Coincidence Matrix Research Articles

The GANDALF 128-Channel Time-to-Digital Converter

The GANDALF 6U-VME64x/VXS module has been designed to cope with a variety of readout tasks in high energy and nuclear physics experiments, in particular the COMPASS experiment at CERN. The exchangeable mezzanine cards allow for an employment of the system in very different applications such as analog-to-digital or time-to-digital conversions, coincidence matrix formation, fast pattern recognition or fast trigger generation. Based on this platform, we present a 128-channel TDC which is implemented in a single Xilinx Virtex-5 FPGA using a shifted clock sampling method. In this concept each input signal is continuously sampled by 16 flip-flops using equidistant phase-shifted clocks. Compared to previous FPGA designs, usually based on delay lines and comprising few TDC channels with resolutions in the order of 10 ps, our design permits the implementation of a large number of TDC channels with a resolution of 64 ps in a single FPGA. Predictable placement of logic components and uniform routing inside the FPGA fabric is a particular challenge of this design. We present measurement results for the time resolution and the nonlinearity of the TDC readout system.

Lifetimes of odd-spin yrast states inHg182

Lifetimes of excited states in $^{182}\mathrm{Hg}$ were extracted from recoil-gated $\ensuremath{\gamma}$-ray spectra and recoil-gated $\ensuremath{\gamma}\ensuremath{\gamma}$-coincidence matrices using the recoil distance Doppler-shift method. States were populated using the $^{96}\mathrm{Mo}$($^{88}\mathrm{Sr}$,$2n$)$^{182}\mathrm{Hg}$ fusion-evaporation reaction. Measured lifetimes allowed transition probabilities, transition quadrupole moments, quadrupole deformation parameters, and transition dipole moments to be deduced for the band formed by the odd-spin yrast states. The experimental results confirm the low degree of octupole collectivity in this mass region.

Investigating Global and Local Categorical Map Configuration Comparisons Based on Coincidence Matrices

The simple and intuitive nature of the coincidence matrix has not only made it the current “gold standard” for accuracy assessment (based on a sample of map pixels), but also a common tool for describing difference between two categorical maps (when all pixels are enumerated). It is this latter case of map comparison that this article explores. Coincidence matrices, although providing significant information regarding thematic agreement between two categorical maps (composition), can lack significantly in terms of conveying information about differences or similarities in the spatial arrangement (configuration) of those map categories in geographic space. This article introduces means for distilling the available configuration information from a coincidence matrix while demonstrating some simple categorical map comparisons. Specifically, while the coincidence matrix summarizes per‐pixel compositional persistence or change, the introduced technique further quantifies the global and local configurational uncertainty between compared maps. I demonstrate how this quantification of configurational uncertainty can be used to gauge which thematic mismatch types are most significant and how to measure/present local configurational uncertainty in a spatial context. Implementation is through a straightforward mathematical algorithm in R that is illustrated by several examples.

Periodic solutions for nonlinear second-order difference equations

This paper is devoted to introduce a new approach to investigate the existence of periodic solutions for nonlinear difference equations. Transforming a second-order nonlinear difference equation on a finite discrete segment with periodic boundary conditions into a continuous system, we obtain the existence conditions of periodic solutions of the equation. The proof relies on coincidence degree theory and matrix theory without using Green’s function.

The Muon Spectrometer Barrel Level-1 Trigger of the ATLAS Experiment at LHC

The proton-proton beam crossing at the LHC accelerator at CERN will have a rate of 40 MHz at the project luminosity. The ATLAS Trigger System has been designed in three levels in order to select only interesting physics events reducing from that rate of 40 MHz to the foreseen storage rate of about 200 Hz. The First Level reduces the output rate to about 100 kHz. The ATLAS Muon Spectrometer has been designed to perform stand-alone triggering and measurement of Muon transverse momentum up to 1 TeV/c with good resolution (from 3% at 10 GeV/c up to 10% at 1 TeV/c). In the Barrel region of the Muon Spectrometer the Level-1 trigger is given by means of three layers of resistive plate chamber detectors (RPC): a gaseous detector working in avalanche mode composed by two plates of high-resistivity bakelite and two orthogonal planes of read-out strips. The logic of the Level-1 barrel Muon trigger is based on the search of patterns of RPC hits in the three layers consistent with a high transverse momentum Muon track originated from the interaction vertex. The associated trigger electronics is based on dedicated processors, the Coincidence Matrix boards, performing space coincidences and time gates and providing the RPC readout as well. A detailed simulation of the ATLAS Experiment and of both the hardware components and the logic of the Level-1 Muon Trigger in the barrel of the Muon Spectrometer has been performed. This simulation has been used not only to evaluate the performances of the system but also to define the hardware set-up such as the cabling of both the trigger detectors and the trigger electronics modules. A description of both the Level-1 Muon Trigger system in the barrel and the RPC detectors, with their cosmic rays quality tests, will be presented together with the trigger performances and rates calculations evaluated for Muons over a wide range of pT and preliminary studies on the impact of accidental triggers due to low energy background particles in the experimental area

Assessing cellular automata model behaviour using a sensitivity analysis approach

Rapid advances in computer and geospatial technology have made it increasingly possible to design and develop urban models to efficiently simulate spatial growth patterns. An approach commonly used in geography and urban growth modelling is based on cellular automata theory and the GIS framework. However, the behaviour of cellular automaton (CA) models is affected by uncertainties arising from the interaction between model elements, structures, and the quality of data sources used as model input. The uncertainty of CA models has not been sufficiently addressed in the research literature. The objective of this study is to analyze the behaviour of a GIS-based CA urban growth model using sensitivity analysis (SA). The proposed SA approach has both qualitative and quantitative components. These components were operationalized using the cross-tabulation map, KAPPA index with coincidence matrices, and spatial metrics. The research focus was on the impacts of CA neighbourhood size and type on the model outcomes. A total of 432 simulations were generated and the results suggest that CA neighbourhood size and type configurations have a significant influence on the CA model output. This study provides insights about the limitations of CA model behaviour and contributes to enhancing existing spatial urban growth modelling procedures.

Confidence in coincidence

We present a simple simulation scheme to derive confidence intervals for measures computed based on a coincidence matrix. Our approach is based on the conditional distributions between two categorical maps, and is a direct interpretation of how much information one map (usually the classified image) carries about the other map (usually the reference image). The simulation algorithm creates a realization of the map created by visiting each pixel and drawing a random sample from the conditional distribution of reference categories (conditioned on the category of the pixel of the classified image). Confidence intervals can be derived by repeating the simulation many times and computing the coincidence measure(s). Handling the coincidence matrix as a set of conditional distributions also allows the comparison of maps with different numbers of categories. This approach is an extension of the traditional methodology widely used in accuracy assessment of data derived from remotely sensed images. We illustrate the usage and interpretation of the approach on artificial and Canadian land cover mapping data.

Efficient fitting algorithms applied to analysis of coincidence γ-ray spectra

In the paper efficient nonlinear fitting algorithms without matrix inversion are described. The algorithms were applied to the analysis of two- and three-fold coincidence γ-ray spectra. They were used to process coincidence matrices from fission data from the multidetector GAMMASPHERE spectrometer.

Integration of forest inventory and satellite imagery:: a Canadian status assessment and research issues

Canada's ability to sustainably manage approximately 10% of the global forest cover is a critical environmental and economic issue. The capacity to meet such demands and to deliver on national and international commitments regarding forest management is enabled through collaboration between federal, provincial, and territorial agencies. A principal collaborator is the National Forest Inventory (NFI); a systematic photo-plot based monitoring system designed specifically for reporting purposes and as an important input for scientific models. Satellite imagery is illustrated here as a support data set to ensure the quality of the NFI, for auditing the photo-plot contents, and to detect spatial biases. The Canadian Forest Service, in collaboration with the Canadian Space Agency and other federal and provincial agencies, is producing a national land cover database of the forested area of Canada (Earth Observation for Sustainable Development of Forests (EOSD)) using Landsat-7 ETM+ data for circa 2000 conditions. The integration between the plot-based NFI with classified EOSD data is presented for central British Columbia, an area comprising 6 Landsat scenes and 324 2 km × 2 km photo-plots. Traditional accuracy assessment measures based on the analysis of coincidence matrices are reported as levels of agreement for hierarchically aggregated land cover categories (overall agreements of 91%, 79%, 64% and 26% for 3, 4, 6 and 20 classes respectively) to demonstrate coincidence between the different data products. Local agreement between NFI and EOSD is demonstrated as a means of photo-plot auditing while spatial biases are detected through investigations of geographic pattern in the coincidence values. The illustrated approaches may be expanded or applied to different mapped attributes (e.g., biomass) that are of utility to those attempting to characterize large areas in a consistent and rigorous fashion.

Analysis of temporal sar and optical data for rice mapping

This study investigates the potential of multi-temporal signature analysis of satellite imagery to map rice area in South 24 Paraganas district of West Bengal. Two optical data (IRS ID LISS III) and three RADARSAT SAR data of different dates were acquired during 2001. Multi-temporal SAR backscatter signatures of different landcovers were incorporated into knowledge based decision rules and kharif landcover map was generated. Based on the spectral variation in signature, the optical data acquired during rabi (January) and summer (March) season were classified using supervised maximum likelihood classifier. A co-incidence matrix was generated using logical approach for a combined “rabi-summer” and “kharif-rabi-summer” landcover mapping. The major landcovers obtained in South 24 Paraganas using remote sensing data are rice, water, aquaculture ponds, homestead, mangrove, and urban area. The classification accuracy of rice area was 98.2% using SAR data. However, while generating combined “kharif-rabi-summer” landcovers, the classification accuracy of rice area was improved from 81.6% (optical data) to 96.6% (combined SAR-Optical). The primary aim of the study is to achieve better accuracy in classifying rice area using the synergy between the two kinds of remotely sensed data.

Evidence for chiral symmetry breaking inEu140?

High spin states in $^{140}\mathrm{Eu}$ were populated following the reaction $^{92}\mathrm{Mo}(^{51}\mathrm{V},2pn)$ at a beam energy of $205\phantom{\rule{0.3em}{0ex}}\text{MeV}$ by the ESTU accelerator at the Wright Nuclear Structure Laboratory, Yale University. A total of 5 bands and 69 transitions were assigned to $^{140}\mathrm{Eu}$. The assignments were based on ${K}_{\ensuremath{\alpha}}$ x-ray coincidences and on excitation function measurements. $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ and $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence matrices were created. Directional correlation of oriented states analysis, angular distributions, and Compton asymmetry measurements were performed and $B(M1)∕B(E2)$ branching ratios were extracted. The band assignments and structures are discussed in terms of the rotational model and interpreted following a series of cranked shell model and total Routhian surface calculations. In particular, two pairs of bands, one pair based on the $\ensuremath{\pi}{h}_{11∕2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11∕2}$ configuration, the other based on the $\ensuremath{\pi}({g}_{7∕2},{d}_{5∕2})\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11∕2}$ configuration, are identified. These bands show some features expected of either chiral partners or shape coexistence, based on triaxial shapes with $\ensuremath{\gamma}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}25\ifmmode^\circ\else\textdegree\fi{}$. Further measurements are required to distinguish between these two possibilities.

The coincidence matrix ASIC of the level-1 muon barrel trigger of the ATLAS experiment

The ATLAS barrel level-1 muon trigger processes hit information from the resistive plate chamber detector, identifying candidate muon tracks and assigning them to a programmable p/sub T/ range and to a unique bunch crossing number. The trigger system uses up to seven detector layers and seeks hit patterns compatible with muon tracks in the bending and nonbending projection. The basic principle of the algorithm is to demand a coincidence of hits in the different chamber layers within a path. The width of the road is related to the p/sub T/ threshold to be applied. The system is split into an on-detector and an off-detector part. The on-detector electronics reduces the information from about 350 k channels to about 400 32-bit data words sent via optical fiber to the so-called sector logic (SL). The off-detector SL electronics collects muon candidates and associates them to detector regions-of-interest of /spl Delta//spl eta//spl times//spl Delta//spl Phi/ of 0.1/spl times/0.1. The core of the on-detector electronics is the coincidence matrix ASIC (CMA), which fulfils both the trigger algorithm and the readout of the RPC detector. Each CMA is able to process and readout 192 RPC strips from as many as four detector layers. In order to keep the full level-1 system latency below 2 /spl mu/s, the CMA has to find candidate muon tracks with a latency of a few 25 ns bunch crossing periods. The readout part of the CMA is able to time tag incoming RPC hits with a time interpolator running at the trigger pipeline frequency of 320 MHz and to send the data to the readout system via a serial link. The design of the trigger system and the performances of the ASIC, based on a CMOS 0.18 /spl mu/m technology, are presented.

Stability analysis of a delayed Hopfield neural network

In this paper, we study a class of neural networks, which includes bidirectional associative memory networks and cellular neural networks as its special cases. By Brouwer's fixed point theorem, a continuation theorem based on Gains and Mawhin's coincidence degree, matrix theory, and inequality analysis, we not only obtain some different sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium but also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity.

Study of thermally excited nuclei through E1 and E2 decay from collective modes

The nuclear system at the limit of excitation energy and angular momentum is here studied in the case of the superdeformed nucleus 143 Eu using $\gamma$ -spectroscopy techniques. The data are based on a EUROBALL experiment using the reaction 37 Cl + 110 Pd $\to^{143}$ Eu + 4n. The influence of thermal energy on superdeformed configurations is investigated through the analysis of the quasi-continuum spectra formed by E2 transitions among states of excited rotational bands with energy extending up to 4-5 MeV above the yrast line. In particular, the effective lifetimes of the discrete rotational bands forming ridge structures in $\gamma$ - $\gamma$ coincidence matrices is measured by a Doppler Shift Attenuation Method. The deduced quadrupole deformation of $Q_t \approx$ 10 eb indicates that the nucleus maintains its collectivity with increasing excitation energy, supporting the superdeformed character of the excited nuclear rotation. The obtained number of superdeformed discrete bands forming the ridge structures is found in good agreement with microscopic cranked shell model calculations including the decay-out process into the lower deformation minimum. In addition, the nuclear properties at higher excitation energies are investigated through the E1 $\gamma$ -decay of the giant dipole resonance (GDR). It is found that the intensity of the superdeformed yrast and excited bands increases by a factor of approximately 1.6 when a coincidence with a high-energy $\gamma$ -ray is required, showing the importance of the E1 cooling in the feeding mechanism of the superdeformed states.

Multistep rotational energy correlations probed by high fold $γ$ coincidence data

The number of discrete rotational bands in the nucleus 168Yb is obtained by a fluctuation analysis of the rotational ridge structure in double and triple γ coincidence matrices. The data are compared with cranked shell model calculations including a surface delta interaction. It is found that the number of calculated bands strongly depends on the interaction strength V0, and agreement between data and calculations supports the standard value V0= 27.5/A MeV.

Method and program for decay scheme reconstruction based on formal logical analysis of gamma-gamma coincidence matrix

A new, rigorously substantiated approach to construction of decay schemes on the basis of γ-γ coincidence data is described. Complete decay modes (concrete cascades of transition from excited to the ground state of a nucleus excited in a decay or a reaction) and continuity regions in complete modes (regions of successive transitions) are isolated by logical operations with rows (columns) of a symmetrical coincidence matrix where rows (columns) correspond to energies of coinciding transitions and matrix elements are unities and zeros, depending on the presence or absence of the given coincidence. To reject false complete modes and continuity regions arising from incompleteness of the coincidence data and errors in them, energy selection is introduced for complete modes and continuity regions. This requires that the total energy of their constituent transitions should be equal to the total energy of some other complete modes and continuity regions and to the energies of singles. With the continuity regions found, it is possible to order transitions in the selected complete modes and to algorithmize matching of complete modes into a decay scheme.

A pipelined first-level trigger for the H1 forward-muon spectrometer

We have built a fast, pipelined first-level trigger processor for the H1 experiment at HERA. The trigger finds tracks in the forward-muon spectrometer which point back to the interaction vertex. The inputs to the trigger come from drift chambers with a 6 cm drift space corresponding to a maximum drift time of 1.2 μs. These chambers consist of two layers of drift cells whose staggered configuration makes it possible to extract the time at which a particle traversed the chambers to better than one HERA bunch-crossing period, 96 ns. The trigger hardware exploits this characteristic in a real-time operation, and is able to find pointing tracks and associate them to production in a specific electron-proton crossing. The trigger processor must be deadtime free. It operates in a pipelined mode with 48 ns steps and has a latency of about 22 HERA bunch-crossing periods. The compact design is based on two semi-custom integrated circuits. Both are field-programmable 32 × 32 coincidence matrices, one having serial loading of its inputs and the other using parallel loading. The system was installed in the H1 experiment early in 1993 and has run successfully since then.

Extracting energies and intensities from complex coincidence matrices

Coincidence intensities and uncertainties are extracted at the statistical limits from γ-γ coincidence matrices. The matrices are decomposed into continuum, ridges and peaks. The continuum is successfully modeled by the product of two vectors which describe the Compton distributions in the coincident detectors or groups of detectors. The ridges are represented by the corresponding continuum vector scaled according to the intensity and energy of the associated γ-ray. The peaks are fitted as the product of two, one-dimensional Gaussians. This technique has been applied to the analysis of prompt gamma-rays from the spontaneous fission of 252Cf and the high spin states in 163Lu populated via the 122Sn( 45Sc, 4n) reaction.

Study of the high-spin structure of 144Gd

High-spin states in 144Gd have been investigated through the 108Pd( 40Ar, 4n) reaction. An extended level scheme is proposed. A ridge structure has been observed in a γγ coincidence matrix, consistent with energy spacings in the superdeformed bands of neighbouring nuclei. Several discrete high-spin sequences have been observed. They are interpreted in the context of cranked-Strutinsky-type calculations in terms of different coexisting shapes.

A rotational band in82Zr

The neutron deficient nucleus82Zr has been studied through the reaction58Ni(28Si, 2p 2n)82Zr with a calculated cross section of 0.3% of the total fusion cross section atE(28Si)=128 MeV. Gamma rays from excited states of82Zr were measured and identified using the NORDBALL escape-suppression array at the Niels Bohr Institute. Reaction channel selection was performed by use of neutron and charged particle detector arrays in conjunction with the germanium detectors. A rotational band in82Zr has been identified with spins up to 20 ħ by analysis of reaction channel selectedγ-γ coincidence matrices. Band crossings were identified at frequencies 0.57 and 0.69 MeV.