Related papers: Probability Distributions of Positioning Errors fo…
The center of gravity is one of the most frequently used algorithm for position reconstruction with different analytical forms for the noise optimization. The error distributions of the different forms are essential instruments to improve…
To complete a previous paper, the probability density functions of the center-of-gravity as positioning algorithm are derived with classical methods. These methods, as suggested by the textbook of Probability, require the preliminary…
To complete a previous work, the probability density functions for the errors in the center-of-gravity as positioning algorithm are derived with the usual methods of the cumulative distribution functions. These methods introduce substantial…
The construction of a well tuned probability distributions is illustrated in synthetic way, these probability distributions produce faithful realizations of the impact point distributions for particles in silicon strip detector. Their use…
The realistic probability distributions of a previous article are applied to the reconstruction of tracks in constant magnetic field. The complete forms and their schematic approximations produce excellent momentum estimations, drastically…
The optimizations of the track fittings require complex simulations of silicon strip detectors to be compliant with the fundamental properties of the hit heteroscedasticity. Many different generations of random numbers must be available…
An experimental set up, dedicated to isolate an error present in the $\eta$-algorithm, gave an unexpected result. The average of a center of gravity algorithm at orthogonal particle incidence turns out to be non zero. This non zero average…
The center of gravity $x_{g}= \sum_{i}E_{i} x_{i}/\sum_{i} E_{i}$ as an algorithm for position measurements is carefully analyzed. Many mathematical consequences of discretization are extracted. The origin of the systematic error of the…
The center of gravity as an algorithm for position measurements is analyzed for a two-dimensional geometry. Several mathematical consequences of discretization for various types of detector arrays are extracted. Arrays with rectangular,…
The algorithms for position reconstruction in silicon micro-strip detectors are studied, and the signals of a minimum ionizing particle are simulated. The center-of-gravity distributions of the data events allow the fine tuning of the…
In our paper published earlier we discussed forecasts of earthquake focal mechanism and ways to test the forecast efficiency. Several verification methods were proposed, but they were based on ad-hoc, empirical assumptions, thus their…
We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods -- geometric fit, Kasa fit, Pratt fit, and Taubin fit -- is…
A simple way of obtaining robust estimates of the "center" (or the "location") and of the "scatter" of a dataset is to use the maximum likelihood estimate with a class of heavy-tailed distributions, regardless of the "true" distribution…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
We study statistics of the gaps in Random Average Process (RAP) on a ring with particles hopping symmetrically, except one tracer particle which could be driven. These particles hop either to the left or to the right by a random fraction…
The topic of the paper is the position reconstruction from signals of segmented detectors. With the help of a simple simulation, it is shown that the position reconstruction using the centre-of-gravity method is strongly biased, if the…
Estimates of seismic wave speeds in the Earth (seismic velocity models) are key input parameters to earthquake simulations for ground motion prediction. Owing to the non-uniqueness of the seismic inverse problem, typically many velocity…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
Many astrophysical analyses depend on estimates of redshifts (a proxy for distance) determined from photometric (i.e., imaging) data alone. Inaccurate estimates of photometric redshift uncertainties can result in large systematic errors.…
In this paper, we discuss the worst-case of distortion riskmetrics for general distributions when only partial information (mean and variance) is known. This result is applicable to general class of distortion risk measures and variability…