Root Isolation of Zero-dimensional Polynomial Systems with Linear Univariate Representation

In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the roots of the equation system are represented as linear combinations of roots of several univariate polynomial equations. The main advantage of this representation is that the precision of the roots can be easily controlled. In fact, based on the linear univariate representation, we can give the exact precisions needed for roots of the univariate equations in order to obtain the roots of the equation system to a given precision. As a consequence, a root isolation algorithm for a zero-dimensional polynomial equation system can be easily derived from its linear univariate representation.Comment: 19 pages,2 figures; MM-Preprint of KLMM, Vol. 29, 92-111, Aug. 201

Prototype as Query for Few Shot Semantic Segmentation

Few-shot Semantic Segmentation (FSS) was proposed to segment unseen classes in a query image, referring to only a few annotated examples named support images. One of the characteristics of FSS is spatial inconsistency between query and support targets, e.g., texture or appearance. This greatly challenges the generalization ability of methods for FSS, which requires to effectively exploit the dependency of the query image and the support examples. Most existing methods abstracted support features into prototype vectors and implemented the interaction with query features using cosine similarity or feature concatenation. However, this simple interaction may not capture spatial details in query features. To alleviate this limitation, a few methods utilized all pixel-wise support information via computing the pixel-wise correlations between paired query and support features implemented with the attention mechanism of Transformer. These approaches suffer from heavy computation on the dot-product attention between all pixels of support and query features. In this paper, we propose a simple yet effective framework built upon Transformer termed as ProtoFormer to fully capture spatial details in query features. It views the abstracted prototype of the target class in support features as Query and the query features as Key and Value embeddings, which are input to the Transformer decoder. In this way, the spatial details can be better captured and the semantic features of target class in the query image can be focused. The output of the Transformer-based module can be viewed as semantic-aware dynamic kernels to filter out the segmentation mask from the enriched query features. Extensive experiments on PASCAL-$5^{i}$ and COCO-$20^{i}$ show that our ProtoFormer significantly advances the state-of-the-art methods.Comment: under revie

A Theory of Complex Adaptive Learning Based on an Intelligent Trading Probability Wave Equation

Complex adaptive learning is intelligent and crucial in living and inanimate complex systems. A complex system comprises many interacting individuals or units, shows hidden patterns as they interact, and widely occurs in almost every traditional discipline, from natural to social sciences. A recent study has demonstrated a so-called architected material capable of learning. It stimulates scientists to explore the mechanism of complex systems formulation. However, it is very challenging. Here the authors attempt to extract a universal rule or a law of complex adaptive learning subject to local dynamic equilibrium in complex systems from a trading volume-price probability wave equation and apply it to complex quantum systems as its application. It proves particles capable of intelligence-like properties in interactive coherence if the momentum force exerted on the complex quantum systems is non-localized. It is the cumulative probability of the moving particles observed in a time interval. Thus, it assumes that particles in complex quantum systems have a complex adaptive learning- or intelligence-like property in a reinforced coordinate, governed by the exact complex adaptive learning mechanism as that of traders in the complexity of the financial markets. With this assumption, the authors propose an innovative interpretation of entanglement in quantum mechanics. It concludes that quantum entanglement is not a state of the superposition of coherent states as the mainstream Copenhagen school of thought maintains. It is a coherent state in the interaction between two opposite, complementary, and variable forces. The authors look forward to the experimental results to examine its validity and further improve the theory until it is perfect, suggesting industrial production of entanglement resources in new technical routes availableComment: 22 pages in total (double spaces and including a title page and a popular summary), 2 figures, and 20 reference

Diabetes Cognitive Impairments and the Effect of Traditional Chinese Herbs

The problem of cognitive impairment resulting from diabetes is gaining more acceptance and attention. Both type 1 and type 2 diabetes mellitus have been proved to be associated with reduced performance on numerous domains of cognitive function. Although the exact mechanisms of cognitive impairments in diabetes have not been completely understood, hyperglycemia and insulin resistance seem to play significant roles. And other possible risk factors such as hypoglycemia, insulin deficiency, vascular risk factors, hyperactive HPA axis, depression, and altered neurotransmitters will also be examined. In the meanwhile, this review analyzed the role of the active ingredient of Chinese herbal medicine in the treatment of diabetes cognitive impairments

AWTE-BERT:Attending to Wordpiece Tokenization Explicitly on BERT for Joint Intent Classification and SlotFilling

Intent classification and slot filling are two core tasks in natural language understanding (NLU). The interaction nature of the two tasks makes the joint models often outperform the single designs. One of the promising solutions, called BERT (Bidirectional Encoder Representations from Transformers), achieves the joint optimization of the two tasks. BERT adopts the wordpiece to tokenize each input token into multiple sub-tokens, which causes a mismatch between the tokens and the labels lengths. Previous methods utilize the hidden states corresponding to the first sub-token as input to the classifier, which limits performance improvement since some hidden semantic informations is discarded in the fine-tune process. To address this issue, we propose a novel joint model based on BERT, which explicitly models the multiple sub-tokens features after wordpiece tokenization, thereby generating the context features that contribute to slot filling. Specifically, we encode the hidden states corresponding to multiple sub-tokens into a context vector via the attention mechanism. Then, we feed each context vector into the slot filling encoder, which preserves the integrity of the sentence. Experimental results demonstrate that our proposed model achieves significant improvement on intent classification accuracy, slot filling F1, and sentence-level semantic frame accuracy on two public benchmark datasets. The F1 score of the slot filling in particular has been improved from 96.1 to 98.2 (2.1% absolute) on the ATIS dataset

Curcumin Inhibits Neuronal and Vascular Degeneration in Retina after Ischemia and Reperfusion Injury

Neuron loss, glial activation and vascular degeneration are common sequelae of ischemia-reperfusion (I/R) injury in ocular diseases. The present study was conducted to explore the ability of curcumin to inhibit retinal I/R injury, and to investigate underlying mechanisms of the drug effects.Different dosages of curcumin were administered. I/R injury was induced by elevating the intraocular pressure for 60 min followed by reperfusion. Cell bodies, brn3a stained cells and TUNEL positive apoptotic cells in the ganglion cell layer (GCL) were quantitated, and the number of degenerate capillaries was assessed. The activation of glial cells was measured by the expression level of GFAP. Signaling pathways including IKK-IκBα, JAK-STAT1/3, ERK/MAPK and the expression levels of β-tubulin III and MCP-1 were measured by western blot analysis. Pre-treatment using 0.01%-0.25% curcumin in diets significantly inhibited I/R-induced cell loss in GCL. 0.05% curcumin pre-treatment inhibited I/R-induced degeneration of retinal capillaries, TUNEL-positive apoptotic cell death in the GCL, brn3a stained cell loss, the I/R-induced up-regulation of MCP-1, IKKα, p-IκBα and p-STAT3 (Tyr), and down-regulation of β-tubulin III. This dose showed no effect on injury-induced GFAP overexpression. Moreover, 0.05% curcumin administered 2 days after the injury also showed a vaso-protective effect.Curcumin protects retinal neurons and microvessels against I/R injury. The beneficial effects of curcumin on neurovascular degeneration may occur through its inhibitory effects on injury-induced activation of NF-κB and STAT3, and on over-expression of MCP-1. Curcumin may therefore serve as a promising candidate for retinal ischemic diseases

Efficient metal halide perovskite light-emitting diodes with significantly improved light extraction on nanophotonic substrates.

Metal halide perovskite has emerged as a promising material for light-emitting diodes. In the past, the performance of devices has been improved mainly by optimizing the active and charge injection layers. However, the large refractive index difference among different materials limits the overall light extraction. Herein, we fabricate efficient methylammonium lead bromide light-emitting diodes on nanophotonic substrates with an optimal device external quantum efficiency of 17.5% which is around twice of the record for the planar device based on this material system. Furthermore, optical modelling shows that a high light extraction efficiency of 73.6% can be achieved as a result of a two-step light extraction process involving nanodome light couplers and nanowire optical antennas on the nanophotonic substrate. These results suggest that utilization of nanophotonic structures can be an effective approach to achieve high performance perovskite light-emitting diodes

Construction of genetic map in barley using sequence-related amplified polymorphism markers, a new molecular marker technique

Sequence-related amplified polymorphism (SRAP) markers, a novel polymerase chain reaction (PCR)-based molecular marker technique, were successfully applied in map construction, cultivar identification, diversity evaluation, comparative genomics and gene location of different plant species. The molecular genetic map of SRAP markers in Steptoe / Morex doubled haploid (DH) population was constructed in this study, using 216 SRAP markers and 312 simple sequence repeat (SSR) markers. Overall, 21 of the 216 SRAP markers generated 78 polymorphic loci, and 98 of 312 SSR markers produced 107 polymorphic loci. Among the 185 loci, 175 loci (70 SRAP loci and 105 SSR loci) were assigned to nine linkage groups. The map covered 1475 cM with a mean density of 8.7 cM per locus. In total, 33 of all the loci (17.84%) showed significant segregation distortion. Moreover, 23 of the 33 loci (69.7%) skewed towards the parent Steptoe, whereas the remaining loci (21.3%) deviated towards the parent Morex and some of these distorted loci tended to cluster at the end of linkage groups, while others were dispersed on linkage groups in a decentralized fashion. The three putative segregation distortion regions (SDRs) were detected on chromosomes 2H, 4H and 5H, respectively. This linkage map indicates its importance in quantitative trait loci (QTLs) mapping, marker-assisted selection (MAS) and integrative analysis for further genetic studies with other linkage maps in barley.Keywords: Barley, sequence-related amplified polymorphism (SRAP), molecular genetic map, simple sequence repeat (SSR), doubled haploid (DH) populatio