Broad histograms

One particular case of Eq. (A 12) has attracted considerable attention. If one sets M = E and considers the infinite temperature limit, the probabilities of the macrostates ) and Ej can be replaced by the associated values of the density-of-states function G(Ej) and G(Ej). The resulting equation has been christened the broad-histogram relation [128] it forms the core of extensive studies of transition probability methods referred to variously as flat histogram [129] and transition matrix [130]. Applications of these formulations seem to have been restricted to the situation where the energy is the macrovariable, and the energy spectmm is discrete. 

Y. Wu, M. Kbrner, L. Coloima-Romano, S. Trebst, H. Gould, J. Machta, and M. Troyer (2005) Overcoming the critical slowing down of fiat-histogram Monte Carlo simulations Cluster updates and optimized broad-histogram ensembles. Phys. Rev. E 72, p. 046704... 

Figure 17a shows, as an example, the plateau data-point histograms of T3 at three bias voltages. Each histogram, constructed from more than 1,000 individual traces, reveals a distinct maximum. The peak positions from individual experiments are very reproducible for low bias voltages Vbias < 0-30 V. The broad asymmetric tail region toward higher conductance values is attributed to contributions from... 

The histograms of Fig. 7 indicate that the distributions are extremely broad and complex. 

The energy landscape approach can elucidate such general properties of molecular recognition as the nature of the thermodynamic phases and barriers on the ligand-protein association pathway [127,128]. This method evaluates equilibrium thermodynamic properties of the system from Monte Carlo simulations of the system at a broad temperature range with the aid of the optimized data analysis and the weighted histogram analysis technique [148-153],... 

Fig. 15.5. Transformation of force-extension traces into the molecular coordinate contour length, (a) The rupture force and the extension xi and X2 are subject to fluctuations and exhibit a broad distribution. Furthermore, they depend on experimental parameters as described in the text. The characteristic parameter of a folding state is the free contour length as illustrated in (b). Each data point (Fi, Xi) is transformed into force-contour length space (Fi, Li) by means of inverse models for polymer elasticity. The transformed data points are accumulated into histograms, which directly show the barrier positions Li and L2 along the contour length, (c) The barrier positions of TK in the absence (black) and presence (red) of ATP were determined with a relative error of 2% corresponding to only a few amino acids. The number of amino acids (346 6) agrees well with the actual number (344). (b) Ig/Fn domains serve as an internal verification. The determined mean number of 95 2 amino acids agrees again with the value of 96 aa...

Fig. 1. Relative probability histograms of Slave craton detrital zircons (continuous curve with black infill below based on data from Sircombe et al. 2001), Ar/ Ar ages of impact spherules in lunar soil samples (dash-dot curve after Culler et al. 2000), and Ar/ Ar ages of impact glasses in lunar meteorites (dashed curve after Cohen et al. 2000). Time interval spans from 4500 Ma, the approximate age of formation of the Moon, to 2500 Ma, the defined Archaean-Proterozoic boundary. Vertical scales of the three curves are independent. Shaded age bars with roman numerals represent main events in basement of the Slave craton that were initially defined on the basis of individual rock age and their inheritance (see Bleeker Davis 1999). The detrital zircon data represent c. 300 zircon grains from five widely distributed samples of a c. 2800 Ma quartzite unit overlying the Mesoarchaean to Hadean-age basement complex of the Slave craton. These data represent a least-biased record of pre-2.8 Ga components of the Slave craton. The broad complementarity in the datasets should be noted. With the first major peak in Slave crustal ages (event V 3100-3200 Ma) immediately following the last major peak in the lunar spherule data. Both lunar soil and meteorite data sets support a lunar cataclysm or late heavy bombardment that appears to have erased or swamped out the pre-4.0Ga lunar record.

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