On embeddings in cycles

We prove several exact results for the dilation of well-known interconnection networks in cycles, namely : ${\rm dil}(T_{t,r},C_{(t^{r-1}-1)/(r-1)})=\lceil t(t^{r-1}-1)/(2(r-1)(t-1))\rceil,$ for complete $r$-level $t$-ary trees, ${\rm dil}(Q_n,C_{2^n}) =\sum_{k=0}^{n-1}{k\choose \lfloor \frac{k}{2}\rfloor },$ for $n$-dimensional hypercubes, ${\rm dil}(P_n\times P_n\times P_n,C_{n^3})= \lfloor 3n^2/4+n/2\rfloor,$ for 3-dimensional meshes (where $P_n$ is an $n$-vertex path) and ${\rm dil}(P_m\times P_n,C_{mn})= {\rm dil}(C_m\times P_n,C_{mn})={\rm dil}(C_m\times C_n,C_{mn})=\min\{m,n\},$ for 2-dimensional ordinary, cylindrical and toroidal meshes, respectively. The last results solve three remaining open problems of the type $"{\rm dil}(X\times Y, Z)=?"$, where $X,\ Y$ and $Z$ are paths or cycles. The previously known dilations are: ${\rm dil}(P_m\times P_n,P_{mn})= \min \{m,n\}$, ${\rm dil}(C_m\times P_n,P_{mn})=\min \{m,2n\}$ and ${\rm dil}(C_m\times C_n,P_{mn}) =2\min \{m,n\}$, if $m\neq n$, otherwise ${\rm dil}(C_n\times C_n)=2n-1$ . The proofs of the above stated results are based on the following technique. We find a suficient condition for a graph $G$ which assures the equality ${\rm dil}(G,C_n)={\rm dil}(G,P_n)$. We prove that trees, X-trees, meshes, hypercubes, pyramides and tree of meshes satisfy the condition. Using known optimal dilations of complete trees, hypercubes and 2- and 3-dimensional meshes in path we get the above exact result

Is livestock grazing a key factor for changing vegetation patterns in lime rich coastal dunes in the Netherlands?

In 1990, livestock grazing was introduced in Meijendel, a 1800 ha lime-rich coastal dune area, at a density of 0.06–0.07 LLU.ha-1.year−1 (1:12–18 ha) to counteract encroachment of tall grasses and shrubland on dune grassland and increase the bare sand area. Monitoring was based on four digital orthophotos (1975–1990–2001-2009) with a high spatial resolution (pixel size 25 × 25 cm). The changes were tested using Generalized Estimating Equations. Habitat changes occurred, but contradicting our hypothesis, there was no significant impact from the grazing on bare sand, grassland or shrubland within 11 and 19 years post livestock introduction. (1) After several decennia of decreasing bare sand, there was a significant increase between 2001 and 2009, irrespective of livestock presence. (2) The changes in grasslands and shrublands are independent of the livestock, but dependent on distance to the coast. (3) Bare sand and shrub cover determine the space left for the dune grasslands. It appears other factors than livestock grazing must have induced the changes. Changes in climate conditions and nitrogen load might have stimulated bare sand. An interaction with the end of Marram planting in 1990 cannot be concluded from available data. The disease-led reduction of rabbit grazing from the mid-1950s led to an expansion of the dominant shrub Hippophae rhamnoides. However, Hippophae shrubland typically regresses to grasslands on its collapse after 25–40 years. Tree species like Crataegus, Betula and Quercus will gradually dominate the landscape for far longer. Active removal of these indigenous species is necessary to prevent future loss of dune grasslands.</p

On the Point-Splitting Method of the Commutator Anomaly of the Gauss Law Operators

We analyze the generalized point-splitting method and Jo's result for the commutator anomaly. We find that certain classes of general regularization kernels satisfying integral conditions provide a unique result, which, however differs from Faddeev's cohomological result.Comment: 16 pages, RevTex, 1 figure + 1 table, uses psbox.te

Parameter Identification in a Probabilistic Setting

Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g. through a measurement, by connecting it to Bayes's theorem. The unknown quantity is modelled as a (may be high-dimensional) random variable. Such a description has two constituents, the measurable function and the measure. One group of methods is identified as updating the measure, the other group changes the measurable function. We connect both groups with the relatively recent methods of functional approximation of stochastic problems, and introduce especially in combination with the second group of methods a new procedure which does not need any sampling, hence works completely deterministically. It also seems to be the fastest and more reliable when compared with other methods. We show by example that it also works for highly nonlinear non-smooth problems with non-Gaussian measures.Comment: 29 pages, 16 figure

Quantum Bayes rule

We state a quantum version of Bayes's rule for statistical inference and give a simple general derivation within the framework of generalized measurements. The rule can be applied to measurements on N copies of a system if the initial state of the N copies is exchangeable. As an illustration, we apply the rule to N qubits. Finally, we show that quantum state estimates derived via the principle of maximum entropy are fundamentally different from those obtained via the quantum Bayes rule.Comment: REVTEX, 9 page

Sample-Averaged Biexciton Quantum Yield Measured by Solution-Phase Photon Correlation

The brightness of nanoscale optical materials such as semiconductor nanocrystals is currently limited in high excitation flux applications by inefficient multiexciton fluorescence. We have devised a solution-phase photon correlation measurement that can conveniently and reliably measure the average biexciton-to-exciton quantum yield ratio of an entire sample without user selection bias. This technique can be used to investigate the multiexciton recombination dynamics of a broad scope of synthetically underdeveloped materials, including those with low exciton quantum yields and poor fluorescence stability. Here, we have applied this method to measure weak biexciton fluorescence in samples of visible-emitting InP/ZnS and InAs/ZnS core/shell nanocrystals, and to demonstrate that a rapid CdS shell growth procedure can markedly increase the biexciton fluorescence of CdSe nanocrystals.United States. Dept. of Energy. Office of Basic Energy Sciences (DE-FG02-07ER46454)United States. Dept. of Energy. Office of Basic Energy Sciences (DE-SC0001088)National Institutes of Health (U.S.) (9P41EB015871-26A1

The Winchcombe meteorite, a unique and pristine witness from the outer solar system.

Direct links between carbonaceous chondrites and their parent bodies in the solar system are rare. The Winchcombe meteorite is the most accurately recorded carbonaceous chondrite fall. Its pre-atmospheric orbit and cosmic-ray exposure age confirm that it arrived on Earth shortly after ejection from a primitive asteroid. Recovered only hours after falling, the composition of the Winchcombe meteorite is largely unmodified by the terrestrial environment. It contains abundant hydrated silicates formed during fluid-rock reactions, and carbon- and nitrogen-bearing organic matter including soluble protein amino acids. The near-pristine hydrogen isotopic composition of the Winchcombe meteorite is comparable to the terrestrial hydrosphere, providing further evidence that volatile-rich carbonaceous asteroids played an important role in the origin of Earth's water

Certified reference materials for radionuclides in Bikini Atoll sediment (IAEA-410) and Pacific Ocean sediment (IAEA-412)

The preparation and characterization of certified reference materials (CRMs) for radionuclide content in sediments collected offshore of Bikini Atoll (IAEA-410) and in the open northwest Pacific Ocean (IAEA-412) are described and the results of the certification process are presented. The certified radionuclides include: 40K, 210Pb (210Po), 226Ra, 228Ra, 228Th, 232Th, 234U, 238U, 239Pu, 239+240Pu and 241Am for IAEA-410 and 40K, 137Cs, 210Pb (210Po), 226Ra, 228Ra, 228Th, 232Th, 235U, 238U, 239Pu, 240Pu and 239+240Pu for IAEA-412. The CRMs can be used for quality assurance and quality control purposes in the analysis of radionuclides in sediments, for development and validation of analytical methods and for staff training