Affine embeddings and intersections of Cantor sets

Let $E, F\subset \R^d$ be two self-similar sets. Under mild conditions, we show that $F$ can be $C^1$-embedded into $E$ if and only if it can be affinely embedded into $E$; furthermore if $F$ can not be affinely embedded into $E$, then the Hausdorff dimension of the intersection $E\cap f(F)$ is strictly less than that of $F$ for any $C^1$-diffeomorphism $f$ on $\R^d$. Under certain circumstances, we prove the logarithmic commensurability between the contraction ratios of $E$ and $F$ if $F$ can be affinely embedded into $E$. As an application, we show that $\dim_HE\cap f(F)<\min\{\dim_HE, \dim_HF\}$ when $E$ is any Cantor-$p$ set and $F$ any Cantor-$q$ set, where $p,q\geq 2$ are two integers with \log p/\log q\not \in \Q. This is related to a conjecture of Furtenberg about the intersections of Cantor sets.Comment: The paper will appear in J. Math. Pure. App

Box-counting measure of metric spaces

In this paper, we introduce a new notion called the \emph{box-counting measure} of a metric space. We show that for a doubling metric space, an Ahlfors regular measure is always a box-counting measure; consequently, if $E$ is a self-similar set satisfying the open set condition, then the Hausdorff measure restricted to $E$ is a box-counting measure. We show two classes of self-affine sets, the generalized Lalley-Gatzouras type self-affine sponges and Bara\'nski carpets, always admit box-counting measures; this also provides a very simple method to calculate the box-dimension of these fractals. Moreover, among others, we show that if two doubling metric spaces admit box-counting measures, then the multi-fractal spectra of the box-counting measures coincide provided the two spaces are Lipschitz equivalent

Magnetic resonance morphologic features predict progression of incidental pancreatic cystic lesions during follow-up

PURPOSEWe aimed to evaluate which morphologic features on magnetic resonance imaging (MRI) could predict the progression of pancreatic cystic lesions (PCLs) that are suitable for follow-up.METHODSA total of 2176 MRI findings of PCLs were retrospectively reviewed between January 2009 and December 2016. The study population was composed of 223 patients. Clinical data and morphologic features of PCLs were recorded. We divided the individuals into two sub-groups according to the final features on MRI. Univariable and multivariable regression analyses were performed to identify independent risk factors for progression of PCLs.RESULTSA total of 84 PCLs (37.7%) progressed during follow-up, while 139 PCLs (62.3%) were stable. Age (odds ratio [OR], 1.042; P = 0.017), number of lesions (OR, 0.491; P = 0.048), communication to pancreatic duct (PD) (OR, 2.425; P = 0.007) and presence of septa (OR, 6.105; P < 0.001) were significant independent factors for progression of PCLs. Among 84 lesions that progressed, 23 lesions (27.4%) increased to ≥ 30 mm in diameter or showed worrisome imaging features at the end of follow-up that needed clinical intervention. The initial size and communication to PD were independent factors for progression of PCLs necessitating clinical intervention (P < 0.001 and P = 0.011, respectively).CONCLUSIONAge, number of the lesions, communication to PD and presence of septa were independent risk factors for the progression of PCLs, and the initial size and communication to PD could potentially predict PCLs needing clinical intervention

MR quantitative 3D shape analysis helps to distinguish mucinous cystic neoplasm from serous oligocystic adenoma

PURPOSEWe aimed to assess the performance of quantitative 3D shape analysis in the differential diagno- sis of pancreatic serous oligocystic adenoma (SOA) and mucinous cystic neoplasm (MCN).METHODSFour hundred thirty-two patients diagnosed with serous cystic neoplasms (SCNs) or MCNs were retrospectively reviewed from August 2014 to July 2019 and finally 87 patients with MCNs (n = 45) and SOAs (n = 42) were included. Clinical data and magnetic resonance morphologic fea- tures with 3D shape analysis of lesions (shape sphericity, compacity, and volume) were recorded and compared between MCNs and SOAs according to the pathology. Univariable and multivari- able regression analyses were used to identify independent impact factors for differentiating MCN from SOA.RESULTSThe age of MCN patients was younger than SOAs (43.02 ± 10.83 years vs. 52.78 ± 12.31 years; OR = 0.275; 95% CI: 0.098-0.768; P = .014). MCN has a higher female/male ratio than SOA (43/2 vs. 27/15; OR = 40.418; 95% CI: 2.704-604.171; P = .007) and was more often located in the distal of pancreas (OR = 31.403; 95% CI: 2.985-330.342; P = .004). Shape_Sphericity derived from 3D shape analysis was a significant independent factor in the multivariable analysis and the value of MCN was closer to 1 than SOA (OR = 35.153; 95% CI: 5.301-237.585; P < .001). Area under the receiver operating characteristic curve (AUC) of Shape_Sphericity was 0.923 (optimal cutoff value was 0.964876).CONCLUSIONShape_Sphericity in combination with age, sex, and location could help to distinguish MCN from SOA

miR-638 is a new biomarker for outcome prediction of non-small cell lung cancer patients receiving chemotherapy.

MicroRNAs (miRNAs), a class of small non-coding RNAs, mediate gene expression by either cleaving target mRNAs or inhibiting their translation. They have key roles in the tumorigenesis of several cancers, including non-small cell lung cancer (NSCLC). The aim of this study was to investigate the clinical significance of miR-638 in the evaluation of NSCLC patient prognosis in response to chemotherapy. First, we detected miR-638 expression levels in vitro in the culture supernatants of the NSCLC cell line SPC-A1 treated with cisplatin, as well as the apoptosis rates of SPC-A1. Second, serum miR-638 expression levels were detected in vivo by using nude mice xenograft models bearing SPC-A1 with and without cisplatin treatment. In the clinic, the serum miR-638 levels of 200 cases of NSCLC patients before and after chemotherapy were determined by quantitative real-time PCR, and the associations of clinicopathological features with miR-638 expression patterns after chemotherapy were analyzed. Our data helped in demonstrating that cisplatin induced apoptosis of the SPC-A1 cells in a dose- and time-dependent manner accompanied by increased miR-638 expression levels in the culture supernatants. In vivo data further revealed that cisplatin induced miR-638 upregulation in the serum derived from mice xenograft models, and in NSCLC patient sera, miR-638 expression patterns after chemotherapy significantly correlated with lymph node metastasis. Moreover, survival analyses revealed that patients who had increased miR-638 levels after chemotherapy showed significantly longer survival time than those who had decreased miR-638 levels. Our findings suggest that serum miR-638 levels are associated with the survival of NSCLC patients and may be considered a potential independent predictor for NSCLC prognosis

Paraholcoglossum and Tsiorchis, Two New Orchid Genera Established by Molecular and Morphological Analyses of the Holcoglossum Alliance

BACKGROUND: Holcoglossum is a small orchid genus of 12 species ranging from SW China to Thailand and NE India. Although molecular and morphological analyses have been performed to establish the phylogenetic relationships within this genus, the interspecific relations and its relations with allied genera, such as Rhynchostylis, Aerides and Vanda, remain unclear. METHODOLOGY/PRINCIPAL FINDINGS: In addition to morphological analysis, maximum parsimony, maximum likelihood, and Bayesian inference analyses were performed based on fragments of the nuclear ITS and chloroplast trnL-F and matK genes of 31 taxa (15 Holcoglossum, 14 Aeridinae, 2 outgroups) representing all major clades of the Holcoglossum alliance. The results suggest that Holcoglossum is triphyletic, comprising three clades: the Holcoglossum clade, its sister clade, and a distant clade more closely related to Rhynchostylis, Aerides, and Vanda than to the Holcoglossum clade. The Holcoglossum clade is further divided into three subclades; the genetic distances between these three subclades also support this delimitation. The molecular conclusion is consistent with their distinct morphological characters. CONCLUSIONS: We propose that the latter two clades comprise two new genera, Paraholcoglossum and Tsiorchis, and Holcoglossum clade divides into three sections. In addition, a new section, Holcoglossum sect. Nujiangensia, and a new species, Holcoglossum linearifolium, are proposed. Some new combinations are made, and a new scheme is provided for the classification of all species of Holcoglossum, Paraholcoglossum, and Tsiorchis

Neottia bifidus (Orchidaceae, Epidendroideae, Neottieae), a new mycoheterotrophic species from Guizhou, China

Neottia bifidus, a new mycoheterotrophic orchid, found in Maolan National Nature Reserve in Guizhou Province, China, is described and illustrated here. The new species is close to N. nidus-avis, N. kiusiana and N. papilligera but differs in having a finely pubescent rachis with fewer flowers, a finely pubescent pedicel, and a fishtail-shaped lip that is deeply bilobed to the middle of the lip, with the lobes diverging at an acute angle (45°) to each other and mesochile with many papillae. Additionally, N. bifidus is well supported as a new species by molecular phylogenetic results based on ITS and chloroplast genome. The chloroplast genome of the novelty, which contains an LSC region of 33,819 bp, SSC region of 5,312 bp and IRs of 46,762 bp was assembled and annotated. A key to mycoheterotrophic Neottia species in China is also provided

Time-reversal symmetry breaking driven topological phase transition in EuB6_6

The interplay between time-reversal symmetry (TRS) and band topology plays a crucial role in topological states of quantum matter. In time-reversal-invariant (TRI) systems, the inversion of spin-degenerate bands with opposite parity leads to nontrivial topological states, such as topological insulators and Dirac semimetals. When the TRS is broken, the exchange field induces spin splitting of the bands. The inversion of a pair of spin-splitting subbands can generate more exotic topological states, such as quantum anomalous Hall insulators and magnetic Weyl semimetals. So far, such topological phase transitions driven by the TRS breaking have not been visualized. In this work, using angle-resolved photoemission spectroscopy, we have demonstrated that the TRS breaking induces a band inversion of a pair of spin-splitting subbands at the TRI points of Brillouin zone in EuB$_6$, when a long-range ferromagnetic order is developed. The dramatic changes in the electronic structure result in a topological phase transition from a TRI ordinary insulator state to a TRS-broken topological semimetal (TSM) state. Remarkably, the magnetic TSM state has an ideal electronic structure, in which the band crossings are located at the Fermi level without any interference from other bands. Our findings not only reveal the topological phase transition driven by the TRS breaking, but also provide an excellent platform to explore novel physical behavior in the magnetic topological states of quantum matter.Comment: 22 pages, 7 figures, accepted by Phys. Rev.