A relation between chiral central charge and ground state degeneracy in 2+1-dimensional topological orders

A bosonic topological order on $d$-dimensional closed space $\Sigma^d$ may have degenerate ground states. The space $\Sigma^d$ with different shapes (different metrics) form a moduli space ${\cal M}_{\Sigma^d}$. Thus the degenerate ground states on every point in the moduli space ${\cal M}_{\Sigma^d}$ form a complex vector bundle over ${\cal M}_{\Sigma^d}$. It was suggested that the collection of such vector bundles for $d$-dimensional closed spaces of all topologies completely characterizes the topological order. Using such a point of view, we propose a direct relation between two seemingly unrelated properties of 2+1-dimensional topological orders: (1) the chiral central charge $c$ that describes the many-body density of states for edge excitations (or more precisely the thermal Hall conductance of the edge), (2) the ground state degeneracy $D_g$ on closed genus $g$ surface. We show that $c D_g/2 \in \mathbb{Z},\ g\geq 3$ for bosonic topological orders. We explicitly checked the validity of this relation for over 140 simple topological orders. For fermionic topological orders, let $D_{g,\sigma}^{e}$ ($D_{g,\sigma}^{o}$) be the degeneracy with even (odd) number of fermions for genus-$g$ surface with spin structure $\sigma$. Then we have $2c D_{g,\sigma}^{e} \in \mathbb{Z}$ and $2c D_{g,\sigma}^{o} \in \mathbb{Z}$ for $g\geq 3$.Comment: 8 pages. This paper supersedes Section XIV of an unpublished work arXiv:1405.5858. We add new results on fermionic topological orders and some numerical check

Entrepreneurship Education and Entrepreneurial Intention: Perspectives on Institutional Theory

Entrepreneurial intentions have been considered a critical element understanding the formation of new venture creations that have been seen in creating jobs and economic growth in a country. This study draws upon institutional environment theory to clarify and test the model using multiple linear regression on entrepreneurship education and three determinants of institutional environment dimensions, namely, regulatory, cogni-tive, and normative dimensions toward entrepreneurial intentions in the context of Esto-nia. A questionnaire-based survey on 265 Estonian university students was conducted to validate the hypotheses of the study. The results suggest that entrepreneurship education has a significant influence on university students’ entrepreneurial intention. Additionally, all three institutional environment determinants moderate the positive relationship be-tween entrepreneurship education and entrepreneurial intention. Interestingly, interaction terms among normative environment, entrepreneurship education, and entrepreneurial intention are statistically significant. Therefore, the results of this study advance institu-tional theory and its application in entrepreneurship research in the context of Estonia. Research paper Keywords: Entrepreneurship education, Entrepreneurial intentions, Institutional environment theory, Estonia, University students Reference to this paper should be made as follows: Wannamakok, W., & Liang, W. (2019). Entrepreneurship Education and Entrepreneurial Intention: Perspectives on Institutional Theory, Journal of Entrepreneurship, Business and Economics, 7(2), 106–129.&nbsp

Vanishing Mean Oscillation Spaces Associated with Operators Satisfying Davies-Gaffney Estimates

Let $(\mathcal{X}, d, \mu)$ be a metric measure space, $L$ a linear operator which has a bounded $H_\infty$ functional calculus and satisfies the Davies-Gaffney estimate, $\Phi$ a concave function on $(0,\infty)$ of critical lower type $p_\Phi^-\in(0,1]$ and $\rho(t)\equiv t^{-1}/\Phi^{-1}(t^{-1})$ for all $t\in(0,\infty)$. In this paper, the authors introduce the generalized VMO space ${\mathrm {VMO}}_{\rho,L}({\mathcal X})$ associated with $L$, and establish its characterization via the tent space. As applications, the authors show that $({\mathrm {VMO}}_{\rho,L}({\mathcal X}))^*=B_{\Phi,L^*}({\mathcal X})$, where $L^*$ denotes the adjoint operator of $L$ in $L^2({\mathcal X})$ and $B_{\Phi,L^*}({\mathcal X})$ the Banach completion of the Orlicz-Hardy space $H_{\Phi,L^*}({\mathcal X})$.Comment: 40 pages, Kyoto J. Math. (to appear

Regularized Wasserstein Means for Aligning Distributional Data

We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the variational transportation to distribute a sparse discrete measure into the target domain. The resulting sparse representation well captures the desired property of the domain while reducing the mapping cost. We demonstrate the scalability and robustness of our method with examples in domain adaptation, point set registration, and skeleton layout

Mining Circumgalactic Baryons in the Low-Redshift Universe

(Abridged) This paper presents an absorption-line study of the multiphase circumgalactic medium (CGM) based on observations of Lya, CII, CIV, SiII, SiIII, and SiIV absorption transitions in the vicinities of 195 galaxies at redshift z<0.176. The galaxy sample is established based on a cross-comparison between public galaxy and QSO survey data and is characterized by a median redshift of =0.041, a median projected distance of =362 kpc to the sightline of the background QSO, and a median stellar mass of log(M_star/M_sun) = 9.7 \pm 1.1. Comparing the absorber features identified in the QSO apectra with known galaxy properties has led to strong constraints for the CGM absorption properties at z<~0.176. First, abundant hydrogen gas is observed out to d~500 kpc, well beyond the dark matter halo radius Rh of individual galaxies, with a mean covering fraction of ~60%. In contrast, no heavy elements are detected at d>~0.7 Rh from either low-mass dwarfs or high-mass galaxies. The lack of detected heavy elements in low- and high-ionization states suggests that either there exists a chemical enrichment edge at d~0.7 Rh or gaseous clumps giving rise to the observed absorption lines cannot survive at these large distances. Considering all galaxies at d>Rh leads to a strict upper limit for the covering fraction of heavy elements of ~3% (at a 95% confidence level) over d=(1-9) Rh. At d<Rh, differential covering fraction between low- and high-ionization gas is observed, suggesting that the CGM becomes progressively more ionized from d<0.3 Rh to larger distances. Comparing CGM absorption observations at low and high redshifts shows that at a fixed-fraction of Rh the CGM exhibits stronger mean absorption at z=2.2 than at z~0. We discuss possible pseudo-evolution of the CGM as a result of misrepresentation of halo radius.Comment: 25 pages, 13 figures; accepted for publication in MNRA