Well-posedness of a class of perturbed optimization problems in Banach spaces

AbstractLet X be a Banach space and Z a nonempty subset of X. Let J:Z→R be a lower semicontinuous function bounded from below and p⩾1. This paper is concerned with the perturbed optimization problem of finding z0∈Z such that ‖x−z0‖p+J(z0)=infz∈Z{‖x−z‖p+J(z)}, which is denoted by minJ(x,Z). The notions of the J-strictly convex with respect to Z and of the Kadec with respect to Z are introduced and used in the present paper. It is proved that if X is a Kadec Banach space with respect to Z and Z is a closed relatively boundedly weakly compact subset, then the set of all x∈X for which every minimizing sequence of the problem minJ(x,Z) has a converging subsequence is a dense Gδ-subset of X∖Z0, where Z0 is the set of all points z∈Z such that z is a solution of the problem minJ(z,Z). If additionally p>1 and X is J-strictly convex with respect to Z, then the set of all x∈X for which the problem minJ(x,Z) is well-posed is a dense Gδ-subset of X∖Z0

Motor neuron-derived Thsd7a is essential for zebrafish vascular development via the Notch-dll4 signaling pathway.

BackgroundDevelopment of neural and vascular systems displays astonishing similarities among vertebrates. This parallelism is under a precise control of complex guidance signals and neurovascular interactions. Previously, our group identified a highly conserved neural protein called thrombospondin type I domain containing 7A (THSD7A). Soluble THSD7A promoted and guided endothelial cell migration, tube formation and sprouting. In addition, we showed that thsd7a could be detected in the nervous system and was required for intersegmental vessels (ISV) patterning during zebrafish development. However, the exact origin of THSD7A and its effect on neurovascular interaction remains unclear.ResultsIn this study, we discovered that zebrafish thsd7a was expressed in the primary motor neurons. Knockdown of Thsd7a disrupted normal primary motor neuron formation and ISV sprouting in the Tg(kdr:EGFP/mnx1:TagRFP) double transgenic zebrafish. Interestingly, we found that Thsd7a morphants displayed distinct phenotypes that are very similar to the loss of Notch-delta like 4 (dll4) signaling. Transcript profiling further revealed that expression levels of notch1b and its downstream targets, vegfr2/3 and nrarpb, were down-regulated in the Thsd7a morphants. These data supported that zebrafish Thsd7a could regulate angiogenic sprouting via Notch-dll4 signaling during development.ConclusionsOur results suggested that motor neuron-derived Thsd7a plays a significant role in neurovascular interactions. Thsd7a could regulate ISV angiogenesis via Notch-dll4 signaling. Thus, Thsd7a is a potent angioneurin involved in the development of both neural and vascular systems

Optical Forces in Coupled Chiral Particles

Structural chirality can induce counter-intuitive optical forces due to inherent symmetry properties. While optical forces on a single chiral particle in the Rayleigh regime have been well studied, optical forces in coupled chiral particles remain less explored. By using full-wave numerical simulations and analytical methods of source representation and coupled mode theory, we investigated the optical forces induced by a plane wave on two chiral particles coupling with each other via the evanescent near fields. We found that the induced electric and magnetic dipoles of the chiral particles have complicated couplings that give rise to dark and bright modes. The interaction force between the particles can be either attractive or repulsive, and its magnitude can be significantly enhanced by the resonance modes. The attractive force is much stronger if two particles are of opposite handedness compared with the case of same handedness. The electric dipole force and the magnetic dipole force have the same sign for two particles with the same handedness, while they are of different signs for two particles with opposite handedness. The results can lead to a better understanding of chirality-induced optical forces with potential applications in optical manipulations and chiral light-matter interactions.Comment: 11 pages, 13 figure

Herd Behavior In Global Online Shopping Carnival

We have witnessed the magnificent power of herd behavior exhibited by the frantic crowd during the Alibaba’s global online shopping carnival (OSC) which has made 9 Ginness world’s records within 24 hours. This study explores the cognitive herding process and the critical factors facilitating herd behavior in OSC. Meanwhile, applying the theory of carnival, this study identifies three OSC behaviors which spread through the OSC herd. Using 473 samples from OSC participants, the hypotheses are supported by the empirical results. Information incentive (e.g. promotion motivation and review information) and social influence (e.g. peer mimicry and endorsement influence) are two crucial preconditions for herd behavior; participation, interaction and playfulness capture the essence of OSC behavior. The results provide insights to: (1). the cognitive process of herd behavior; (2). the critical factors facilitating herd behavior in OSC; (3) the important OSC behavior imitated during the herding process

The Immunomodulatory Effect of You-Gui-Wan on Dermatogoides-pteronyssinus-Induced Asthma

The traditional Chinese medicine You-Gui-Wan (YGW) contains ten species of medicinal plants and has been used to improve health in remissive states of asthma for hundreds of years in Asia. However, little is known about the immunomodulatory mechanisms in vivo. Therefore, this study investigated the pathologic and immunologic responses to YGW in mice that had been repeatedly exposed to Dermatogoides-pteronyssinus (Der p). YGW reduced Der-p-induced airway hyperresponsiveness and total IgE in serum. It also inhibited eosinophil infiltration by downregulating the protein expression of IL-5 in serum and changed the Th2-bios in BALF by upregulating IL-12. Results of the collagen assay and histopathologic examination showed that YGW reduced airway remodeling in the lung. In addition, after YGW treatment there was a relative decrease in mRNA expression of TGF-β1, IL-13, eotaxin, RANTES, and MCP-1 in lung in the YGW group. The results of EMSA and immunohistochemistry revealed that YGW inhibited NF-κB expression in epithelial lung cells. YGW exerts its regulative effects in chronic allergic asthmatic mice via its anti-inflammatory activity and by inhibiting the progression of airway remodeling

De-wetting of evaporating drops on regular patterns of triangular posts

Directional wicking and spreading of liquids can be achieved by regular micro-patterns of specifically designed topographic features that break the reflection symmetry of the underlying pattern. The present study aims to understand the formation and stability of wetting films during the evaporation of volatile liquid drops on surfaces with a micro-pattern of triangular posts arranged in a rectangular lattice. Depending on the density and aspect ratio of the posts, we observe either spherical-cap shaped drops with a mobile three-phase contact line or the formation of circular or angular drops with a pinned three-phase contact line. Drops of the latter class eventually evolve into a liquid film extending to the initial footprint of the drop and a shrinking cap-shaped drop sitting on the film. The drop evolution is controlled by the density and aspect ratio of the posts, while no influence of the orientation of the triangular posts on the contact line mobility becomes evident. Our experiments corroborate previous results of systematic numerical energy minimization, predicting that conditions for a spontaneous retraction of a wicking liquid film depend weakly on the orientation of the film edge relative to the micro-pattern

Bifurcation and hysteresis of flow pattern transition in a shallow molten silicon pool with Cz configuration

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