Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry

We introduce the notion of algebraic higher symmetry, which generalizes higher symmetry and is beyond higher group. We show that an algebraic higher symmetry in a bosonic system in $n$-dimensional space is characterized and classified by a local fusion $n$-category. We find another way to describe algebraic higher symmetry by restricting to symmetric sub Hilbert space where symmetry transformations all become trivial. In this case, algebraic higher symmetry can be fully characterized by a non-invertible gravitational anomaly (i.e. an topological order in one higher dimension). Thus we also refer to non-invertible gravitational anomaly as categorical symmetry to stress its connection to symmetry. This provides a holographic and entanglement view of symmetries. For a system with a categorical symmetry, its gapped state must spontaneously break part (not all) of the symmetry, and the state with the full symmetry must be gapless. Using such a holographic point of view, we obtain (1) the gauging of the algebraic higher symmetry; (2) the classification of anomalies for an algebraic higher symmetry; (3) the equivalence between classes of systems, with different (potentially anomalous) algebraic higher symmetries or different sets of low energy excitations, as long as they have the same categorical symmetry; (4) the classification of gapped liquid phases for bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of a topological order in one higher dimension (that corresponds to the categorical symmetry). This classification includes symmetry protected trivial (SPT) orders and symmetry enriched topological (SET) orders with an algebraic higher symmetry.Comment: 61 pages, 31 figure

Contact Stress Prediction Model for Variable Hyperbolic Circular Arc Gear Based on the Optimized Kriging-Response Surface Model

In order to study the influence of design parameters (pressure angle, tooth width, tooth line radius, modulus, and moment) on contact stress of variable hyperbolic circular arc gear (VHCAG) and to obtain the best manufacturing parameters, The Kriging-Response Surface Model, a hybrid surrogate model with adaptive quantum particle swarm optimization (QPSO) algorithm was proposed to establish the expression prediction model for the relation between design parameters and contact stress. An intelligent quantum particle swarm optimization algorithm based on adaptive weight and natural selection is proposed to optimize the parameters of Gaussian variation function of the kriging surrogate model to improve its fitting accuracy. The global search ability of quantum particles is improved, and the accuracy and stability of the algorithm are improved by adjusting the weight of quantum particles adaptively and by optimizing the elimination iteration process, and the response relationship between design parameters and contact stress was established. The binomial response surface model of gear design parameters and contact stress is established based on the output obtained through the improved kriging model; this simplifies the complex expression of the kriging model. The effects of parameters and their cross-terms on contact stress are analysed based on the contact stress prediction model established by using the optimized Kriging-Response Surface Model hybrid surrogate model. The hybrid Kriging-Response Surface Model surrogate model lays a foundation for the research on the reliability and robust optimization of cylindrical gears with variable hyperbolic arc tooth profile

Calcineurin B-Like Proteins CBL4 and CBL10 Mediate Two Independent Salt Tolerance Pathways in Arabidopsis.

In Arabidopsis, the salt overly sensitive (SOS) pathway, consisting of calcineurin B-like protein 4 (CBL4/SOS3), CBL-interacting protein kinase 24 (CIPK24/SOS2) and SOS1, has been well defined as a crucial mechanism to control cellular ion homoeostasis by extruding Na+ to the extracellular space, thus conferring salt tolerance in plants. CBL10 also plays a critical role in salt tolerance possibly by the activation of Na+ compartmentation into the vacuole. However, the functional relationship of the SOS and CBL10-regulated processes remains unclear. Here, we analyzed the genetic interaction between CBL4 and CBL10 and found that the cbl4 cbl10 double mutant was dramatically more sensitive to salt as compared to the cbl4 and cbl10 single mutants, suggesting that CBL4 and CBL10 each directs a different salt-tolerance pathway. Furthermore, the cbl4 cbl10 and cipk24 cbl10 double mutants were more sensitive than the cipk24 single mutant, suggesting that CBL10 directs a process involving CIPK24 and other partners different from the SOS pathway. Although the cbl4 cbl10, cipk24 cbl10, and sos1 cbl10 double mutants showed comparable salt-sensitive phenotype to sos1 at the whole plant level, they all accumulated much lower Na+ as compared to sos1 under high salt conditions, suggesting that CBL10 regulates additional unknown transport processes that play distinct roles from the SOS1 in Na+ homeostasis

Design of Plant Protection UAV Variable Spray System Based on Neural Networks

Recently, unmanned aerial vehicles (UAVs) have rapidly emerged as a new technology in the fields of plant protection and pest control in China. Based on existing variable spray research, a plant protection UAV variable spray system integrating neural network based decision making is designed. Using the existing data on plant protection UAV operations, combined with artificial neural network (ANN) technology, an error back propagation (BP) neural network model between the factors affecting droplet deposition is trained. The factors affecting droplet deposition include ambient temperature, ambient humidity, wind speed, flight speed, flight altitude, propeller pitch, nozzles pitch and prescription value. Subsequently, the BP neural network model is combined with variable rate spray control for plant protection UAVs, and real-time information is collected by multi-sensor. The deposition rate is determined by the neural network model, and the flow rate of the spray system is regulated according to the predicted deposition amount. The amount of droplet deposition can meet the prescription requirement. The results show that the training variance of the ANN is 0.003, and thus, the model is stable and reliable. The outdoor tests show that the error between the predicted droplet deposition and actual droplet deposition is less than 20%. The ratio of droplet deposition to prescription value in each unit is approximately equal, and a variable spray operation under different conditions is realized

Transplantation of a Peripheral Nerve with Neural Stem Cells Plus Lithium Chloride Injection Promote the Recovery of Rat Spinal Cord Injury

Transplantation of neural stem cells (NSCs) holds great potential for the treatment of spinal cord injury (SCI). However, transplanted NSCs poorly survive in the SCI environment. We injected NSCs into tibial nerve and transplanted tibial nerve into a hemisected spinal cord and investigated the effects of lithium chloride (LiCl) on the survival of spinal neurons, axonal regeneration, and functional recovery. Our results show that most of the transplanted NSCs expressed glial fibrillary acidic protein, while there was no obvious expression of nestin, neuronal nuclei, or acetyltransferase found in NSCs. LiCl treatment produced less macrosialin (ED1) expression and axonal degeneration in tibial nerve after NSC injection. Our results also show that a regimen of LiCl treatment promoted NSC differentiation into NF200-positive neurons with neurite extension into the host spinal cord. The combination of tibial nerve transplantation with NSCs and LiCl injection resulted in more host motoneurons surviving in the spinal cord, more regenerated axons in tibial nerve, less glial scar area, and decreased ED1 expression. We conclude that lithium may have therapeutic potential in cell replacement strategies for central nervous system injury due to its ability to promote survival and neuronal generation of grafted NSCs and reduced host immune reaction

Design of Plant Protection UAV Variable Spray System Based on Neural Networks

Recently, unmanned aerial vehicles (UAVs) have rapidly emerged as a new technology in the fields of plant protection and pest control in China. Based on existing variable spray research, a plant protection UAV variable spray system integrating neural network based decision making is designed. Using the existing data on plant protection UAV operations, combined with artificial neural network (ANN) technology, an error back propagation (BP) neural network model between the factors affecting droplet deposition is trained. The factors affecting droplet deposition include ambient temperature, ambient humidity, wind speed, flight speed, flight altitude, propeller pitch, nozzles pitch and prescription value. Subsequently, the BP neural network model is combined with variable rate spray control for plant protection UAVs, and real-time information is collected by multi-sensor. The deposition rate is determined by the neural network model, and the flow rate of the spray system is regulated according to the predicted deposition amount. The amount of droplet deposition can meet the prescription requirement. The results show that the training variance of the ANN is 0.003, and thus, the model is stable and reliable. The outdoor tests show that the error between the predicted droplet deposition and actual droplet deposition is less than 20%. The ratio of droplet deposition to prescription value in each unit is approximately equal, and a variable spray operation under different conditions is realized

Antioxidant Properties of Polysaccharide from the Brown Seaweed Sargassum graminifolium (Turn.), and Its Effects on Calcium Oxalate Crystallization

We investigated the effects of polysaccharides from the brown seaweed Sargassum graminifolium (Turn.) (SGP) on calcium oxalate crystallization, and determined its antioxidant activities. To examine the effects of SGP on calcium oxalate crystallization, we monitored nucleation and aggregation of calcium oxalate monohydrate crystals, using trisodium citrate as a positive control. We assessed antioxidant activities of SGP by determining its reducing power, its ability to scavenge superoxide radicals, and its activity in the 1,1-diphenyl-2-picrylhydrazyl (DPPH) assay. The nucleation inhibition ratio of trisodium citrate and SGP was 58.5 and 69.2%, respectively, and crystal aggregation was inhibited by 71.4 and 76.8%, respectively. Increasing concentrations of SGP resulted in increased scavenging of superoxide anions and DPPH radicals (IC50 = 1.9 and 0.6 mg/mL, respectively). These results suggest that SGP could be a candidate for treating urinary stones because of its ability to inhibit calcium oxalate crystallization and its antioxidant properties

Classification of topological phases with finite internal symmetries in all dimensions

We develop a mathematical theory of symmetry protected trivial (SPT) orders and anomaly-free symmetry enriched topological (SET) orders in all dimensions via two different approaches with an emphasis on the second approach. The first approach is to gauge the symmetry in the same dimension by adding topological excitations as it was done in the 2d case, in which the gauging process is mathematically described by the minimal modular extensions of unitary braided fusion 1-categories. This 2d result immediately generalizes to all dimensions except in 1d, which is treated with special care. The second approach is to use the 1-dimensional higher bulk of the SPT/SET order and the boundary-bulk relation. This approach also leads us to a precise mathematical description and a classification of SPT/SET orders in all dimensions. The equivalence of these two approaches, together with known physical results, provides us with many precise mathematical predictions.Comment: 41 pages, 6 figures; add more results on anomalies; final version to appear in JHE