Cholesky Decomposition Research Articles

Finite-field Cholesky decomposed coupled-cluster techniques (ff-CD-CC): theory and application to pressure broadening of Mg by a He atmosphere and a strong magnetic field.

For the interpretation of spectra of magnetic stellar objects such as magnetic white dwarfs (WDs), highly accurate quantum chemical predictions for atoms and molecules in finite magnetic field are required. Especially the accurate description of electronically excited states and their properties requires established methods such as those from coupled-cluster (CC) theory. However, respective calculations are computationally challenging even for medium-sized systems. Cholesky decomposition (CD) techniques may be used to alleviate memory bottlenecks. In finite magnetic field computations, the latter are increased due to the reduction of permutational symmetry within the electron-repulsion-integrals (ERIs) as well as the need for complex-valued data types. CD enables a memory-efficient, approximate description of the ERIs with rigorous error control and thus the treatment of larger systems at the CC level becomes feasible. In order to treat molecules in a finite magnetic field, we present in this work the working equations of the left and right-hand side equations for finite field (ff)-EOM-CD-CCSD for various EOM flavours as well as for the approximate ff-EOM-CD-CC2 method. The methods are applied to the study of the modification of the spectral lines of a magnesium transition by a helium atmosphere that can be found on magnetic WD stars.

Generalized Fused Lasso for Treatment Pooling in Network Meta-Analysis.

This work develops a generalized fused lasso (GFL) approach to fitting contrast-based network meta-analysis (NMA) models. The GFL method penalizes all pairwise differences between treatment effects, resulting in the pooling of treatments that are not sufficiently different. This approach offers an intriguing avenue for potentially mitigating biases in treatment rankings and reducing sparsity in networks. To fit contrast-based NMA models within the GFL framework, we formulate the models as generalized least squares problems, where the precision matrix depends on the standard error in the data, the estimated between-study heterogeneity and the correlation between contrasts in multi-arm studies. By utilizing a Cholesky decomposition of the precision matrix, we linearly transform the data vector and design matrix to frame NMA within the GFL framework. We demonstrate how to construct the GFL penalty such that every pairwise difference is penalized similarly. The model is straightforward to implement in R via the "genlasso" package, and runs instantaneously, contrary to other regularization approaches that are Bayesian. A two-step GFL-NMA approach is recommended to obtain measures of uncertainty associated with the (pooled) relative treatment effects. Two simulation studies confirm the GFL approach's ability to pool treatments that have the same (or similar) effects while also revealing when incorrect pooling may occur, and its potential benefits against alternative methods. The novel GFL-NMA method is successfully applied to a real-world dataset on diabetes where the standard NMA model was not favored compared to the best-fitting GFL-NMA model with AICc selection of the tuning parameter ( .

Adding gastrointestinal parasite resistance to the breeding objective in hair sheep: initial steps.

The U.S. Maternal Hair index was designed by the National Sheep Improvement Program (NSIP) to increase total weight of lamb weaned per ewe lambing (TW). Producers are interested in adding gastrointestinal nematode (GIN) resistance to this breeding objective since parasitism causes substantial economic losses. The NSIP provides producers with estimated breeding values (EBV) for post-weaning fecal egg count (PFEC), an indicator of GIN resistance. Our objective was to gauge the effects of including PFEC as another selection criterion and goal trait. Selection index theory was used to construct 11 indexes. First was a benchmark index with TW as the goal. Weaning weight, and number of lambs born and weaned, were selection criteria. An index was then designed with PFEC added as a selection criterion. In 9 more indices, PFEC was also included as a goal trait, where the economic value of TW was scaled relative to that of PFEC. PFEC received a scaled economic value of -1 with that of TW increasing from +1 to +5 at +0.5 increments. Selection criteria were modelled as EBV or phenotypes. Annual genetic responses in goal traits were predicted. The top 3% of males and 26% of females were selected. Breeding values and phenotypes were simulated for 200 lambs by Cholesky decomposition and used to generate index scores, with 100 replicates run. Concordances with the animals selected in the benchmark scenario were determined. Using EBV as selection criteria, TW increased by 1.46kg/yr in the benchmark scenario. However, unfavorably, PFEC increased by 2.24%/yr. When using phenotypic criteria, TW increased by 0.52kg/yr and PFEC by 0.28%/yr. Once added as a goal trait, PFEC decreased regardless of the scaled economic value of TW. However, responses in TW were also reduced, although less so as its scaled economic value increased. A scaled economic value of +3 for TW appeared reasonable over other choices with 79% of the emphasis placed on TW in the breeding objective. With EBV as selection criteria, PFEC declined by 7.96%/yr with 98% of the response in TW retained. Also, on average, 64% of males and 80% of females were chosen in common with the benchmark. With phenotypic selection criteria, PFEC declined by 5.13%/yr and 94% of the response in TW was retained; 61% of males and 80% of females were chosen in common with the benchmark. Implementing an index with scaled economic values of +3 for TW and -1 for PFEC would balance gains in TW with reductions in PFEC.

A Consistent Comparison of Upper Subcritical Limit Methods

This study conducts a consistent and comprehensive comparison of several methods for estimating upper subcritical limits (USLs) for nuclear criticality safety analysis. To eliminate inconsistency caused by the discrepancy between the estimated covariance data and the true degree of uncertainty present in nuclear data, the experimental system eigenvalues k exp were assumed to equal the calculated eigenvalue for the systems using nominal ENDF/B-VII.1 cross sections, and the estimated calculated eigenvalue k calc was assumed to equal the calculated eigenvalue for the systems using nuclear data from one perturbed cross-section library. USLs are estimated for a variety of validation application cases using the Whisper, TSURFER, and USLSTATS tools and are compared to a reference 95/95 limit. The TSURFER approach produced the strongest agreement with the reference USLs; the Whisper produced USLs that were reliably conservative compared to the reference USL; and the USLSTATS approach experienced difficulty consistently producing accurate USL estimates. Last, this study observed a noteworthy discrepancy when using Cholesky decomposition to randomly sample neutron cross-section covariance data that are small in magnitude.

Iterative Methods for Vecchia-Laplace Approximations for Latent Gaussian Process Models

Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is a fast method with asymptotic convergence guarantees to approximate marginal likelihoods and posterior predictive distributions for non-Gaussian likelihoods. Unfortunately, the computational complexity of combined Vecchia-Laplace approximations grows faster than linearly in the sample size when used in combination with direct solver methods such as the Cholesky decomposition. Computations with Vecchia-Laplace approximations can thus become prohibitively slow precisely when the approximations are usually the most accurate, i.e., on large data sets. In this article, we present iterative methods to overcome this drawback. Among other things, we introduce and analyze several preconditioners, derive new convergence results, and propose novel methods for accurately approximating predictive variances. We analyze our proposed methods theoretically and in experiments with simulated and real-world data. In particular, we obtain a speed-up of an order of magnitude compared to Cholesky-based calculations and a threefold increase in prediction accuracy in terms of the continuous ranked probability score compared to a state-of-the-art method on a large satellite data set. All methods are implemented in a free C++ software library with high-level Python and R packages. 4

Multivariate prototype representation for domain-generalized incremental learning

Deep learning models often suffer from catastrophic forgetting when fine-tuned with samples of new classes. This issue becomes even more challenging when there is a domain shift between training and testing data. In this paper, we address the critical yet less explored Domain-Generalized Class-Incremental Learning (DGCIL) task. We propose a DGCIL approach designed to memorize old classes, adapt to new classes, and reliably classify objects from unseen domains. Specifically, our loss formulation maintains classification boundaries while suppressing domain-specific information for each class. Without storing old exemplars, we employ knowledge distillation and estimate the drift of old class prototypes as incremental training progresses. Our prototype representations are based on multivariate Normal distributions, with means and covariances continually adapted to reflect evolving model features, providing effective representations for old classes. We then sample pseudo-features for these old classes from the adapted Normal distributions using Cholesky decomposition. Unlike previous pseudo-feature sampling strategies that rely solely on average mean prototypes, our method captures richer semantic variations. Experiments on several benchmarks demonstrate the superior performance of our method compared to the state of the art.

Statistically sound identification of compounds by low-resolution GC-MS: Identification of tear agents in tear gas sprays

Gas-chromatography hyphenated with low-resolution mass spectrometry is a very flexible tool for the cost-effective identification and quantification of volatile compounds in complex matrices. In some analytical fields, criteria for the agreement between retention time and mass spectra of the analyte in calibrators and samples are defined based on the general understanding of the performance of these parameters. However, since this harmonization is not based on experimental performance observed for specific GC-MS conditions and analyte it leads to false identifications. This research proposes a novel and robust tool for defining statistically sound criteria for the identification of compounds by GC-MS and LC-MS using experimental data. The Monte Carlo Method (MCM) simulation of the correlated abundance of characteristic ions of analyte mass spectrum allows simulating the abundance ratio difference of the analyte in a calibrator and sample used for statistically sound identifications. The Cholesky decomposition of the covariance matrix of ion abundances for MCM simulations allows the reliable use of many ion abundance ratios in identifications. The developed methodology was implemented in a user-friendly Excel spreadsheet and applied to the identification of tear gas agents in tear gas sprays. Criteria defined by SANTE for identifying pesticide residues in foodstuffs were compared with the developed tool. The cross-validation of computational and SANTE tools allowed concluding that the statistical control of retention time and mass spectra performs according to the defined confidence level. On the other hand, the SANTE criteria can produce up to 92% false identifications for being too strict considering signal dispersion.

Cholesky Decomposition in Spin-Free Dirac-Coulomb Coupled-Cluster Calculations.

We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost comparable to those of their nonrelativistic counterparts. While for nonrelativistic CC calculations, atomic-orbital (AO)-based algorithms, due to their significantly reduced disk-space requirements, are the key to efficient large-scale computations, such algorithms are less advantageous in the SFDC case due to their increased computational cost in that case. Here, molecular-orbital (MO)-based algorithms exploiting the CD of the two-electron integrals allow us to reduce disk-space requirements and lead to computational cost in the CC step that is more or less the same as in the nonrelativistic case. The only remaining overhead in a CD-SFDC-CC calculation is due to the need to compute additional two-electron integrals, the somewhat higher cost of the Hartree-Fock calculation in the SFDC case, and additional cost in the transformation of the Cholesky vectors from the AO to the MO representation. However, these additional costs typically amount to less than 5-15% of the total wall time and are thus acceptable. We illustrate the efficiency of our CD scheme for SFDC-CC calculations on a series of illustrative calculations for the X(CO)4 molecules with X = Ni, Pd, Pt.

Performance analysis of multiuser mmWave DCT-spread CP-Less OFDM communication system

In this paper, we propose a framework for multiuser mmWave DCT-Spread CP-less OFDM communication system and analyze it comprehensively. Due to excessive cyclic prefix (CP) usage in conventional multicarrier systems, spectral efficiency reduces and increases transmission latency. Our proposed system enhances spectral efficiency and reduces transmission latency. We introduce an image encryption algorithm based on DNA encoding combined with a chaotic map is introduced to enhance physical layer security (PLS). The impact of block diagonalization (BD) channel precoding for multiuser interference (MUI) reduction and designed subcarrier mapping with time-domain Tukey windowing for out-of-band (OOB) power emission reduction are investigated. In addition, the paper studies the applicability of discrete cosine transforms (DCT)-Spreading for peak-to-average power ratio (PAPR) reduction. Simulation results demonstrate that Turbo and Repeat and Accumulate (RA) channel coding and minimum mean square error (MMSE) and Cholesky decomposition (CD)-based zero-forcing (ZF) signal detection schemes improve bit error rate (BER) performance of the proposed system for different users.

Social isolation and poor mental health in young people: testing genetic and environmental influences in a longitudinal cohort study.

We assessed genetic and environmental influences on social isolation across childhood and the overlap between social isolation and mental health symptoms including depression symptoms, conduct problems, and psychotic-like experiences from adolescence to young adulthood. Participants included 2,232 children from the Environmental Risk Longitudinal Twin Study. Social isolation was measured at ages 5, 7, 10, 12, and 18. A Cholesky decomposition was specified to estimate the genetic and environmental influences on social isolation across ages 5, 7, 10, and 12. An independent pathway model was used to assess additive genetic (A), shared environmental (C), and non-shared environmental (E) influences on the overlap between social isolation and mental health problems from age 12 to 18. Genetic and non-shared environmental influences accounted for half of the variance in childhood social isolation. Genetic influences contributed to the continuity of social isolation across childhood, while non-shared environmental influences were age-specific. The longitudinal overlap between social isolation and mental health symptoms was largely explained by genetic influences for depression symptoms (r = 0.15-0.24: 82-84% A, 11-12% C, and 5-6% E) and psychotic-like experiences (r = 0.13-0.15: 81-91% A, 0-8% C, and 9-11% E) but not conduct problems (r = 0.13-0.16; 0-42% A, 42-81% C, 16-24% E). Our findings emphasise that rather than a risk factor or an outcome, social isolation is aetiologically intertwined with the experience of poor mental health. An integrative assessment of social isolation could be a helpful indicator of underlying mental health symptoms in young people.

Testing the Deliberate Practice Theory: Does Practice Reduce the Heritability of Musical Expertise?

The deliberate practice (DP) theory claims that expertise essentially reflects the accumulated amount of deliberate practice, and that with sufficient practice, genetic influences on expertise will be bypassed. Thus, a core prediction of the DP theory is that genetic effects on performance decrease as a function of practice. Here, we test this prediction using music as a model domain. Musical expertise (measured with a musical auditory discrimination test) and lifetime practice hours were determined in 6471 twins including 1302 complete twin pairs. We fitted a bivariate Cholesky decomposition with practice hours as a moderator to determine to what extent genetic and environmental influences on musical expertise are influenced by practice hours. On average, 50% of individual differences in musical expertise were due to genetic influences, whereas shared environmental and residual influences each explained about 25%. Importantly, music practice significantly moderated these estimates. Variation in musical expertise decreased with more practice hours due to decreased shared environmental and residual variance. In contrast, the overall genetic component was unaffected by the number of practice hours. Consequently, the relative genetic contribution (heritability) increased with more practice hours. These findings are in contrast with predictions from the DP theory and suggest that genetic predisposition remains important for musical expertise even after prolonged practice.

The Linear Algebra of the Pell-Lucas Matrix

In this paper, we introduce the Pell-Lucas and the symmetric Pell-Lucas matrices. The study delves into the linear algebra aspects of these matrices, analyzing their mathematical properties and relationships. We construct decompositions for both the Pell-Lucas matrix and its inverse matrix. We present the Cholesky factorization of the symmetric Pell-Lucas matrices. Furthermore, we derive some valuable identities and bounds for the eigenvalues of these symmetric matrices through the application of majorization notation.

Randomized Cholesky Factorization With Threshold-Based Multisampling for Power Grid Simulation

Randomized Cholesky Factorization With Threshold-Based Multisampling for Power Grid Simulation

Central bank information effects in Japan: the role of uncertainty channel

AbstractThis study identifies central bank information shocks and pure monetary policy shocks for Japan by combining high-frequency identification with sign restrictions. The empirical findings provide robust evidence of the central bank information effect in Japan. Specifically, the central bank’s optimistic outlook, conveyed through contractionary monetary actions, reduces economic uncertainty and leads to increases in stock prices and output. Additionally, changes in uncertainty play a significant role in the transmission of the central bank’s information effect. The overall impact of monetary policy and information shocks, as identified through our method, is found to be larger than that identified using conventional techniques such as Cholesky decomposition.

Quantum geometrodynamics revived: II. Hilbert space of positive definite metrics

Abstract This paper represents the second in a series of works aimed at reinvigorating the quantum geometrodynamics program. Our approach introduces a lattice regularization of the hypersurface deformation algebra, such that each lattice site carries a set of canonical variables given by the components of the spatial metric and the corresponding conjugate momenta. In order to quantize this theory, we describe a representation of the canonical commutation relations that enforces the positivity of the operators q_{ab} s^a s^b for all choices of s. Moreover, symmetry of q_{ab} and p^{ab} is ensured. This reflects the physical requirement that the spatial metric should be a positive definite, symmetric tensor. To achieve this end, we resort to the Cholesky decomposition of the spatial metric into upper triangular matrices with positive diagonal entries. Moreover, our Hilbert space also carries a representation of the vielbein fields and naturally separates the physical and gauge degrees of freedom. Finally, we introduce a generalization of the Weyl quantization for our representation. We want to emphasize that our proposed methodology is amenable to applications in other fields of physics, particularly
in scenarios where the configuration space is restricted by complicated relationships among the degrees of freedom.

The imprint of conservation laws on correlated particle production

The study of event-by-event fluctuations of net-baryon number in a subspace of full phase space is a promising direction for deciphering the structure of strongly interacting matter created in collisions of relativistic heavy nuclei. Such fluctuations are generally suppressed by exact baryon number conservation. Moreover, the suppression is stronger if baryon number is conserved locally. In this report we present a conceptually new approach to quantify correlations in rapidity space between baryon-antibaryon, baryon-baryon, and antibaryon-antibaryon pairs and demonstrate their impact on net-baryon number fluctuations. For the special case of Gaussian rapidity distributions, we use the Cholesky factorization of the covariance matrix, while the general case is introduced by exploiting the well-known Metropolis and Simulated Annealing methods. The approach is based on the use of the canonical ensemble of statistical mechanics for baryon number and can be applied to study correlations between baryons as well as strange and/or charm hadrons. It can also be applied to describe relativistic nuclear collisions leading to the production of multi-particle final states. One application of our method is the search for formation of proton clusters at low collision energies emerging as a harbinger of the anticipated first-order chiral phase transition. In a first step, the results obtained are compared to the recent measurements from the CERN ALICE collaboration. Such investigations are key to explore the phase diagram of strongly interacting matter and baryon production mechanisms at energy scales from several GeV to several TeV.

A Line-Search-Based Algorithm for Multiphase Flash Calculations with CO2-Hydrocarbon System.

Multiphase flash calculations are pivotal in compositional simulation, necessitating a robust and efficient computational algorithm. In this work, we have developed a line-search-based algorithm framework for stability analysis and multiphase flash calculations. This algorithm is rooted in the modified Newton step and line-search method. The modified Newton step, derived from modified Cholesky factorization, ensures a descent direction, while the line search determines the degree of decrease. This combination facilitates convergence even in challenging regions for phase stability analysis and multiphase flash calculations, exhibiting superlinear convergence speed. Unlike traditional approaches that rely on successive substitution iteration and may resort to Newton iteration only if the Hessian matrix is positive definite, our algorithm incorporates modification via modified Cholesky factorization upon encountering a nonpositive definite Hessian matrix. We tested our algorithm with several classical fluids, demonstrating its efficiency and robustness. Furthermore, we assessed the algorithm's performance by computing the pressure-composition diagram for the CO2-hydrocarbon system, where all calculations achieved rapid convergence without failure. This newly developed algorithm for phase stability analysis and multiphase flash calculations represents a significant advancement for compositional or chemical process simulations.

Response surface method-based efficient approach for the load and resistance factors calibration of breakwater foundation considering soil spatial variability

This study aims to propose an efficient approach to calibrate the load and resistance factors (LRFs) for the limit state design of breakwater foundations. The spatial variability of soil was considered by employing the Cholesky decomposition technique. To overcome the low computational efficiency of the Monte Carlo simulation (MCS), a response surface method (RSM) was utilized. Additionally, an efficient algorithm, namely the adaptive boundary-based particle filtering algorithm (ABB-PFA), was proposed with the use of RSM to automatically and quickly search optimal nominal values of random variables in the LRF calibration process. Noticeably, the optimal number of particles and values of the modification factor used in the ABB-PFA were observed to enhance the efficiency of the calibration process. The results showed that the computational efficiency of the calibration process is significantly increased by utilizing the response surface method and the proposed ABB-PFA. The efficiency increases the most if the number of particles is one and the value of the modification factor is 0.5 or 0.6. The influences of the random field element size on the efficiency of the calibration process were also investigated. By using the appropriate size, the efficiency is significantly increased while still obtaining a high accuracy of the LRFs calibration process.

A methodology to correlate river inflows in state sampling Monte Carlo simulation

This paper proposes a methodology to sample inflow states of run-of-the-river hydropower plants that are spatially correlated, preserving the statistical dependence among them, in Non-Sequential Monte Carlo Simulation (MCS). The technique used to correlate the inflows of hydro plants in the Brazilian synthetic series generation model, which is based on the correlation matrix and Cholesky Decomposition, is adapted to be used in the sampling stage. Nataf transformation is used for addressing non-normality of the inflow data. The solution method is such that no assumption about the data probability distribution is necessary. Although the methodology is applied to inflows in this paper, it can be applied to any other quantity, such as winds. A case study is proposed to evaluate the correlation of the sampled inflows and the impact on the reliability indices. Besides, it is investigated the effect when inflows states are clustered to reduce the number of states in the system for better computational efficiency. Case study shows that the reliability indices obtained with the proposed methodology are within the confidence interval of the indices calculated by the Sequential MCS with an execution time as fast as the Non-Sequential one, while the non-consideration of correlation causes very significant errors. Simulation with 50 clusters produces equally good results with a reduction of 75 % of the execution time. Sensitivity analysis showed that halving the number of clusters maintains the accuracy of the results, while 10 clusters results in overestimating system reliability. Different degrees of correlation have been simulated, showing that the higher the correlation among the hydro plants, the less reliable the system becomes.

EEG Motor Imagery Classification: Tangent Space with Gate-Generated Weight Classifier.

Individuals grappling with severe central nervous system injuries often face significant challenges related to sensorimotor function and communication abilities. In response, brain-computer interface (BCI) technology has emerged as a promising solution by offering innovative interaction methods and intelligent rehabilitation training. By leveraging electroencephalographic (EEG) signals, BCIs unlock intriguing possibilities in patient care and neurological rehabilitation. Recent research has utilized covariance matrices as signal descriptors. In this study, we introduce two methodologies for covariance matrix analysis: multiple tangent space projections (M-TSPs) and Cholesky decomposition. Both approaches incorporate a classifier that integrates linear and nonlinear features, resulting in a significant enhancement in classification accuracy, as evidenced by meticulous experimental evaluations. The M-TSP method demonstrates superior performance with an average accuracy improvement of 6.79% over Cholesky decomposition. Additionally, a gender-based analysis reveals a preference for men in the obtained results, with an average improvement of 9.16% over women. These findings underscore the potential of our methodologies to improve BCI performance and highlight gender-specific performance differences to be examined further in our future studies.