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The J-PET scanner, which allows for single bed imaging of the whole human body, is currently under development at the Jagiellonian University. The dis- cussed detector offers improvement of the Time of Flight (TOF) resolution due to the use of fast plastic scintillators and dedicated electronics allowing for sam- pling in the voltage domain of signals with durations of few nanoseconds. In this paper we show that recovery of the whole signal, based on only a few samples, is possible. In order to do that, we incorporate the training signals into the Tikhonov regularization framework and we perform the Principal Component Analysis decomposition, which is well known for its compaction properties. The method yields a simple closed form analytical solution that does not require iter- ative processing. Moreover, from the Bayes theory the properties of regularized solution, especially its covariance matrix, may be easily derived. This is the key to introduce and prove the formula for calculations of the signal recovery error. In this paper we show that an average recovery error is approximately inversely proportional to the number of acquired samples.

J-PET analysis framework is a flexible, lightweight, ROOT-based software package which provides the tools to develop reconstruction and calibration procedures for PET tomography. In this article we present the implementation of the full data-processing chain in the J-PET framework which is used for the data analysis of the J-PET tomography scanner. The Framework incorporates automated handling of PET setup parameters' database as well as high level tools for building data reconstruction procedures. Each of these components is briefly discussed., Comment: 6 pages, 1 figure

In this article we present a novel method of hit time and hit position reconstruction in long scintillator detectors. We take advantage of the fact that for this kind of detectors amplitude and shape of registered signals depends strongly on the position where particle hit the detector. The reconstruction is based on determination of the degree of similarity between measured and averaged signals stored in a library for a set of well-defined positions along the scintillator. Preliminary results of validation of the introduced method with experimental data obtained by means of the double strip prototype of the J-PET detector are presented.

We present a fast GPU implementation of the image reconstruction routine, for a novel two strip PET detector that relies solely on the time of flight measurements.

Novel Positron Emission Tomography system, based on plastic scintillators, is developed by the J-PET collaboration. In order to optimize geometrical configuration of built device, advanced computer simulations are performed. Detailed study is presented of background given by accidental coincidences and multiple scattering of gamma quanta., Comment: 18 pages, 16 figures

For the first time a molecule of 2-(4-styrylphenyl)benzoxazole containing benzoxazole and stilbene groups is applied as a scintillator dopant acting as a wavelength shifter. In this article a light yield of the plastic scintillator, prepared from styrene doped with 2 wt% of 2,5-diphenylbenzoxazole and 0.03 wt% of 2-(4-styrylphenyl)benzoxazole, is determined to be as large as 60% $\pm$ 2% of the anthracene light output. There is a potential to improve this value in the future by the optimization of the additives concentrations.

We prove that every congruence distributive variety has directed J\'{o}nsson terms, and every congruence modular variety has directed Gumm terms. The directed terms we construct witness every case of absorption witnessed by the original J\'{o}nsson or Gumm terms. This result is equivalent to a pair of claims about absorption for admissible preorders in CD and CM varieties, respectively. For finite algebras, these absorption theorems have already seen significant applications, but until now, it was not clear if the theorems hold for general algebras as well. Our method also yields a novel proof of a result by P. Lipparini about the existence a chain of terms (which we call Pixley terms) in varieties that are at the same time congruence distributive and $k$-permutable for some $k$., Comment: 17 pages

A novel method of hit time and hit position reconstruction in scintillator detectors is described. The method is based on comparison of detector signals with results stored in a library of synchronized model signals registered for a set of well-defined positions of scintillation points. The hit position is reconstructed as the one corresponding to the signal from the library which is most similar to the measurement signal. The time of the interaction is determined as a relative time between the measured signal and the most similar one in the library. A degree of similarity of measured and model signals is defined as the distance between points representing the measurement- and model-signal in the multi-dimensional measurement space. Novelty of the method lies also in the proposed way of synchronization of model signals enabling direct determination of the difference between time-of-flights (TOF) of annihilation quanta from the annihilation point to the detectors. The introduced method was validated using experimental data obtained by means of the double strip prototype of the J-PET detector and $^{22}$Na sodium isotope as a source of annihilation gamma quanta.The detector was built out from plastic scintillator strips with dimensions of 5 mm x 19 mm x 300 mm, optically connected at both sides to photomultipliers,from which signals were sampled by means of the Serial Data Analyzer.Using the introduced method, the spatial and TOF resolution of about 1.3 cm ($\sigma$) and 125 ps ($\sigma$) were established, respectively.

We present a new approach, called a lazy matching, to the problem of on-line matching on bipartite graphs. Imagine that one side of a graph is given and the vertices of the other side are arriving on-line. Originally, incoming vertex is either irrevocably matched to an another element or stays forever unmatched. A lazy algorithm is allowed to match a new vertex to a group of elements (possibly empty) and afterwords, forced against next vertices, may give up parts of the group. The restriction is that all the time each element is in at most one group. We present an optimal lazy algorithm (deterministic) and prove that its competitive ratio equals $1-\pi/\cosh(\frac{\sqrt{3}}{2}\pi)\approx 0.588$. The lazy approach allows us to break the barrier of $1/2$, which is the best competitive ratio that can be guaranteed by any deterministic algorithm in the classical on-line matching.

The paper deals with extremal problems concerning colorings of hypergraphs. By using a random recoloring algorithm we show that any $n$-uniform simple (i.e. every two distinct edges share at most one vertex) hypergraph $H$ with maximum edge degree at most \[ \Delta(H)\leq c\cdot nr^{n-1}, \] is $r$-colorable, where $c>0$ is an absolute constant. %We prove also that similar result holds for $b$-simple hypergraphs. As an application of our proof technique we establish a new lower bound for Van der Waerden number $W(n,r)$, the minimum $N$ such that in any $r$-coloring of the set $\{1,...,N\}$ there exists a monochromatic arithmetic progression of length $n$. We show that \[ W(n,r)>c\cdot r^{n-1}, \] for some absolute constant $c>0$., Comment: 16 pages

We study attractively interacting fermions on a square lattice with dispersion relations exhibiting strong spin-dependent anisotropy. The resulting Fermi surface mismatch suppresses the s-wave BCS-type instability, clearing the way for unconventional types of order. Unbiased sampling of the Feynman diagrammatic series using Diagrammatic Monte Carlo methods reveals a rich phase diagram in the regime of intermediate coupling strength. Instead of a proposed Cooper-pair Bose metal phase [A. E. Feiguin and M. P. A. Fisher, Phys. Rev. Lett. 103, 025303 (2009)] we find an incommensurate density wave at strong anisotropy and two different p-wave superfluid states with unconventional symmetry at intermediate anisotropy., Comment: published version, supplemental material included as appendix, 4+4 pages, 5+7 figures

A significant part of the phase diagram of the two-dimensional fermionic Hubbard model for moderate interactions and filling factors ($U < 4, \, n<0.7$) is governed by effective Fermi liquid physics with weak BCS-type instabilities. We access this regime in a controlled way by a combination of the bold-line diagrammatic Monte Carlo method with an additional ladder-diagram summation trick and semi-analytic treatment of the weak instability in the Cooper channel. We obtain the corresponding ground-state phase diagram in the $(n,U)$ plane describing the competition between the $p-$ and $d-$wave superfluid states. We also claim the values of the dimensionless BCS coupling constants controlling the superfluid $T_c$ at the phase boundaries, which prove to be very small up to $U=4, n = 0.6$., Comment: 5 pages, 5 figures

Currently inorganic scintillator detectors are used in all commercial Time of Flight Positron Emission Tomograph (TOF-PET) devices. The J-PET collaboration investigates a possibility of construction of a PET scanner from plastic scintillators which would allow for single bed imaging of the whole human body. This paper describes a novel method of hit-position reconstruction based on sampled signals and an example of an application of the method for a single module with a 30 cm long plastic strip, read out on both ends by Hamamatsu R4998 photomultipliers. The sampling scheme to generate a vector with samples of a PET event waveform with respect to four user-defined amplitudes is introduced. The experimental setup provides irradiation of a chosen position in the plastic scintillator strip with an annihilation gamma quanta of energy 511~keV. The statistical test for a multivariate normal (MVN) distribution of measured vectors at a given position is developed, and it is shown that signals sampled at four thresholds in a voltage domain are approximately normally distributed variables. With the presented method of a vector analysis made out of waveform samples acquired with four thresholds, we obtain a spatial resolution of about 1 cm and a timing resolution of about 80 ps

Time of Flight Positron Emission Tomography scanner based on plastic scintillators is being developed at the Jagiellonian University by the J-PET collaboration. The main challenge of the conducted research lies in the elaboration of a method allowing application of plastic scintillators for the detection of low energy gamma quanta. In this article we report on tests of a single detection module built out from BC-420 plastic scintillator strip (with dimensions of 5x19x300mm^3) read out at two ends by Hamamatsu R5320 photomultipliers. The measurements were performed using collimated beam of annihilation quanta from the 68Ge isotope and applying the Serial Data Analyzer (Lecroy SDA6000A) which enabled sampling of signals with 50ps intervals. The time resolution of the prototype module was established to be better than 80ps (sigma) for a single level discrimination. The spatial resolution of the determination of the hit position along the strip was determined to be about 0.93cm (sigma) for the annihilation quanta. The fractional energy resolution for the energy E deposited by the annihilation quanta via the Compton scattering amounts to sigma(E)/E = 0.044/sqrt(E[MeV]) and corresponds to the sigma(E)/E of 7.5% at the Compton edge., Comment: 12 pages, 6 figures; Updated with editorial corrections related to publication in NIM A

The Luttinger-Ward functional $\Phi[\mathbf{G}]$, which expresses the thermodynamic grand potential in terms of the interacting single-particle Green's function $\mathbf{G}$, is found to be ill-defined for fermionic models with the Hubbard on-site interaction. In particular, we show that the self-energy $\mathbf{\Sigma}[\mathbf{G}] \propto \delta\Phi[\mathbf{G}]/\delta \mathbf{G}$ is not a single-valued functional of $\mathbf{G}$: in addition to the physical solution for $\mathbf{\Sigma}[\mathbf{G}]$, there exists at least one qualitatively distinct unphysical branch. This result is demonstrated for several models: the Hubbard atom, the Anderson impurity model, and the full two-dimensional Hubbard model. Despite this pathology, the skeleton Feynman diagrammatic series for $\mathbf{\Sigma}$ in terms of $\mathbf{G}$ is found to converge at least for moderately low temperatures. However, at strong interactions, its convergence is to the unphysical branch. This reveals a new scenario of breaking down of diagrammatic expansions. In contrast, the bare series in terms of the non-interacting Green's function $\mathbf{G}_0$ converges to the correct physical branch of $\mathbf{\Sigma}$ in all cases currently accessible by diagrammatic Monte Carlo. Besides their conceptual importance, these observations have important implications for techniques based on the explicit summation of diagrammatic series., Comment: 5 pages, 5 figures

We propose two strategies for Presenter in on-line graph coloring games. The first one constructs bipartite graphs and forces any on-line coloring algorithm to use $2\log_2 n - 10$ colors, where $n$ is the number of vertices in the constructed graph. This is best possible up to an additive constant. The second strategy constructs graphs that contain neither $C_3$ nor $C_5$ as a subgraph and forces $\Omega(\frac{n}{\log n}^\frac{1}{3})$ colors. The best known on-line coloring algorithm for these graphs uses $O(n^{\frac{1}{2}})$ colors.

The role of the services described in this paper is to support decisions in the Critical Infrastructure Protection (CIP) domain. Those services are perceived as the most fundamental functionalities, that will serve as a basis for the planned European simulation centre for modelling the behaviour of Critical Infrastructures (CI). The proposed services are: CI-related data accessing and gathering, threat forecasting and visualisation, consequence analysis, crowd management, as well as resources and capability management. In general, services proposed in the current paper will contribute to reducing the problem of overwhelming decision makers by too large amount of information. In the crisis, their decisions are made on the basis of the large amount of data related to the current situation, such as the status of CI, localisation of capabilities, weather and threat forecasts etc. The design of the services has been established with the help of the future end-users. The work presented in this paper is the result of preliminary activities performed in the FP7 project CIPRNet., Comment: EDCC-2014, BIG4CIP-2014, CIP, CIPRNet project, decision support, services

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP languages to weighted algebras. We show that the difficulty of VCSP depends only on the weighted variety generated by the associated weighted algebra. Paralleling the results for CSPs we exhibit a reduction to cores and rigid cores which allows us to focus on idempotent weighted varieties. Further, we propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the hardness direction and verify that it agrees with known results for VCSPs on two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny 2013] and conservative VCSPs [Kolmogorov and Zivny 2013]., Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other authors

A novel PET detector consisting of strips of polymer scintillators is being developed by the J-PET Collaboration. The map of efficiency and the map of geometrical acceptance of the 2-strip J-PET scanner are presented. Map of efficiency was determined using the Monte Carlo simulation software GATE based on GEANT4. Both maps were compared using method based on the chi2 test., Comment: 14 pages, 9 figures, proceeding from conference Symposium on Positron Emission Tomography: http://koza.if.uj.edu.pl/pet-symposium-2013/

A study of identification properties of a Si-Si DE-E telescope exploiting an underdepleted residual-energy detector has been performed. Five different bias voltages have been used, one corresponding to full depletion, the others associated with a depleted layer ranging from 90% to 60% of the detector thickness. Fragment identification has been performed using either the DE-E technique or Pulse Shape Analysis (PSA). Both detectors are reverse mounted: particles enter from the low field side, to enhance the PSA performance. The achieved charge and mass resolution has been quantitatively expressed using a Figure of Merit (FoM). Charge collection efficiency has been evaluated and the possibility of energy calibration corrections has been considered. We find that the DE-E performance is not affected by incomplete depletion even when only 60% of the wafer is depleted. Isotopic separation capability improves at lower bias voltages with respect to full depletion, though charge identification thresholds are higher than at full depletion. Good isotopic identification via PSA has been obtained from a partially depleted detector whose doping uniformity is not good enough for isotopic identification at full depletion., Comment: 13 pages, 10 figures 5 tables; submitted to European Physical Journal A

The complexity of the hardware and the amount of data collected during the PET imaging process require application of modern methods of efficient data organization and processing. In this article we will discuss the data structures and the flow of collected data from the novel TOF-PET medical scanner which is being developed at the Jagiellonian University. The developed data format reflects: registration process of the gamma quanta emitted from positron-electron annihilation, Front-End Electronic (FEE) structure and required input information for the image reconstruction. In addition, the system database fulfills possible demands of the evolving J-PET project., Comment: 6 p, 3 figs, based on talk given at Symposium on Positron Emission Tomography, Sept. 19-22, 2013, Jagiellonian University, Krak\'ow PL, submitted to Bio-Algorithms and Med-Systems

We discuss computing issues for data analysis and image reconstruction of PET-TOF medical scanner or other medical scanning devices producing large volumes of data. Service architecture based on the grid and cloud concepts for distributed processing is proposed and critically discussed., Comment: 9 p, 3 figs, based on talk given at Symposium on Positron Emission Tomography, Sept. 19-22, 2013, Jagiellonian University, Krak\'ow, Pl

Photomultipliers are commonly used in commercial PET scanner as devices which convert light produced in scintillator by gamma quanta from positron-electron annihilation into electrical signal. For proper analysis of obtained electrical signal, a photomultiplier gain curve must be known, since gain can be significantly different even between photomultipliers of the same model. In this article we describe single photoelectron method used for photomultipliers calibration applied for J-PET scanner, a novel PET detector being developed at the Jagiellonian University. Description of calibration method, an example of calibration curve and gain of few R4998 Hamamatsu photomultipliers are presented., Comment: Submitted to Bio-Algorithms and Med-Systems (12 pages, 6 figures)