2-permutations of lattice vertex operator algebras: Higher rank
The fusion rules of the 2-permutation orbifold of an arbitrary lattice vertex operator algebra are determined by using the theory of quantum dimension.
math.QA↗
arXiv subjects
Feng Xu
Publications and source records attributed to Feng Xu.
Constraining A String Gauge Field by Galaxy Rotation Curves and Perihelion Precession of Planets
We discuss a cosmological model in which the string gauge field coupled universally to matter gives rise to an extra centripetal force and will have observable signatures on cosmological and astronomical observations. Several tests are performed using data including galaxy rotation curves of 22 spiral galaxies of varied luminosities and sizes, and perihelion precessions of planets in the solar system. The rotation curves of the same group of galaxies are independently fit using a dark matter model with the generalized Navarro--Frenk--White (NFW) profile and the string model. A Remarkable fit of galaxy rotation curves is achieved using the one-parameter string model as compared to the three-parameter dark matter model with the NFW profile. The average $χ^2$ value of the NFW fit is 9\% better than that of the string model at a price of two more free parameters. Furthermore, from the string model, we can give a dynamical explanation for the phenomenological Tully-Fisher relation. We are able to derive a relation between field strength, galaxy size and luminosity, which can be verified with data from the 22 galaxies. To further test the hypothesis of the universal existence of the string gauge field, we apply our string model to the solar system. Constraint on the magnitude of the string field in the solar system is deduced from the current ranges for any anomalous perihelion precession of planets allowed by the latest observations. The field distribution resembles a dipole field originating from the Sun. The string field strength deduced from the solar system observations is of a similar magnitude as the field strength needed to sustain the rotational speed of the Sun inside the Milky Way. This hypothesis can be tested further by future observations with higher precision.
hep-th↗
Shear-Exfoliated Phosphorene for Rechargeable Nanoscale Battery
Discovery of atomically thin black phosphorus (called phosphorene) holds promise to be used as an alternative two-dimensional material to graphene and transition metal dichalcogenides especially as an anode material for lithium-ion batteries (LIBs). However, at present bulk black phosphorus (BP) still suffers from rapid capacity fading that results in poor rechargeable performance. Here, for the first time, we use in situ transmission electron microscopy (TEM) to construct nanoscale phosphorene LIBs and visualize the capacity fading mechanism in thick multilayer phosphorene by real time capturing delithiation-induced structural decomposition that reduces electrical conductivity and thus causes irreversibility of lithiated Li3P phase. We further demonstrate that few-layer phosphorene successfully circumvents the structural decomposition and holds superior structural restorability, even subjected to multi-cycle lithiation/delithiation processes and concomitant huge volume expansion. This finding affords new experimental insights into thickness-dependent lithium diffusion kinetics in phosphorene. Additionally, a scalable liquid-phase shear exfoliation route has been developed to produce high-quality ultrathin (monolayer or few-layer) phosphorene, only by a high-speed shear mixer or even a household kitchen blender with the shear rate threshold, which will pave the way for potential large-scale applications in LIBs once the rechargeable phosphorene nanoscale batteries can be transferred to industrialized enlargement in the future.
cond-mat.mtrl-sci↗
On Orbifold Theory
Let V be a simple vertex operator algebra and G a finite automorphism group of V such that V^G is regular. It is proved that every irreducible V^G-module occurs in an irreducible g-twisted V-module for some g in G. Moreover, the quantum dimensions of each irreducible V^G-module are determined and a global dimension formula for V in terms of twisted modules is obtained.
math.QA↗
Cyclic permutations of lattice vertex operator algebras
The irreducible modules of the 2-cycle permutation orbifold models of lattice vertex operator algebras of rank 1 are classified, the quantum dimensions of irreducible modules and the fusion rules are determined.
math.QA↗
N=2 superconformal nets
We provide an Operator Algebraic approach to N=2 chiral Conformal Field Theory and set up the Noncommutative Geometric framework. Compared to the N=1 case, the structure here is much richer. There are naturally associated nets of spectral triples and the JLO cocycles separate the Ramond sectors. We construct the N=2 superconformal nets of von Neumann algebras in general, classify them in the discrete series c<3, and we define and study an operator algebraic version of the N=2 spectral flow. We prove the coset identification for the N=2 super-Virasoro nets with c<3, a key result whose equivalent in the vertex algebra context has seemingly not been completely proved so far. Finally, the chiral ring is discussed in terms of net representations.
math.OA↗
A Generalized Linear Transport Model for Spatially-Correlated Stochastic Media
We formulate a new model for transport in stochastic media with long-range spatial correlations where exponential attenuation (controlling the propagation part of the transport) becomes power law. Direct transmission over optical distance $τ(s)$, for fixed physical distance $s$, thus becomes $(1+τ(s)/a)^{-a}$, with standard exponential decay recovered when $a\to\infty$. Atmospheric turbulence phenomenology for fluctuating optical properties rationalizes this switch. Foundational equations for this generalized transport model are stated in integral form for $d=1,2,3$ spatial dimensions. A deterministic numerical solution is developed in $d=1$ using Markov Chain formalism, verified with Monte Carlo, and used to investigate internal radiation fields. Standard two-stream theory, where diffusion is exact, is recovered when $a=\infty$. Differential diffusion equations are not presently known when $a<\infty$, nor is the integro-differential form of the generalized transport equation. Monte Carlo simulations are performed in $d=2$, as a model for transport on random surfaces, to explore scaling behavior of transmittance $T$ when transport optical thickness $τ_\text{t} \gg 1$. Random walk theory correctly predicts $T \propto τ_\text{t}^{-\min\{1,a/2\}}$ in the absence of absorption. Finally, single scattering theory in $d=3$ highlights the model's violation of angular reciprocity when $a<\infty$, a desirable property at least in atmospheric applications. This violation is traced back to a key trait of generalized transport theory, namely, that we must distinguish more carefully between two kinds of propagation: one that ends in a virtual or actual detection, the other in a transition from one position to another in the medium.
physics.optics↗
Conformal embeddings and simple current extensions
In this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.
math.RT↗
Assessment of mortgage default risk via Bayesian state space models
Managing risk at the aggregate level is crucial for banks and financial institutions as required by the Basel III framework. In this paper, we introduce discrete time Bayesian state space models with Poisson measurements to model aggregate mortgage default rate. We discuss parameter updating, filtering, smoothing, forecasting and estimation using Markov chain Monte Carlo methods. In addition, we investigate the dynamic behavior of the default rate and the effects of macroeconomic variables. We illustrate the use of the proposed models using actual U.S. residential mortgage data and discuss insights gained from Bayesian analysis.
stat.AP↗
Want a Good Answer? Ask a Good Question First!
Community Question Answering (CQA) websites have become valuable repositories which host a massive volume of human knowledge. To maximize the utility of such knowledge, it is essential to evaluate the quality of an existing question or answer, especially soon after it is posted on the CQA website. In this paper, we study the problem of inferring the quality of questions and answers through a case study of a software CQA (Stack Overflow). Our key finding is that the quality of an answer is strongly positively correlated with that of its question. Armed with this observation, we propose a family of algorithms to jointly predict the quality of questions and answers, for both quantifying numerical quality scores and differentiating the high-quality questions/answers from those of low quality. We conduct extensive experimental evaluations to demonstrate the effectiveness and efficiency of our methods.
cs.DB↗
Modeling complex spatial dynamics of two-population interaction in urbanization process
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed. Subsequently a logistic equation on percentage urban is derived from the urbanization model so that spatial interaction can be connected mathematically with logistic growth. The numerical experiment by using the discretized urban-rural population interaction model of urbanization shows a period-doubling bifurcation and chaotic behavior, which is identical in patterns to those from the simple mathematical models of logistic growth in ecology. This suggests that the complicated dynamics of logistic growth may come from some kind of the nonlinear interaction. The results from this study help to understand urbanization, urban-rural population interaction, chaotic dynamics, and spatial complexity of geographical systems.
physics.soc-ph↗
Redefining the Attraction Measure, Scaling Exponent and Impedance Function of the Gravity Model
The attraction measure, scaling exponent, and impedance function of the gravity model are redefined using the concepts from fractals and spatial complexity. Firstly, the attraction measure of spatial interaction in human systems is defined by the product of traffic inflow and outflow. Based on the new definition, the gravity model originating from the Newtonian analogy is differentiated from Wilson's spatial interaction model deriving from entropy-maximizing principle. Secondly, the scaling exponent of the gravity model based on the inverse distance relationship is revealed to be the ratio of the fractal dimension of networks of cities to that of hierarchies of cities. The value of the scaling exponent is then shown to approach to 2, which corresponds to the value of the power exponent of the law of gravity in classical physics. Thirdly, the inverse power function is demonstrated to be more acceptable than the negative exponential function as an impedance function of the gravity model. The limits of application of different gravity models based on different impedance functions are brought to light. Applying the expanded theory and models to China's interregional flows yields satisfying results, which in turn lend further support to the expanded theory and models.
physics.soc-ph↗
Mirror Extensions of Vertex Operator Algebras
The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.
math.QA↗
MaTrust: An Effective Multi-Aspect Trust Inference Model
Trust is a fundamental concept in many real-world applications such as e-commerce and peer-to-peer networks. In these applications, users can generate local opinions about the counterparts based on direct experiences, and these opinions can then be aggregated to build trust among unknown users. The mechanism to build new trust relationships based on existing ones is referred to as trust inference. State-of-the-art trust inference approaches employ the transitivity property of trust by propagating trust along connected users. In this paper, we propose a novel trust inference model (MaTrust) by exploring an equally important property of trust, i.e., the multi-aspect property. MaTrust directly characterizes multiple latent factors for each trustor and trustee from the locally-generated trust relationships. Furthermore, it can naturally incorporate prior knowledge as specified factors. These factors in turn serve as the basis to infer the unseen trustworthiness scores. Experimental evaluations on real data sets show that the proposed MaTrust significantly outperforms several benchmark trust inference models in both effectiveness and efficiency.
cs.DB↗
On examples of intermediate subfactors from conformal field theory
Motivated by our subfactor generalization of Wall's conjecture, in this paper we determine all intermediate subfactors for conformal subnets corresponding to four infinite series of conformal inclusions, and as a consequence we verify that these series of subfactors verify our conjecture. Our results can be stated in the framework of Vertex Operator Algebras. We also verify our conjecture for Jones-Wassermann subfactors from representations of Loop groups extending our earlier results.
math.OA↗
On generalized universal irrational rotation algebras and the operator $u+v$
We introduce a class of generalized universal irrational rotation $C^*$-algebras $A_{θ,γ}=C^*(x,w)$ which is characterized by the relations $w^*w=ww^*=1$, $x^*x=γ(w)$, $xx^*=γ(e^{-2πiθ}w)$, and $xw=e^{-2πiθ}wx$, where $θ$ is an irrational number and $γ(z)\in C(\mathbb{T})$ is a positive function. We characterize tracial linear functionals, simplicity, and $K$-groups of $A_{θ,γ}$ in terms of zero points of $γ(z)$. We show that if $A_{θ,γ}$ is simple then $A_{θ,γ}$ is an $A{\mathbb T}$-algebra of real rank zero. We classify $A_{θ,γ}$ in terms of $θ$ and zero points of $γ(z)$. Let $A_θ=C^*(u,v)$ be the universal irrational rotation $C^*$-algebra with $vu=e^{2πiθ}uv$. Then $C^*(u+v)\cong A_{θ,|1+z|^2}$. As an application, we show that $C^*(u+v)$ is a proper simple $C^*$-subalgebra of $A_θ$ which has a unique trace, $K_1(C^*(u+v))\cong \mathbb{Z}$, and there is an order isomorphism of $K_0(C^*(u+v))$ onto $\mathbb{Z}+\mathbb{Z}θ$. {Moreover, $C^*(u+v)$ is a unital simple $A{\mathbb T}$-algebra of real rank zero.} We also calculate the spectrum and the Brown measure of $u+v$.
math.OA↗
Quantum Dimensions and Quantum Galois Theory
The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents of a rational vertex operator algebra is given. A full Galois theory for rational vertex operator algebras is established using the quantum dimensions.
math.QA↗
Twistor theory and the harmonic hull
We use twistor theory to identify the harmonic hull of an arbitrary connected open subset U of R^{2m} for m at least 2. It is the natural domain of analytic continuation in C^{2m} for harmonic functions on U.
math.DG↗