Correlation functions and correlation times for models with multiplicative white noise

Correlation functions and correlation times for the Stratonovich and Verhulst model are investigated. By transforming the Fourier transform of the corresponding Fokker-Planck equation into a tridiagonal vector recurrence relation, the Fourier transform of the correlation function and the correlation time are expressed in terms of matrix continued fractions or by similar iterations and are thus obtained numerically. By using the inverse Fourier transform, the correlation function itself is calculated. Furthermore an analytic expression in terms of an integral is obtained for the correlation time, which is evaluated exactly in the Verhulst model and asymptotically for large and weak noise strength in the Stratonovich model. A Padé expansion approximating the correlation time for all noise strength is also given.     

Evaluation of the dosimetric characteristics of a radiophotoluminescent glass dosimeter for high-energy photon and electron beams in the field of radiotherapy

We aimed to evaluate the suitability of a glass dosimeter (GD) for high-energy photon and electron beams in experimental and clinical use, especially for radiation therapy. We examined the expanded dosimetric characteristics of GDs including dose linearity up to 500 Gy, uniformity among GD lots and for individual GDs, the angular dependence, and energy dependence of 4 therapeutic x-ray qualities. In addition, we measured the dosimetric features (dose linearity, uniformity, angular dependence, and energy dependence) of the GD for electron beams of 10 different electron energy qualities. All measurements with the exception of dose linearity for photon beam were performed in a water phantom. For high-energy photon beams, dose linearity has a linear relationship for a dose ranging from 1 to 500 Gy with the coefficient of determination; R² of 0.998. The uniformity of each GD of dose measurements was within ±0.5% for four GD lots and within ±1.2% for 80 GDs. In terms of the effects of photon beam angle, lower absorbed doses of within 1.0% were observed between 60° and 105° than at 90°. The GD energy dependence of 4 photon beam energy qualities was within ±2.0%. On the other hand, the result of the dose linearity for high-energy electron beams showed well fitted regression line with the coefficient of determination; R² of 0.999 between 6 and 20 MeV. The uniformity of GDs exposed to the nominal electron energies 6, 9, 12, 16, and 20 MeV was ±1.2%. In terms of the angular dependence to electron beams, absorbed doses were within 2.0% between 60° and 105° than at 90°. In evaluation of the energy dependence of the GD at nominal electron energies between 5 and 20 MeV, we obtained responses between 1.1% and 3.5% lower than that for a cobalt-60 beam. Our results show that GDs can be used as a detector for determining doses when a high-energy photon beam is used, and that it also has considerable potential for dose measurement of high-energy electron beam.     

Charged particle multiplicity distributions ine + e − annihilation at 29 GeV: a comparison with hadronic data

The charged particle multiplicity distributions for two-jet events ine ⁺ e ^? annihilation at 29 GeV have been measured using the High Resolution Spectrometer at PEP. A Poisson distribution describes the data for both the complete event and for the single jets. In addition, no correlation is observed between the multiplicities in the two jets of an event. For fixed values of the prong number of the complete event, the multiplicity sharing between the two jets is in good agreement with a binomial distribution. The rapidity gap distribution is exponential with a slope equal to the mean rapidity density. These observations, which are consistent with a picture of independent emission of single particles, are contrasted to the results from soft hadronic collisions and conclusions are drawn about the nature of clusters.     

A Decision Criterion for the Optimal Number of Clusters in Hierarchical Clustering

Clustering has been widely used to partition data into groups so that the degree of association is high among members of the same group and low among members of different groups. Though many effective and efficient clustering algorithms have been developed and deployed, most of them still suffer from the lack of automatic or online decision for optimal number of clusters. In this paper, we define clustering gain as a measure for clustering optimality, which is based on the squared error sum as a clustering algorithm proceeds. When the measure is applied to a hierarchical clustering algorithm, an optimal number of clusters can be found. Our clustering measure shows good performance producing intuitively reasonable clustering configurations in Euclidean space according to the evidence from experimental results. Furthermore, the measure can be utilized to estimate the desired number of clusters for partitional clustering methods as well. Therefore, the clustering gain measure provides a promising technique for achieving a higher level of quality for a wide range of clustering methods.     

Off-peak saturation effects of beam-plasma instability

For beam-plasma instability in the absence of a magnetic field, hybrid simulations produce almost identical results to those of particle simulations (both agree with linear and nonlinear analyses), but with much reduced computing cost and noise level. With the verification by simulations, it is shown that the saturation level is very strongly influenced by the discrete wave number spectrum, sometimes giving different, by an order of magnitude, results by choosing slightly different off-peak (in growth rate curve) parameters, which must be considered in most simulations (whether hybrid or particle or whether magnetized or unmagnetized)     

Dynamic Point Location in General Subdivisions

The dynamic planar point location problem is the task of maintaining a dynamic set S of n nonintersecting (except possibly at endpoints) line segments in the plane under the following operations:

• Locate (: point): Report the segment immediately above , i.e., the first segment intersected by an upward vertical ray starting at ;

• Insert (: segment): Add segment to the collection of segments;

• Delete (: segment): Remove segment from the collection of segments.

We present a solution which requires space O(n) and has query and insertion time O(log n log log n) and deletion time O(log²n). The bounds for insertions and deletions are amortized. A query time below O(log²n) was previously only known for monotone subdivisions and subdivisions consisting of horizontal segments and required nonlinear space.     

A remark on nilpotent Lie Algebras

Letf(n) denoted the number of essential parameters which are needed to classifyn-dimensional nilpotent Lie Algebras over the complex number field. Then $f(2n) \geqslant \tfrac{{n(n2 - 7)}}{6} - 2$ .