Performance of three-photon PET imaging: Monte Carlo simulations

We have recently introduced the idea of making use of three-photon positron annihilations in positron emission tomography. In this paper the basic characteristics of the three-gamma imaging in PET are studied by means of Monte Carlo simulations and analytical computations. Two typical configurations of human and small animal scanners are considered. Three-photon imaging requires high energy resolution detectors. Parameters currently attainable by CdZnTe semiconductor detectors, the technology of choice for the future development of radiation imaging, are assumed. Spatial resolution is calculated as a function of detector energy resolution and size, position in the field of view, scanner size, and the energies of the three gamma annihilation photons. Possible ways to improve the spatial resolution obtained for nominal parameters: 1.5 cm and 3.2 mm FWHM for human and small animal scanners, respectively, are indicated. Counting rates of true and random three-photon events for typical human and small animal scanning configurations are assessed. A simple formula for minimum size of lesions detectable in the three-gamma based images is derived. Depending on the contrast and total number of registered counts, lesions of a few mm size for human and sub mm for small animal scanners can be detected

Volatility clustering and scaling for financial time series due to attractor bubbling

A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time thermal bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering. For a proper choice of the model parameters the probability distributions of returns exhibit power-law tails with scaling exponents close to the empirical ones.Comment: For related publications see http://www.helbing.or

U.S. stock market interaction network as learned by the Boltzmann Machine

We study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented analysis shows that binarization preserves market correlation structure. Properties of distributions of external fields and couplings as well as industry sector clustering structure are studied for different historical dates and moving window sizes. We found that a heavy positive tail in the distribution of couplings is responsible for the sparse market clustering structure. We also show that discrepancies between the model parameters might be used as a precursor of financial instabilities.Comment: 15 pages, 17 figures, 1 tabl

Recovery and normalization of triple coincidences in PET

Purpose: Triple coincidences in positron emission tomography (PET) are events in which three γ-rays are detected simultaneously. These events, though potentially useful for enhancing the sensitivity of PET scanners, are discarded or processed without special consideration in current systems, because there is not a clear criterion for assigning them to a unique line-of-response (LOR). Methods proposed for recovering such events usually rely on the use of highly specialized detection systems, hampering general adoption, and/or are based on Compton-scatter kinematics and, consequently, are limited in accuracy by the energy resolution of standard PET detectors. In this work, the authors propose a simple and general solution for recovering triple coincidences, which does not require specialized detectors or additional energy resolution requirements.Methods: To recover triple coincidences, the authors’ method distributes such events among their possible LORs using the relative proportions of double coincidences in these LORs. The authors show analytically that this assignment scheme represents the maximum-likelihood solution for the triple-coincidence distribution problem. The PET component of a preclinical PET/CT scanner was adapted to enable the acquisition and processing of triple coincidences. Since the efficiencies for detecting double and triple events were found to be different throughout the scanner field-of-view, a normalization procedure specific for triple coincidences was also developed. The effect of including triple coincidences using their method was compared against the cases of equally weighting the triples among their possible LORs and discarding all the triple events. The authors used as figures of merit for this comparison sensitivity, noise-equivalent count (NEC) rates and image quality calculated as described in the NEMA NU-4 protocol for the assessment of preclinical PET scanners.Results: The addition of triple-coincidence events with the authors’ method increased peak NEC rates of the scanner by 26.6% and 32% for mouse- and rat-sized objects, respectively. This increase in NEC-rate performance was also reflected in the image-quality metrics. Images reconstructed using double and triple coincidences recovered using their method had better signal-to-noise ratio than those obtained using only double coincidences, while preserving spatial resolution and contrast. Distribution of triple coincidences using an equal-weighting scheme increased apparent system sensitivity but degraded image quality. The performance boost provided by the inclusion of triple coincidences using their method allowed to reduce the acquisition time of standard imaging procedures by up to ∼25%.Conclusions: Recovering triple coincidences with the proposed method can effectively increase the sensitivity of current clinical and preclinical PET systems without compromising other parameters like spatial resolution or contrast.This work was funded by Consejería de Educación, Juventud y Deporte de la Comunidad de Madrid (Spain) through the Madrid-MIT M + Visión Consortium. The authors also acknowledge the company Sedecal S.A. (Madrid, Spain) and the M + Visión Faculty for their support during this work.Publicad

Strategies for an Efficient Official Publicity Campaign

We consider the process of opinion formation, in a society where there is a set of rules B that indicates whether a social instance is acceptable. Public opinion is formed by the integration of the voters’ attitudes which can be either conservative (mostly in agreement with B) or liberal (mostly in disagreement with B and in agreement with peer voters). These attitudes are represented by stable fixed points in the phase space of the system. In this article we study the properties of a perturbative term, mimicking the effects of a publicity campaign, that pushes the system from the basin of attraction of the liberal fixed point into the basin of the conservative point, when both fixed points are equally likely

Nuclear Interactions Of Super High Energy Cosmic-rays Observed In Mountain Emulsion Chambers

Here we present a summary of joint discussions on the results of three mountain experiments with large-scale emulsion chambers, at Pamir, Mt. Fuji and Chacaltaya. Observations cover gamma quanta, hadrons and their clusters (called "families"). The following topics are covered, concerning the characteristics of nuclear interactions the energy region 1014-1016 eV: (i) rapid dissipation seen in atmospheric diffusion of high-energy cosmic-rays; (ii) multiplicity and Pt increase in produced pi-mesons in the fragmentation region; (iii) existence of large-Pt jets, (iv) extremely hadron-rich family of the Centauro type; (v) exotic phenomena in the extremely high energy region beyond 1016 eV. © 1981.1911125(1977) Acta Univ. Lodz ser. II, (60)(1973) 13th Int. Cosmic-ray Conf., 3, p. 2228(1975) 14th Int. Cosmic-Ray Conf., 7, p. 2365(1979) AIP Conf. Proc. no. 49, p. 334(1979) 16th Int. Cosmic-ray Conf., 6, p. 344(1979) 16th Int. Cosmic-ray Conf., 7, p. 6816th Int. Cosmic-ray Conf. (1979) 16th Int. Cosmic-ray Conf., 7, p. 284(1979) 16th Int. Cosmic-ray Conf., 7, p. 294(1979) 16th Int. Cosmic-ray Conf., 13, p. 87(1979) 16th Int. Cosmic-ray Conf., 13, p. 92(1979) 16th Int. Cosmic-ray Conf., 13, p. 98(1979) AIP Conf. Proc. no. 49, p. 94(1979) AIP Conf. Proc. no. 49, p. 145(1979) AIP Conf. Proc. no. 49, p. 317(1979) 16th Int. Cosmic-ray Conf., 6, p. 350(1979) 16th Int. Cosmic-ray Conf., 6, p. 356(1979) 16th Int. Cosmic-ray Conf., 6, p. 362Nikolsky, Proc. 9th Int. High-energy Symp. (1978) CSSR, 21. , ToborMiyake, (1978) Proc. 19th Int. Conf. on High-energy physics, p. 433Vernov, (1977) Physica, 3, p. 1601Khristiansen, (1978) JETP Lett., 28, p. 124(1973) 13th Int. Cosmic-ray Conf., 3, p. 2219Izv. Acad. Nauk USSR, ser Phys. (1974) Izv. Acad. Nauk USSR, ser Phys., 38, p. 918(1975) 14th Int. Cosmic-ray Conf., 7, p. 2365(1979) 16th Int. Cosmic-ray Conf., 7, p. 68Dunaevsky, Urysson, Emelyanov, Shorin, Tashimov, (1975) FIAN preprint no. 150Dunaevsky, Urysson, Emelyanov, Shorin, Tashinov, (1979) Acta Univ. Lodz ser. II, (60), p. 199Ivanenko, Kanevskya, Roganova, (1978) JETP Lett., 40, p. 704Ivanenko, Kanevsky, Roganova, (1979) 16th Int. Cosmic-ray Conf., 7, p. 101Ivanenko, Kanevsky, Roganova, (1979) 16th Int. Cosmic-ray Conf., 7, p. 198Wrotniak, (1977) Acta Univ. Lodz ser. II, (60), p. 165Krys, Tomaszevski, Wrotniak, (1979) 16th Int. Cosmic-ray Conf., 7, p. 182Krys, Tomaszevski, Wrotniak, (1979) 16th Int. Cosmic-ray Conf., 7, p. 186Fomin, Kempa, Khristiansen, Levina, Piotrowska, Wdowczyk, (1977) 15th Int. Cosmic-ray Conf., 7, p. 248Fomin, Kempa, Khristiansen, Levina, Piotrowska, Wdowczyk, (1979) 16th Int. Cosmic-ray Conf., 13, p. 82Azimov, Mullazhanov, Yuldashbayev, (1979) 16th Int. Cosmic-ray Conf., 7, p. 262Azimov, Mullazhanov, Yuldashbayev, (1977) Acta Univ. Lodz ser. II, (60), p. 275Kasahara, Torri, Yuda, (1979) 16th Int. Cosmic-ray Conf., 13, p. 70Kasahara, Torii, Yuda, (1979) 16th Int. Cosmic-ray Conf., 13, p. 79Shibata, (1979) 16th Int. Cosmic-ray Conf., 7, p. 176H. Semba, T. Shibata and T. Tabuki, Suppl. Prog. Theor. Phys., to be publishedZhdanov, Roinishvilli, Smorodin, Tomaszevski, (1975) FIAN preprint no. 163Lattes, Fujimoto, Hasegawa, Hadronic interactions of high energy cosmic-ray observed by emulsion chambers (1980) Physics Reports, 65, p. 152Ellsworth, Gaisser, Yodh, (1981) Phys. Rev., 23 D, p. 764Baradzei, Smorodin, (1974) FIAN preprint nos. 103, 104Baradzei, Smorodin, (1977) Acta Univ. Lodz ser. II, (60), p. 51Zhdanov, (1980) FIAN preprint no. 140H. Semba, T. Shibata and T. Tabuki, Suppl. Prog. Theor. Phys., to be publishedShibata, (1980) Phys. Rev., 22 D, p. 100Slavatinsky, (1980) Proc. 7th European Symp. on Cosmic rays, , Leningrad, to be published(1979) AIP Conference Proc. no. 49, p. 145Azimov, Abduzhamilov, Chudakov, (1963) JETP (Sov. Phys.), 45, p. 40713th Int. Cosmic-ray Conf. (1973) 13th Int. Cosmic-ray Conf., 5, p. 326Acharya, Rao, Sivaprasad, Rao, (1979) 16th Int. Cosmic-ray Conf., 6, p. 289Ellsworth, Goodman, Yodh, Gaisser, Stanev, (1981) Phys. Rev., 23 D, p. 771Bariburina, Guseva, Denisova, (1980) Acta Univ. Lodz, 1, p. 9415th Int. Cosmic-ray Conf. (1977) 15th Int. Cosmic-ray Conf., 7, p. 184(1979) AIP Conf. Proc. no. 49, p. 33

Numerical analysis of concentration distribution of floating particles in mechanically agitated suspension

W pracy przedstawiono wyniki symulacji numerycznych rozkładów stężenia cząstek lekkich w zawiesinie wytwarzanej w cylindrycznym zbiorniku z przegrodami i mieszadłem turbinowym z sześcioma łopatkami pochylonymi pod kątem 45°. Uzyskane numerycznie rozkłady stężeń cząstek w cieczy przedstawiono graficznie w postaci profili oraz konturów stężenia cząstek ciała stałego. Zidentyfikowano obszary stagnacji cząstek w objętości mieszanej cieczy.The results of numerical simulations concerning the concentration distribution of floating particles in suspension produced in an agitated vessel equipped with the baffles and pitched blade turbine (PBT 45) are presented. Numerically obtained distributions of particles concentration in liquid are shown in a form of profiles and contours. Stagnation regions for particles in the agitated liquid volume were identified

Modeling of turbulence kinetic energy distribution and their dissipation rate in mechanically agitated floating suspension of particles

Przedstawiono wyniki modelowania numerycznego energii kinetycznej burzliwości i szybkości jej dyssypacji w zbiorniku z mieszadłem do wytwarzania zawiesiny lekkiej. Uzyskano kontury oraz profi le tych wielkości dla burzliwego ruchu płynu w mieszalniku i trzech modeli burzliwości k-ε, k-ω, lub SST. Zidentyfikowano strefy, w których modelowane zmienne przyjmują największe wartości i w których rozpraszanie cząstek ciała stałego jest najbardziej efektywne.Results of numerical modeling of turbulence kinetic energy and its dissipation rate in mechanically agitated floating particles’ suspension are presented. Contours and profiles of these quantities were found for turbulent fluid flow in an agitated vessel and three turbulence 'models k-ε, k-ω or SST. The agitated vessel zones in which modeled quantities took the greatest values and where the best dispersion of floating particles was obtained were identified