A Note on the Monge-Kantorovich Problem in the Plane

The Monge-Kantorovich mass-transportation problem has been shown to be fundamental for various basic problems in analysis and geometry in recent years. Shen and Zheng (2010) proposed a probability method to transform the celebrated Monge-Kantorovich problem in a bounded region of the Euclidean plane into a Dirichlet boundary problem associated to a nonlinear elliptic equation. Their results are original and sound, however, their arguments leading to the main results are skipped and difficult to follow. In the present paper, we adopt a different approach and give a short and easy-followed detailed proof for their main results

Explaining cocktail party effect and McGurk effect with a spiking neural network improved by Motif-topology

Network architectures and learning principles have been critical in developing complex cognitive capabilities in artificial neural networks (ANNs). Spiking neural networks (SNNs) are a subset of ANNs that incorporate additional biological features such as dynamic spiking neurons, biologically specified architectures, and efficient and useful paradigms. Here we focus more on network architectures in SNNs, such as the meta operator called 3-node network motifs, which is borrowed from the biological network. We proposed a Motif-topology improved SNN (M-SNN), which is further verified efficient in explaining key cognitive phenomenon such as the cocktail party effect (a typical noise-robust speech-recognition task) and McGurk effect (a typical multi-sensory integration task). For M-SNN, the Motif topology is obtained by integrating the spatial and temporal motifs. These spatial and temporal motifs are first generated from the pre-training of spatial (e.g., MNIST) and temporal (e.g., TIDigits) datasets, respectively, and then applied to the previously introduced two cognitive effect tasks. The experimental results showed a lower computational cost and higher accuracy and a better explanation of some key phenomena of these two effects, such as new concept generation and anti-background noise. This mesoscale network motifs topology has much room for the future

Particle transfer and fusion cross-section for Super-heavy nuclei in dinuclear system

Within the dinuclear system (DNS) conception, instead of solving Fokker-Planck Equation (FPE) analytically, the Master equation is solved numerically to calculate the fusion probability of super-heavy nuclei, so that the harmonic oscillator approximation to the potential energy of the DNS is avoided. The relative motion concerning the energy, the angular momentum, and the fragment deformation relaxations is explicitly treated to couple with the diffusion process, so that the nucleon transition probabilities, which are derived microscopically, are time-dependent. Comparing with the analytical solution of FPE, our results preserve more dynamical effects. The calculated evaporation residue cross sections for one-neutron emission channel of Pb-based reactions are basically in agreement with the known experimental data within one order of magnitude.Comment: 19 pages, plus 6 figures, submitted to Phys. Rev.

Efficacy and safety of the compound Chinese medicine SaiLuoTong in vascular dementia: A randomized clinical trial

Introduction: No licensed medications are available to treat vascular dementia (VaD). Methods: Patients were randomly assigned to experimental groups (SaiLuoTong [SLT] 360 or 240 mg for groups A and B for 52 weeks, respectively) or placebo group (SLT 360 mg and 240 mg for group C only from weeks 27 to 52, respectively). Results: Three hundred twenty-five patients were included in final analysis. At week 26, the difference in VaD Assessment Scale-cognitive subscale scores was 2.67 (95% confidence interval, 1.54 to 3.81) for groups A versus C, and 2.48 (1.34 to 3.62) for groups B versus C (both Discussion: This study suggests that SLT is effective for treatment of VaD, and this compound Chinese medicine may represent a better choice to treat VaD

Short- and long-term effects of manganese, zinc and copper ions on nitrogen removal in nitritation-anammox process

This study provided a deep insight into the impacts of trace elements (Mn2+, Zn2+ and Cu2+) on nitritation-anammox process. For short-term exposure, all the three elements could improve the nitrogen removal rate (NRR) and the optimal concentrations were 2.0 mg/L, 2.0 mg/L and 0.5 mg/L for Mn2+, Zn2+ and Cu2+, respectively. Accordingly, the NRR were enhanced 54.62%, 45.93% and 44.09%. The long-term experiments were carried out in lab-scale sequencing batch reactors. The surprising results showed that only Mn2+ addition could enhance the long-term nitritation-anammox process, and the NRR increased from 0.35 ± 0.01 kg N/m3/d (control, no extra trace element addition) to 0.49 ± 0.03 kg N/m3/d. Vice versa, the amendment of Zn2+ reduced the NRR to 0.28 ± 0.02 kg N/m3/d, and Cu2+ had no significant effect on the NRR (0.36 ± 0.01 kg N/m3/d). From the analysis of microbial community structure, it was explained by the increasing abundance of anaerobic ammonium oxidizing bacteria (AnAOB) only in Mn2+ treatment, whereas Zn2+ predominantly promoted ammonium oxidizing bacteria (AOB). Additionally, the majority of Mn2+ was identified inside AnAOB cells, and Zn2+ and Cu2+ were mainly located in AOB. Our results indicated the synergistic effects of trace elements on nitritation-anammox, both short-term encouraging activities of AnAOB and long-term altering microbial community structure. This work implies the importance of trace elements addition in nitritation-anammox process

Differential Effects Of Conifer And Broadleaf Litter Inputs On Soil Organic Carbon Chemical Composition Through Altered Soil Microbial Community Composition

A strategic selection of tree species will shift the type and quality of litter input, and subsequently magnitude and composition of the soil organic carbon (SOC) through soil microbial community. We conducted a manipulative experiment in randomized block design with leaf litter inputs of four native subtropical tree species in a Pinus massoniana plantation in southern China and found that the chemical composition of SOC did not differ significantly among treatments until after 28 months of the experiment. Contrasting leaf litter inputs had significant impacts on the amounts of total microbial, Gram-positive bacterial, and actinomycic PLFAs, but not on the amounts of total bacterial, Gramnegative bacterial, and fungal PLFAs. There were significant differences in alkyl/O-alkyl C in soils among the leaf litter input treatments, but no apparent differences in the proportions of chemical compositions (alkyl, O-alkyl, aromatic, and carbonyl C) in SOC. Soil alkyl/O-alkyl C was significantly related to the amounts of total microbial, and Gram-positive bacterial PLFAs, but not to the chemical compositions of leaf litter. Our findings suggest that changes in forest leaf litter inputs could result in changes in chemical stability of SOC through the altered microbial community composition