Strategic Asset Seeking and Innovation Performance: The Role of Innovation Capabilities and Host Country Institutions

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Multipole Gravitational Lensing and High-order Perturbations on the Quadrupole Lens

An arbitrary surface mass density of gravitational lens can be decomposed into multipole components. We simulate the ray-tracing for the multipolar mass distribution of generalized SIS (Singular Isothermal Sphere) model, based on the deflection angles which are analytically calculated. The magnification patterns in the source plane are then derived from inverse shooting technique. As have been found, the caustics of odd mode lenses are composed of two overlapping layers for some lens models. When a point source traverses such kind of overlapping caustics, the image numbers change by \pm 4, rather than \pm 2. There are two kinds of images for the caustics. One is the critical curve and the other is the transition locus. It is found that the image number of the fold is exactly the average value of image numbers on two sides of the fold, while the image number of the cusp is equal to the smaller one. We also focus on the magnification patterns of the quadrupole (m = 2) lenses under the perturbations of m = 3, 4 and 5 mode components, and found that one, two, and three butterfly or swallowtail singularities can be produced respectively. With the increasing intensity of the high-order perturbations, the singularities grow up to bring sixfold image regions. If these perturbations are large enough to let two or three of the butterflies or swallowtails contact, eightfold or tenfold image regions can be produced as well. The possible astronomical applications are discussed.Comment: 24 pages, 6 figure

Is the Number of Giant Arcs in LCDM Consistent With Observations?

We use high-resolution N-body simulations to study the galaxy-cluster cross-sections and the abundance of giant arcs in the $\Lambda$CDM model. Clusters are selected from the simulations using the friends-of-friends method, and their cross-sections for forming giant arcs are analyzed. The background sources are assumed to follow a uniform ellipticity distribution from 0 to 0.5 and to have an area identical to a circular source with diameter 1\arcsec. We find that the optical depth scales as the source redshift approximately as \tau_{1''} = 2.25 \times 10^{-6}/[1+(\zs/3.14)^{-3.42}] (0.6<\zs<7). The amplitude is about 50% higher for an effective source diameter of 0.5\arcsec. The optimal lens redshift for giant arcs with the length-to-width ratio ($L/W$) larger than 10 increases from 0.3 for \zs=1, to 0.5 for \zs=2, and to 0.7-0.8 for \zs>3. The optical depth is sensitive to the source redshift, in qualitative agreement with Wambsganss et al. (2004). However, our overall optical depth appears to be only $\sim$ 10% to 70% of those from previous studies. The differences can be mostly explained by different power spectrum normalizations ($\sigma_8$) used and different ways of determining the $L/W$ ratio. Finite source size and ellipticity have modest effects on the optical depth. We also found that the number of highly magnified (with magnification $|\mu|>10$) and ``undistorted'' images (with $L/W<3$) is comparable to the number of giant arcs with $|\mu|>10$ and $L/W>10$. We conclude that our predicted rate of giant arcs may be lower than the observed rate, although the precise `discrepancy' is still unclear due to uncertainties both in theory and observations.Comment: Revised version after the referee's reports (32 pages,13figures). The paper has been significantly revised with many additions. The new version includes more detailed comparisons with previous studies, including the effects of source size and ellipticity. New discussions about the redshift distribution of lensing clusters and the width of giant arcs have been adde

The p-spectral radius of k-partite and k-chromatic uniform hypergraphs

We characterize the r-graph with maximal p-spectral radius among the k-partite r-graphs of order n, and the 3-graph with maximal p-spectral radius among the k-chromatic 3-graphs of order n.Comment: 23 page

Modulatory effects of the landscape sequences on pedestrians emotional states using EEG

This study aimed to investigate the impact of specific landscape elements on pedestrians’ emotional experiences during walking. During the study, footages were recorded by participants while walking to obtain real-time visual element data, including greenery, building and road visibility. And electroencephalogram (EEG) indicators of β/α, (α+θ)/β, θ/β and θ/α ratio were collected to represent levels of arousal, fatigue, attention and relaxation. Our findings suggested strong correlations between θ/α ratio with both greenery and road visibility. Conversely, other indicators were primarily influenced by greenery and building visibility. Regarding the combined impact of elements, the most positive emotions were observed when green visibility exceeded 51%. However, the peak alertness was achieved with building visibility between 5.2% and 31%. The lowest fatigue and the highest attention level were recorded under building visibility less than 5.2%, and the highest level of relaxation occurred with road visibility less than 10%. In terms of the influence of time, the entire walking process could be delineated by the five and 8 min marks, classified into novelty, adaptation and sustained phase based on the patterns of emotional changes observed in the participants. Consequently, the visual elements and their combinations, and duration play regulatory roles in pedestrians' emotional experiences

The colonic macrophage transcription factor RBP-J orchestrates intestinal immunity against bacterial pathogens

Macrophages play pleiotropic roles in maintaining the balance between immune tolerance and inflammatory responses in the gut. Here, we identified transcription factor RBP-J as a crucial regulator of colonic macrophage-mediated immune responses against the enteric pathogen Citrobacter rodentium. In the immune response phase, RBP-J promoted pathogen clearance by enhancing intestinal macrophage-elicited Th17 cell immune responses, which was achieved by maintenance of C/EBPβ-dependent IL-6 production by overcoming miRNA-17∼92-mediated suppressive effects. RBP-J deficiency-associated phenotypes could be genetically corrected by further deleting miRNA-17∼92 in macrophages. In the late phase, noneradicated pathogens in RBP-J KO mice recruited abundant IL-1β-expressing CD64+Ly6C+ colonic macrophages and thereby promoted persistence of ILC3-derived IL-22 to compensate for the impaired innate and adaptive immune responses, leading to ultimate clearance of pathogens. These results demonstrated that colonic macrophage-intrinsic RBP-J dynamically orchestrates intestinal immunity against pathogen infections by interfacing with key immune cells of T and innate lymphoid cell lineages