A non-negative matrix factorization model based on the zero-inflated Tweedie distribution

Non-negative matrix factorization (NMF) is a technique of multivariate analysis used to approximate a given matrix containing non-negative data using two non-negative factor matrices that has been applied to a number of fields. However, when a matrix containing non-negative data has many zeroes, NMF encounters an approximation difficulty. This zero-inflated situation occurs often when a data matrix is given as count data, and becomes more challenging with matrices of increasing size. To solve this problem, we propose a new NMF model for zero-inflated non-negative matrices. Our model is based on the zero-inflated Tweedie distribution. The Tweedie distribution is a generalization of the normal, the Poisson, and the gamma distributions, and differs from each of the other distributions in the degree of robustness of its estimated parameters. In this paper, we show through numerical examples that the proposed model is superior to the basic NMF model in terms of approximation of zero-inflated data. Furthermore, we show the differences between the estimated basis vectors found using the basic and the proposed NMF models for \(\beta \) divergence by applying it to real purchasing data.     

A switching for all strongly regular collinearity graphs from polar spaces

We describe a general construction of strongly regular graphs from the collinearity graph of a finite classical polar spaces of rank at least 3 over a finite field of order q. We show that these graphs are non-isomorphic to the collinearity graphs and have the same parameters. For most of these parameters, the collinearity graphs were the only known examples, and so many of our examples are new.     

Competitive analysis of price online inventory problem with cost function

In this paper, a new price is given to the online decision maker at the beginning of each day. The trader must decide how many items to purchase according to the current price. We present three variants and an online algorithm based on cost function. The competitive ratio of the online algorithm is given for each variant, which is a performance measure of an online algorithm. More importantly, we show that the online algorithm is optimal.     

Applications of Hyphenated Liquid Chromatography Techniques for Polymer Analysis

We find polymers everywhere in our daily activities, for example, as a part of consumer electronics products, healthcare devices, vehicles, etc. Analytical characterization of such materials is an important step towards understanding their properties and behavior in various applications. The increase of material complexity driven by highly demanding requirements for many applications necessitates the use of sophisticated analytical techniques to obtain sufficient insight into the structure of these materials. Coupling of liquid chromatography with other information-rich instrumental techniques becomes more and more important in the field of polymer characterization. Such combination can enable simultaneous separation, identification, and quantification of polymer sample components. In addition, it can provide information on interdependence of two polymer properties, e.g., molecular weight and chemical composition. Different hyphenated systems may be applied to address different problems in polymer research and development and a selection of the right technique may not be an easy and straightforward task. In this paper, the applications of LC-NMR, LC-IR, LC-Raman, LC-MS, LC-MALDI, LC × LC, and LC × Py-GC for polymer analysis are reviewed, their advantages and limitations are discussed, and practical challenges for the implementation of these techniques in a lab are addressed. Different hyphenated options are compared to facilitate selection of a suitable instrument for the particular problem at hand.     

Analysis of Glycocholic Acid in Human Plasma and Urine from Hepatocellular Carcinoma Patients

Glycocholic acid (GCA) has been identified as endogenous biomarker for hepatocellular carcinoma (HCC). To dissolve protein and liberate GCA from protein, ionic liquids (ILs) that contain chaotropic ions were used for pretreatment of liquid biological samples. Coupling with solid-phase extraction (SPE) and reversed-phase high-performance liquid chromatography (RP-HPLC), the novel sample pretreatment method was applied for quantitative determination of GCA in urine and plasma samples. Compared with the traditional organic solvents pretreatment of biological samples, the proposed method is “greener” and simpler, due to no use of volatile organic solvent, and avoiding centrifugation. Under the optimal conditions, when the GCA-free urine and plasma samples were spiked with GCA at 0.05–1.0 and 0.2–10 μmol L^?1, the recoveries of GCA ranged between 95.8–101.6 and 96.9–100.4%, respectively. These procedures only required 1 mL of urine and 3 mL of 3 mM ILs aqueous solution and 100 μL of plasma and 4 mL of 2 mM ILs aqueous solution, respectively. The proposed method has been successfully validated on a small sample size of 14 HCC patients and 14 healthy volunteers. For HCC patients, the mean concentration of GCA was 24.79 ± 6.86 and 31.98 ± 11.12 μmol L^?1 in urine and plasma samples, and was about 3 times and 24 times as much as in healthy people, respectively. The proposed method opens up a new possibility in early diagnosis of HCC.