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In this paper, we will deal with the following two classes of best approximation problems about the linear manifolds: Problem 1. Given matrices $ A_1, B_1, C_1, $ and $ D_1 \in {\mathbb R}^{ m \times n} $, find $ d(L_1, L_2) = \min_{X\in L_1, Y\in L_2}\|X-Y\|, $ and find $ \hat{X}\in L_1, \hat{Y}\in L_2 $ such that $ \|\hat{X}-\hat{Y}\| = d(L_1, L_2) $, where $ L_1 = \left\{{X \in {\mathbb {SR}} ^{n \times n} \left|{\ \|A_1X-B_1\| = \min}\right.} \right\} $ and $ L_2 = \left\{{Y \in {\mathbb {SR}} ^{n \times n} \left|{\ \|C_1Y-D_1\| = \min}\right.} \right\} $. Problem 2. Given matrices $ A_2, B_2, E_2, F_2 \in {\mathbb R}^{ m \times n} $ and $ C_2, D_2, G_2, H_2 \in {\mathbb R}^{ n \times p} $, find $ d(L_3, L_4) = \min_{X\in L_3, Y\in L_4}\|X-Y\|, $ and find $ \tilde{X}\in L_3, \tilde{Y}\in L_4 $ such that $ \|\tilde{X}-\tilde{Y}\| = d(L_3, L_4) $, where $ L_3 = \left\{{X \in {\mathbb {R}}^{n \times n} \left|{\ \|A_2X-B_2\|^2+||XC_2-D_2\|^2 = \min}\right.} \right\} $ and $ L_4 = \left\{{Y \in {\mathbb {R}} ^{n \times n} \left|{\ \|E_2Y-F_2\|^2+||YG_2-H_2\|^2 = \min}\right.} \right\} $. We obtain explicit formulas for $ d(L_1, L_2) $ and $ d(L_3, L_4), $ and all the matrices in question by using the singular value decompositions and the canonical correlation decompositions of matrices.

ABSTRACTAlthough evidence has shown that vitamin D (VD) influences gut homeostasis, limited knowledge is available how VD regulates intestinal immunity against bacterial infection. In the present study, cyp2r1 mutant zebrafish, lacking the capacity to metabolize VD, and zebrafish fed a diet devoid of VD, were utilized as VD-deficient animal models. Our results confirmed that the expression of antimicrobial peptides (AMPs) and IL-22 was restrained and the susceptibility to bacterial infection was increased in VD-deficient zebrafish. Furthermore, VD induced AMP expression in zebrafish intestine by activating IL-22 signaling, which was dependent on the microbiota. Further analysis uncovered that the abundance of the acetate-producer Cetobacterium in VD-deficient zebrafish was reduced compared to WT fish. Unexpectedly, VD promoted the growth and acetate production of Cetobacterium somerae under culture in vitro. Importantly, acetate treatment rescued the suppressed expression of β-defensins in VD-deficient zebrafish. Finally, neutrophils contributed to VD-induced AMP expression in zebrafish. In conclusion, our study elucidated that VD modulated gut microbiota composition and production of short-chain fatty acids (SCFAs) in zebrafish intestine, leading to enhanced immunity.

Vitamin D (VD) is a major regulator of calcium metabolism in many living organisms. In addition, VD plays a key role in regulating innate and adaptive immunity in vertebrates. Neutrophils constitute an important part of the first line of defense against invading microbes; however, the potential effect of VD on neutrophils remains elusive. Thus, in this study zebrafish in different developmental stages were utilized to identify the potential role of VD in the basal homeostasis and functions of neutrophils. Our results showed that addition of exogenous VD3 promoted granulopoiesis in zebrafish larvae. Reciprocally, neutrophil abundance in the intestine of adult zebrafish with a cyp2r1 mutant, lacking the capacity to 25-hydroxylate VD, was reduced. Moreover, VD-mediated granulopoiesis was still observed in gnotobiotic zebrafish larvae, indicating that VD regulates neutrophil generation independent of the microbiota during early development. In contrast, VD was incapable to influence granulopoiesis in adult zebrafish when the commensal bacteria were depleted by antibiotic treatment, suggesting that VD might modulate neutrophil activity via different mechanisms depending on the developmental stage. In addition, we found that VD3 augmented the expression of il-8 and neutrophil recruitment to the site of caudal fin amputation. Finally, VD3 treatment significantly decreased bacterial counts and mortality in zebrafish infected with Edwardsiella tarda (E. tarda) in a neutrophil-dependent manner. Combined, these findings demonstrate that VD regulates granulopoiesis and neutrophil function in zebrafish immunity.

Memory is an intricate process involving various faculties of the brain and is a central component in human cognition. However, the exact mechanism that brings about memory in our brain remains elusive and the performance of the existing memory models is not satisfactory. To overcome these problems, this paper puts forward a brain-inspired spatio-temporal sequential memory model based on spiking neural networks (SNNs). Inspired by the structure of the neocortex, the proposed model is structured by many mini-columns composed of biological spiking neurons. Each mini-column represents one memory item, and the firing of different spiking neurons in the mini-column depends on the context of the previous inputs. The Spike-Timing-Dependant Plasticity (STDP) is used to update the connections between excitatory neurons and formulates association between two memory items. In addition, the inhibitory neurons are employed to prevent incorrect prediction, which contributes to improving the retrieval accuracy. Experimental results demonstrate that the proposed model can effectively store a huge number of data and accurately retrieve them when sufficient context is provided. This work not only provides a new memory model but also suggests how memory could be formulated with excitatory/inhibitory neurons, spike-based encoding, and mini-column structure.

Short-chain fatty acids (SCFAs) are mainly produced by microbiota through the fermentation of carbohydrates in the intestine. Acetate, propionate, and butyrate are the most abundant SCFA metabolites and have been shown to be important in the maintenance of host health. In this study, head kidney macrophages (HKMs) were isolated and cultured from turbots. We found that the antibacterial activity of HKMs was increased after these cells were incubated with sodium butyrate, sodium propionate or sodium acetate. Interestingly, our results showed that all three SCFAs enhanced the expression of hypoxia inducible factor-1 α (HIF-1α) in HKMs, and further study confirmed that butyrate augmented the oxygen consumption of these cells. Moreover, HIF-1α inhibition diminished the butyrate-promoted intracellular bacterial killing activity of macrophages, and SCFAs also raised the gene expression and activity of lysozymes in HKMs via HIF-1α signaling. In addition, our results suggested that butyrate induced HIF-1α expression and the bactericidal activity of HKMs through histone deacetylase inhibition, while G protein-coupled receptors did not contribute to this effect. Finally, we demonstrated that butyrate induced a similar response in the murine macrophage cell line RAW264.7. In conclusion, our results demonstrated that SCFAs promoted HIF-1α expression via histone deacetylase inhibition, leading to the enhanced production of antibacterial effectors and increased bacterial killing of macrophages.

In order to investigate the ecotoxicological effects of nano-ZnO particles and seawater acidification on marine bivalves, the thick shell mussels, Mytilus coruscus were subjected to joint treatments with different nano-ZnO concentrations (0 [control], 2.5 [medium] and 10 mg L-1 [high]) under two pH levels (7.7 [low]and 8.1 [control]) for 14 days. The results showed that respiration rate (RR), absorption efficiency (AE), clearance rate (CR), O:N ratio and scope for growth (SFG) were significantly reduced with nano-ZnO concentration increase, but ammonium excretion rate (ER) was increased. Low pH significantly reduced CR, RR, SFG, and O:N ratio of the mussels especially under high nano-ZnO conditions, and significantly increased ER. Principal component analysis (PCA) showed consistent relationships among most tested parameters, especially among SFG, RR, O:N ratio and CR under the normal pH and 0 nano-ZnO conditions. Therefore, seawater acidification and nano-ZnO interactively impact the ecophysiological responses of mussels and cause more severe effects when they appear concurrently.

With the release of large amounts of CO2, ocean acidification is intensifying and affecting aquatic organisms. In addition, salinity also plays an important role for marine organisms and fluctuates greatly in estuarine and coastal ecosystem, where ocean acidification frequently occurs. In present study, flow cytometry was used to investigate immune parameters of haemocytes in the thick shell mussel Mytilus coruscus exposed to different salinities (15, 25, and 35‰) and two pH levels (7.3 and 8.1). A 7-day in vivo and a 5-h in vitro experiments were performed. In both experiments, low pH had significant effects on all tested immune parameters. When exposed to decreased pH, total haemocyte count (THC), phagocytosis (Pha), esterase (Est), and lysosomal content (Lyso) were significantly decreased, whereas haemocyte mortality (HM) and reactive oxygen species (ROS) were increased. High salinity had no significant effects on the immune parameters of haemocytes as compared with low salinity. However, an interaction between pH and salinity was observed in both experiments for most tested haemocyte parameters. This study showed that high salinity, low salinity and low pH have negative and interactive effects on haemocytes of mussels. As a consequence, it can be expected that the combined effect of low pH and changed salinity will have more severe effects on mussel health than predicted by single exposure.

Vitamin D (VD) is a fat-soluble sterol that possesses a wide range of physiological functions. The present study aimed to evaluate the effects of VD on folate metabolism in zebrafish and further investigated the underlying mechanism. Wild-type (WT) zebrafish were fed with a diet containing 0 IU/kg VD3 or 800 IU/kg VD3 for 3 wk. Meanwhile, cyp2r1 mutant zebrafish with impaired VD metabolism was used as another model of VD deficiency. Our results showed that VD deficiency in zebrafish suppressed the gene expression of folate transporters, including reduced folate carrier (RFC) and proton-coupled folate transporter (PCFT) in the intestine. Moreover, VD influenced the gene expression of several enzymes related to cellular folate metabolism in the intestine and liver of zebrafish. Importantly, VD-deficient zebrafish contained a remarkably lower level of folate content in the liver. Notably, VD was incapable of altering folate metabolism in zebrafish when gut microbiota was depleted by antibiotic treatment. Further studies proved that gut commensals from VD-deficient fish displayed a lower capacity to produce folate than those from WT fish. Our study revealed the potential correlation between VD and folate metabolism in zebrafish, and gut microbiota played a key role in VD-regulated folate metabolism in zebrafish. [ABSTRACT FROM AUTHOR]