Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation

It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The integer part is a discrete random variable (we call it Planck variable) whose distribution is just the Bose distribution yielding the Planck law of black-body radiation. The fractional part is the dark part (we call is dark variable) with a continuous distribution, which is, of course, not observed in the experiments. It is proved that the Bose distribution is infinitely divisible, and the irreducible decomposition of it is given. The Planck variable can be decomposed into an infinite sum of independent binary random variables representing the binary photons (more accurately photo-molecules or photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons follow the Fermi statistics. Consequently, the black-body radiation can be viewed as a mixture of statistically and thermodynamically independent fermion gases consisting of binary photons. The binary photons give a natural tool for the dyadic expansion of arbitrary (but not coherent) ordinary photon excitations. It is shown that the binary photons have wave-particle fluctuations of fermions. These fluctuations combine to give the wave-particle fluctuations of the original bosonic photons expressed by the Einstein fluctuation formula.Comment: 29 page

The reproductive biology of the porbeage shark (Lamna nasus) in the western North Atlantic Ocean

Reproductive organs from 393 male and 382 female porbeagles (Lamna nasus), caught in the western North Atlantic Ocean, were examined to determine size at maturity and reproductive cycle. Males ranged in size from 86 to 246 cm fork length (FL) and females ranged from 94 to 288 cm FL. Maturity in males was best described by an inflection in the relationship of clasper length to fork length when combined with clasper calcification. Males matured between 162 and 185 cm FL and 50% were mature at 174 cm FL. In females, all reproductive organ measurements related to body length showed a strong inflection around the size of maturity. Females matured between 210 and 230 cm FL and 50% were mature at 218 cm FL. After a protracted fall mating period (September–November), females give birth to an average of 4.0 young in spring (April−June). As in other lamnids, young are nourished through oophagy. Evidence from this study indicated a one-year reproductive cycle and gestation period lasting 8–9 months

Einstein's fluctuation formula. A historical overview

A historical overview is given on the basic results which appeared by the year 1926 concerning Einstein's fluctuation formula of black-body radiation, in the context of light-quanta and wave-particle duality. On the basis of the original publications (from Planck's derivation of the black-body spectrum and Einstein's introduction of the photons up to the results of Born, Heisenberg and Jordan on the quantization of a continuum) a comparative study is presented on the first line of thoughts that led to the concept of quanta. The nature of the particle-like fluctuations and the wave-like fluctuations are analysed by using several approaches. With the help of the classical probability theory, it is shown that the infinite divisibility of the Bose distribution leads to the new concept of classical poissonian photo-multiplets or to the binary photo-multiplets of fermionic character. As an application, Einstein's fluctuation formula is derived as a sum of fermion type fluctuations of the binary photo-multiplets.Comment: 34 page

Application of Bomb Radiocarbon Chronologies to Shortfin Mako (Isurus oxyrinchus)

There is an ongoing disagreement regarding the aging of the shortfin mako due to a difference of interpretation in the periodic deposition of vertebral growth band pairs, especially for the larger size classes. Using analysis of length-month information, tagging data, and length-frequency analysis, concluded that two band pairs were formed in the vertebral centrum every year (biannual band-pair interpretation). Cailliet et al. (1983), however, presented growth parameters based on the common assumption that one band pair forms annually (annual band-pair interpretation). Therefore, growth rates obtained by Pratt & Casey (1983) were twice that of Cailliet et al. (1983) and could lead to age discrepancies of about 15 years for maximum estimated ages on the order of 30 from the annual band-pair interpretation. Serious consequences in the population dynamics could occur for this species if inputs are based on an invalid age interpretation. The latest Fishery Management Plan (FMP) for Highly Migratory Species (HMS), for example, adopted the biannual band pair deposition hypothesis because it apparently fit the observed growth patterns best (Pacific Fishery Management Council 2003). However, the ongoing uncertainty about the aging of the shortfin mako was acknowledged and it was recommended that an endeavor to resolve this issue be made. Since 1983, five additional studies on the age and growth of the shortfin mako have been conducted (Chan 2001, Campana et al. 2002, Hsu 2003, Ribot-Carballal et al. 2005, Bishop et al. 2006). Using Marginal Increment Ratio (MIR), Hsu (2003) indicated the formation of annual translucent bands from July to September in western North Pacific Ocean shortfin makos. Using Marginal Increment Analysis (MIA) Ribot-Carballal et al. (2005) supported the annual band-pair interpretation for 109 shortfin makos collected in the eastern Pacific Ocean. Although the study provided support for annual band-pair deposition, no statistical test was performed and the number of samples for MIA analysis was insufficient for some months. Hence, unequivocal validation of shortfin mako age estimates has yet to be accomplished. Atmospheric testing of thermonuclear devices in the 1950s and 1960s effectively doubled the natural atmospheric radiocarbon ({sup 14}C). The elevated {sup 14}C levels were first recorded in 1957-58, with a peak around 1963. As a consequence, {sup 14}C entered the ocean through gas exchange with the atmosphere at the ocean surface and in terrestrial runoff. Despite variable oceanographic conditions, a worldwide rise of the bomb {sup 14}C signal entered the ocean mixed layer as dissolved inorganic carbon (DIC) in 1957-58. The large amounts of {sup 14}C released from the bomb tests produced a signature that can be followed through time, throughout the marine food web, and into deeper waters. The marked increase of radiocarbon levels was first measured in the DIC of seawater and in biogenic marine carbonates of hermatypic corals in Florida. Subsequently, this record was documented in corals from other regions and in the thallus of rhodoliths. The accumulation of radiocarbon in the hard parts of most marine organisms in the mixed layer (such as fish otoliths and bivalves) was synchronous with the coral time-series. This technique has been used to validate age estimates and longevity of numerous bony fishes to date, as well as to establish bomb radiocarbon chronologies from different oceans. In the first application of this technique to lamnoid sharks, validated annual band-pair deposition in vertebral growth bands for the porbeagle (Lamna nasus) aged up to 26 years. Radiocarbon values from samples obtained from 15 porbeagle caught in the western North Atlantic Ocean (some of which were known-age) produced a chronology similar in magnitude to the reference carbonate chronology for that region. The observed phase shift of about 3 years was attributed to different sources of carbon between vertebrae and those for otoliths, bivalves and corals. In the same study by Campana et al. (2002), a single vertebra from a shortfin mako caught in 1977 was aged at 21 and 10 years, using the annual versus the biannual deposition hypotheses, respectively. Vertebral samples were extracted from the first, last, and two intermediate bands and were assayed for radiocarbon. The results indicated the aging interpretation for the vertebra from this fish best fit the timing of the porbeagle time-series by adopting the annual band-pair interpretation. To provide a more comprehensive basis for valid aging criteria and a definitive growth function for the shortfin mako, more radiocarbon assays were required. The goal of our research was to take heed of this suggestion and continue the use of bomb radiocarbon to validate the aging of the shortfin mako, and specifically to resolve the validity of either annual or biannual band-pair age interpretations

Global Phylogeography of the Dusky Shark Carcharhinus obscurus: Implications for Fisheries Management and Monitoring the Shark Fin Trade

Genetic stock structure information is needed to delineate management units and monitor trade in sharks, many of which are heavily exploited and declining. The dusky shark Carcharhinus obscurus is a large apex predator that is sought after for its fins and is considered highly susceptible to overexploitation. The International Union for the Conservation of Nature (IUCN) classifies this species as ‘Vulnerable’ globally and ‘Endangered’ in the northwest Atlantic. We make the first assessment of global stock structure of C. obscurus by analyzing part of the mitochondrial control region (mtCR) in 255 individuals sampled from 8 geographically dispersed locations. We found 25 mtCR haplotypes and rejected a null hypothesis of panmixia (analysis of molecular variance, ΦST = 0.55, p \u3c 0.000001), detecting significant differentiation between 3 management units: US Atlantic (USATL), South Africa (SAF), and Australia (AUS). We also found preliminary evidence of population structure between the USATL and southwest Atlantic (Brazil). There were no shared haplotypes between the western Atlantic and Indo-Pacific. These analyses suggest that replenishment of the collapsed USATL management unit via immigration of females from elsewhere is unlikely. Mixed stock analysis (MSA) simulations show that reconstruction of the relative contributions of USATL, SAF, and AUS management units to the Asian fin trade is possible using these mtCR sequences. We suggest avenues for obtaining samples to conduct MSA of the shark fin trade, which could enhance management of dusky sharks and other species that are exploited for their fins

An elementary proof of an equivalence theorem relevant in the theory of optimization

The authors give an elementary proof of an equivalence theorem of analysis which is often used in optimization theory. The theorem asserts that certain conditions are equivalent to weak convergence in L 1 . One is the Dunford-Pettis condition concerning absolute integrability. Two others are expressed in terms of Nagumo functions, and can be thought of as growth properties. The original proofs of the various parts of the theorem are scattered in different and specialized mathematical publications. The authors feel it useful to present here a straightforward proof of the various parts in terms of standard Lebesgue integration theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45221/1/10957_2004_Article_BF00938425.pd

Engineering tyrosine-based electron flow pathways in proteins: The case of aplysia myoglobin

Tyrosine residues can act as redox cofactors that provide an electron transfer ("hole-hopping") route that enhances the rate of ferryl heme iron reduction by externally added reductants, for example, ascorbate. Aplysia fasciata myoglobin, having no naturally occurring tyrosines but 15 phenylalanines that can be selectively mutated to tyrosine residues, provides an ideal protein with which to study such through-protein electron transfer pathways and ways to manipulate them. Two surface exposed phenylalanines that are close to the heme have been mutated to tyrosines (F42Y, F98Y). In both of these, the rate of ferryl heme reduction increased by up to 3 orders of magnitude. This result cannot be explained in terms of distance or redox potential change between donor and acceptor but indicates that tyrosines, by virtue of their ability to form radicals, act as redox cofactors in a new pathway. The mechanism is discussed in terms of the Marcus theory and the specific protonation/deprotonation states of the oxoferryl iron and tyrosine. Tyrosine radicals have been observed and quantified by EPR spectroscopy in both mutants, consistent with the proposed mechanism. The location of each radical is unambiguous and allows us to validate theoretical methods that assign radical location on the basis of EPR hyperfine structure. Mutation to tyrosine decreases the lipid peroxidase activity of this myoglobin in the presence of low concentrations of reductant, and the possibility of decreasing the intrinsic toxicity of hemoglobin by introduction of these pathways is discussed. © 2012 American Chemical Society

Quasi-normal frequencies: Key analytic results

The study of exact quasi-normal modes [QNMs], and their associated quasi-normal frequencies [QNFs], has had a long and convoluted history - replete with many rediscoveries of previously known results. In this article we shall collect and survey a number of known analytic results, and develop several new analytic results - specifically we shall provide several new QNF results and estimates, in a form amenable for comparison with the extant literature. Apart from their intrinsic interest, these exact and approximate results serve as a backdrop and a consistency check on ongoing efforts to find general model-independent estimates for QNFs, and general model-independent bounds on transmission probabilities. Our calculations also provide yet another physics application of the Lambert W function. These ideas have relevance to fields as diverse as black hole physics, (where they are related to the damped oscillations of astrophysical black holes, to greybody factors for the Hawking radiation, and to more speculative state-counting models for the Bekenstein entropy), to quantum field theory (where they are related to Casimir energies in unbounded systems), through to condensed matter physics, (where one may literally be interested in an electron tunelling through a physical barrier).Comment: V1: 29 pages; V2: Reformatted, 31 pages. Title changed to reflect major additions and revisions. Now describes exact QNFs for the double-delta potential in terms of the Lambert W function. V3: Minor edits for clarity. Four references added. No physics changes. Still 31 page

Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum

A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any desired order. This leads to an efficient procedure to compute quantum reaction rates and the associated Gamov-Siegert resonances. In the classical limit the QNF reduces to the classical normal form which leads to the recently developed phase space realisation of Wigner's transition state theory. It is shown that the phase space structures that govern the classical reaction d ynamicsform a skeleton for the quantum scattering and resonance wavefunctions which can also be computed from the QNF. Several examples are worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008) R1-R11