Low-momentum ring diagrams of neutron matter at and near the unitary limit

We study neutron matter at and near the unitary limit using a low-momentum ring diagram approach. By slightly tuning the meson-exchange CD-Bonn potential, neutron-neutron potentials with various $^1S_0$ scattering lengths such as $a_s=-12070fm$ and $+21fm$ are constructed. Such potentials are renormalized with rigorous procedures to give the corresponding $a_s$-equivalent low-momentum potentials $V_{low-k}$, with which the low-momentum particle-particle hole-hole ring diagrams are summed up to all orders, giving the ground state energy $E_0$ of neutron matter for various scattering lengths. At the limit of $a_s\to \pm \infty$, our calculated ratio of $E_0$ to that of the non-interacting case is found remarkably close to a constant of 0.44 over a wide range of Fermi-momenta. This result reveals an universality that is well consistent with the recent experimental and Monte-Carlo computational study on low-density cold Fermi gas at the unitary limit. The overall behavior of this ratio obtained with various scattering lengths is presented and discussed. Ring-diagram results obtained with $V_{low-k}$ and those with $G$-matrix interactions are compared.Comment: 9 pages, 7 figure

White learning methodology: a case study of cancer-related disease factors analysis in real-time PACS environment

Bayesian network is a probabilistic model of which the prediction accuracy may not be one of the highest in the machine learning family. Deep learning (DL) on the other hand possess of higher predictive power than many other models. How reliable the result is, how it is deduced, how interpretable the prediction by DL mean to users, remain obscure. DL functions like a black box. As a result, many medical practitioners are reductant to use deep learning as the only tool for critical machine learning application, such as aiding tool for cancer diagnosis. In this paper, a framework of white learning is being proposed which takes advantages of both black box learning and white box learning. Usually, black box learning will give a high standard of accuracy and white box learning will provide an explainable direct acyclic graph. According to our design, there are 3 stages of White Learning, loosely coupled WL, semi coupled WL and tightly coupled WL based on degree of fusion of the white box learning and black box learning. In our design, a case of loosely coupled WL is tested on breast cancer dataset. This approach uses deep learning and an incremental version of Naïve Bayes network. White learning is largely defied as a systemic fusion of machine learning models which result in an explainable Bayes network which could find out the hidden relations between features and class and deep learning which would give a higher accuracy of prediction than other algorithms. We designed a series of experiments for this loosely coupled WL model. The simulation results show that using WL compared to standard black-box deep learning, the levels of accuracy and kappa statistics could be enhanced up to 50%. The performance of WL seems more stable too in extreme conditions such as noise and high dimensional data. The relations by Bayesian network of WL are more concise and stronger in affinity too. The experiments results deliver positive signals that WL is possible to output both high classification accuracy and explainable relations graph between features and class. [Abstract copyright: Copyright © 2020. Published by Elsevier B.V.

Local syzygies of multiplier ideals

In recent years, multiplier ideals have found many applications in local and global algebraic geometry. Because of their importance, there has been some interest in the question of which ideals on a smooth complex variety can be realized as multiplier ideals. Other than integral closure no local obstructions have been known up to now, and in dimension two it was established by Favre-Jonsson and Lipman-Watanabe that any integrally closed ideal is locally a multiplier ideal. We prove the somewhat unexpected result that multiplier ideals in fact satisfy some rather strong algebraic properties involving higher syzygies. It follows that in dimensions three and higher, multiplier ideals are very special among all integrally closed ideals.Comment: 8 page

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Interpolation in non-positively curved K\"ahler manifolds

We extend to any simply connected K\"ahler manifold with non-positive sectional curvature some conditions for interpolation in $\mathbb{C}$ and in the unit disk given by Berndtsson, Ortega-Cerd\`a and Seip. The main tool is a comparison theorem for the Hessian in K\"ahler geometry due to Greene, Wu and Siu, Yau.Comment: 9 pages, Late

Unitarity potentials and neutron matter at the unitary limit

We study the equation of state of neutron matter using a family of unitarity potentials all of which are constructed to have infinite $^1S_0$ scattering lengths $a_s$. For such system, a quantity of much interest is the ratio $\xi=E_0/E_0^{free}$ where $E_0$ is the true ground-state energy of the system, and $E_0^{free}$ is that for the non-interacting system. In the limit of $a_s\to \pm \infty$, often referred to as the unitary limit, this ratio is expected to approach a universal constant, namely $\xi\sim 0.44(1)$. In the present work we calculate this ratio $\xi$ using a family of hard-core square-well potentials whose $a_s$ can be exactly obtained, thus enabling us to have many potentials of different ranges and strengths, all with infinite $a_s$. We have also calculated $\xi$ using a unitarity CDBonn potential obtained by slightly scaling its meson parameters. The ratios $\xi$ given by these different unitarity potentials are all close to each other and also remarkably close to 0.44, suggesting that the above ratio $\xi$ is indifferent to the details of the underlying interactions as long as they have infinite scattering length. A sum-rule and scaling constraint for the renormalized low-momentum interaction in neutron matter at the unitary limit is discussed.Comment: 7.5 pages, 7 figure

Mobile access to moodle activities: student usage and perceptions

Parallel Sessions 4Theme: Mobile Learning MOOCs and 21st Century-learningWith the rapidly increasing use of handheld mobile devices among staff and students in higher education, it has become more and more common for them to access teaching and learning related information and services using mobile devices (Peters, 2009). A 2011 survey on mobile services in academic libraries in Hong Kong and Singapore reveals that the possession rate of mobile devices was 93.4% among Hong Kong college students, and 61.9% of them used smartphones to access the Internet (Ang, 2012). It is not uncommon to see university students use smartphones to access learning resources on Moodle and other LMSs. However, how students use Moodle via mobile phones and what their perceptions of mobile access to Moodle have rarely been formally investigated. The current research aims at filling this gap by looking at which Moodle activities students would use mobile phones to access and exploring possible reasons behind the usage patterns.postprin