Full Model Space Research Articles

Indispensability of cross-shell contributions in neutron resonance spacing

Spin- and parity-dependent nuclear level densities (NLDs) are obtained for a configuration interaction shell model using a numerically efficient spectral distribution method. The calculations are performed for 24Na and 25,26,27Mg nuclei using full sd-pf model space that incorporates the cross-shell excitations from the sd to the pf-shell. The obtained NLDs are then employed to determine the s-wave neutron resonance spacing (D0), which is one of the crucial inputs for the predictions of astrophysical reaction rates. Although the considered nuclei are not neutron-rich, the contributions from cross-shell excitations to the pf-shell are indispensable for explaining the experimental data for D0, which otherwise are significantly overestimated.

Direct Measurement of Hexacontatetrapole, E6 γ Decay from Fe53m

The only proposed observation of a discrete, hexacontatetrapole (E6) transition in nature occurs from the T_{1/2}=2.54(2)-min decay of ^{53m}Fe. However, there are conflicting claims concerning its γ-decay branching ratio, and a rigorous interrogation of γ-ray sum contributions is lacking. Experiments performed at the Australian Heavy Ion Accelerator Facility were used to study the decay of ^{53m}Fe. For the first time, sum-coincidence contributions to the weak E6 and M5 decay branches have been firmly quantified using complementary experimental and computational methods. Agreement across the different approaches confirms the existence of the real E6 transition; the M5 branching ratio and transition rate have also been revised. Shell model calculations performed in the full fp model space suggest that the effective proton charge for high-multipole, E4 and E6, transitions is quenched to approximately two-thirds of the collective E2 value. Correlations between nucleons may offer an explanation of this unexpected phenomenon, which is in stark contrast to the collective nature of lower-multipole, electric transitions observed in atomic nuclei.

Electromagnetic multipoles of positive parity states in 27Al by elastic and inelastic electron scattering

Nuclear structure of 27Al nucleus has been investigated using shell model with self-consistent Hartree–Fock calculations. Shell model calculations are performed with full sd model space for positive parity states. For all selected excited states, Skyrme interactions are adopted to generate from them a one-body potential in Hartrre-Fock theory to calculate the single-particle matrix elements and compared with those of the harmonic oscillator. The deduced results are discussed for the longitudinal and transverse form factors and compared with the available experimental data. It has been found that the core-polarization effects are essential in obtaining a reasonable description of the data.

Probing the single-particle behavior above Sn132 via electromagnetic moments of Sb133,134 and N=82 isotones

Magnetic and quadrupole moments of the $7/{2}^{+}$ ground state in $^{133}\mathrm{Sb}$ and the $({7}^{\ensuremath{-}})$ isomer in $^{134}\mathrm{Sb}$ have been measured by collinear laser spectroscopy to investigate the single-particle behavior above the doubly magic nucleus $^{132}\mathrm{Sn}$. The comparison of experimental data of the $7/{2}^{+}$ states in $^{133}\mathrm{Sb}$ and neighboring $N=82$ isotones to shell-model calculations reveals the sensitivity of magnetic moments to the splitting of the spin-orbit partners $\ensuremath{\pi}0{g}_{9/2}$ and $\ensuremath{\pi}0{g}_{7/2}$ across the proton shell closure at $Z=50$. In contrast, quadrupole moments of the $N=82$ isotones are insensitive to cross-shell excitations, but require the full proton model space from $Z=50\phantom{\rule{4.pt}{0ex}}\text{to}\phantom{\rule{4.pt}{0ex}}82$ for their accurate description. In fact, the linear trend of the quadrupole moment follows approximately the expectation of the seniority scheme when filling the $\ensuremath{\pi}0{g}_{7/2}$ orbital. As far as the isomer in $^{134}\mathrm{Sb}$ is concerned, its electromagnetic moments can be perfectly described by the additivity rule employing the moments of $^{133}\mathrm{Sb}$ and $^{133}\mathrm{Sn}$, respectively. These findings agree with shell-model calculations and thus confirm the weak coupling between the valence proton and neutron in $^{134}\mathrm{Sb}$.

On tomography velocity uncertainty in relation with structural imaging

Evaluating structural uncertainties associated with seismic imaging and target horizons can be of critical importance for decision making related to oil and gas exploration and production. An important breakthrough for industrial applications has been made with the development of industrial approaches to velocity model building. We have developed an extension of these approaches, sampling an equiprobable contour of the tomography posterior probability density function (PDF) rather than the full PDF, and using nonlinear slope tomography. Our approach allows for assessing the quality of uncertainty-related assumptions (linearity and Gaussian hypothesis within the Bayesian theory) and estimating volumetric migration positioning uncertainties (a generalization of horizon uncertainties), in addition to the advantages in terms of computational efficiency. We derive the theoretical concepts underlying this approach and unify our derivations with those of previous publications. Because the method works in the full model space rather than in a preconditioned one, we split the analysis into resolved and unresolved tomography spaces. We argue that resolved space uncertainties are to be used in further steps leading to decision making and can be related to the output of methods that work in a preconditioned model space. Unresolved space uncertainties represent a qualitative by-product specific to our method, strongly highlighting the most uncertain gross areas, thus useful for quality control. These concepts are developed on a synthetic data set. In addition, the industrial viability of the method is determined on two different 3D field data sets. The first one consists of a merge of different seismic surveys in the North Sea and indicates the corresponding structural uncertainties. The second one consists of a marine data set and indicates the impact of structural uncertainties on gross-rock volume computation.

Bayesian rock-physics inversion: Application to CO2 storage monitoring

Risk assessment of [Formula: see text] storage requires the use of geophysical monitoring techniques to quantify changes in selected reservoir properties such as [Formula: see text] saturation, pore pressure, and porosity. Conformance monitoring and the associated decision making rest upon the quantified properties derived from geophysical data, with uncertainty assessment. We have developed a general framework combining seismic and controlled-source electromagnetic (CSEM) inversions with rock-physics inversion with fully Bayesian formulations for proper quantification of uncertainty. The Bayesian rock-physics inversion rests upon two stages. First, a search stage consists of exploring the model space and deriving models with the associated probability density function (PDF). Second, an appraisal or importance sampling stage is used as a “correction” step to ensure that the full model space is explored and that the estimated posterior PDF can be used to derive quantities such as marginal probability densities. Both steps are based on the neighborhood algorithm. The approach does not require any linearization of the rock-physics model or assumption about the model parameters’ distribution. After describing the [Formula: see text] storage context, the available data at the Sleipner field before and after [Formula: see text] injection (baseline and monitor), and the rock-physics models, we perform an extended sensitivity study. We find that prior information is crucial, especially in the monitor case. We determine that joint inversion of seismic and CSEM data is also key to properly quantifying [Formula: see text] saturations. Finally, we apply the full inversion strategy to real data from Sleipner. We obtain rock frame moduli, porosity, saturation, and patchiness exponent distributions and the associated uncertainties along a 1D profile before and after injection. The results are consistent with geology knowledge and reservoir simulations, i.e., that the [Formula: see text] saturations are larger under the caprock confirming the [Formula: see text] upward migration by buoyancy effect. The estimates of the patchiness exponent have a larger uncertainty, suggesting semipatchy mixing behavior.

Characterizing Network Search Algorithms Developed for Dynamic Causal Modeling.

Dynamic causal modeling (DCM) is a widely used tool to estimate the effective connectivity of specified models of a brain network. Finding the model explaining measured data is one of the most important outstanding problems in Bayesian modeling. Using heuristic model search algorithms enables us to find an optimal model without having to define a model set a priori. However, the development of such methods is cumbersome in the case of large model-spaces. We aimed to utilize commonly used graph theoretical search algorithms for DCM to create a framework for characterizing them, and to investigate relevance of such methods for single-subject and group-level studies. Because of the enormous computational demand of DCM calculations, we separated the model estimation procedure from the search algorithm by providing a database containing the parameters of all models in a full model-space. For test data a publicly available fMRI dataset of 60 subjects was used. First, we reimplemented the deterministic bilinear DCM algorithm in the ReDCM R package, increasing computational speed during model estimation. Then, three network search algorithms have been adapted for DCM, and we demonstrated how modifications to these methods, based on DCM posterior parameter estimates, can enhance search performance. Comparison of the results are based on model evidence, structural similarities and the number of model estimations needed during search. An analytical approach using Bayesian model reduction (BMR) for efficient network discovery is already available for DCM. Comparing model search methods we found that topological algorithms often outperform analytical methods for single-subject analysis and achieve similar results for recovering common network properties of the winning model family, or set of models, obtained by multi-subject family-wise analysis. However, network search methods show their limitations in higher level statistical analysis of parametric empirical Bayes. Optimizing such linear modeling schemes the BMR methods are still considered the recommended approach. We envision the freely available database of estimated model-spaces to help further studies of the DCM model-space, and the ReDCM package to be a useful contribution for Bayesian inference within and beyond the field of neuroscience.

Single-particle shell strengths near the doubly magic nucleus 56Ni and the 56Ni(p,γ)57Cu reaction rate in explosive astrophysical burning

Angle-integrated cross-section measurements of the 56Ni(d,n) and (d,p) stripping reactions have been performed to determine the single-particle strengths of low-lying excited states in the mirror nuclei pair 57Cu−57Ni situated adjacent to the doubly magic nucleus 56Ni. The reactions were studied in inverse kinematics utilizing a beam of radioactive 56Ni ions in conjunction with the GRETINA γ-array. Spectroscopic factors are compared with new shell-model calculations using a full pf model space with the GPFX1A Hamiltonian for the isospin-conserving strong interaction plus Coulomb and charge-dependent Hamiltonians. These results were used to set new constraints on the 56Ni(p,γ)57Cu reaction rate for explosive burning conditions in x-ray bursts, where 56Ni represents a key waiting point in the astrophysical rp-process.

Multi-messenger investigation of the Pygmy Dipole Resonance in 140Ce

We report on the first (p,p′γ) experiments at Ep=80 MeV to investigate the Pygmy Dipole Resonance (PDR) in the semi-magic nucleus 140Ce. This experiment is the latest in a series of experiments to investigate the PDR with different complementary probes to provide a multi-messenger data set on the properties of the PDR in 140Ce. In addition, calculations within the Quasi-particle Phonon Model (QPM) have been performed. Cross sections have been calculated for proton- as well as α-scattering reactions based on the transition densities obtained from the QPM, not only at the RPA level, but including the full model space of up to 3p–3h configurations. This allows for the first time to compare the calculations to the experimental results on an absolute scale for single excitations. Agreement between QPM and experiment is observed, which proves the high accuracy of the calculated transition densities for individual PDR states.

Neutrino Spectra from Nuclear Weak Interactions in sd-Shell Nuclei under Astrophysical Conditions

Abstract We present shell model calculations of nuclear neutrino energy spectra for 70 sd-shell nuclei over the mass number range A = 21–35. Our calculations include nuclear excited states as appropriate for the hot and dense conditions characteristic of pre-collapse massive stars. We consider neutrinos produced by charged lepton captures and decays, and for the first time in tabular form, neutral current nuclear deexcitation, providing neutrino energy spectra on the Fuller–Fowler–Newman temperature–density grid for these interaction channels for each nucleus. We use the full sd-shell model space to compute initial nuclear states up to 20 MeV excitation with transitions to final states up to 35–40 MeV, employing a modification of the Brink-Axel hypothesis to handle high-temperature population factors and the nuclear partition functions.

Shell-model calculations for upper pf-shell nuclei with an effective interaction

Results obtained for the energy spectra and the low-lying positive-parity energy eigenstates of the upper p f -shell nuclei 64Ge and 68Se with the use of the effective interaction JUN45 are reported. We address the question of how appropriate is the possibility to construct a symmetry-adapted shell model in a single oscillator shell using a Pairing-plus-Quadrupole Hamiltonian. Specifically, we study the goodness of the symmetries pseudo SU(3) and O(6) in the structure of the energy eigenstates. Finally, we relate our results to a proposed mixed-symmetry approach which is able to simultaneously account for the presence of both the pairing and the quadrupole modes as the most important ingredients in the effective interaction while using a restricted part of the full model space.

Shell model results for T = 1 and T = 0 bands in 66As

The results of comprehensive shell model (SM) analyses, within the full model space, of the recently available experimental data (Ruotsalainen et al (2013) Phys. Rec. C 88 024320) with four T = 0 bands and one T = 1 band in the odd–odd N = Z nucleus 66As are presented. The calculations are performed by using the jj44b effective interaction developed recently by Brown and Lisetskiy for this model space. For the lowest two T = 0 bands and the T = 1 band, the results are in reasonable agreement with experimental data and the deformed shell model is used to identify their intrinsic structure. For the T = 1 band, a structural change at is predicted. For the third band with T = 0, the shell model values and quadrupole moments (in addition to energies) are consistent with the interpretation in terms of an aligned isoscalar np pair in a orbit coupled to the 64Ge ground band. Similarly, the level of band 4 and a close-lying level are found to be isomeric states in the analysis. Finally, the energies of the band 5 members, calculated using the shell model with both positive and negative parity, show that the observed levels are most likely negative parity levels. The shell model results with jj44b are compared with results obtained using the JUN45 interaction.

The Hamming Ball Sampler

ABSTRACTWe introduce the Hamming ball sampler, a novel Markov chain Monte Carlo algorithm, for efficient inference in statistical models involving high-dimensional discrete state spaces. The sampling scheme uses an auxiliary variable construction that adaptively truncates the model space allowing iterative exploration of the full model space. The approach generalizes conventional Gibbs sampling schemes for discrete spaces and provides an intuitive means for user-controlled balance between statistical efficiency and computational tractability. We illustrate the generic utility of our sampling algorithm through application to a range of statistical models. Supplementary materials for this article are available online.

A proposed Fast algorithm to construct the system matrices for a reduced-order groundwater model

Past research has demonstrated that a reduced-order model (ROM) can be two-to-three orders of magnitude smaller than the original model and run considerably faster with acceptable error. A standard method to construct the system matrices for a ROM is Proper Orthogonal Decomposition (POD), which projects the system matrices from the full model space onto a subspace whose range spans the full model space but has a much smaller dimension than the full model space. This projection can be prohibitively expensive to compute if it must be done repeatedly, as with a Monte Carlo simulation. We propose a Fast Algorithm to reduce the computational burden of constructing the system matrices for a parameterized, reduced-order groundwater model (i.e. one whose parameters are represented by zones or interpolation functions). The proposed algorithm decomposes the expensive system matrix projection into a set of simple scalar-matrix multiplications. This allows the algorithm to efficiently construct the system matrices of a POD reduced-order model at a significantly reduced computational cost compared with the standard projection-based method. The developed algorithm is applied to three test cases for demonstration purposes. The first test case is a small, two-dimensional, zoned-parameter, finite-difference model; the second test case is a small, two-dimensional, interpolated-parameter, finite-difference model; and the third test case is a realistically-scaled, two-dimensional, zoned-parameter, finite-element model. In each case, the algorithm is able to accurately and efficiently construct the system matrices of the reduced-order model.

Approximate Model Spaces for Model-Robust Experiment Design

Optimal designs depend upon a prespecified model form. A popular and effective model-robust alternative is to design with respect to a set of models instead of just one. However, model spaces associated with experiments of interest are often prohibitively large and so algorithmically generated designs are infeasible. Here, we present a simple method that largely eliminates this problem by choosing a small set of models that approximates the full set and finding designs that are explicitly robust for this small set. We build our procedure on a restricted columnwise-pairwise algorithm, and explore its effectiveness for two model spaces in the literature. For smaller full model spaces, we find that the designs constructed with the new method compare favorably with robust designs that use the full model space, with construction times reduced by orders of magnitude. We also construct designs that heretofore have been unobtainable due to the size of their model spaces. Supplementary material (available online) includes code, designs, and additional results.

Estimation and Impact of Nonuniform Horizontal Correlation Length Scales for Global Ocean Physical Analyses

Abstract Optimally modeling background-error horizontal correlations is crucial in ocean data assimilation. This paper investigates the impact of releasing the assumption of uniform background-error correlations in a global ocean variational analysis system. Spatially varying horizontal correlations are introduced in the recursive filter operator, which is used for modeling horizontal covariances in the Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC) analysis system. The horizontal correlation length scales (HCLSs) were defined on the full three-dimensional model space and computed from both a dataset of monthly anomalies with respect to the monthly climatology and through the so-called National Meteorological Center (NMC) method. Different formulas for estimating the correlation length scale are also discussed and applied to the two forecast error datasets. The new formulation is tested within a 12-yr period (2000–11) in the ½° resolution system. The comparison with the data assimilation system using uniform background-error horizontal correlations indicates the superiority of the former, especially in eddy-dominated areas. Verification skill scores report a significant reduction of RMSE, and the use of nonuniform length scales improves the representation of the eddy kinetic energy at midlatitudes, suggesting that uniform, latitude, or Rossby radius-dependent formulations are insufficient to represent the geographical variations of the background-error correlations. Furthermore, a small tuning of the globally uniform value of the length scale was found to have a small impact on the analysis system. The use of either anomalies or NMC-derived correlation length scales also has a marginal effect with respect to the use of nonuniform HCLSs. On the other hand, the application of overestimated length scales has proved to be detrimental to the analysis system in all areas and for all parameters.

Detecting transient signals in geodetic time series using sparse estimation techniques

AbstractWe present a new method for automatically detecting transient deformation signals from geodetic time series. We cast the detection problem as a least squares procedure where the design matrix corresponds to a highly overcomplete, nonorthogonal dictionary of displacement functions in time that resemble transient signals of various timescales. The addition of a sparsity‐inducing regularization term to the cost function limits the total number of dictionary elements needed to reconstruct the signal. Sparsity‐inducing regularization enhances interpretability of the resultant time‐dependent model by localizing the dominant timescales and onset times of the transient signals. Transient detection can then be performed using convex optimization software where detection sensitivity is dependent on the strength of the applied sparsity‐inducing regularization. To assess uncertainties associated with estimation of the dictionary coefficients, we compare solutions with those found through a Bayesian inference approach to sample the full model space for each dictionary element. In addition to providing uncertainty bounds on the coefficients and confirming the optimization results, Bayesian sampling reveals trade‐offs between dictionary elements that have nearly equal probability in modeling a transient signal. Thus, we can rigorously assess the probabilities of the occurrence of transient signals and their characteristic temporal evolution. The detection algorithm is applied on several synthetic time series and real observed GPS time series for the Cascadia region. For the latter data set, we incorporate a spatial weighting scheme that self‐adjusts to the local network density and filters for spatially coherent signals. The weighting allows for the automatic detection of repeating slow slip events.

Experimental design for estimating unknown groundwater pumping using genetic algorithm and reduced order model

[1] An optimal experimental design algorithm is developed to select locations for a network of observation wells that provide maximum information about unknown groundwater pumping in a confined, anisotropic aquifer. The design uses a maximal information criterion that chooses, among competing designs, the design that maximizes the sum of squared sensitivities while conforming to specified design constraints. The formulated optimization problem is non-convex and contains integer variables necessitating a combinatorial search. Given a realistic large-scale model, the size of the combinatorial search required can make the problem difficult, if not impossible, to solve using traditional mathematical programming techniques. Genetic algorithms (GAs) can be used to perform the global search; however, because a GA requires a large number of calls to a groundwater model, the formulated optimization problem still may be infeasible to solve. As a result, proper orthogonal decomposition (POD) is applied to the groundwater model to reduce its dimensionality. Then, the information matrix in the full model space can be searched without solving the full model. Results from a small-scale test case show identical optimal solutions among the GA, integer programming, and exhaustive search methods. This demonstrates the GA's ability to determine the optimal solution. In addition, the results show that a GA with POD model reduction is several orders of magnitude faster in finding the optimal solution than a GA using the full model. The proposed experimental design algorithm is applied to a realistic, two-dimensional, large-scale groundwater problem. The GA converged to a solution for this large-scale problem.

Hidden Markov Acoustic Modeling With Bootstrap and Restructuring for Low-Resourced Languages

This paper proposes an acoustic modeling approach based on bootstrap and restructuring to dealing with data sparsity for low-resourced languages. The goal of the approach is to improve the statistical reliability of acoustic modeling for automatic speech recognition (ASR) in the context of speed, memory and response latency requirements for real-world applications. In this approach, randomized hidden Markov models (HMMs) estimated from the bootstrapped training data are aggregated for reliable sequence prediction. The aggregation leads to an HMM with superior prediction capability at cost of a substantially larger size. For practical usage the aggregated HMM is restructured by Gaussian clustering followed by model refinement. The restructuring aims at reducing the aggregated HMM to a desirable model size while maintaining its performance close to the original aggregated HMM. To that end, various Gaussian clustering criteria and model refinement algorithms have been investigated in the full covariance model space before the conversion to the diagonal covariance model space in the last stage of the restructuring. Large vocabulary continuous speech recognition (LVCSR) experiments on Pashto and Dari have shown that acoustic models obtained by the proposed approach can yield superior performance over the conventional training procedure with almost the same run-time memory consumption and decoding speed.

Evaluation of overlaps between arbitrary fermionic quasiparticle vacua

We derive an expression that allows for the unambiguous evaluation of the overlap between two arbitrary quasiparticle vacua, including its sign. Our expression is based on the Pfaffian of a skew-symmetric matrix, extending the formula recently proposed by [L. M. Robledo, Phys. Rev. C 79, 021302(R) (2009)] to the most general case, including the one of the overlap between two different blocked n-quasiparticle states for either even or odd systems. The powerfulness of the method is illustrated for a few typical matrix elements that appear in realistic angular-momentum-restored Generator-Coordinate Method calculations when breaking time-reversal invariance and using the full model space of occupied single-particle states.