Decomposition of Integral Self-Affine Multi-Tiles

In this paper, we propose a method to decompose an integral self-affine ${\mathbb Z}^n$-tiling set $K$ into measure disjoint pieces $K_j$ satisfying $K=\displaystyle\bigcup K_j$ in such a way that the collection of sets $K_j$ forms an integral self-affine collection associated with the matrix $B$ and this with a minimum number of pieces $K_j$. When used on a given measurable $\mathbb{Z}^n$-tiling set $K\subset\mathbb{R}^n$, this decomposition terminates after finitely many steps if and only if the set $K$ is an integral self-affine multi-tile. Furthermore, we show that the minimal decomposition we provide is unique.Comment: 15pages, 5figures, added references, typo correction

Spectrality of Self-Similar Tiles

We call a set $K \subset {\mathbb R}^s$ with positive Lebesgue measure a {\it spectral set} if $L^2(K)$ admits an exponential orthonormal basis. It was conjectured that $K$ is a spectral set if and only if $K$ is a tile (Fuglede's conjecture). Despite the conjecture was proved to be false on ${\mathbb R}^s$, $s\geq 3$ ([T], [KM2]), it still poses challenging questions with additional assumptions. In this paper, our additional assumption is self-similarity. We study the spectral properties for the class of self-similar tiles $K$ in ${\mathbb R}$ that has a product structure on the associated digit sets. We show that any strict product-form tiles and the associated modulo product-form tiles are spectral sets. As for the converse question, we give a pilot study for the self-similar set $K$ generated by arbitrary digit sets with four elements. We investigate the zeros of its Fourier transform due to the orthogonality, and verify Fuglede's conjecture for this special case.Comment: 22page

Style Transfer in Text: Exploration and Evaluation

Style transfer is an important problem in natural language processing (NLP). However, the progress in language style transfer is lagged behind other domains, such as computer vision, mainly because of the lack of parallel data and principle evaluation metrics. In this paper, we propose to learn style transfer with non-parallel data. We explore two models to achieve this goal, and the key idea behind the proposed models is to learn separate content representations and style representations using adversarial networks. We also propose novel evaluation metrics which measure two aspects of style transfer: transfer strength and content preservation. We access our models and the evaluation metrics on two tasks: paper-news title transfer, and positive-negative review transfer. Results show that the proposed content preservation metric is highly correlate to human judgments, and the proposed models are able to generate sentences with higher style transfer strength and similar content preservation score comparing to auto-encoder.Comment: To appear in AAAI-1

Association between body fat and sarcopenia in older adults with type 2 diabetes mellitus: A cross-sectional study

ObjectivesTo investigate the association between body fat (BF%) and sarcopenia in older adults with type 2 diabetes mellitus (T2DM) and potential link with increased levels of inflammatory indicators and insulin resistance.MethodsA total of 543 older adults with T2DM were included in this cross-sectional study. Appendicular skeletal muscle (ASM), handgrip strength and gait speed were measured to diagnose sarcopenia according to the updated Asian Working Group for Sarcopenia (AWGS) 2019 criteria. Body composition data were tested using dual-energy X-ray absorptiometry (DEXA). Levels of serum high-sensitive C-reactive protein (hs-CRP), interleukin-6, fasting blood insulin (FINS), hemoglobin A1c (HbA1c), 25-hydroxyvitamin D3 [25(OH) D3] were also determined.ResultsThe prevalence of sarcopenia in all participants was 8.84%, of which 11.90% were male and 5.84% females. The Pearson’s correlation analysis revealed that BF% was negatively correlated with gait speed in men and women (R =-0.195, P=0.001; R = -0.136, P =0.025, respectively). After adjusting for all potential confounders, sarcopenia was positive associated with BF% (male, OR: 1.38, 95% CI: 1.15–1.65, P< 0.001; female, OR: 1.30, 95% CI: 1.07–1.56, P=0.007), and negatively associated with body mass index (BMI) (male, OR: 0.57, 95% CI: 0.44–0.73, P<0.001; female, OR: 0.48, 95% CI: 0.33–0.70, P<0.001). No significant differences were found in hs-CRP, interleukin-6, and insulin resistance between older T2DM adults with and without sarcopenia.ConclusionHigher BF% was linked to an increased risk of sarcopenia in older adults with T2DM, suggesting the importance of assessing BF% rather than BMI alone to manage sarcopenia

Source attribution of particulate matter pollution over North China with the adjoint method

We quantify the source contributions to surface PM2.5 (fine particulate matter) pollution over North China from January 2013 to 2015 using the GEOS-Chem chemical transport model and its adjoint with improved model horizontal resolution (1/4 degrees x 5/16 degrees) and aqueous-phase chemistry for sulfate production. The adjoint method attributes the PM2.5 pollution to emissions from different source sectors and chemical species at the model resolution. Wintertime surface PM2.5 over Beijing is contributed by emissions of organic carbon (27% of the total source contribution), anthropogenic fine dust (27%), and SO2 (14%), which are mainly from residential and industrial sources, followed by NH3 (13%) primarily from agricultural activities. About half of the Beijing pollution originates from sources outside of the city municipality. Adjoint analyses for other cities in North China all show significant regional pollution transport, supporting a joint regional control policy for effectively mitigating the PM2.5 air pollution.China's National Basic Research Program [2014CB441303]; National Natural Science Foundation of China [41205103, 41475112]SCI(E)[email protected]

Air pollution–aerosol interactions produce more bioavailable iron for ocean ecosystems

It has long been hypothesized that acids formed from anthropogenic pollutants and natural emissions dissolve iron (Fe) in airborne particles, enhancing the supply of bioavailable Fe to the oceans. However, field observations have yet to provide indisputable evidence to confirm this hypothesis. Single-particle chemical analysis for hundreds of individual atmospheric particles collected over the East China Sea shows that Fe-rich particles from coal combustion and steel industries were coated with thick layers of sulfate after 1 to 2 days of atmospheric residence. The Fe in aged particles was present as a “hotspot” of (insoluble) iron oxides and throughout the acidic sulfate coating in the form of (soluble) Fe sulfate, which increases with degree of aging (thickness of coating). This provides the “smoking gun” for acid iron dissolution, because iron sulfate was not detected in the freshly emitted particles and there is no other source or mechanism of iron sulfate formation in the atmosphere