Presence and Absence of Barren Plateaus in Tensor-Network Based Machine Learning.

Tensor networks are efficient representations of high-dimensional tensors with widespread applications in quantum many-body physics. Recently, they have been adapted to the field of machine learning, giving rise to an emergent research frontier that has attracted considerable attention. Here, we study the trainability of tensor-network based machine learning models by exploring the landscapes of different loss functions, with a focus on the matrix product states (also called tensor trains) architecture. In particular, we rigorously prove that barren plateaus (i.e., exponentially vanishing gradients) prevail in the training process of the machine learning algorithms with global loss functions. Whereas, for local loss functions the gradients with respect to variational parameters near the local observables do not vanish as the system size increases. Therefore, the barren plateaus are absent in this case and the corresponding models could be efficiently trainable. Our results reveal a crucial aspect of tensor-network based machine learning in a rigorous fashion, which provide a valuable guide for both practical applications and theoretical studies in the future.

Unsupervised Learning of Non-Hermitian Topological Phases.

Non-Hermitian topological phases bear a number of exotic properties, such as the non-Hermitian skin effect and the breakdown of conventional bulk-boundary correspondence. In this Letter, we introduce an unsupervised machine learning approach to classify non-Hermitian topological phases based on diffusion maps, which are widely used in manifold learning. We find that the non-Hermitian skin effect will pose a notable obstacle, rendering the straightforward extension of unsupervised learning approaches to topological phases for Hermitian systems ineffective in clustering non-Hermitian topological phases. Through theoretical analysis and numerical simulations of two prototypical models, we show that this difficulty can be circumvented by choosing the "on-site" elements of the projective matrix as the input data. Our results provide a valuable guidance for future studies on learning non-Hermitian topological phases in an unsupervised fashion, both in theory and experiment.

[Research on Application of Fourier Transform Infrared Spectrometry in the Diagnosis of Lymph Node Metastasis in Gastric Cancer].

To explore the feasibility of quick intraoperative in situ and noninvasive diagnosis of lymph node metastasis in gastric cancer by Fourier transform infrared (FTIR) spectrometry. FTIR spectra of surgically removed fresh lymph nodes were measured by FTIR via probe of attenuated total reflection (ATR). For each spectrum, 13 bands were indentified and assigned between 3 000 and 1 000 cm(-1). Peaks in the spectra were measured and relative intensity ratios were calculated and compared between the spectra of Metastatic lymph nodes (MLN) and Non-metastatic lymph nodes (NMLN). Standard statistic analysis was performed. 720 lymph nodes were measured in 38 gastric cancer patients. Results show that there were significant differences between the FTIR of 540 MLN and 180 NMLN. (1) For the band related to nucleic acid: The ratios of I1240/I1460 (p = 0.015) and I1080/I1460 (p = 0.034) increased in MLN, which shows that the relative quantity of nucleic acid was more in MLN than that in NMLN. (2) For the bands related to protein: The ratios of I1640 /I1460 (p = 0.001) and I146/I1460 (p = 0.027) increased in MLN, which shows that the relative quantity of protein was more in MLN. (3) For the bands related to lipid: The ratio of I2855/I460 and I1740/I1460 decreased in MLN FTIR spectrum, indicating the lower relative quantity of lipid in MLN. (4) For the bands related to carbohydrate: The ratio of I1160/I1460 (p = 0.023) decreased in MLN FTIR spectrum, indicating the lower relative quantity of carbohydrate in MLN. The results demonstrate that the FTIR spectroscopy technique maybe develop into a promising method for in situ and quick intraoperative differential diagnosis of lymph node metastasis in gastric cancer.

miR-10a and miR-10b target the 3'-untranslated region of TBX5 to repress its expression.

As a well-known transcription factor, TBX5 is involved in embryonic cardiac development. Although TBX5 functions in a dose-dependent manner, the posttranscriptional regulation of human TBX5 is poorly understood. Thus, this study aimed to identify microRNAs that modulate TBX5 expression. Luciferase assays were used to screen miRNAs predicted to modulate TBX5 expression. Using quantitative reverse transcriptase-polymerase chain reaction and Western blot analysis, the authors found that miR-10a and miR-10b significantly repressed TBX5 expression and decreased TBX5 protein levels by targeting the TBX5 3'-untranslated region. In addition, miR-10a and miR-10b expression levels were respectively 2.77 and 3.51 times higher in the heart tissues of congenital heart disease patients than in healthy control subjects, suggesting that they are potential diagnostic biomarkers. In conclusion, the study results indicate that miR-10a and miR-10b inhibit TBX5 expression at the level of translation. Higher levels of miR-10a and miR-10b expression are associated with a higher risk of congenital heart defects.

[Post-transcriptional protein modification of Gata4].

Gata4 is an important transcription factor in heart development. Gata4 post-transcriptional protein modification regulates transcriptional activity and DNA binding, which in turn affects expression of downstream genes and transcription factors, differentiation of embryonic stem cells and cardiogenesis. This article summarizes the effect of post-transcriptional protein modification on transcriptional activity of Gata4 and the relationship between this effect and congenital heart disease. It was shown that acetylation, phosphorylation and SUMOylation upregulate transcriptional activity, DNA binding, downstream gene expression and embryonic stem cell differentiation. On the other hand, methylation and deacetylation downregulate Gata4 transcriptional activity. Post-transcriptional protein modification of Gata4 is very important in clinical research on congenital and other heart diseases.

A TBX5 3'UTR variant increases the risk of congenital heart disease in the Han Chinese population.

TBX5 is a vital transcription factor involved in cardiac development in a dosage-dependent manner. But little is known about the potential association of TBX5 3' untranslated region (UTR) variations with congenital cardiac malformations. This study aimed to investigate the relationship between TBX5 3'UTR variants and risk for congenital heart disease (CHD) susceptibility in two Han Chinese populations, and to reveal its molecular mechanism. The relationship between TBX5 3'UTR variants and CHD susceptibility was examined in 1 177 CHD patients and 990 healthy controls in two independent case-control studies. Variant rs6489956 C>T was found to be associated with increased CHD susceptibility in both cohorts. The combined CHD risk for the CT and TT genotype carriers was 1.83 times higher than that of CC genotype, while the risk for CT or TT genotype was 1.94 times and 2.31 times higher than that of CC carriers, respectively. Quantitative real-time PCR and western blot analysis showed that T allele carriers exhibited reduced TBX5 mRNA and protein levels in CHDs tissues. Compared with C allele, T allele showed increased binding affinity to miR-9 and miR-30a in both luciferase assays and surface plasmon resonance analysis. Functional analysis confirmed that miR-9 and miR-30a downregulated TBX5 expression at the transcriptional and translational levels, respectively. The assays in zebrafish model were in support of the interaction of miR-9/30a and TBX5 3'UTR (C and T allele). We concluded that TBX5 3'UTR variant rs6489956 increased susceptibility of CHD in the Han Chinese population because it changes the binding affinity of two target miRNAs that specifically mediate TBX5 expression.

Differences in airway remodeling and airway inflammation among moderate-severe asthma clinical phenotypes.

BACKGROUND: To identify asthma clinical phenotypes using cluster analysis and improve our understanding of heterogeneity in asthma. METHODS: Clustering approaches were applied to 203 patients who were diagnosed with asthma in XinHua Hospital (January 2012 to December 2015). One hundred and twenty patients underwent multi-slice spiral computed tomography (MSCT) examination and 30 underwent bronchial mucosal biopsy for evaluation of airway remodeling and airway inflammation among the phenotypes. RESULTS: Four groups were identified. Patients in cluster 1 (n=52) had early onset atopic asthma and patients in cluster 2 (n=65) had small airway obstruction and atopic asthma. Cluster 3 (n=52) was a unique group of patients with late-onset and non-atopic asthma. Patients in cluster 4 (n=34) had severe airflow obstruction and obvious airway remodeling as observed on MSCT (P<0.05). According to the immunohistochemistry of IL-5 and IL-17 (P<0.05), the results of clusters 1 and 2 may be attributable to the Th2 immune response, whereas those of clusters 3 and 4 to the Th17 immune response. CONCLUSIONS: Four distinct clinical phenotypes of asthma were identified by cluster analysis. The results of the MSCT and pathological examinations may suggest specific pathogeneses among the phenotypes.

ℤ3 parafermionic chain emerging from Yang-Baxter equation.

We construct the 1D ℤ3 parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the ℤ3 parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the ℤ3 parafermionic model is a direct generalization of 1D ℤ2 Kitaev model. Both the ℤ2 and ℤ3 model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian H123 based on Yang-Baxter equation. Different from the Majorana doubling, the H123 holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P [formula in text] and emergent parafermionic operator Γ, which are the generalizations of parity PM and emergent Majorana operator in Lee-Wilczek model, respectively. Both the ℤ3 parafermionic model and H123 can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.

Mild decrease in TBX20 promoter activity is a potentially protective factor against congenital heart defects in the Han Chinese population.

Congenital heart defects (CHDs) are one of the most common human birth defects worldwide. TBX20 is a crucial transcription factor for the development of embryonic cardiovascular system. Previous studies have demonstrated that mutations in the TBX20 coding region contribute to familial and sporadic CHD occurrence. However, it remains largely unknown whether variants in the TBX20 regulatory region are also related to CHDs. In this study, we sequenced the 2 kb region upstream of the TBX20 transcription start site in 228 CHD patients and 292 controls in a Han Chinese population. Among the 8 single nucleotide polymorphisms (SNPs) identified, six SNPs are in strong linkage disequilibrium and the minor alleles are associated with lower CHD risk (for rs10235849 chosen as tag SNP, p = 0.0069, OR (95% CI) = 0.68 (0.51-0.90)). Functional analysis showed that the minor alleles have lower transcriptional activity than major alleles in both human heart tissues and three cell lines. The electrophoretic mobility shift assay suggested that TBX20 minor alleles may exhibit higher binding affinity with certain transcription repressors. Our results indicate that a moderately lower TBX20 activity potentially reduces CHD risk in the Han Chinese population, providing new insight in the study of CHD etiology.

[Molecular mechanism of cyclooxygenase-2 inhibitor in inhibition of proliferation of colon cancer cells by modulating Stat5 signal transduction pathway].

OBJECTIVE: To investigate the role of NS398, a selective cyclooxygenase (COX)-2 inhibitor, in proliferation and apoptosis of colorectal cancer, and to reveal the mechanism of inhibiting colon cancer by NS-398 Independent of COX-2. METHODS: Human colon cancer cells of the line SW480 were cultured and then divided into 2 groups: experimental group and control group. NS398 of the concentrations of 12.5, 25, 50, 75, 100, and 125 micromol/L was added into the culture fluid of the experimental group. MTT assay was used to observe the proliferation of the cells, flow cytometry was used to test the cell cycle, RT-PCR analysis was performed to examine COX-2 mRNA expression, and Western blotting analysis was performed to detect the expression of Stat5, peroxisome proliferators-activated receptors (PPARs), cyclin D1 and Bcl-x(L). RESULTS: Expression of COX-2 mRNA was not detected in the SW480 colon cancer cells. 72 hours after the addition of NS398 75 micromol/L the proliferative level of the SW480 cells was decreased; the rate of the cells at the G(1) stage increased from 31.2% to 40.6%, and the rate of cells at the S stage decreased from 52.8% to 41.2%. The expression of Stat5, PPARdelta, cyclin D1 and Bcl-x(L) decreased along with the elongation of time of NS398 action. CONCLUSION: COX-2 inhibitor, such as NS-398 inhibits the colon cancer cell proliferation and induces apoptosis of colon cancer cells with the possible mechanism of inhibiting the proliferation and inducing the apoptosis of colon cancer cells through a pathway independent of COX-2.

More about the doubling degeneracy operators associated with Majorana fermions and Yang-Baxter equation.

A new realization of doubling degeneracy based on emergent Majorana operator Γ presented by Lee-Wilczek has been made. The Hamiltonian can be obtained through the new type of solution of Yang-Baxter equation, i.e. -matrix. For 2-body interaction, R(θ) gives the "superconducting" chain that is the same as 1D Kitaev chain model. The 3-body Hamiltonian commuting with Γ is derived by 3-body R123-matrix, we thus show that the essence of the doubling degeneracy is due to [R(θ), Γ=0]. We also show that the extended Γ'-operator is an invariant of braid group BN for odd N. Moreover, with the extended Γ'-operator, we construct the high dimensional matrix representation of solution to Yang-Baxter equation and find its application in constructing 2N-qubit Greenberger-Horne-Zeilinger state for odd N.

A simplified approach for evaluation of the polarity parameters for polymer using the K coefficient of the Mark-Houwink-Sakurada equation.

Since two solvent polarity parameters, e.g., the Et(30) defined by Reichardt and the pi* defined by Kamlet and Taft, respectively, plotted with the K coefficient of the Mark-Houwink-Sakurada equation, presented good linear fits, this paper suggests applying the extrapolating method in the same way as the Zisman plot to obtain similar polarity parameters for polymers. In order to verify those obtained polarity parameter values for various polymers, literature-reported polarity values determined using other techniques are referenced and indicate that this paper introduced a simplified approach that can be applied to evaluate the polarity parameters for polymers. In this paper, since we observe that various polymers are of interest to present absolutely different slope tendencies, e.g., positive and negative, it is also suggested that polarity properties of polymers may be reinterpreted.

[Analysis of prognostic and clinicopathologic factors in gastrointestinal stromal tumors of the stomach].

OBJECTIVE: To identify the clinical pathological characteristics and prognostic factors in patients with gastrointestinal stromal tumors of the stomach. METHODS: The data of 98 patients of gastric stromal tumors, leiomyomas, leiomyosarcomas, leiomyoblastomas, schwannomas and neurofibromas, collected from Mar. 1983 to Dec. 2001 in our hospital with complete clinical and pathological data, were investigated retrospectively. Gastric stromal tumors were diagnosed by reviewing the tumor slides stained with hematoxylin and eosin (H&E). Two histomorphologically representative areas of each tumor slides were identified and arrayed on a tissue microarray. Immunohistochemistry staining were performed using antibodies to c-kit (CD117), CD34, smooth muscle actin (SMA), Desmin and S-100 proteins. The relations of various clinicopathologic characteristics and outcomes were tested by univariate analysis and multivariate analysis. RESULTS: Ninety-one patients were clearly identified as gastric stromal tumors from the 98 patients, who were diagnosed as gastric stromal tumor, leiomyoma, leiomyosarcoma, leiomyoblastoma schwannoma and neurofibroma (92.9%). The follow-up rate was 91% and the median follow up time was 54 months. The patient survival rates at 1, 5 and 10 years were 88.8%, 79.6% and 63.7% respectively. Univariate analysis showed that tumor size, mitotic count, tumor necrosis, nuclear pleomorphism, cell type, cell density, surgical procedure, mucosal invasion, age and lable index of Ki-67 were associated with prognosis (P<0.05). Multivariate analysis showed that tumor size, mitotic count, mucosal invasion and tumor necrosis were predictors of prognosis (P<0.05). CONCLUSION: Tumor size of >10 cm, mitotic count of >10 mitoses per 50 high power fields, necrosis and mucosal invasion are often associated with an aggressive clinical course in gastric stromal tumors.

[Intra-abdomen extragastrointestinal stromal tumors: a clinicopathologic study on 30 cases].

OBJECTIVE: To investigate the clinicopathological characteristics and prognostic factors in patients with intra-abdomen extragastrointestinal stromal tumors (EGISTs). METHODS: The data of 47 patients of mesenchymal neoplasms that arose from the abdominal cavity and retroperitoneum, collected from July 1987 to June 2003 in our hospital with complete clinical and pathological data, were investigated retrospectively. EGISTs were diagnosed by reviewing the tumor slides stained with hematoxylin and eosin (H&E). Immunohistochemistry staining were performed on CD117, CD34, smooth muscle actin, Desmin and S-100 proteins. The relations of various clinicopathologic characteristics and outcomes were examined. RESULTS: Among the 47 cases, 30 tumors were confirmed to be EGISTs. Twelve cases arose from the mesentery, six from small omentum, eight from retroperitoneum and four from the abdominal cavity. The size of tumors ranged from 4 to 30 cm (median 12.5 cm) in diameter and the tumor cell components mainly included spindle cells (23 cases), epithelioid cells (4 cases), and mixed cells (3 cases). The follow-up rate was 90% and the median follow up time was 44 months. The patient survival rates at 1, 5 and 10 years were 79.7%, 59.5% and 45.4% respectively. Univariate analysis showed that tumor size >10 cm, tumor necrosis, mitoses > or =5/50HPF, obvious nuclear atypia, moderate and poor differentiated tumor cells were predictors of poor prognosis. CONCLUSIONS: EGISTs have specific clinical behaviors. The parameters used for predicting GISTs prognosis are not completely applicable for EGISTs. Tumor necrosis, obvious nuclear atypia and mitoses > or =5/50HPF help to predict aggressive behaviors in EGISTs.