Hankel determinants, Pad\'e approximations, and irrationality exponents

The irrationality exponent of an irrational number $\xi$, which measures the approximation rate of $\xi$ by rationals, is in general extremely difficult to compute explicitly, unless we know the continued fraction expansion of $\xi$. Results obtained so far are rather fragmentary, and often treated case by case. In this work, we shall unify all the known results on the subject by showing that the irrationality exponents of large classes of automatic numbers and Mahler numbers (which are transcendental) are exactly equal to $2$. Our classes contain the Thue--Morse--Mahler numbers, the sum of the reciprocals of the Fermat numbers, the regular paperfolding numbers, which have been previously considered respectively by Bugeaud, Coons, and Guo, Wu and Wen, but also new classes such as the Stern numbers and so on. Among other ingredients, our proofs use results on Hankel determinants obtained recently by Han.Comment: International Mathematics Research Notices 201

Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors

Based on the NMR measurements on Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (La-Bi2201) in strong magnetic fields, we identify the non-superconducting pseudogap phase in the cuprates as a Luttinger-volume violating Fermi liquid (LvvFL). This state is a zero temperature quantum liquid that does not break translational symmetry, and yet, the Fermi surface encloses a volume smaller than the large one given by the Luttinger theorem. The particle number enclosed by the small Fermi surface in the LvvFL equals the doping level $p$, not the total electron number $n_e=1-p$. Both the phase string theory and the dopon theory are introduced to describe the LvvFL. For the dopon theory, we can obtain a semi-quantitative agreement with the NMR experiments.Comment: The final version in PR

What Women With Disabilities Write in Personal Blogs About Pregnancy and Early Motherhood: Qualitative Analysis of Blogs.

BackgroundMore than 1 in 10 women of reproductive age identify as having some type of disability. Most of these women are able to become pregnant and have similar desires for motherhood as women without disability. Women with disability, however, face greater stigma and stereotyping, additional risk factors, and may be less likely to receive adequate reproductive health care compared with their peers without disability. More and more individuals, including those with disability, are utilizing the internet to seek information and peer support. Blogs are one source of peer-to-peer social media engagement that may provide a forum for women with disability to both share and obtain peer-to-peer information and support. Nevertheless, it is not clear what content about reproductive health and pregnancy and/or motherhood is featured in personal blogs authored by women with spinal cord injury (SCI), traumatic brain injury (TBI), spina bifida, and autism.ObjectiveThe objective of this study was twofold: (1) to examine the information being shared in blogs by women with 4 types of disabilities, namely, SCI, TBI, spina bifida, and autism, about reproductive health, disability, health care, pregnancy, and motherhood; and (2) to classify the content of reproductive health experiences addressed by bloggers to better understand what they viewed as important.MethodsPersonal blogs were identified by searching Google with keywords related to disabilities, SCI, TBI, spina bifida, and autism, and a variety of keywords related to reproductive health. The first 10 pages of each database search in Google, based on the relevance of the search terms, were reviewed and all blogs in these pages were included. Blog inclusion criteria were as follows: (1) written by a woman or care partner (ie, parent or spouse) of a woman with a self-identified diagnosis of SCI, TBI, spina bifida, or autism; (2) focused on the personal experience of health and health care during the prepregnancy, prenatal, antepartum, intrapartum, and/or postpartum periods; (3) written in English; and (4) published between 2013 and 2017. A descriptive and thematic qualitative analysis of blogs and corresponding comments was facilitated with NVivo software and matrix analysis.ResultsOur search strategy identified 125 blogs that met all the inclusion criteria; no blogs written by women with spina bifida were identified. We identified 4 reproductive health themes featured in the blog of women with disabilities: (1) (in)accessible motherhood, (2) (un)supportive others, (3) different, but not different, and (4) society questioning motherhood.ConclusionsThis analysis of personal blogs about pregnancy and health care written by women with SCI, TBI, and autism provides a glimpse into their experiences. The challenges faced by these women and the adaptations they made to successfully navigate pregnancy and early motherhood provide insights that can be used to shape future research

Developing a Low-Cost Force Treadmill via Dynamic Modeling

By incorporating force transducers into treadmills, force platform-instrumented treadmills (commonly called force treadmills) can collect large amounts of gait data and enable the ground reaction force (GRF) to be calculated. However, the high cost of force treadmills has limited their adoption. This paper proposes a low-cost force treadmill system with force sensors installed underneath a standard exercise treadmill. It identifies and compensates for the force transmission dynamics from the actual GRF applied on the treadmill track surface to the force transmitted to the force sensors underneath the treadmill body. This study also proposes a testing procedure to assess the GRF measurement accuracy of force treadmills. Using this procedure in estimating the GRF of “walk-on-the-spot motion,” it was found that the total harmonic distortion of the tested force treadmill system was about 1.69%, demonstrating the effectiveness of the approach

Assessing Postural Stability Via the Correlation Patterns of Vertical Ground Reaction Force Components

Background Many methods have been proposed to assess the stability of human postural balance by using a force plate. While most of these approaches characterize postural stability by extracting features from the trajectory of the center of pressure (COP), this work develops stability measures derived from components of the ground reaction force (GRF). Methods In comparison with previous GRF-based approaches that extract stability features from the GRF resultant force, this study proposes three feature sets derived from the correlation patterns among the vertical GRF (VGRF) components. The first and second feature sets quantitatively assess the strength and changing speed of the correlation patterns, respectively. The third feature set is used to quantify the stabilizing effect of the GRF coordination patterns on the COP. Results In addition to experimentally demonstrating the reliability of the proposed features, the efficacy of the proposed features has also been tested by using them to classify two age groups (18–24 and 65–73 years) in quiet standing. The experimental results show that the proposed features are considerably more sensitive to aging than one of the most effective conventional COP features and two recently proposed COM features. Conclusions By extracting information from the correlation patterns of the VGRF components, this study proposes three sets of features to assess human postural stability during quiet standing. As demonstrated by the experimental results, the proposed features are not only robust to inter-trial variability but also more accurate than the tested COP and COM features in classifying the older and younger age groups. An additional advantage of the proposed approach is that it reduces the force sensing requirement from 3D to 1D, substantially reducing the cost of the force plate measurement system

Cross-lingual part-of-speech tagging using word embedding

As one of semi-supervised learning approach, cross-lingual projection leverages existing resources from a resource-rich language when building tools for resource-poor languages. In this paper we attempt to make use of word embedding with anchor based label propagation to improve the accuracy of a cross-lingual projection task: cross-lingual part-of-speech tagging under the graph-based framework. Our approach uses bilingual parallel corpora and labeled data from the resource-rich side assuming that there is no labeled data or only a few labeled data in resource-poor language. The results suggest the efficacy of our approach over traditional label propagation with lexical feature for projecting part-of-speech information across languages, and show that a few of labeled data help to enhance the effect a lot in cross-lingual task

Stochastic bifurcation characteristics of cantilevered piezoelectric energy harvester

Stochastic bifurcation characteristics of cantilevered piezoelectric energy harvester were studied in this paper. Von de Pol differencial item was introduced to interpret the hysteretic phenomena of piezoelectric ceramics, and then the nonlinear dynamic model of piezoelectric cantilever beam subjected to axial stochastic excitation was developed. The stochastic stability of the system was analyzed, and the steady-state probability density function and the joint probability density function of the dynamic response of the system were obtained, and then the conditions of stochastic Hopf bifurcation were analyzed. Numerical simulation shows that stochastic Hopf bifurcation appears when bifurcation parameter varies, which can increase vibration amplitude of cantilever beam system and improve the efficiency of piezoelectric energy harvester. Finally, the theoretical and numerical results were proved by experiments. The results of this paper are helpful to application of cantilevered piezoelectric energy harvester in engineering fields