The lowest discriminant ideal of a Cayley-Hamilton Hopf algebra

Discriminant ideals of noncommutative algebras $A$, which are module finite over a central sublagebra $C$, are key invariants that carry important information about $A$, such as the sum of the squares of the dimensions of its irreducible modules with a given central character. There has been substantial research on the computation of discriminants, but very little is known about the computation of discriminant ideals. In this paper we carry out a detailed investigation of the lowest discriminant ideals of Cayley-Hamilton Hopf algebras in the sense of De Concini, Reshetikhin, Rosso and Procesi, whose identity fiber algebras are basic. The lowest discriminant ideals are the most complicated ones, because they capture the most degenerate behaviour of the fibers in the exact opposite spectrum of the picture from the Azumaya locus. We provide a description of the zero sets of the lowest discriminant ideals of Cayley-Hamilton Hopf algebras in terms of maximally stable modules of Hopf algebras, irreducible modules that are stable under tensoring with the maximal possible number of irreducible modules with trivial central character. In important situations, this is shown to be governed by the actions of the winding automorphism groups. The results are illustrated with applications to the group algebras of central extensions of abelian groups, big quantum Borel subalgebras at roots of unity and quantum coordinate rings at roots of unity.Comment: 33 page

OPTIMIZATION OF MUNICIPAL SOLID WASTE COLLECTION SYSTEM IN HEFEI CITY OF CHINA

The refuse collection spot is the central part in the municipal solid waste collecting system. The wrong collecting way would lead to environmental problem and disturb the life of citizens. With the demand of source separation in China, the waste collecting sites need to be improved. Nowadays there have three different types of wastes collecting in Hefei, capital city in Anhui province, China. The advantages and disadvantages of such waste collection system were compared and discussed. The suggestions were put forward. Concerning about special example for agricultural market waste collection, taking Hefei Wanguo market as a sample, the research was made to optimize the present collection system. Compared with traditional waste collecting sites, the results showed the agricultural market waste collecting sites were better in both environmental and social efficiency

LSTM Learning with Bayesian and Gaussian Processing for Anomaly Detection in Industrial IoT

The data generated by millions of sensors in Industrial Internet of Things (IIoT) is extremely dynamic, heterogeneous, and large scale. It poses great challenges on the real-time analysis and decision making for anomaly detection in IIoT. In this paper, we propose a LSTM-Gauss-NBayes method, which is a synergy of the long short-term memory neural network (LSTM-NN) and the Gaussian Bayes model for outlier detection in IIoT. In a nutshell, the LSTM-NN builds model on normal time series. It detects outliers by utilising the predictive error for the Gaussian Naive Bayes model. Our method exploits advantages of both LSTM and Gaussian Naive Bayes models, which not only has strong prediction capability of LSTM for future time point data, but also achieves an excellent classification performance of Gaussian Naive Bayes model through the predictive error. Empirical studies demonstrate our solution outperforms the best-known competitors, which is a preferable choice for detecting anomalies

Atomic Ramsey interferometry with S- and D-band in a triangular optical lattice

Ramsey interferometers have wide applications in science and engineering. Compared with the traditional interferometer based on internal states, the interferometer with external quantum states has advantages in some applications for quantum simulation and precision measurement. Here, we develop a Ramsey interferometry with Bloch states in S- and D-band of a triangular optical lattice for the first time. The key to realizing this interferometer in two-dimensionally coupled lattice is that we use the shortcut method to construct $\pi/2$ pulse. We observe clear Ramsey fringes and analyze the decoherence mechanism of fringes. Further, we design an echo $\pi$ pulse between S- and D-band, which significantly improves the coherence time. This Ramsey interferometer in the dimensionally coupled lattice has potential applications in the quantum simulations of topological physics, frustrated effects, and motional qubits manipulation

Observation of Temperature-Induced Crossover to an Orbital-Selective Mott Phase in Ax_{x}Fe2−y_{2-y}Se2_2 (A=K, Rb) Superconductors

In this work, we study the A$_{x}$Fe$_{2-y}$Se$_2$ (A=K, Rb) superconductors using angle-resolved photoemission spectroscopy. In the low temperature state, we observe an orbital-dependent renormalization for the bands near the Fermi level in which the dxy bands are heavily renormliazed compared to the dxz/dyz bands. Upon increasing temperature to above 150K, the system evolves into a state in which the dxy bands have diminished spectral weight while the dxz/dyz bands remain metallic. Combined with theoretical calculations, our observations can be consistently understood as a temperature induced crossover from a metallic state at low temperature to an orbital-selective Mott phase (OSMP) at high temperatures. Furthermore, the fact that the superconducting state of A$_{x}$Fe$_{2-y}$Se$_2$ is near the boundary of such an OSMP constraints the system to have sufficiently strong on-site Coulomb interactions and Hund's coupling, and hence highlight the non-trivial role of electron correlation in this family of iron superconductors

Role of gonadally synthesized steroid hormones in the colorectal cancer microenvironment

ObjectiveTo understand the relationship between steroid hormones synthesized by the gonads and colorectal cancer as well as its tumor microenvironment, in the expectation of providing new ideas in order to detect and treat colorectal cancer.MethodsThrough reviewing the relevant literature at home and abroad, we summarized that androgens promote the growth of colorectal cancer, and estrogens and progesterone help prevent bowel cancer from developing; these three hormones also have a relevant role in the cellular and other non-cellular components of the tumor microenvironment of colorectal cancer.ConclusionThe current literature suggests that androgens, estrogens, and progesterone are valuable in diagnosing and treating colorectal cancer, and that androgens promote the growth of colorectal cancer whereas estrogens and progesterone inhibit colorectal cancer, and that, in addition, the receptors associated with them are implicated in the modulation of a variety of cellular components of the microenvironment of colorectal cancer

Investigating causal associations among gut microbiota, metabolites, and liver diseases: a Mendelian randomization study

ObjectiveThere is some evidence for an association between gut microbiota and nonalcoholic fatty liver disease (NAFLD), alcoholic liver disease (ALD), and viral hepatitis, but no studies have explored their causal relationship.MethodsInstrumental variables of the gut microbiota (N = 13266) and gut microbiota-derived metabolites (N = 7824) were acquired, and a Mendelian randomization study was performed to explore their influence on NAFLD (1483 European cases and 17,781 European controls), ALD (2513 European cases and 332,951 European controls), and viral hepatitis risk (1971 European cases and 340,528 European controls). The main method for examining causality is inverse variance weighting (IVW).ResultsIVW results confirmed that Anaerotruncus (p = 0.0249), Intestinimonas (p = 0.0237), Lachnoclostridium (p = 0.0245), Lachnospiraceae NC2004 group (p = 0.0083), Olsenella (p = 0.0163), and Peptococcus (p = 0.0472) were protective factors for NAFLD, and Ruminococcus 1 (p = 0.0120) was detrimental for NAFLD. The higher abundance of three genera, Lachnospira (p = 0.0388), Desulfovibrio (p = 0.0252), and Ruminococcus torques group (p = 0.0364), was correlated with a lower risk of ALD, while Ruminococcaceae UCG 002 level was associated with a higher risk of ALD (p = 0.0371). The Alistipes (p = 0.0069) and Ruminococcaceae NK4A214 group (p = 0.0195) were related to a higher risk of viral hepatitis. Besides, alanine (p = 0.0076) and phenyllactate (p = 0.0100) were found to be negatively correlated with NAFLD, while stachydrine (Op = 0.0244) was found to be positively associated with NAFLD. The phenylacetate (p = 0.0353) and ursodeoxycholate (p = 0.0144) had a protective effect on ALD, while the threonate (p = 0.0370) exerted a detrimental influence on ALD. The IVW estimates of alanine (p = 0.0408) and cholate (p = 0.0293) showed their suggestive harmful effects against viral hepatitis, while threonate (p = 0.0401) displayed its suggestive protective effect against viral hepatitis.ConclusionIn conclusion, our research supported causal links between the gut microbiome and its metabolites and NAFLD, ALD, and viral hepatitis