Rank-One Matrix Completion with Automatic Rank Estimation via L1-Norm Regularization

Completing a matrix from a small subset of its entries, i.e., matrix completion is a challenging problem arising from many real-world applications, such as machine learning and computer vision. One popular approach to solve the matrix completion problem is based on low-rank decomposition/factorization. Low-rank matrix decomposition-based methods often require a prespecified rank, which is difficult to determine in practice. In this paper, we propose a novel low-rank decomposition-based matrix completion method with automatic rank estimation. Our method is based on rank-one approximation, where a matrix is represented as a weighted summation of a set of rank-one matrices. To automatically determine the rank of an incomplete matrix, we impose L1-norm regularization on the weight vector and simultaneously minimize the reconstruction error. After obtaining the rank, we further remove the L1-norm regularizer and refine recovery results. With a correctly estimated rank, we can obtain the optimal solution under certain conditions. Experimental results on both synthetic and real-world data demonstrate that the proposed method not only has good performance in rank estimation, but also achieves better recovery accuracy than competing methods

Tensor Rank Estimation and Completion via CP-based Nuclear Norm

Tensor completion (TC) is a challenging problem of recovering missing entries of a tensor from its partial observation. One main TC approach is based on CP/Tucker decomposition. However, this approach often requires the determination of a tensor rank a priori. This rank estimation problem is difficult in practice. Several Bayesian solutions have been proposed but they often under/overestimate the tensor rank while being quite slow. To address this problem of rank estimation with missing entries, we view the weight vector of the orthogonal CP decomposition of a tensor to be analogous to the vector of singular values of a matrix. Subsequently, we define a new CP-based tensor nuclear norm as the L1-norm of this weight vector. We then propose Tensor Rank Estimation based on L1-regularized orthogonal CP decomposition (TREL1) for both CP-rank and Tucker-rank. Specifically, we incorporate a regularization with CP-based tensor nuclear norm when minimizing the reconstruction error in TC to automatically determine the rank of an incomplete tensor. Experimental results on both synthetic and real data show that: 1) Given sufficient observed entries, TREL1 can estimate the true rank (both CP-rank and Tucker-rank) of incomplete tensors well; 2) The rank estimated by TREL1 can consistently improve recovery accuracy of decomposition-based TC methods; 3) TREL1 is not sensitive to its parameters in general and more efficient than existing rank estimation methods

Bilinear Probabilistic Canonical Correlation Analysis via Hybrid Concatenations

Canonical Correlation Analysis (CCA) is a classical technique for two-view correlation analysis, while Probabilistic CCA (PCCA) provides a generative and more general viewpoint for this task. Recently, PCCA has been extended to bilinear cases for dealing with two-view matrices in order to preserve and exploit the matrix structures in PCCA. However, existing bilinear PCCAs impose restrictive model assumptions for matrix structure preservation, sacrificing generative correctness or model flexibility. To overcome these drawbacks, we propose BPCCA, a new bilinear extension of PCCA, by introducing a hybrid joint model. Our new model preserves matrix structures indirectly via hybrid vector-based and matrix-based concatenations. This enables BPCCA to gain more model flexibility in capturing two-view correlations and obtain close-form solutions in parameter estimation. Experimental results on two real-world applications demonstrate the superior performance of BPCCA over competing methods

Dislocation constriction and cross-slip in Al and Ag: an ab initio study

A novel model based on the Peierls framework of dislocations is developed. The new theory can deal with a dislocation spreading at more than one slip planes. As an example, we study dislocation cross-slip and constriction process of two fcc metals, Al and Ag. The energetic parameters entering the model are determined from ab initio calculations. We find that the screw dislocation in Al can cross-slip spontaneously in contrast with that in Ag, which splits into partials and cannot cross-slip without first being constricted. The dislocation response to an external stress is examined in detail. We determine dislocation constriction energy and critical stress for cross-slip, and from the latter, we estimate the cross-slip energy barrier for the straight screw dislocations

Modeling and Optimization of the Dilute Sulfuric Acid Treatment on Corn Stover at Low Temperature

Corn stover was hydrolyzed using dilute sulfuric acid at concentrations of 2, 4, and 6% over reaction times up to 300 minutes at 80oC. The concentrations of sugars (xylose and glucose) and degradation product (furfural) were determined and the kinetic parameters of mathematical models for predicting them in the hydrolysates were obtained. According to the models, an optimal condition for hydrolysis was achieved which was 5% H2SO4 at 80°C for 240min and the liquor contained up to 13.21g/l xylose, 5.07g /l glucose and 0.80g/l furfural. The hydrolysates obtained from corn stover can be used to produce hydrogen and methane by anaerobic fermentation process. The models could be used successfully to predict the concentrations of xylose, glucose and furfural within 0-300min under experimental acid concentration

Restructuring of colloidal aggregates in shear flow: Coupling interparticle contact models with Stokesian dynamics

A method to couple interparticle contact models with Stokesian dynamics (SD) is introduced to simulate colloidal aggregates under flow conditions. The contact model mimics both the elastic and plastic behavior of the cohesive connections between particles within clusters. Owing to this, clusters can maintain their structures under low stress while restructuring or even breakage may occur under sufficiently high stress conditions. SD is an efficient method to deal with the long-ranged and many-body nature of hydrodynamic interactions for low Reynolds number flows. By using such a coupled model, the restructuring of colloidal aggregates under stepwise increasing shear flows was studied. Irreversible compaction occurs due to the increase of hydrodynamic stress on clusters. Results show that the greater part of the fractal clusters are compacted to rod-shaped packed structures, while the others show isotropic compaction.Comment: A simulation movie be found at http://www-levich.engr.ccny.cuny.edu/~seto/sites/colloidal_aggregates_shearflow.htm

Detecting Current Noise with a Josephson Junction in the Macroscopic Quantum Tunneling Regime

We discuss the use of a hysteretic Josephson junction to detect current fluctuations with frequencies below the plasma frequency of the junction. These adiabatic fluctuations are probed by switching measurements observing the noise-affected average rate of macroscopic quantum tunneling of the detector junction out of its zero-voltage state. In a proposed experimental scheme, frequencies of the noise are limited by an on-chip filtering circuit. The third cumulant of current fluctuations at the detector is related to an asymmetry of the switching rates.Comment: 26 pages, 10 figures. To appear in Journal of Low Temperature Physics in the proceedings of the ULTI conference organized in Lammi, Finland (2006

A causal inference study: The impact of the combined administration of Donepezil and Memantine on decreasing hospital and emergency department visits of Alzheimer’s disease patients

Alzheimer’s disease is the most common type of dementia that currently affects over 6.5 million people in the U.S. Currently there is no cure and the existing drug therapies attempt to delay the mental decline and improve cognitive abilities. Two of the most commonly prescribed such drugs are Donepezil and Memantine. We formally tested and confirmed the presence of a beneficial drug-drug interaction of Donepezil and Memantine using a causal inference analysis. We applied doubly robust estimators to one of the largest and high-quality medical databases to estimate the effect of two commonly prescribed Alzheimer’s disease (AD) medications, Donepezil and Memantine, on the average number of hospital or emergency department visits per year among patients diagnosed with AD. Our results show that, compared to the absence of medication scenario, the Memantine monotherapy, and the Donepezil monotherapy, the combined use of Donepezil and Memantine treatment significantly reduces the average number of hospital or emergency department visits per year by 0.078 (13.8%), 0.144 (25.5%), and 0.132 days (23.4%), respectively. The assessed decline in the average number of hospital or emergency department visits per year is consequently associated with a substantial reduction in medical costs. As of 2022, according to the Alzheimer’s Disease Association, there were over 6.5 million individuals aged 65 and older living with AD in the US alone. If patients who are currently on no drug treatment or using either Donepezil or Memantine alone were switched to the combined used of Donepezil and Memantine therapy, the average number of hospital or emergency department visits could decrease by over 613 thousand visits per year. This, in turn, would lead to a remarkable reduction in medical expenses associated with hospitalization of AD patients in the US, totaling over 940 million dollars per year

OmOm Diagnostic for Dilaton Dark Energy

$Om$ diagnostic can differentiate between different models of dark energy without the accurate current value of matter density. We apply this geometric diagnostic to dilaton dark energy(DDE) model and differentiate DDE model from LCDM. We also investigate the influence of coupled parameter $\alpha$ on the evolutive behavior of $Om$ with respect to redshift $z$. According to the numerical result of $Om$, we get the current value of equation of state $\omega_{\sigma0}$=-0.952 which fits the WMAP5+BAO+SN very well.Comment: 6 pages and 6 figures

Health and social care service utilisation and associated expenditure among community-dwelling older adults with depressive symptoms

AIMS: Late-life depression has substantial impacts on individuals, families and society. Knowledge gaps remain in estimating the economic impacts associated with late-life depression by symptom severity, which has implications for resource prioritisation and research design (such as in modelling). This study examined the incremental health and social care expenditure of depressive symptoms by severity. METHODS: We analysed data collected from 2707 older adults aged 60 years and over in Hong Kong. The Patient Health Questionnaire-9 (PHQ-9) and the Client Service Receipt Inventory were used, respectively, to measure depressive symptoms and service utilisation as a basis for calculating care expenditure. Two-part models were used to estimate the incremental expenditure associated with symptom severity over 1 year. RESULTS: The average PHQ-9 score was 6.3 (standard deviation, s.d. = 4.0). The percentages of respondents with mild, moderate and moderately severe symptoms and non-depressed were 51.8%, 13.5%, 3.7% and 31.0%, respectively. Overall, the moderately severe group generated the largest average incremental expenditure (US$5886; 95$3849; 95% CI 2520-5177 or a 176% increase) and the moderate group (US$1843; 95$691; 95% CI 444-939), then gradually fell to negative between scores of 12 (US$- 35; 95$ -171; 95% CI - 417 to 76) and soared to positive and rebounded at the score of 23 (US$601; 95% CI -1652 to 2854). CONCLUSIONS: The association between depressive symptoms and care expenditure is stronger among older adults with mild and moderately severe symptoms. Older adults with the same symptom severity have different care utilisation and expenditure patterns. Non-psychiatric healthcare is the major cost element. These findings inform ways to optimise policy efforts to improve the financial sustainability of health and long-term care systems, including the involvement of primary care physicians and other geriatric healthcare providers in preventing and treating depression among older adults and related budgeting and accounting issues across services