arXiv subjects

Weiwei Pan

Publications and source records attributed to Weiwei Pan.

41 records · Page 3Linked to original sources

arXiv2018

The sl_3 web algebra

In this paper we use Kuperberg's $\mathfrak{sl}_3$-webs and Khovanov's $\mathfrak{sl}_3$-foams to define a new algebra $K^S$, which we call the $\mathfrak{sl}_3$-web algebra. It is the $\mathfrak{sl}_3$ analogue of Khovanov's arc algebra. We prove that $K^S$ is a graded symmetric Frobenius algebra. Furthermore, we categorify an instance of $q$-skew Howe duality, which allows us to prove that $K^S$ is Morita equivalent to a certain cyclotomic KLR-algebra of level 3. This allows us to determine the split Grothendieck group $K^{\oplus}_0(\mathcal{W}^S)_{\mathbb{Q}(q)}$, to show that its center is isomorphic to the cohomology ring of a certain Spaltenstein variety, and to prove that $K^S$ is a graded cellular algebra.

math.QA↗

arXiv2017

Weighted Tensor Decomposition for Learning Latent Variables with Partial Data

Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this work, we consider the case in which certain dimensions of the data are not always observed---common in applied settings, where not all measurements may be taken for all observations---resulting in moment estimates of varying quality. We derive a weighted tensor decomposition approach that is computationally as efficient as the non-weighted approach, and demonstrate that it outperforms methods that do not appropriately leverage these less-observed dimensions.

stat.ML↗

arXiv2016

An Empirical Comparison of Sampling Quality Metrics: A Case Study for Bayesian Nonnegative Matrix Factorization

In this work, we empirically explore the question: how can we assess the quality of samples from some target distribution? We assume that the samples are provided by some valid Monte Carlo procedure, so we are guaranteed that the collection of samples will asymptotically approximate the true distribution. Most current evaluation approaches focus on two questions: (1) Has the chain mixed, that is, is it sampling from the distribution? and (2) How independent are the samples (as MCMC procedures produce correlated samples)? Focusing on the case of Bayesian nonnegative matrix factorization, we empirically evaluate standard metrics of sampler quality as well as propose new metrics to capture aspects that these measures fail to expose. The aspect of sampling that is of particular interest to us is the ability (or inability) of sampling methods to move between multiple optima in NMF problems. As a proxy, we propose and study a number of metrics that might quantify the diversity of a set of NMF factorizations obtained by a sampler through quantifying the coverage of the posterior distribution. We compare the performance of a number of standard sampling methods for NMF in terms of these new metrics.

cs.LG↗

arXiv2011

Microstructure and magnetic anisotropy of electrospun Cu$_{1-x}$Zn$_x$Fe$_2$O$_4$ nanofibers: A local probe study

Understanding the phenomena at the nanometer scale is of fundamental importance for future improvements of desired properties of nanomaterials. We report a detailed investigation of the microstructure and the resulting magnetic anisotropy by magnetic, transmission electron microscope (TEM) and Mössbauer measurements of the electrospun Cu$_{1-x}$Zn$_x$Fe$_2$O$_4$ nanofibers. Our results show that the electrospun Cu$_{1-x}$Zn$_x$Fe$_2$O$_4$ nanofibers exhibit nearly isotropic magnetic anisotropy. TEM measurements indicate that the nanofibers are composed of loosely connected and randomly aligned nanograins. As revealed by the Henkel plot, these nanofibers and the nanograins within the nanofibers are dipolar coupled, which reduces the effective shape anisotropy leading to a nearly random configuration of the magnetic moments inside the nanofibers, hence, the observed nearly isotropic magnetic anisotropy can be easily understood.

cond-mat.mes-hall↗

arXiv2011

Effect of Zn substitution on morphology and magnetic properties of copper ferrite nanofibers

Spinel ferrite Cu1-xZnxFe2O4 nanofibers over a compositional range 0 < x < 1 were prepared by electrospinning combined with sol-gel method. The influence of Zn2+ ions substitution on morphology, structure, and magnetic properties of copper ferrite has been investigated. The results show that surface of CuFe2O4 nanofibers consists of small open porosity, while surface of doped nanofibers reveals smooth and densified nature. With increasing Zn substitution, saturation magnetization initially increases and then decreases with a maximum value of 58.4 emu/g at x = 0.4, coercivity and square ratio all decrease. The influence of substitution on magnetic properties is related with the cation distraction and exchange interactions between spinel lattices.

cond-mat.mtrl-sci↗