NBLDA: Negative Binomial Linear Discriminant Analysis for RNA-Seq Data

RNA-sequencing (RNA-Seq) has become a powerful technology to characterize gene expression profiles because it is more accurate and comprehensive than microarrays. Although statistical methods that have been developed for microarray data can be applied to RNA-Seq data, they are not ideal due to the discrete nature of RNA-Seq data. The Poisson distribution and negative binomial distribution are commonly used to model count data. Recently, Witten (2011) proposed a Poisson linear discriminant analysis for RNA-Seq data. The Poisson assumption may not be as appropriate as negative binomial distribution when biological replicates are available and in the presence of overdispersion (i.e., when the variance is larger than the mean). However, it is more complicated to model negative binomial variables because they involve a dispersion parameter that needs to be estimated. In this paper, we propose a negative binomial linear discriminant analysis for RNA-Seq data. By Bayes' rule, we construct the classifier by fitting a negative binomial model, and propose some plug-in rules to estimate the unknown parameters in the classifier. The relationship between the negative binomial classifier and the Poisson classifier is explored, with a numerical investigation of the impact of dispersion on the discriminant score. Simulation results show the superiority of our proposed method. We also analyze four real RNA-Seq data sets to demonstrate the advantage of our method in real-world applications

Anyon exclusions statistics on surfaces with gapped boundaries

An anyon exclusion statistics, which generalizes the Bose-Einstein and Fermi-Dirac statistics of bosons and fermions, was proposed by Haldane[1]. The relevant past studies had considered only anyon systems without any physical boundary but boundaries often appear in real-life materials. When fusion of anyons is involved, certain `pseudo-species' anyons appear in the exotic statistical weights of non-Abelian anyon systems; however, the meaning and significance of pseudo-species remains an open problem. In this paper, we propose an extended anyon exclusion statistics on surfaces with gapped boundaries, introducing mutual exclusion statistics between anyons as well as the boundary components. Motivated by Refs. [2, 3], we present a formula for the statistical weight of many-anyon states obeying the proposed statistics. We develop a systematic basis construction for non-Abelian anyons on any Riemann surfaces with gapped boundaries. From the basis construction, we have a standard way to read off a canonical set of statistics parameters and hence write down the extended statistical weight of the anyon system being studied. The basis construction reveals the meaning of pseudo-species. A pseudo-species has different `excitation' modes, each corresponding to an anyon species. The `excitation' modes of pseudo-species corresponds to good quantum numbers of subsystems of a non-Abelian anyon system. This is important because often (e.g., in topological quantum computing) we may be concerned about only the entanglement between such subsystems.Comment: 36 pages, 14 figure

Perceptions of CAI tools in English/Chinese Interpreting Practice, perspectives of professional interpreters and trainers

This article analyses the perceptions of computer-assisted interpreting tools in interpreting practice and training based on the findings of a survey distributed to English/Chinese interpreters and trainers. Results analysis show that most respondents are positive about the application of CAI tools albeit without much application experience yet. Professional interpreters and trainers are optimistic about the existing CAI tools but mainly used them in preparation and post-interpreting stages. Secondly, user feedback shows CAI assists mainly in the science & technology domain. Thirdly, CAI tools are welcomed in interpreter training but trainers insist on the acquisition of skills before integration of technologies

AI Moral Decision Making : Human Control and Cultural Impact

We conducted a survey to explore how much control we wish to have when we allow an autonomous AI to handle a situation like Trolley problem. The survey received 771 responses from three countries, United States, India, and Nigeria. A preliminary analysis indicated each country group have distinctive response to survey questions. There is possible influence both from national culture and demographics. We are currently working on more extensive analysis to find out how such differences are caused by culture and demographics and whether they are consistent with existing studies

Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders

We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are compatible with the bulk Hamoltonian. Given the bulk Hamiltonian defined by a gauge group $G$ and a four-cocycle $\omega$ in the fourth cohomology group of $G$ over $U(1)$, a boundary Hamiltonian can be defined by a subgroup $K$ of $G$ and a three-cochain $\alpha$ in the third cochain group of $K$ over $U(1)$. The boundary Hamiltonian to be constructed must be gapped and invariant under the topological renormalization group flow (via Pachner moves), leading to a generalized Frobenius condition. Given $K$, a solution to the generalized Frobenius condition specifies a gapped boundary condition. We derive a closed-form formula of the ground state degeneracy of the model on a three-cylinder, which can be naturally generalized to three-spaces with more boundaries. We also derive the explicit ground-state wavefunction of the model on a three-ball. The ground state degeneracy and ground-state wavefunction are both presented solely in terms of the input data of the model, namely, $\{G,\omega,K,\alpha\}$

Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae

We investigate interdomain excitations in composite systems of topological orders separated by gapped domain walls. We derive two domain-wall Verlinde formulae that relate the braiding between interdomain excitations and domain-wall quasiparticles to the fusion rules of interdomain excitations and the fusion rules of domain-wall quasiparticles. We show how to compute such braiding and fusion with explicit non-Abelian examples and find that the fusion rules of interdomain excitations are generally fractional or irrational. By exploring the correspondence between composite systems and anyon condensation, we uncover why such fusion rules should be called symmetry fractionalized (irrationalized) fusion rules. Our domain-wall Verlinde formulae generalize the Verlinde formula of a single topological order and the defect Verlinde formula found in [C. Shen and L.-Y. Hung, Phys. Rev. Lett. 123, 051602 (2019)]. Our results may find applications in topological quantum computing, topological field theories, and conformal field theories.Comment: 13 pages, 7 figure

Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries

In this paper, we apply the method of Fourier transform and basis rewriting developed in arXiv:1910.13441 for the two-dimensional quantum double model of topological orders to the three-dimensional gauge theory model (with a gauge group $G$) of three-dimensional topological orders. We find that the gapped boundary condition of the gauge theory model is characterized by a Frobenius algebra in the representation category $\mathcal Rep(G)$ of $G$, which also describes the charge splitting and condensation on the boundary. We also show that our Fourier transform maps the three-dimensional gauge theory model with input data $G$ to the Walker-Wang model with input data $\mathcal Rep(G)$ on a trivalent lattice with dangling edges, after truncating the Hilbert space by projecting all dangling edges to the trivial representation of $G$. This Fourier transform also provides a systematic construction of the gapped boundary theory of the Walker-Wang model. This establishes a correspondence between two types of topological field theories: the extended Dijkgraaf-Witten and extended Crane-Yetter theories.Comment: 39 pages, 9 figure