A Conway–Maxwell–Poisson (CMP) model to address data dispersion on positron emission tomography

Positron emission tomography (PET) in medicine exploits the properties of positron-emitting unstable nuclei. The pairs of γ- rays emitted after annihilation are revealed by coincidence detectors and stored as projections in a sinogram. It is well known that radioactive decay follows a Poisson distribution; however, deviation from Poisson statistics occurs on PET projection data prior to reconstruction due to physical effects, measurement errors, correction of deadtime, scatter, and random coincidences. A model that describes the statistical behavior of measured and corrected PET data can aid in understanding the statistical nature of the data: it is a prerequisite to develop efficient reconstruction and processing methods and to reduce noise. The deviation from Poisson statistics in PET data could be described by the Conway-Maxwell-Poisson (CMP) distribution model, which is characterized by the centring parameter λ and the dispersion parameter ν, the latter quantifying the deviation from a Poisson distribution model. In particular, the parameter ν allows quantifying over-dispersion (ν<1) or under-dispersion (ν>1) of data. A simple and efficient method for λ and ν parameters estimation is introduced and assessed using Monte Carlo simulation for a wide range of activity values. The application of the method to simulated and experimental PET phantom data demonstrated that the CMP distribution parameters could detect deviation from the Poisson distribution both in raw and corrected PET data. It may be usefully implemented in image reconstruction algorithms and quantitative PET data analysis, especially in low counting emission data, as in dynamic PET data, where the method demonstrated the best accuracy

Series in Le Roy Type Functions: Theorems in the Complex Plane

Series defined by means of the Le Roy type functions are considered in this paper. These series are studied in the complex plane and their behaviour is investigated ‘near’ the boundaries of their domains of convergence.Bilateral Res. Projects ‘Operators, differential equations and special functions of Fractional Calculus – numerics and applications’ between BAS and SANU and ‘Analysis, Geometry and Topology’ between BAS and MANU; COST program, COST Action CA15225 ‘Fractional’

Series in Le Roy Type Functions: A Set of Results in the Complex Plane-A Survey

This study is based on a part of the results obtained in the author’s publications. An enumerable family of the Le Roy type functions is considered herein. The asymptotic formula for these special functions in the cases of ‘large’ values of indices, that has been previously obtained, is provided. Further, series defined by means of the Le Roy type functions are considered. These series are studied in the complex plane. Their domains of convergence are given and their behaviour is investigated ‘near’ the boundaries of the domains of convergence. The discussed asymptotic formula is used in the proofs of the convergence theorems for the considered series. A theorem of the Cauchy–Hadamard type is provided. Results of Abel, Tauber and Littlewood type, which are analogues to the corresponding theorems for the classical power series, are also proved. At last, various interesting particular cases of the discussed special functions are considered

Reports to the President

A compilation of annual reports for the 1999-2000 academic year, including a report from the President of the Massachusetts Institute of Technology, as well as reports from the academic and administrative units of the Institute. The reports outline the year's goals, accomplishments, honors and awards, and future plans

The HBP1 tumor suppressor is a negative epigenetic regulator of MYCN driven neuroblastoma through interaction with the PRC2 complex

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