Integration of Summary Information from External Studies for Semiparametric Models

With the development of biomedical science, researchers have increasing access to an abundance of studies focusing on similar research questions. There is a growing interest in the integration of summary information from those studies to enhance the efficiency of estimation in their own internal studies. In this work, we present a comprehensive framework on integration of summary information from external studies when the data are modeled by semiparametric models. Our novel framework offers straightforward estimators that update conventional estimations with auxiliary information. It addresses computational challenges by capitalizing on the intricate mathematical structure inherent to the problem. We demonstrate the conditions when the proposed estimators are theoretically more efficient than initial estimate based solely on internal data. Several special cases such as proportional hazards model in survival analysis are provided with numerical examples

Novel Constructions of Mutually Unbiased Tripartite Absolutely Maximally Entangled Bases

We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in $\mathbb{C}^{d} \otimes \mathbb{C}^{d} \otimes \mathbb{C}^{d}$ based on mutually orthogonal Latin squares. Then we generalize the approach to the case of $\mathbb{C}^{d_{1}} \otimes \mathbb{C}^{d_{2}} \otimes \mathbb{C}^{d_{1}d_{2}}$ by mutually weak orthogonal Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Detailed examples in $\mathbb{C}^{3} \otimes \mathbb{C}^{3} \otimes \mathbb{C}^{3},$ $\mathbb{C}^{2} \otimes \mathbb{C}^{2} \otimes \mathbb{C}^{4}$ and $\mathbb{C}^{2} \otimes \mathbb{C}^{5} \otimes \mathbb{C}^{10}$ are provided to illustrate the advantages of our approach

Quantum kk-uniform states from quantum orthogonal arrays

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of $N$ systems with dimension of prime power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform states of $N$-qubit systems for arbitrary $N\geq 6$ and $N\neq 7,8,9,11$; 3-uniform states of $N$ systems with dimension of prime power $d\geq 7$ for arbitrary $N\geq 7$.Comment: 26 pages, 1 figure

Mutually unbiased maximally entangled bases from difference matrices

Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish $q$ mutually unbiased bases with $q-1$ maximally entangled bases and one product basis in $\mathbb{C}^q\otimes \mathbb{C}^q$ for arbitrary prime power $q$. In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in $\mathbb{C}^{12}\otimes \mathbb{C}^{12}$ and $\mathbb{C}^{21}\otimes\mathbb{C}^{21}$, which improve the known lower bounds for $d=3m$, with $(3,m)=1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we construct $p+1$ mutually unbiased bases with $p$ maximally entangled bases and one product basis in $\mathbb{C}^p\otimes \mathbb{C}^{p^2}$ for arbitrary prime number $p$.Comment: 24 page

An Efficient Feature Extraction Method, Global Between Maximum and Local Within Minimum, and Its Applications

Feature extraction plays an important role in preprocessing procedure in dealing with small sample size problems. Considering the fact that LDA, LPP, and many other existing methods are confined to one case of the data set. To solve this problem, we propose an efficient method in this paper, named global between maximum and local within minimum. It not only considers the global structure of the data set, but also makes the best of the local geometry of the data set through dividing the data set into four domains. This method preserves relations of the nearest neighborhood, as well as demonstrates an excellent performance in classification. Superiority of the proposed method in this paper is manifested in many experiments on data visualization, face representative, and face recognition

(5,5′-Dicarboxy­biphenyl-2,2′-dicarboxyl­ato-κ2 O 2,O 2′)bis­(1,10-phenanthroline-κ2 N,N′)zinc(II) dihydrate

In the title compound, [Zn(C16H8O8)(C12H8N2)2]·2H2O, the ZnII atom is located on a twofold rotation axis and is six-coordinated by two O atoms from a 5,5′-dicarboxy­biphenyl-2,2′-dicarboxyl­ate ligand and four N atoms from two 1,10-phenanthroline mol­ecules in a distorted octa­hedral geometry. The crystal structure involves O—H⋯O hydrogen bonds

Response surface optimization of light conditions for organic matter accumulation in two different shapes of Arthrospira platensis

Arthrospira platensis has attracted wide attention as a cyanobacteria with high nutritional value. In this research, the response surface method was used to study the effects of light cycle, light intensity and red-blue LED conditions on the growth and organic matter accumulation in spiral shaped strain A. platensis OUC623 and linear shaped strain A. platensis OUC793. The light conditions suitable for A. platensis OUC623 were as follows: growth (light time 12.01 h, light intensity 35.64 μmol/m2s, LED red: blue = 6.38:1); chlorophyll a (light time 12.75 h, light intensity 31.06 μmol/m2s, red: blue = 6.25:1); carotenoid (light time 13.12 h, light intensity 32.25 μmol/m2s, red: blue = 5.79:1); polysaccharide (light time 16.00 h, light intensity 31.32 μmol/m2s, blue: red = 6.24:1); protein (light time 12.18 h, light intensity 6.12 μmol/m2s, blue: red = 7.95:1); phycocyanin (light time12.00 h, light intensity 5.00 μmol/m2s, blue: red = 8.00:1). The light conditions suitable for A. platensis OUC793 were as follows: growth (light time 13.52 h, light intensity 40.22 μmol/m2s, red: blue = 5.98:1); chlorophyll a (light time 14.22 h, light intensity 44.96 μmol/m2s, red: blue = 5.94:1); carotenoid (light time 14.13 h, light intensity 44.50 μmol/m2s, red: blue = 6.02:1); polysaccharide (light time 16.00 h, light intensity 31.85 μmol/m2s, blue: red = 6.08:1); protein (light time12.00 h, light intensity 5.00 μmol/m2s, blue: red = 8.00:1); phycocyanin (light time12.01 h, light intensity 5.01 μmol/m2s, blue: red = 8.00:1). Under the theoretical optimal light conditions, compared with white LED, the growth rate, chlorophyll a, carotenoid, phycocyanin, protein and polysaccharide contents in strain 623 increased by 91.67%, 114.70%, 85.05%, 563.54%, 386.14%, 201.18%, and in strain 793 increased by 75.00%, 150.94%, 113.43%, 427.09%, 1284.71%, 312.38%, respectively. The two strains showed different advantages. Growth rate, chlorophyll a, polysaccharide, protein and phycocyanin content of strain 623 were higher than those of strain 793, while carotenoid was higher in strain 793. After optimization, both strains could reach a good growth state, and the growth rate and organic matter content were close. And then a 20 L photobioreactor was used to expand the culture of the two strains, validating the theoretical optimal light conditions of response surface method. This study laid the foundation for the establishment of optical conditions for organic matter accumulation in two different strains of A. platensis, which provided more options for meeting the industrialization needs of A. platensis