On Degenerate Doubly Nonnegative Projection Problems

The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely positive cone. The major difficulty for implementing a Newton-type method to compute the projection of a given large-scale matrix onto the DNN cone lies in the possible failure of the constraint nondegeneracy, a generalization of the linear independence constraint qualification for nonlinear programming. Such a failure results in the singularity of the Jacobian of the nonsmooth equation representing the Karush–Kuhn–Tucker optimality condition that prevents the semismooth Newton–conjugate gradient method from solving it with a desirable convergence rate. In this paper, we overcome the aforementioned difficulty by solving a sequence of better conditioned nonsmooth equations generated by the augmented Lagrangian method (ALM) instead of solving one aforementioned singular equation. By leveraging the metric subregularity of the normal cone associated with the positive semidefinite cone, we derive sufficient conditions to ensure the dual quadratic growth condition of the underlying problem, which further leads to the asymptotically superlinear convergence of the proposed ALM. Numerical results on difficult randomly generated instances and from the semidefinite programming library are presented to demonstrate the efficiency of the algorithm for computing the DNN projection to a very high accuracy.

Determination of Service Priority Areas as an Effort to Increase Urban Solid Waste Service Coverage (Case study Ngawi Regency)

Limited budget and infrastructure require that a selection be made, which areas prioritize solid waste services. The priority of waste services is determined based on the results of the assessment of the interest scale matrix of the service area. Regions with the highest matrix scores receive priority, followed by sites with lower scores. This study aims to determine the importance of increasing the solid waste service area in Ngawi district, with 19 sub-districts. The results showed that the Ngawi sub-district, as the district capital, Ngawi sub-district was the priority to improve solid waste services, followed by Kedunggalar, Karangjati, Mantingan, and Padas sub-districts.

An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

Attitude estimation is a basic task for most spacecraft missions in aerospace engineering and many Kalman type attitude estimators have been applied to the guidance and navigation of spacecraft systems. By building the attitude dynamics on matrix Lie groups, the invariant Kalman filter (IKF) was developed according to the invariance properties of symmetry groups. However, the Gaussian noise assumption of Kalman theory may be violated when a spacecraft maneuvers severely and the process noise might be heavy-tailed, which is prone to degrade IKF’s performance for attitude estimation. To address the attitude estimation problem with heavy-tailed process noise, this paper proposes a hierarchical Gaussian state-space model for invariant Kalman filtering: The probability density function of state prediction is defined based on student’s t distribution, while the conjugate prior distributions of the scale matrix and degrees of freedom (dofs) parameter are respectively formulated as the inverse Wishart and Gamma distribution. For the constructed hierarchical Gaussian attitude estimation state-space model, the Lie groups rotation matrix of spacecraft attitude is inferred together with the scale matrix and dof parameter using the variational Bayesian iteration. Numerical simulation results illustrate that the proposed approach can significantly improve the filtering robustness of invariant Kalman filter for Lie groups spacecraft attitude estimation problems with heavy-tailed process uncertainty.

An Optimized Experimental Investigation of Foam-Assisted N2 Huff-n-Puff Enhanced Oil Recovery in Fractured Shale Cores

Sustainable development of shale reservoirs and enhanced oil recovery have become a challenge for the oil industry in recent years. Shale reservoirs are typically characterized by nano Darcy-scale matrix, natural fractures, and artificially fractures with high permeability. Some of earlier studies have confirmed that gas huff-n-puff has been investigated and demonstrated as the most effective and promising solution for improving oil recovery in tight shale reservoirs with ultra-low permeability. Fractures provide an advantage in enhancing recovery from shale reservoirs but they also pose serious problems such as severe gas channeling, which led to rapid decline production from a single well. More studies are needed to optimize the process. This paper studies the method of foam-assisted N2 huff-n-puff to enhance oil recovery in fractured shale cores. The influence of foam on oil recovery was analyzed. The effect of matrix permeability, cycle number and production time on oil recovery are also considered. The shale core used in the experiment was from Sichuan Basin, China. For the purpose of comparation and validation, two groups of tests were conducted. One group of tests was N2 huff-n-puff, and the other was foam-N2 huff-n-puff. In the optimization experiment, matrix permeabilities were set as 0.01mD, 0.008mD and 0.001mD, cycle numbers ranged from one to five, the production time is designed to be 1 hour and 24 hours respectively. During the puff period of experiments, the history of oil recovery was closely monitored to reveal the mechanism. During a round of gas injection of fractured shale cores, foam-assisted N2 huff-n-puff oil recovery is 4.59%, which is significantly higher than that of N2 huff-n-puff is only 0.0126%, and the contrast becomes more obvious with the increase of matrix permeability. The results also showed that the cumulative oil recovery increased as the number of cycles was increased, with the same experimental conditions. There is an optimal production time to achieve maximum oil recovery. The cycle numbers, matrix permeability, and production time played important roles in foam-assisted N2 huff-n-puff injection process. Therefore, under certain conditions, foam-N2 huff-n-puff has a positive effect on oil development in fractured shale.

Bacterial Multicellularity: The Biology of Escherichia coli Building Large-Scale Biofilm Communities

Biofilms are a widespread multicellular form of bacterial life. The spatial structure and emergent properties of these communities depend on a polymeric extracellular matrix architecture that is orders of magnitude larger than the cells that build it. Using as a model the wrinkly macrocolony biofilms of Escherichia coli, which contain amyloid curli fibers and phosphoethanolamine (pEtN)-modified cellulose as matrix components, we summarize here the structure, building, and function of this large-scale matrix architecture. Based on different sigma and other transcription factors as well as second messengers, the underlying regulatory network reflects the fundamental trade-off between growth and survival. It controls matrix production spatially in response to long-range chemical gradients, but it also generates distinct patterns of short-range matrix heterogeneity that are crucial for tissue-like elasticity and macroscopic morphogenesis. Overall, these biofilms confer protection and a potential for homeostasis, thereby reducing maintenance energy, which makes multicellularity an emergent property of life itself. Expected final online publication date for the Annual Review of Microbiology, Volume 75 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

On Randomized Trace Estimates for Indefinite Matrices with an Application to Determinants

Randomized trace estimation is a popular and well-studied technique that approximates the trace of a large-scale matrix B by computing the average of $$x^T Bx$$ x T B x for many samples of a random vector X. Often, B is symmetric positive definite (SPD) but a number of applications give rise to indefinite B. Most notably, this is the case for log-determinant estimation, a task that features prominently in statistical learning, for instance in maximum likelihood estimation for Gaussian process regression. The analysis of randomized trace estimates, including tail bounds, has mostly focused on the SPD case. In this work, we derive new tail bounds for randomized trace estimates applied to indefinite B with Rademacher or Gaussian random vectors. These bounds significantly improve existing results for indefinite B, reducing the number of required samples by a factor n or even more, where n is the size of B. Even for an SPD matrix, our work improves an existing result by Roosta-Khorasani and Ascher (Found Comput Math, 15(5):1187–1212, 2015) for Rademacher vectors. This work also analyzes the combination of randomized trace estimates with the Lanczos method for approximating the trace of f(B). Particular attention is paid to the matrix logarithm, which is needed for log-determinant estimation. We improve and extend an existing result, to not only cover Rademacher but also Gaussian random vectors.

Assessment of Successful Drivers of Crowdfunding Projects Based on Visual Analogue Scale Matrix for Criteria Weighting Method

When investing in crowdfunding projects, every investor has some difficulties in selecting the right one. The most important issue is choosing criteria that show the value of the specific project. The aim of this study was to determine which of the criteria are the most important for investors when selecting various crowdfunding projects to fund. A visual analogue scale matrix for criteria weighting (VASMA weighting) methodology was used to determine the main criteria that affect investors’ decisions to invest. The VASMA methodology can capture both objective and subjective parts of criteria weighting. In addition, the risk factor was considered a success driver of crowdfunding projects. The main findings reveal that the criteria of the three risk groups have the highest weights of the VASMA weighting methodology. In this research, only investor preferences were chosen and analyzed for successful crowdfunding project investment. The VASMA weighting methodology’s criteria ranking might help investors select the most exciting crowdfunding project to fund.

Efficient Noninteractive Outsourcing of Large-Scale QR and LU Factorizations

QR and LU factorizations are two basic mathematical methods for decomposition and dimensionality reduction of large-scale matrices. However, they are too complicated to be executed for a limited client because of big data. Outsourcing computation allows a client to delegate the tasks to a cloud server with powerful resources and therefore greatly reduces the client’s computation cost. However, the previous methods of QR and LU outsourcing factorizations need multiple interactions between the client and cloud server or have low accuracy and efficiency in large-scale matrix applications. In this paper, we propose a noninteractive and efficient outsourcing algorithm of large-scale QR and LU factorizations. The proposed scheme is based on the specific perturbation method including a series of consecutive and sparse matrices, which can be used to protect the original matrix and obtain the results of factorizations. The generation and inversion of sparse matrix has small workloads on the client’s side, and the communication cost is also small since the client does not need to interact with the cloud server in the outsourcing algorithms. Moreover, the client can verify the outsourcing result with a probability of approximated to 1. The experimental results manifest that as for the client, the proposed algorithms reduce the computational overhead of direct computation successfully, and it is most efficient compare with the previous ones.