are searching for special shapes, called Fano varieties, that are the “elements” in our “periodic table of shapes”. We created the images above when analyzing 3-dimensional Fano varieties. It is difficult to visualize a complex 3-dimensional shape, but one way to do it is to look at slices through the shape. For example, to visualize the human brain (which is also a complex 3-dimensional shape!) you can take slices using an MRI scanner, and then assemble these slices to view the whole brain, like this: (Thanks to Dr Daniel Bulte at the University of Oxford for the animation.)

Note: Abelian/non-abelian correspondence is similar for pairs $X_{ab}/X_{na}$ and $V_{ab}/V_{na}$. Mirror symmetry.

Dr Coates has recently won a prestigious Philip Leverhulme Prize worth GBP70,000 from the Leverhulme Trust.

To follow the research project in real time, visit his blog.

## fredag 25 februari 2011

### The Selling of the Female Orgasm.

Big Pharma has got a big prey in sight; all unsatisfyed women. Of course men has nothing to do with this? Men are always willing, always capable? So it must be something wrong with women? Maybe a pill would help? A quick fix.

After all Viagra has been a big success. That the same pill has become a nightmare for many women the 'pill industry' doesn't bother about. They sell dreams and fantasies, not reality.

The fact that there is a Viagra pill contradict the statement of 'men always capable'. Also that they ignore.

Everything must have a reason, and a pill is the answer to everything? So thinks Big Pharma. A pill is so easy to swallow. The cure is easy, and brings money to Big Pharma. What if it also brings happiness? What would be better?

The Selling of the Female Orgasm.
70 percent of women don’t reach orgasm during coitus. It is quite normal.
A provocative new documentary targets Big Pharma’s quest for a female Viagra. They didn't tell that in this video? The video has been taken away. How greedy can they be?
The film is a desperately needed antidote to all the hype generated by pharmaceutical companies pursuing their holy grail: a female Viagra — something called “female sexual dysfunction”. “They were telling me that 43 percent of women had this disorder, which I found amazing, how could that be true if I had never heard of it before?” Women often suffered profoundly because their sex lives didn’t live up to the glowing imagery displayed in popular culture. She found that the often-cited 43 percent figure actually refers to a 1994 study of all kinds of sexual problems, including a lack of sexual desire, anxiety about performance, and pain during intercourse. Canner ultimately concluded that the catch-all female sexual dysfunction is essentially a phony disease made up by pharmaceutical companies.“A lot of this is about marketing,” she says. “They are trying to sell disorders.”

No single drug could possibly cure all of women’s sexual problems because there are so many potential causes for a woman’s inability to enjoy sex. Male impotence is essentially a mechanical problem that can be cured by a medication that enables erection. But women may turn away from sex for many reasons: physical, emotional, psychological. I think there is a great danger that many healthy women could end up taking drugs that could harm them to fix a disease they don’t have.” What does make a woman more receptive to sex? That’s still something of a mystery.

There may be cheaper and faster ways to reduce inhibition—like a glass of wine and a more attentive partner. And the European women didn’t experience the same benefit from creams and pills as their North American sisters, perhaps because they already are less inhibited.

Neuroscience about how the brain works to influence sexual desire is still primitive, Tiefer says. “The idea that you have to rebalance your brain? That’s just ludicrous.”

Pay more attention! This consider both men and women, but especially men should not think that sex is just an act in the bedroom. Sex is something much more. It is the openness to each other. No pill can fix that. Humans are more than animals. Humans need 'souls'.

## torsdag 24 februari 2011

### Carbon complexity and origin of life.

Carbon is primordial!
We don’t know how diamonds grow. There are diamonds the size of potatoes, but where did they come from?” Hazen said. Diamonds shoot up through the crust from a depth of 100 kilometers “without getting degraded into graphite. It must happen in an hour,” mineralogists believe. “How do fluids move that fast?”

The Hunt For Earth's Missing Carbon the 'most important element' on Earth.

The Deep Carbon Observatory aims to reshape our fundamental understanding of carbon's role in the biology, chemistry, and physics of Earth's interior. Carbon is among the most important chemical elements to humans. It forms the basis of life as we know it, is the central ingredient in many energy sources and plays a key part in our climate. In a planetary-scale machine called the carbon cycle, the element circulates among the oceans and atmosphere, into and out of the Earth's crust, and through living creatures. But even this immense cycle is thought to contain only a small part of total amount of carbon in our planet, with the rest locked deep beneath the surface. The goal of the project is to answer basic science questions, but industry already has its eyes on the research.

Eric Betz, 20.2.11. Inside Science News Service writes:
Deep beneath the surface of the Earth, a vast and unseen community of strange, microscopic lifeforms quietly subsists on the heat rising from our planet's interior.
In its total mass, this life might rival all that walks, crawls, stands, swims and soars above it, but scientists don't know for sure. Life has already been found in the deepest layer of Earth's crust, nearly one mile down, but scientists expect to find life thriving even deeper. Studying mysteries like this one is a task for the Deep Carbon Observatory, a new project that will search out not just life but everything carbon-related that lies beneath our feet.
“Twenty years ago, the idea that there was a deep underground biosphere would have been laughed at, now know there is, because anywhere you drill you find life. We're learning fascinating things about a biosphere that lives in very different conditions than we're familiar with.”

Scientists believe that the subterranean microbes, some of them isolated from Earth's surface since before the dawn of humanity, crucially influence the engines that drive our planet's interior. The microbes process carbon relatively quickly, making them an important step in the carbon cycle.

“Science is not cataloging all the things we know, it's exploring the things we don't know.”
• Carbon Cycle at Depth, by Katrina Edwards, USC, explains how isotopic evidence indicates that a deep biosphere of microbes both scrubs ocean fluids of organic matter and produces new, yet old, organic carbon in situ.
• by Dave Goldberg, LDEO, explores how basalt sills at young seafloor spreading centers may heat overlying sediments inducing natural carbon release while basalt flows elsewhere may serve to sequester anthropogenic carbon.
• Bassez, M., Is high-pressure water the cradle of life, J. Phys.: Condens. Mat. 15, L353-L361, 2003.
• More publications here.
Did deep biochemistry play a central role in life’s origins?
White paper.
Surprising discoveries of deep microbial life in terrestrial and oceanic environments point to a rich subsurface biota that, by some estimates, may rival all surface life in total biomass. Though many key discoveries have been made, we don’t know how life adapts to deep environments, what novel biochemical pathways sustain life at high P-T, or the extreme limits of life. Life holds only a small fraction of Earth’s carbon, yet biological cycling of carbon is relatively rapid.

Microbes are the principal innovators of Earth’s biogeochemical cycles. Their cell numbers in terrestrial and aquatic environments exceed 5 X 10^30 organisms with cellular carbon in excess of 10^17 grams. Yet we know very little about the abundance, distribution, diversity and activity of deep subsurface microbial life. One recent study indicates that deep subsurface life can persist in complete isolation: fixing its own carbon and nitrogen and living in complete indifference to photosynthesis-derived organics and O2. Such discoveries demand a profound recalibration of long-held principles of biology and ecology.
Carbon dynamics.
The dynamics in planet scale is poorly understood. The situation suggests that some very important piece might be missing from the existing models.

Pitkänen, Quantum Astrophysics: The vision about dark matter as a quantum phase with a gigantic Planck constant is an excellent candidate for this missing piece.
The hierarchy of Planck constants is realized by generalizing the notion of imbedding
space such that one has a book like structure with various almost-copies of imbedding space glued together like pages of book. Each page of book correspond to a particular level of dark matter hierarchy and darkness means that there are no Feynman diagrams in which particles with different value of Planck constant would appear. The interactions between di erent levels of hierarchy involve the transfer of the particles mediating the interaction between di erent pages of the book. Physically this means a phase transition changing the value of Planck constant assignable to the particle so that particle's quantum size is scaled. At classical level the interactions correspond to the leakage of magnetic and electric fluxes and radiation fields between di fferent pages of the book.

Quantum cosmology predicts that astrophysical objects do not follow cosmic expansion except in jerk-wise quantum leaps increasing the value of the gravitational Planck constant. This assumption provides explanation for the apparent cosmological constant. Also planets are predicted to expand in this manner. This provides a new version of Expanding Earth theory (R/2) originally postulated to explain the intriguing findings suggesting that continents have once formed a connected continent covering the entire surface of Earth but with radius which was one half of the recent one.
The most modern version of Expanding Earth theory is by Australian geologist Samuel W. Carey. He calculated that in Cambrian period (about 500 million years ago) all continents were stuck together and covered the entire Earth. Deep seas began to evolve then.
Physics and Chemistry of Carbon.
At their September 2010 meeting, the DCO Founders Committee voted to create this fourth directorate to focus on the physics and chemistry of deep carbon and carbon under extreme conditions.

White paper.
Excerpts.
One of the main goals of DCO is to understand the present distribution of carbon throughout Earth (core, mantle, and surface) as a result of processes active during planetary accretion and the subsequent thermal and chemical evolution of Earth. During Earth’s formation, volatiles were incorporated by accreting planetesimals. Initially, the growth of small planetesimals did not involve significant heating; toward the end stages of the generation of (possibly mutltiple) magma oceans. The solubility of carbon and other volatiles in the magma ocean and the depth of the magma ocean determine how much carbon remains within the mantle and how much is outgassed to the atmosphere as the magma ocean cools.

It is generally accepted that the origin of methane and related light hydrocarbons found in surface and near-surface reservoirs is due to one of two mechanistic pathways: microbial-based digestion of organic matter or by thermal degradation of organic compounds. This long-held view has been challenged by reports of high-temperature methane-rich fluids venting from sediment-poor mid-ocean ridges, hydrocarbon seepages from terrestrial regions dominated by ultramafic rocks, methane-bearing fluids from Precambrian shields, and fluid inclusions in mantle and igneous rocks. Geochemical indicators, such as CH4/C2H6 + C3H8) ratios, and carbon and hydrogen isotope compositions of methane, heretofore thought to be adequate for distinguishing methane of different origins, have been brought into question for certain hydrocarbon occurrences.

In the context of the carbon cycle the origin and behavior of both oxidized and reduced carbon species are certainly better understood for near-surface reservoirs compared to the deep Earth where the distribution and behavior are poorly constrained. It is clear, however, that a fundamental knowledge of deep Earth carbon is necessary because of its potential impact on geodynamic processes and because of the influence of the deep carbon cycle on surface processes such as secular variations in atmospheric composition and the rate of production of hydrocarbon deposits.

Thermodynamics of Carbon-bearing systems.
A large integrated experimental-theoretical effort is needed to compile reliable thermodynamic data for the (C, H, O, salt) system and the solubility of carbon dissolved as a trace constituent in other phases under the conditions of the deep earth.

To explore the relationship between deep biosphere life and climate.
An improved understanding of the origin and reaction history of methane.
The magnitude of kinetic vs. equilibrium fractionations and effect of T on isotopologues

Geobiochemistry.
How does life interact with its environment, by changing the chemistry of fluids, by catalyzing reactions and mineral growth, and by generating or destroying porosity. Production and processing of nanoparticles produced via biochemical pathways. To find a global minimum structure (as might be present in the natural system) requires a search over configuration space. As the number of degrees of freedom grows the problem becomes intractable. The electrons in these materials are often highly correlated and their correct description might require higher level electronic structure calculations and in some cases new theory.

An area important to the understanding of life processes that has not received much attention is the simulation of bioenzyme reaction mechanisms and their effect on the carbon cycle (e.g., RNA self replication in prebiotic systems effects of mineral surfaces, the exoenzymes involved respiration based on iron minerals, etc). There has been impressive progress at the microbiological level (discovering what is happening) but much less progress on the chemical mechanism (why and how these reaction work, e.g., the atomic level biochemical mechanisms). First principles methods have been used in such applications in pharmaceutical drug design research. Similar concepts and calculations can be applied to the analysis of complex biogeochemical processes in extreme environments. The deeper understanding of the enzyme mechanisms obtained should improve the understanding of the chemistry utilized by living systems in extreme conditions of temperature, pressure and under anaerobic conditions. The better understanding of key enzyme reaction would support the development of biomimetric pathways in enhanced energy recovery strategies (e.g., the better understanding of the mechanism of carbonic anhydrase should lead to more efficient CO2 sequestration strategies).

Remarkably little is known about the physical chemistry of carbon in salt water in equilibrium with minerals at pressures of the deep crust and mantle. This is a major knowledge gap closely related also to thermodynamics and kinetics.

Starting with water itself, we need experimental measurements and theoretical calculations of the fundamental properties of water, water-CO2, and water-CH4 mixtures, including in the presence of salt. Specifically the dielectric constant and the dissociation constant of water at pressures greater than 5.0 kbars and at elevated temperatures are needed.

Theoretical and experimental studies of the potential role of metastability in mineral-water-hydrocarbon systems at elevated temperatures and pressures must be undertaken. Methane (like other hydrocarbons) is not thermodynamically stable but merely metastable over a large range of P, T conditions where it is observed or inferred to exist. It is unknown how high in temperature and pressure this metastability and/or kinetically inhibited stability persists. Incorporation of the results obtained above for water into the databases of chemical mass transfer codes would enable quantitative modelling of mineral-water interactions at high T and P. Specifically, the role of the oxygen fugacity fO2 (or hydrogen fugacity fH2) in such systems in influencing the relative metastabilities of different C-bearing species could be addressed.

Similar knowledge deficiencies plague our understanding of carbonate mineral formation and destruction. Carbonate mineral formation is critical to removing and storing carbon in both the shallow Earth (soils, sediment), and the deep Earth. Whether and how carbonates form, and their rates and mechanisms of precipitation and dissolution, all affect how the climate system works over geologic timescales.

There is good evidence that indicates that over geologic time the rates of sediment delivery have changed, controlled by changing tectonic and climatic triggers. What is unknown is whether modern sediments now entering the ocean are typical of the flux over longer periods of time and how much organic carbon has been locked up in these. Transformative understanding of the carbon cycle and the role of deep carbon will depend on our ability to characterize and describe it in terms of complex structures and their reorganization — i.e. interrogation of “dissipative structures.” In particular we need to quantify the consequences of both positive and negative feedback processes on carbon distributions among key reservoirs such as the atmosphere, oceans, continental waters (e.g. rivers, lakes) and the crust.

Carbomers have the ability to absorb, retain water and swell to many times their original volume, used as thickening, dispersing (a dispersing agent or a plasticizer is either a non-surface active polymer or a surface-active substance added to a suspension, usually a colloid, to improve the separation of particles and to prevent settling or clumping), suspending and emulsifying agents.
Two representations exist for carbo-benzene. one has the aromatic core of benzene expanded, and one has the hydrogen substituents expanded. The substituted benzene derivative hexaethynylbenzene is a known compound, and the core-expanded molecule also exists, although with the hydrogen atoms replaced by phenyl groups. The final step in its organic synthesis is reaction of the triol with stannous chloride and hydrochloric acid in diethyl ether.

Intra-terrestrial hypothesis about the evolution of life is a prediction inTGD. Could the harsh pre-Cambrian conditions have allowed only intra-terrestrial multicellular life? Could the Cambrian explosion correspond to the moment of birth for this life in the very concrete
sense that the magma flow brought it into the day-light? Very many life forms of Cambrian explosion looked like final products of a long evolutionary process. It is quite possible that Earth's mantle contained low temperature water pockets, where the complex life forms might have evolved in an environment shielded from meteoric bombardment and UV radiation.

The vision known as RNA world.
It is assumed that RNA polymers serve all the basic functions associated with DNA, RNA and amino-acids. These functions are based on genetic and catalytic capacity of RNA. Later a genetic takeover occurred involving the emergence of DNA and genetic code in which amino-acids replaced RNA somehow. RNA seems able to serve synthetizing, transfer, messenger and ribosomal functions so that it can guide both its own replication and ordered polymerization of proteins.

King, view of complex systems, the basic mechanisms developed without genetic control and were nally taken under control as the genetic takeover occurred. These kind of generic
structures include proteins and nuclei acids, nucleotide coenzymes, bilayered membrane structures, ion transport and membrane excitability, membrane bound electron transport, glycolysis and the citric acide cycle. In TGD framework one can add to this list topologically quantized classical fields as universal structures. Atoms like C, N, and O and smaller amounts of P and S giving rise to bio-monomers, and metals like Al, Fe, and Zn are the basic building blocks. The formation of various chemical bonds like hydrogen bonds, covalent bonds, and peptide bonds is necessary.
Dr. Cairns-Smith has proposed that so called clay genes appeared as predecessors of genes.

## måndag 21 februari 2011

### Zooming into a fractal. Counting and hierarchy with primes.

The basis for adding and counting are partition numbers. Ken Ono and his research team (and number group) have unlocked the divisibility properties of partitions, and developed a mathematical theory for "seeing" their infinitely repeating superstructure. Partition numbers behave like fractals. And they have devised the first finite formula to calculate the partitions of any number. 1. 2. 3. 4. 5. 6. 7. 8. 9. We don’t mean the partition function that is familiar to most physicists.

"We prove that partition numbers are 'fractal' for every prime, and are self-similar in a shocking way. They are the number theory equivalent of zooming into a fractal," Ono explains. Video here.

Fractals pervade the universe at every level because of their simplicity. They appear to be the most basic way to organize the components of the universe. Expansion through replication of a basic pattern to build, in a sense growing from least to greatest. The same surely occurs with different forms of electromagnetic energy with colors being akin to musical notes in light frequency and radio waves and light like different keys. All built on the oscillations of matter? Or strings? Fractals are mathematical surfaces though.

Partitions can be graphically visualized with Young diagrams (also called Ferrers diagrams). Young tableaux have numerous applications in combinatorics, representation theory, and algebraic geometry. They occur in a number of branches of mathematics and physics, including the study of symmetric polynomials, the symmetric group and in group representation theory in general. Our original function p(n) is just p(1, n).

Ferrers diagrams showing the partitions of positive integers 1 through 8. They are so arranged that images under the reflection about the main diagonal of the square are conjugate partitions (Wikipedia). Listing the number of boxes in each row gives a partition λ of a non-negative integer n, the total number of boxes of the diagram. The Young diagram is said to be of shape λ, and it carries the same information as that partition. Containment of one Young diagram in another defines a partial ordering on the set of all partitions, which is in fact a lattice structure, known as Young's lattice. Listing the number of boxes of a Young diagram in each column gives another partition, the conjugate or transpose partition of λ; one obtains a Young diagram of that shape by reflecting the original diagram along its main diagonal.

A partition is a way of representing a natural number $n$ as the sum of natural numbers (ie. for $n = 3$, we have three partitions, $3$, $2 + 1$, and $1 + 1 + 1$, independent of order). Thus, the partition function, $p(n)$, represents the number of possible partitions of $n$. So, $p(3) = 3$, $p(4) = 5$ (for $n = 4$, we have: $4$, $3 + 1$, $2 + 2$, $2 + 1 + 1$, $1 + 1 + 1 + 1$) , etc..

This reveals divisibility properties of the basic partition function that are astounding. Partition numbers are a crazy sequence of integers which race rapidly off to infinity. The amount of partitions for the number 10 is 42. For the number 100, the partitions explode to more than 190,000,000. This discovery unlock the secret of the complex pattern underlying this rapid growth.

Using the reciprocal of what is now called Euler’s function, we get the generator for $p(n)$ by this infinite product,

$\sum_{n=0}^{\infty} p(n)q^n= \prod_{n=1}^{\infty}\frac{1}{1-q^n}$.

Here, $q^n$ counts the number of ways to write, $n = a_1 + 2a_2 + 3a_3 +\ldots$, for $a_i \in \mathbb{N}$, where each number $i$ appears $a_i$ times.

Ken Ono and colleagues, Jan Bruinier, Amanda Folsom and Zach Kent, got results that include a finite, algebraic formula for partition numbers thanks to the discovering that partitions are fractal. The sequences are all eventually periodic, and they repeat themselves over and over at precise intervals.

A mathematical telescope.
Ramanujan noted strange patterns in partition numbers. In 1919 he wrote: "There appear to be corresponding properties in which the moduli are powers of 5, 7 or 11 … and no simple properties for any moduli involving primes other than these three." (Ono, “The Last Words of a Genius” [pdf]).

It is like taking a"walk" through partition numbers. They found the pattern at a hike. “We realized the process of these numbers folding over on themselves is very much like what you see in the woods,” Ono says. “It was kind of a poetic moment,” he recalls of looking out on a mountainous valley, knowing that nature had helped them crack a mystery that had baffled some of the greatest minds in math.

"We found a partition function, that we call P, that is like a magical oracle," Ono says. "I can take any number, plug it into P, and instantly calculate the partitions of that number. P does not return gruesome numbers with infinitely many decimal places. It's the finite, algebraic formula that we have been looking for."

Related:
How a hike led to 'Eureka!'
New theories reveal the nature of numbers video here, over 1hour, but definitely worth to see.
Ken Ono's public lecture on the new theories
Combinatorics and Number Theory
Selected publications, Ono

References.
Ken Ono, & Jan H. Bruinier (2009). Identities and congruences for the coefficients of Ramanujan’s omega(q) Ramanujan Journal

Ken Ono (2010). The Last Words of a Genius Notices of the American Mathematical Society, 57, 1410-1419

Ken Ono, Amanda Folsom, & Zach Kent (2011). l-adic properties of the partition function American Institute of Mathematics.

Ken Ono & Jan Bruinier (2011). AN ALGEBRAIC FORMULA FOR THE PARTITION FUNCTION American Institute of Mathematics.

There is already an extension on the Ono-Folsom-Kent fractal issue by John Webb called, “An improved “zoom rate” for the Folsom-Kent-Ono l-adic fractal behavior of partition values” [pdf].

The physics tie in?
Could an ability to always explicitly write down partition numbers translate to physics (see pdf for relevant introduction)? In the past methods developed to understand partitions have been applied to physical problems such as the theory of the strong nuclear force or the entropy of black holes.

Asymptotic degrees of freedom?
Asymptotic analysis is a method of describing limiting behavior. The function "f(n) is said to be asymptotically equivalent to n2 as n → ∞", and this is written symbolically as f(n) ~ n2. Does topological defects, etc. explain the same thing, also boundaries? Is this the structure for memory? Intriguing that also savants are extremely talented in computating.

This asymptotic formula was first obtained by G. H. Hardy and Ramanujan in 1918 and independently by J. V. Uspensky in 1920. The proof of Rademacher's formula is interesting in that it involves Ford circles, Farey sequences, modular symmetry and the Dedekind eta function in a central way.

A special case of an asymptotic distribution is when the late entries go to zero—that is, the Zi go to 0 as i goes to infinity. Some instances of "asymptotic distribution" refer only to this special case. Does this reflect the relation between mass and energy?

This is based on the notion of an asymptotic function which cleanly approaches a constant value (the asymptote) as the independent variable goes to infinity; It is often used in time series analysis.

Asymptotic expansions typically arise in the approximation of certain integrals (Laplace's method, saddle-point method, method of steepest descent) or in the approximation of probability distributions (Edgeworth series). The famous Feynman graphs in quantum field theory are another example of asymptotic expansions which often do not converge.

The most known result of this field is the prime number theorem. Some results often neglected include the probability distribution of the likelihood ratio statistic and the expected value.

Wikipedia theory
Asymptotic scale
Twelvefold way

Composite fermions and permutations by Brannen:
Six quadratic equations are generated from the permtuation group on three elements.
The 1-circulant 3 x 3 matrices form a subalgebra of the 3 x 3 matrices; the product or sum of any two such matrices is a matrix of the same sort. Products of two 2-circulant matrices are a 1-circulant, and the product of a 1-circulant and a 2-circulant is 2-circulant. These are the same rules that apply to the diagonal (1-circulant) and o -diagonal (2-circulant) elements of a 2x2 matrix. Consequently, we can assemble P0 and P1 into a 6x6 matrix:

P =

I J K R B G
K I J B G R
J K I G R B
R B G I J K
B G R K I J
G R B J K I

The six coupled equations are de fined by P2 = P.
Matrices of this form are a subalgebra of the 6 x 6 complex matrices. That is, they include 0 and 1, and are closed under negation, addition and multiplication. They can be thought of as de fining a form of multiplication that operates between two 6-element complex vectors, with 8 classes of solutions.

This is also valid for the relativistic bosonic string in 26 dimensional spacetime, except that then you need to multiply by 24 because the one dimensional string can vibrate independently in any of the 24 space dimensions transverse to the string. The partition function for bosonic string theory is therefore given by

Z = Σn P(n) exp( - (24n-1)ħα)

This is merely an “unsurprising” application of the theory of p-adic modular forms and the real breakthrough is in that field. Perhaps we should expect some developments in p-adic string theory. Different small prime numbers have different uses. The way the partition congruences works turns out to depend on the value of [(p-1)/12] – [(p^2-1)/24p] where the square brackets are for the floor function. For 5,7 and 11 this is zero which is why there are many congruences for these primes. For primes up to 31 it equals one, so there are still congruences but they are harder to find. 2 and 3 dont give congruences because they are factors of 24.
The sum of 8 positive integers is 31. Make sure it doesn't have 0 in it. 0 isn't positive.
But if we don't believe in those dimensions? Would there then be 2(4-1) D? Time is the problematic one? Bosonic time, negative time? Time as ZeroEnergyOntology depending on measurement and consciousness? The basic open question is whether in finite primes relate only to the physics of cognition or whether they might allow to say something non-trivial about the physics of matter too.

The hierarchy problem.
As above, so below, was an ancient saying. Today we talk of macrocosmos and microcosmos, topology and fractality.

A free module over a ring? Like the carbon ring/honeycomb lattice with the zero energy ontology field? Galois groups and modules are the same for both p- and l-adic primes. The general strategy of p-adic Hodge theory is to construct certain so-called period rings. Every discrete valuation ring, being a local ring, carries a natural topology and is a topological ring.

Matti: l-adicity is actually a purely technical term and means p-adicity with some primes excluded. The fractal structure for the distribution of primes is highly interesting and I learned that it is completely analogous to p-adic fractality which is the basic element of p-adic physics. In p-adic physics the physical counterpart of this fractaility is local chaos with long range correlations which corresponds to time and length scales coming as powers of p (and sqrt(p)). The partition functions involved relate directly to conformally invariant systems since the degeneracies of states with given conformal weight correspond to partition numbers. For applications to particle physics this p-adic fractality is not however relevant since the conformal weights involved are so small (n=0,1,2!) that these effects are not important. Hmmm...

And in,"Infinite primes"
The natural expectation is that evolution by quantum jumps means dispersion in the space of these sectors and leads to the increase of the p-adic prime characterizing the Universe. As one moves backwards in subjective time (sequence of quantum jumps) one ends up to the situation in which the prime characterizing the universe was p = 2. Should one assume that there was the first quantum jump when everything began? If not, then it would seem that the p-adic prime characterizing the Universe must be infinite.

But the p-adic length scales are finite and if the size scale of Universe is given by p-adic length scale the Universe has finite size. Assumption: the p-adic prime characterizing the entire Universe is literally in finite and that p-adic primes characterizing space-time sheets are finite.
The recipe for constructing infi nite primes is structurally equivalent with a repeated second quantization of an arithmetic super-symmetric quantum field theory. At the lowest level one has fermionic and bosonic states labeled by fi nite primes and infi nite primes correspond to many particle states of this theory. Also in finite primes analogous to bound states are predicted. This hierarchy of quantizations can be continued inde finitely by taking the many particle states of the previous level as elementary particles at the next level. It must be also emphasized that the notion of infinity is relativistic.

Space-time point becomes in finitely richly structured in the sense that one can associate to it a wave function in the space of real (or octonionic) units allowing to represent the WCW spinor fields. One can speak about algebraic holography or number theoretic Brahman=Atman identity and one can also say that the points of imbedding space and space-time surface are subject to a number theoretic evolution.

The Universe of quantum TGD might basically provide a physical representation of number theory? Infi nite integers and reals can be regarded as in finite-dimensional vector spaces with integer and real valued coeffcients respectively.

The notion of finite measurement resolution for angle variables given naturally as a hierarchy
2 pi=pn of resolutions for a given p-adic prime defining a hierarchy of algebraic extension of p-adic numbers is central.

So we have a relation between integer/reals (bottom-up?) and an algebraic structure containing p-adic numbers? A permutation containing a secondary quantization? This is basically the same structure we use in braidings in genetics (Gaussian-probability). A structure for consciousness as top-down hierarchy, seen also in the music? A topinformational structure of non-entanglement = self? The more far away from the diagonal, the more decay/decoherence of information and energy overlap that brings forth the quantization?

Self-modularity.
In TGD, "selves" are defined as sub-systems able to avoid entanglement with the environment (and hence decoherence) in subsequent quantum jumps. These semi-stable, bound states can be both material (atoms, molecules, organisms) and p-adic (individual mind)- defining an infinite hierarchy of organizational levels and "observers".

A spectacular wiev: The most stable configuration is in the middle diagonal of the Young diagram? This is seen in the stable islands of the atoms too, and in the periodic table? The farther away from the diagonal the higher the tension, until it is quantized and vanish out of sight (the Planck constant or alpha changes?) into the dark?

References.
Sautoy, Marcus Du. The Music of the Primes. New York: Perennial-HarperCollins, 2003.

J. P. Boyd, "The Devil's Invention: asymptotic, superasymptotic and hyperasymptotic series", Acta Applicandae Mathematicae, 56: 1-98 (1999). Preprint

TGD as a Generalized Number Theory III: Infinite Primes and the chapter Non-Standard Numbers and TGD of "Physics as a Generalized Number Theory".

Carl Brannen 2008: Density Matrices and the Weak Quantum Numbers, http://brannenworks.com/weakqns.pdf

Michael Aityah, http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.4827v1.pdf
From Euclidean 3-space to complex matrices
Vector bundles over algebraic curves and counting rational points

Amanda Folsom, Zachary A. Kent, and Ken Ono, l-adic properties of the partition function

YANG, Yifan, Congruences of the partition function, http://faculty.math.tsinghua.edu.cn/~lsyin/abstracts.pdf

## fredag 18 februari 2011

### Russian scientist photographs souls.

30 Jul 2010, Moscow.com Weird News. A quote:
The activity of Konstantin Korotkov, deputy director of the St. Petersburg Research Institute of Physical Culture and world-renowned authority on Kirlian photography, was recently highlighted by Life.ru. Korotkov is the developer of the gas-discharge visualization (GDV) technique in Kirlian photography.

## Russian camera can see human soul 22 September, 2010

A publication of the popular Russian tabloid Life.ru gives a dramatic account of the experiments of an inventor from St Petersburg, who has created a device able to see human aura.
Accompanied by pictures suspiciously reminiscent of a series of thermal images of a woman at different temperatures, the report claims they are made with a special “gas discharge camera” built by Konstantin Korotkov, a professor at the Research Institute of Physical Culture and State University of Information Technologies, Mechanics and Optics.
The paper goes on to say that the device can register the circumstances of death, differentiating between a victim of a violent crime and a person who died quietly in bed. It also registers the changes in aura presumably made by a strong psychic working on somebody.
Disregarding the glib comparison of the religious term “soul” with the new age “aura”, the claims – they can hardly even be expected to get support in peer-reviewed scientific papers in our opinion – prompted RT to take a little investigation into the wonder device.

Kirlian photography takes its name from Soviet electrician Semyon Kirlian, who discovered the process in 1939. It was the subject of extensive research in the 1970s in the Soviet Union and the West. It is commonly described as photographing an object’s aura. According to a website associated with Korotkov, he “confirmed earlier observations… that the stimulated electro-photonic glow around human fingertips contained astonishingly coherent and comprehensive information about the human state – both physiological and psychological.”
In other words, the GDV technique, which was developed in the late 1990s, can be used for diagnostic and assessment purposes. It is already used to measure stress and monitor the progress of medical treatments. In its most sophisticated form, the GDV technique is incorporated with computer imaging.
Now scientists have taken GDV photographs of a person as he was dying. In the photos, it could be seen that the area of the belly lost its life force (the purported soul) first, followed by the head. The heart and groin were the last to lose their life force, in that order.
Scientists using the GDV technique say that the aura of those who die unexpectedly or violently differs from those who experience a calm death. The souls of the former remain in a state of confusion for several days and return frequently to their bodies, especially at night. Korotkov ascribes that phenomenon to unused energy retained by the soul. He suggests that the GDV technique will also have applications for distinguishing genuine psychics from frauds.

Welcome to Elecrophotonics World!
Let me invite you to the world of mysterious and attractive "living" glows - world of Electrophotonics. Konstantin Korotkov's world.
Saint-Petersburg Federal Research Institute of Physical Culture
Saint-Petersburg State Technical University of Informational Technologies, Mechanics and optics

Books, a lot.
The influence of mental, emotional and spiritual processes on EPI/GDV images.Many years of experimentation have made it possible to identify bioelectrographic correlates of altered states of consciousness (ASC) [Bundzen et al, 2000; 2002]. These are particular states, which a person enters during meditation, mental training, religious ecstasy, or when under the influence of drugs, psychedelics or anesthesia.

Constant State Of Flux’s experience with the GDV is an interesting read.
This from Dr. Korotkov’s website:
“When we observe the play of light around human body, drop of water or crystal, we understand that everything in the world has interrelationship and any object – biological or inorganic – has its own inner energy. Understanding the fact that our life is not only material body and material existence but, first of all, it is energy, and therefore – Spirit, makes us have new attitude towards our everyday reality. When on real time we observe change of human biological field under influence of therapy, meditation, prayer, love, it makes us see the world round us with different eyes.”

Analysis of energy field.
Bioelectrography by means of a GDV camera according to Prof. Dr. Konstantin Korotkov In case of blockades, illnesses and lack of psychic stability, the energy field appears to be interrupted, laced-up and irregular. This can be depicted on an overall scale or separately on the psychic, physical or mental scale.
We would like to point out that it is not a 'moral' evaluation, but a momentary state of energy that will give hints.

EPC/GDV in Reconnecting healing. article
GDV or Gas Discharge Visualisation

January 2010: Measuring Human Personality by Machine: Could it be true?Paul Dobson & Elena O’Keeffe, Cass Business School, City University London
The physics of gas discharge is well documented (see, for example, Nasser 1971). The Gas Discharge Visualization (GDV) technique (Korotkov 2004) places an object in a high intensive electromagnetic field (EMF). The object is separated from the electrode by a dielectric – a substance that does not conduct electricity but permits an electromagnetic field. With this arrangement, if we apply a voltage between the object and the electrode current does not flow between them but a potential difference builds up until the breakdown voltage is reached. This is the point at which electrons around the object begin to move and a current begins to flow along the surface of the dielectric. As they move the electrons collide with heavier gas molecules wrenching out electrons and emitting quanta of light (photons). Each collision results in two electrons so branching tree like patterns of light result. When an alternating current is used avalanches of ionization moving away or towards the electrode core are overlaid upon each other. The GDV uses a camera to photograph the emitted photons and a computer programme to analyse the captured AVI files. The resulting image parameters are stable and sufficiently distinctive to reliably distinguish between different liquids, metals and gemstones and between electrolytes of different concentrations (see Korotkov 2001, 2004). The nature of the ionisation and photon emission is dependent upon a) the nature of the EMF which in this case is constant (10kV impulses of 10 microseconds duration at a repetition frequency of 1024Hz for 0.5 seconds) b) the ability of the object to hold an electric charge (its capacitance) and hence its breakdown voltage c) the nature of the surrounding gases. The relationship between GDV image area and the capacitance of a metal cylinder is shown below (Korotkov 2008, personal communication). Download

Update 6.9.2013. The article:
Russian scientist photographs the soul leaving the body at death
The image taken using the gas discharge visualization method, an advanced technique of Kirlian photography shows in blue the life force of the person leaving the body gradually.

###### An interview here

Dr. Korotkov can be reached at PL 88 53101, Lapeenranta, Finland, phone: 7-812-112 5627; fax: 7-812-164 8369.

This is interesting, but read it with awareness and care. "Modern science has only just begun to research consciousness", as is said on this page.

## torsdag 17 februari 2011

### The body-mind problem - FQXI-contest 2011.

Dear Ulla Marianne Mattfolk,

Congratulations...your submission to the FQXi Essay Contest has been approved! Your essay is now available for download and discussion on this FQXi forum page.

My FQXI-essay here.

Thanks again for your essay submission, and we look forward to a vibrant discussion of your essay in the FQXi forum!

- The Foundational Questions Institute

This wasn't so easy, because of the small size, 9p only. I would need much more....
The topic is so wast. But after many late nights this is what I achieved. Some said it is impossible for a non-physicist to write a physical essay, but they don't know me:) Few is so stubborn as me. Of course I can write :)

Well, the result is free to judge.

The body-mind problem as a play between coherence and decoherence.
Abstract:
Living matter results from mixed states of quantum and classical physics; the mind and the body. The life as a function from this depends on a digital state function, and the Schrödinger cat is ‘dead and alive’ at the same time. There is no total wave collapse, only partial with interference/superposition. In contrast to non-living systems, they don’t appear to optimize anything, but is intermediate, and reactive.

Life uses noise or dissipation as a tool to create stability and coherence, through formation of decoherence and negentropic states. But life is indeed quantal entanglement, resonance and superposition, with also noise as perceptions from the surroundings, to keep up the quantal states. To be a living matter made of ordinary atoms and molecules the decoherence is needed, and thence we have two different selves, one that we might call the decoherent singular I, and one that we usually call 'the wise man', or 'the magnetic body' in TGD; that is one classic and one quantal self. The longstanding problems of stress, homeostasis and sleep would also get a reasonable understanding.

Perceptions are also both classic, through bodily sensations and senses mostly, including thinking, and quantal in form of cognition, awareness, intention, qualia, and also OBE and paranormal events belonging to experiencies of our quantal self, the magnetic body. Paranormal events would then partly be explained in a simple way.

Write, and discuss, pls.

## onsdag 9 februari 2011

### EDM reveals - antimatter without MSSM and Higgs?

Electrons have a secret? (This is a short variant of the article, look for more details at the link.)

### The shape of the electron. This is one of the most sensitive probes of the difference between matter and antimatter.

We are looking for a deviation from spherical that would indicate a difference in the laws of physics that govern matter and antimatter. This would show that our current theory of particle physics, the Standard Model is incomplete. We know that any deviation from roundness is going to be tiny.
Detecting an electric dipole moment (EDM) would mean electrons, which buzz about atomic nuclei, have internal structure. So far we've checked the roundness of the electron to an incredible degree of precision: the equivalent would be measuring the diameter of the earth to better than the width of one human hair. And so far, we've seen no evidence of non-roundness. Measuring the inner shape of the famous particle could help solve a cosmic mystery, where's all the antimatter? By carefully measuring the shape of the electron, through a particular property known as the electric dipole moment, which would mean that the electron has some kind of internal structure, a bizarre concept for a particle that is supposed to buzz around the nuclear hearts of atoms and molecules with its mass concentrated into an essentially sizeless point. Although no one has yet measured the electron's electric dipole moment, researchers think it should exist and could be within reach of today's modern laboratory setups.

You can learn about the techniques we use, our latest results, what we're planning, and who we are. Trapped polar molecules may be used to measure the electric dipole moment of the electron, a search for physics beyond the standard model. By trapping chiral molecules, it should be possible to study the role of the weak interaction in the emergence of homochirality in biological molecules. Once we have trapped the molecules we hope to cool them further, bringing them into the ultracold regime. Ultracold polar molecules offer a new dimension in cold atom physics, primarily due to their long-range dipole-dipole interactions. By varying the switching timing, the length of the lenses can be varied, which affects the number of stable trajectories along the guide. The electrode geometry was chosen to provide a strongly harmonic field variation; transverse confinement in the high-field Stark limit can be treated as that of a harmonic potential.

"There are good theoretical reasons to think that it isn't too far away," says physicist Larry Hunter of Amherst College in Massachusetts, who has been hunting the electron's electric dipole moment since the 1980s. "What has made us all dedicate our lives to it is the real good chance that something might emerge soon." Within the next few months, scientists at Imperial College London are expected to report the latest limit on the size of the electron electric dipole moment, the first such improvement in a decade.

Physicists suspect that electric dipole moments exist because they allow particles to violate what's known as time-reversal symmetry. Although symmetry sounds like a good thing, scientists know that processes involving other particles (such as B mesons) behave differently whether running forward or backward, a violation of time-reversal symmetry. In order for this to happen, the electron (and other fundamental particles) must have an internal structure, something an electric dipole moment can reveal.

Imagine that the electron has "a cloud of stuff following it and blow that electron cloud up to the size of Earth, and extra positive charge would appear as a tiny dent on the north pole while extra negative charge would be a tiny bulge on the south pole. Given current limits, the size of that dent or bulge would correspond to adding or subtracting no more than about one-thousandth the width of a human hair from either end of the planet.

Reversing time (by switching the direction of a particle's spin) changes the direction of the magnetic dipole (blue) but not the electric dipole (green). This means that possessing an electric dipole moment would give particles a way to violate time-reversal symmetry. Whether a property known as the particle's spin responds differently when the field is switched on in different orientations, which would mean the electron possesses an electric dipole moment. Seeing that difference is the hard part.

Our most recent published measurement of the electron edm is (-0.2 ± 3.2) 10-26 e.cm. [You can find the paper on our publications page]. The current limit has already ruled out the simplest version of a popular idea known as supersymmetry, which tries to explain the cosmic matter/antimatter imbalance by suggesting that every particle has an as-yet-unseen "superpartner." If researchers can push the limit to 10–29, that would rule out another extension to the standard model that tries to solve the matter problem by postulating multiple kinds of the particle known as the Higgs boson, which Europe's Large Hadron Collider was designed to detect. In 2002, Commins' team published the most stringent limit yet: 1.6 × 10–27. The standard model predicts that the electron's electric dipole moment is less than 10–38 in units of electron charge times centimeters.

Any non-zero measurement of the electron edm would be clear evidence for physics beyond the Standard Model. Low-energy particle edm measurements can be viewed as complementary to high-energy accelerator experiments.
The minimal supersymmetric standard model, or MSSM (red), is a standard model extension that holds that every elementary particle has a “superpartner.” One of the simplest versions has been ruled out by the current limit. Another version (blue) of MSSM that sets a parameter dubbed phi to a different value is still a possibility, but it too may be ruled out when researchers lower the bar further. The multi-Higgs model and left-right symmetric models are also ruled out if the new limit is achieved.

What's more, the electric dipole interaction has a property that makes it particularly interesting: it violates time reversal symmetry. That's because the dipole must lie either parallel or anti-parallel to the spin, but the choice of one over the other violates time reversal symmetry. Direct observation of microscopic time-reversal asymmetry would be a profoundly interesting result.

Measurements of particle interactions at the smallest scales seem to indicate that matter and anitmatter are treated in a rather symmetric way. Andrei Sakharov showed that CP-violation is needed to explain the matter dominance of the universe. The degree of CP-violation known in particle physics falls well short of that which would be needed. So, one might reasonably expect that there must be extra CP-violating mechanisms at work - looking for them seems like a good idea. Our measurement of the electron edm could shed light on these mechanisms.

To measure this tiny interaction we use a neat trick. We choose a pair of energy levels that are shifted oppositely by the edm interaction. This gives us a powerful "common mode rejection" of many deleterious effects. We measure the energy difference between our two chosen levels directly using quantum interference. We prepare a coherent superposition of the two energy levels of interest and measure the phase evolution of this superposition interferometrically. We call this technique spin interferometry, and it is described in detail in many of our publications.

An example of interference from two molecular energy levels that have different energies in a tiny magnetic field.
See the cutting edge of research in molecule cooling, manipulation and trapping to build a foundation for the next generation of edm experiment.

From article comments: If the electron has no internal structure, and consists of a real point charge, its energy has to be infinite! And it is impossible to explain its 1/2 spin. (Just claiming that the spin is "intrinsic" is no explanation...)

There already exists a model of the electron that explains its charge and spin, based just on the particles structure/topology and else classical physics (google "neoclassical atom").

Watching An Atom's Electrons Move in Real Time
Physicists have used ultrashort flashes of laser light to directly observe the movement of an atom’s outer electrons for the first time - a process called attosecond absorption spectroscopy.

Researchers were able to time the oscillations between simultaneously produced quantum states of valence electrons with great precision. These oscillations drive electron motion. “This revealed details of a type of electronic motion – coherent superposition – that can control properties in many systems,” says Stephen Leone.

A classical diagram of a krypton atom (background) shows its 36 electrons arranged in shells. Researchers have measured oscillations of quantum states (foreground) in the outer orbitals of an ionized krypton atom, oscillations that drive electron motion.
The crucial role of coherent dynamics in photosynthesis as an example of its importance, (the Graham Fleming group) noting that “the method developed by our team for exploring coherent dynamics has never before been available to researchers. It’s truly general and can be applied to attosecond electronic dynamics problems in the physics and chemistry of liquids, solids, biological systems, everything.” - Leone. Theoretically, however, with longer ionization pulses the production of the ions gets out of phase with the period of the electron wave-packet motion. After just a few cycles of the pump pulse, the coherence is washed out. Thus, says Leone, “Without very short, attosecond-scale probe pulses, we could not have measured the degree of coherence that resulted from ionization.”

Holograms.
Electrons can also be used to create an hologram of the atom.
Scientists have created holograms of atoms using laser-driven electron motion, which could lead to a new type of ultra-fast photoelectron spectroscopy. In the future, this type of holography could enable scientists to study the structures of molecules in a more direct way than before. Ymkje Huismans from the FOM-Institute AMOLF in Amsterdam, The Netherlands, and an international research team have published their study in a recent issue of . They have experimentally demonstrated is that it is possible to make holograms by taking an electron out of a molecule and, using a laser field, redirect the electron toward the molecule.

The scientists beamed an intense infrared laser light at an atom or molecule, which resulted in the atom or molecule becoming ionized and releasing an electron. The laser field causes the liberated electron to oscillate away from and toward the ion. Sometimes, an electron and ion collide, releasing a very short burst of radiation.

Because the is fully coherent, meaning it always has the same phase, the scientists realized that they could apply holographic techniques to record information about the ion and electron. The key to holographic electron imaging is to observe the interference between a reference wave (which is emitted by the electron and doesn’t interact with the ion) and a signal wave (which scatters off the ion and encodes its structure). When the reference wave and signal wave interfere on a detector, the encoded information about the electron and ion is stored and can be viewed in the future. As the scientists explained, the result is a hologram of an atom produced by its own electrons.

The researchers also developed theoretical models to simulate their measurements, confirming that the hologram had stored spatial and temporal information about the and ions. By using the holographic structures to develop a new kind of ultra-fast , researchers could be able to directly measure electron and movements on the attosecond timescale.

References:
Do electrons hold the key to matter/antimatter asymmetry?Sizing up the electron. Science News, Feb. 12, 2011 Sizing up the electron

Eleftherios Goulielmakis, Zhi-Heng Loh, Adrian Wirth, Robin Santra, Nina Rohringer, Vladislav Yakovlev, Sergey Zherebtsov, Thomas Pfeifer, Abdallah Azzeer, Matthias Kling, Stephen Leone, and Ferenc Krausz, “Real-time observation of valence electron motion,” Nature, 466, 739-743 (5 August 2010). Abstract.

Y. Huismans, et al. “Time-Resolved Holography with Photoelectrons.” Science Express. 16 December 2010. DOI:10.1126/science.1198450

Electron EDM. Centre for Cold Matter, Imperial College, London.

The Fleming Group 2010:
1. Spectroscopic elucidation of uncoupled transition energies in the major photosynthetic light-harvesting complex, LHCII, G.S. Schlau-Cohen, T.R. Calhoun, N.S. Ginsberg, M. Ballottari, R. Bassi, G.R. Fleming, PNAS 107 (30), 13276-13281, JUL 2010.
2. Quantum coherence and its interplay with protein dynamics in photosynthetic electronic energy transfer, A. Ishizaki, T.R. Calhoun, G.S. Schlau-Cohen, G.R. Fleming, PHYSICAL CHEMISTRY CHEMICAL PHYSICS 12 (27), 7319-7337, 2010.
3. Quantum entanglement in photosynthetic light-harvesting complexes, M. Sarovar, A. Ishizaki, G.R. Fleming, K.B. Whaley, NATURE PHYSICS 6 (6), 462-467, JUN 2010.
4. Branching Relaxation Pathways from the Hot S2 State of 8′-apo-β-caroten-8′-al, Y. Pang, G.R. Fleming, PHYSICAL CHEMISTRY CHEMICAL PHYSICS 12 (25), 6782-6788, 2010.
5. Ishizaki, G.R. Fleming, NEW JOURNAL OF PHYSICS 12 (5), 055004, May 2010.
6. Ultrafast Spectroscopy of Midinfrared Internal Exciton Transitions in Separated Single-Walled Carbon Nanotubes, J. G. Wang, M. W. Graham,Y.-Z. Ma, G. R. Fleming, R. A. Kaindl, PHYSICAL REVIEW LETTERS 104 (17), APR 30 2010.
7. Exciton annihilation and dephasing dynamics in semiconducting single-walled carbon nanotubes, M. W. Graham, Y.-Z. Ma, G. R. Fleming, A.A. Green, M. C. Hersam, Ultrafast Phenomena in Semiconductors and Nanostructure materials, Proceedings of SPIE, 7600-7613, 2010.
8. Unusual Relaxation Pathway from the Two-Photon Excited First Singlet State of Carotenoids, Y. Pang, G. A. Jones, M. A. Prantil, G. R. Fleming, JOURNAL OF THE AMERICAN CHEMICAL SOCIETY 132 (7), 2264-2273, FEB 24 2010.
Uppdated 4.3.11.