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

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

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

Panoramic Manifold Projection (Panoramap) for Single-Cell Data Dimensionality Reduction and Visualization

Nonlinear dimensionality reduction (NLDR) methods such as t-Distributed Stochastic Neighbour Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP) have been widely used for biological data exploration, especially in single-cell analysis. However, the existing methods have drawbacks in preserving data’s geometric and topological structures. A high-dimensional data analysis method, called Panoramic manifold projection (Panoramap), was developed as an enhanced deep learning framework for structure-preserving NLDR. Panoramap enhances deep neural networks by using cross-layer geometry-preserving constraints. The constraints constitute the loss for deep manifold learning and serve as geometric regularizers for NLDR network training. Therefore, Panoramap has better performance in preserving global structures of the original data. Here, we apply Panoramap to single-cell datasets and show that Panoramap excels at delineating the cell type lineage/hierarchy and can reveal rare cell types. Panoramap can facilitate trajectory inference and has the potential to aid in the early diagnosis of tumors. Panoramap gives improved and more biologically plausible visualization and interpretation of single-cell data. Panoramap can be readily used in single-cell research domains and other research fields that involve high dimensional data analysis

Response of Landscape and Ecological Characteristics to the Optimal Rainwater Harvesting Dual-Element Mulch Covered Soil Model in Beijing

The implementation of energy conservation and emissions reduction in Beijing prompted yearly increases in the area of urban green space, leading to direct increases in urban water consumption. This aggravated an already tense situation of water shortage. Considering the low irrigation water utilization effectives of the urban green space system, the typical urban greening shrub (Ligustrum vicaryi) was selected as the research object of this study. In a pot experiment, three mulch materials were selected: gravel (CH1), pine needles + gravel (CH2), and bark + gravel (CH3). These materials were set to a uniform thickness of 3 cm, and soil water was maintained between 75% and 85% of the field capacity. Using the analytic hierarchy process and fuzzy mathematics model, the physiological and ecological response characteristics of Ligustrum vicaryi were investigated under different combinations of mulch material. The results for various processing, regarding plant growth, showed CH3 > CH2 > CH1 > CK (Control Check). The leaf area, total leaf area, and leaf area index of CH3 were, respectively, 21.4%, 21.9%, and 62.5% larger than those of the control check (CK). Regarding physiological characteristics, photosynthetic rate, evaporation rate, stomatal conductance, and water use efficiency of CH3 were better than for the other treatments. Regarding ecological services, carbon fixation, oxygen release, cooling, and quantity of humidification of CH3 were optimal. Considered comprehensively for the landscape function, physical characteristics, and ecological services of Ligustrum vicaryi, the preliminary thought is that bark and gravel dual-element mulch, with a layer thickness of 3 cm, was the optimal soil cover treatment for the typical city greening shrub Ligustrum vicaryi. Using the analytic hierarchy process (AHP) and the fuzzy mathematical model for the evaluation of the effects of different soil cover treatments on the landscape function, ecological service function, and physiological characteristics of Ligustrum vicaryi was reliable and feasible. The model evaluation results match the actual ones

Concentration-dependent mechanisms of fluoranthene uptake by ryegrass

Fluoranthene (Flu) uptake by plants is affected by plant growth and environmental concentration. Although plant growth processes, including substance synthesis and antioxidant enzyme activities, have been reported to regulate Flu uptake, their contributions have been poorly evaluated. Moreover, the effect of Flu concentration is little known. Here, low concentrations (0, 1, 5, and 10 mg/L) and high concentrations (20, 30, and 40 mg/L) of Flu were set to compare the changes in Flu uptake by ryegrass (Lolium multiflorum Lam.). Indices of plant growth (biomass, root length, root area, root tip number, and photosynthesis and transpiration rates), substance synthesis (indole acetic acid [IAA] content), and antioxidant enzyme activities (superoxide dismutase [SOD], peroxidase [POD], and catalase [CAT]) were recorded to unravel the mechanism of Flu uptake. Findings suggested that the Langmuir model fitted Flu uptake by ryegrass well. Flu absorption capacity in the root was stronger than that that in the leaf. Flu bioconcentration and translocation factors increased then reduced with the increase in Flu concentration and reached the maximum value under 5 mg/L Flu treatment. Plant growth and IAA content had the same pattern as before bioconcentration factor (BCF). SOD and POD activities increased then decreased with Flu concentration and reached their highest levels under 30 and 20 mg/L Flu treatments, respectively, whereas CAT activity decreased continuously and reached its lowest level under 40 mg/L Flu treatment. Variance partitioning analysis indicated that IAA content had the greatest significant effect on Flu uptake under low-concentration Flu treatments, whereas antioxidant enzyme activities had the greatest significant effect on Flu uptake under high-concentration Flu treatments. Revealing the concentration-dependent mechanisms of Flu uptake could provide a basis for regulating pollutant accumulation in plants

Table1_The nutrient preferences of rice and wheat influence fluoranthene uptake.docx

Applications of the key plant nutrient nitrogen (N) increase the uptake and accumulation of pollutants such as polycyclic aromatic hydrocarbons (PAHs). However, it is unclear how a plant’s preference for a particular form of N in the soil affects the uptake and accumulation of PAHs. In this study, we investigated the physiological mechanisms involved in fluoranthene uptake by rice (Oryza sativa L.) and wheat (Triticum aestivum L.) and examined how these mechanisms were affected by different forms of N treatment under an equivalent N supply. Both N form and plant species affected plant fluoranthene uptake. Rice accumulated more fluoranthene than wheat under an equivalent N supply, while the transfer coefficient of fluoranthene in wheat was higher than that in rice. Fluoranthene accumulation in rice and wheat was positively correlated with plant root morphology parameters, and the transfer coefficient was positively correlated with transpiration. Of the treatments examined, ammonium (NH4+-N)-treated rice and nitrate (NO3−-N)-treated wheat accumulated the most fluoranthene at equivalent N supply. Fluoranthene accumulation was positively correlated with plant growth, total nitrogen N content, total protein content, and antioxidant enzyme activities. Based on a partial least squares path model (PLS-PM) analysis, total plant N was the main factor influencing fluoranthene uptake by rice and wheat treated with different forms of N. Overall, ammonium-preferring rice and nitrate-preferring wheat had the highest nutrient content in their preferred N forms, which also promoted fluoranthene uptake. Therefore, regulating the form of N applied to the soil could be a suitable strategy to improve the safety of agricultural products.</p