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

Network-Based Protein Biomarker Discovery Platforms

The advances in mass spectrometry-based proteomics technologies have enabled the generation of global proteome data from tissue or body fluid samples collected from a broad spectrum of human diseases. Comparative proteomic analysis of global proteome data identifies and prioritizes the proteins showing altered abundances, called differentially expressed proteins (DEPs), in disease samples, compared to control samples. Protein biomarker candidates that can serve as indicators of disease states are then selected as key molecules among these proteins. Recently, it has been addressed that cellular pathways can provide better indications of disease states than individual molecules and also network analysis of the DEPs enables effective identification of cellular pathways altered in disease conditions and key molecules representing the altered cellular pathways. Accordingly, a number of network-based approaches to identify disease-related pathways and representative molecules of such pathways have been developed. In this review, we summarize analytical platforms for network-based protein biomarker discovery and key components in the platforms

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 Nonlinear Optimization Model of Advertising Budget Allocation across Multiple Digital Media Channels

The goal of advertisers in the digital marketing industry is to optimize their advertising budgets. Such a budget allocation problem plays a key role in maximizing advertising performance from different marketing channels under planned advertising investment. This study aimed to design a budget-performance-based nonlinear programming model to find an optimized solution for the advertising budget allocation problem. The empirical analysis results of a leading e-business company’s advertising performance data show that the proposed non-LP model generates an optimized solution. The proposed model allows marketers to simulate expected advertising returns, such as conversions or revenues from different channels within their budget constraints

Chromosomal instability in untreated primary prostate cancer as an indicator of metastatic potential.

BackgroundMetastatic prostate cancer (PC) is highly lethal. The ability to identify primary tumors capable of dissemination is an unmet need in the quest to understand lethal biology and improve patient outcomes. Previous studies have linked chromosomal instability (CIN), which generates aneuploidy following chromosomal missegregation during mitosis, to PC progression. Evidence of CIN includes broad copy number alterations (CNAs) spanning > 300 base pairs of DNA, which may also be measured via RNA expression signatures associated with CNA frequency. Signatures of CIN in metastatic PC, however, have not been interrogated or well defined. We examined a published 70-gene CIN signature (CIN70) in untreated and castration-resistant prostate cancer (CRPC) cohorts from The Cancer Genome Atlas (TCGA) and previously published reports. We also performed transcriptome and CNA analysis in a unique cohort of untreated primary tumors collected from diagnostic prostate needle biopsies (PNBX) of localized (M0) and metastatic (M1) cases to determine if CIN was linked to clinical stage and outcome.MethodsPNBX were collected from 99 patients treated in the VA Greater Los Angeles (GLA-VA) Healthcare System between 2000 and 2016. Total RNA was extracted from high-grade cancer areas in PNBX cores, followed by RNA sequencing and/or copy number analysis using OncoScan. Multivariate logistic regression analyses permitted calculation of odds ratios for CIN status (high versus low) in an expanded GLA-VA PNBX cohort (n = 121).ResultsThe CIN70 signature was significantly enriched in primary tumors and CRPC metastases from M1 PC cases. An intersection of gene signatures comprised of differentially expressed genes (DEGs) generated through comparison of M1 versus M0 PNBX and primary CRPC tumors versus metastases revealed a 157-gene "metastasis" signature that was further distilled to 7-genes (PC-CIN) regulating centrosomes, chromosomal segregation, and mitotic spindle assembly. High PC-CIN scores correlated with CRPC, PC-death and all-cause mortality in the expanded GLA-VA PNBX cohort. Interestingly, approximately 1/3 of M1 PNBX cases exhibited low CIN, illuminating differential pathways of lethal PC progression.ConclusionsMeasuring CIN in PNBX by transcriptome profiling is feasible, and the PC-CIN signature may identify patients with a high risk of lethal progression at the time of diagnosis

Systematic analysis of expression signatures of neuronal subpopulations in the VTA

Gene expression profiling across various brain areas at the single-cell resolution enables the identification of molecular markers of neuronal subpopulations and comprehensive characterization of their functional roles. Despite the scientific importance and experimental versatility, systematic methods to analyze such data have not been established yet. To this end, we developed a statistical approach based on in situ hybridization data in the Allen Brain Atlas and thereby identified specific genes for each type of neuron in the ventral tegmental area (VTA). This approach also allowed us to demarcate subregions within the VTA comprising specific neuronal subpopulations. We further identified WW domain-containing oxidoreductase as a molecular marker of a population of VTA neurons that co-express tyrosine hydroxylase and vesicular glutamate transporter 2, and confirmed their region-specific distribution by immunohistochemistry. The results demonstrate the utility of our analytical approach for uncovering expression signatures representing specific cell types and neuronal subpopulations enriched in a given brain area.This work was supported by the grants from National Research Foundations of Korean Ministry of Science and ICT (2018M3C7A1024152, 2018R1A3B1052079, 2019M3A9B6066967, and 2019R1A6A1A10073437) and the Institute for Basic Science (IBS-R013-A1)

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