The Local Orthogonality between Quantum States and Entanglement Decomposition

For a quantum state $\rho$, let $E_{f}(\rho)$ be the entanglement of formation. Professors Horodecki proved the following important results: If $\rho$ is composed of the locally orthogonal pure state ensemble \{\out{\psi_{i}}{\psi_{i}}\}_{i=1}^K with probability distribution $p=(p_i)$ such that \rho =\sum_{i=1}^{K}p_{i}\out{\psi_{i}}{\psi_{i}}, then E_{f}(\rho) = \sum_{i}p_{i}E_{f}(\out{\psi_{i}}{\psi_{i}}). In this paper, we generalize the conclusion to quantum state $\rho$ which is composed of locally orthogonal quantum state ensemble $\{\rho_{a}\}_{a\in\Sigma}$. Finally, we present an interesting example to show that the conditions of these conclusions are existence

Are All Spillovers Created Equal? The Impact of Blockbusters and the Composition of Backers in Online Crowdfunding

Crowdfunding has emerged alongside the IT development. It is believed that overwhelmingly successful projects, blockbusters, would have significant impacts on the overall crowdfunding platform. However, there are notable limitations in previous studies. First, we consider how the advent of blockbusters impact according to the projects’ similarity with inside and outside clusters, rather than pre-determined category. Second, we examine the blockbusters’ heterogeneity with the type of backers that bring different effects. We use project-level dataset and apply novel clustering method to analyze blockbuster effects. We find empirical evidence that blockbusters have a spillover effect on same categories, especially inside clusters experience larger effects than outside clusters. In the long run, these spillover effects decay faster in outside clusters, but last long for inside cluster. Furthermore, this result changes according to the composition of backers. Our study presents a promising avenue for the application of semantic network analysis to the crowdfunding context

A pathogen-derived metabolite induces microglial activation via odorant receptors

Microglia (MG), the principal neuroimmune sentinels in the brain, continuously sense changes in their environment and respond to invading pathogens, toxins, and cellular debris, thereby affecting neuroinflammation. Microbial pathogens produce small metabolites that influence neuroinflammation, but the molecular mechanisms that determine whether pathogen-derived small metabolites affect microglial activation of neuroinflammation remain to be elucidated. We hypothesized that odorant receptors (ORs), the largest subfamily of G protein-coupled receptors, are involved in microglial activation by pathogen-derived small metabolites. We found that MG express high levels of two mouse ORs, Olfr110 and Olfr111, which recognize a pathogenic metabolite, 2-pentylfuran, secreted by Streptococcus pneumoniae. These interactions activate MG to engage in chemotaxis, cytokine production, phagocytosis, and reactive oxygen species generation. These effects were mediated through the G(alpha s)-cyclic adenosine monophosphate-protein kinase A-extracellular signal-regulated kinase and G(beta gamma)-phospholipase C-Ca2+ pathways. Taken together, our results reveal a novel interplay between the pathogen-derived metabolite and ORs, which has major implications for our understanding of microglial activation by pathogen recognition. Database Model data are available in the PMDB database under the accession number PM0082389.N

Directing the Distribution of Potassium Cations in Zeolite-LTL through Crown Ether Addition

We discover that the crystal morphology of zeolite-LTL could be modified by crown ether (21-crown-7, CE), where CE decreases the aspect ratio of zeolite-LTL while increasing the nucleation of domains on the (0001) face and hindering their growth along the <i>c</i>-axes. Moreover, the study using scanning electron microscopy supports that the ratio between the rates for generation of cancrinite columns and bridging cancrinite columns on the {101̅0} face remains constant among the LTL frameworks with different amounts of CE molecules. In addition, X-ray diffraction analysis shows that potassium cations redistribute into pore cavities (<i>t-lil</i>) from cancrinite cages (<i>t-can</i>) and <i>t-ste</i> cages by the strong interactions between potassium and CE as the amount of CE molecules is increased. Additionally, Monte Carlo simulations clarify that stabilization of the <i>t-lil</i> cage via the redistribution of potassium cations at high CE concentration is attributed to the dominant effect in the crystal morphology changes observed. To understand the catalytic and adsorption properties of zeolites, it is important to investigate their structure/property relationships. Especially, studying the morphology of an anisotropic zeolite crystals has been of great interest because of the strong influence on controlling its properties. Thus, morphological control of the material with a particular crystallographic direction is highly desirable to obtain maximum properties for applications

Silver Nanowire/Carbon Sheet Composites for Electrochemical Syngas Generation with Tunable H₂/CO Ratios

Generating syngas (H₂ and CO mixture) from electrochemically reduced CO₂ in an aqueous solution is one of the sustainable strategies utilizing atmospheric CO₂ in value-added products. However, a conventional single-component metal catalyst, such as Ag, Au, or Zn, exhibits potential-dependent CO₂ reduction selectivity, which could result in temporal variation of syngas composition and limit its use in large-scale electrochemical syngas production. Herein, we demonstrate the use of Ag nanowire (NW)/porous carbon sheet composite catalysts in the generation of syngas with tunable H₂/CO ratios having a large potential window to resist power fluctuation. These Ag NW/carbon sheet composite catalysts have a potential window increased by 10 times for generating syngas with the proper H₂/CO ratio (1.7–2.15) for the Fischer–Tropsch process and an increased syngas production rate of about 19 times compared to that of a Ag foil. Additionally, we tuned the H₂/CO ratio from ∼2 to ∼10 by adjusting only the quantity of the Ag NWs under the given electrode potential. We believe that our Ag NW/carbon sheet composite provides new possibilities for designing electrode structures with a large potential window and controlled CO₂ reduction products in aqueous solutions

The Role of Adsorbed CN and Cl on an Au Electrode for Electrochemical CO₂ Reduction

Electrochemical CO₂ reduction is one of the promising ways to convert CO₂ to value-added products such as CO. Many studies have dealt with suppressing the hydrogen evolution reaction (HER) and increasing the CO₂ reduction reaction (CO₂RR) through modification of the metal surface with additives such as anchoring agent, anion, etc. However, there are only a few studies about modifying the Au surface with additives. We present here a theoretical prediction that the addition of the CN and Cl species on an Au electrode would enhance the electrochemical CO₂RR due to van der Waals interactions with these large anionic species. On the basis of this suggestion, we then prepared functionalized Au electrodes by electroplating in an aqueous solution containing CN^– or Cl^– and experimentally verified that the CO₂RR of functionalized Au indeed shows exceptional CO₂RR activity in comparison to pristine Au

Clinical significance of subclinical atherosclerosis in retinal vein occlusion

Abstract Retinal vein occlusion (RVO) is associated with atherosclerotic cardiovascular risk factors; however, its association with the specific markers of subclinical atherosclerosis has not yet been established. To investigate this association, we compared 70 patients with RVO to 70 age- and sex-matched patients without RVO. Low-density lipoprotein cholesterol (LDL-C) levels and brachial-ankle pulse wave velocity (baPWV) were significantly higher in the RVO group than in the control group. Carotid plaques (54.3% vs. 28.6%, p = 0.004) were more frequent in the RVO group. Multivariate logistic regression analysis showed that the presence of carotid plaques (odds ratio [OR]: 3.15, 95% confidence interval [CI] 1.38–7.16, p = 0.006), as well as smoking, LDL-C level, and baPWV were associated with RVO. Additionally, a multinomial logistic regression model showed that the presence of carotid plaques (OR: 3.94, 95% CI 1.65–9.41, p = 0.002) and LDL-C level were associated with branch RVO, whereas smoking and baPWV were associated with central RVO. In conclusion, RVO was associated with subclinical atherosclerosis markers, including carotid plaques and baPWV. These results support the hypothesis that atherosclerosis contributes to the etiology of RVO and suggest the evaluation of subclinical atherosclerosis in patients with RVO