Peakon, pseudo-peakon, and cuspon solutions for two generalized Camassa- Holm equations

In this paper, we study peakon, cuspon, and pseudo-peakon solutions for two generalized Camassa-Holm equations. Based on the method of dynamical systems, the two generalized Camassa-Holm equations are shown to have the parametric representations of the solitary wave solutions such as peakon, cuspon, pseudo-peakons, and periodic cusp solutions. In particular, the pseudo-peakon solution is for the first time proposed in our paper. Moreover, when a traveling system has a singular straight line and a heteroclinic loop, under some parameter conditions, there must be peaked solitary wave solutions appearing

Bifurcations of traveling wave solutions for an integrable equation

This paper deals with the following equation mt= 1/2 1/mk xxx− 1/2 1/mk x, which is proposed by Z. J. Qiao J. Math. Phys. 48, 082701 2007 and Qiao and Liu Chaos, Solitons Fractals 41, 587 2009. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=−2,−1 2 , 1 2 ,2, and parametric representations of all possible bounded traveling wave solutions are given in the different c,g -parameter regions

Tool path planning based on conformal parameterization for meshes

AbstractThe similarity property of conformal parameterization makes it able to locally preserve the shapes between a surface and its parameter domain, as opposed to common parameterization methods. A parametric tool path planning method is proposed in this paper through such parameterization of triangular meshes which is furthermore based on the geodesic on meshes. The parameterization has the properties of local similarity and free boundary which are exploited to simplify the formulas for computing path parameters, which play a fundamentally important role in tool path planning, and keep the path boundary-conformed and smooth. Experimental results are given to illustrate the effectiveness of the proposed methods, as well as the error analysis

An Efficient Threshold-Driven Aggregate-Label Learning Algorithm for Multimodal Information Processing

The aggregate-label learning paradigm tackles the long-standing temporary credit assignment (TCA) problem in neuroscience and machine learning, enabling spiking neural networks to learn multimodal sensory clues with delayed feedback signals. However, the existing aggregate-label learning algorithms only work for single spiking neurons, and with low learning efficiency, which limit their real-world applicability. To address these limitations, we first propose an efficient threshold-driven plasticity algorithm for spiking neurons, namely ETDP. It enables spiking neurons to generate the desired number of spikes that match the magnitude of delayed feedback signals and to learn useful multimodal sensory clues embedded within spontaneous spiking activities. Furthermore, we extend the ETDP algorithm to support multi-layer spiking neural networks (SNNs), which significantly improves the applicability of aggregate-label learning algorithms. We also validate the multi-layer ETDP learning algorithm in a multimodal computation framework for audio-visual pattern recognition. Experimental results on both synthetic and realistic datasets show significant improvements in the learning efficiency and model capacity over the existing aggregate-label learning algorithms. It, therefore, provides many opportunities for solving real-world multimodal pattern recognition tasks with spiking neural networks

An Anonymous System Based on Random Virtual Proxy Mutation

Anonymous systems are usually used to protect users\u27 privacy in network communication. However, even in the low-latency Tor system, it is accompanied by network communication performance degradation, which makes users have to give up using the anonymity system in many applications. Therefore, we propose a novel anonymity system with rotated multi-path accompanying virtual proxy mutation for data transmission. Unlike onion routing, in our system the randomly generated virtual proxies take over the address isolation executing directly on the network layer and expand the anonymity space to all terminals in the network. With the optimal algorithm of selecting the path, the network communication performance improved significantly also. The verification experiments show that the anonymity system terminal sends and receives data at 500 kbps, and only a slight delay jitter occurs at the receiving end, and the other network performance is not significantly reduced

Functional exploration of co-expression networks identifies a nexus for modulating protein and citric acid titres in Aspergillus niger submerged culture

Background: Filamentous fungal cell factories are used to produce numerous proteins, enzymes, and organic acids. Protein secretion and filamentous growth are tightly coupled at the hyphal tip. Additionally, both these processes require ATP and amino acid precursors derived from the citric acid cycle. Despite this interconnection of organic acid production and protein secretion/filamentous growth, few studies in fungi have identified genes which may concomitantly impact all three processes. Results: We applied a novel screen of a global co-expression network in the cell factory Aspergillus niger to identify candidate genes which may concomitantly impact macromorphology, and protein/organic acid fermentation. This identified genes predicted to encode the Golgi localized ArfA GTPase activating protein (GAP, AgeB), and ArfA guanine nucleotide exchange factors (GEFs SecG and GeaB) to be co-expressed with citric acid cycle genes. Consequently, we used CRISPR-based genome editing to place the titratable Tet-on expression system upstream of ageB, secG, and geaB in A. niger. Functional analysis revealed that ageB and geaB are essential whereas secG was dispensable for early filamentous growth. Next, gene expression was titrated during submerged cultivations under conditions for either protein or organic acid production. ArfA regulators played varied and culture-dependent roles on pellet formation. Notably, ageB or geaB expression levels had major impacts on protein secretion, whereas secG was dispensable. In contrast, reduced expression of each predicted ArfA regulator resulted in an absence of citric acid in growth media. Finally, titrated expression of either GEFs resulted in an increase in oxaloacetic acid concentrations in supernatants. Conclusion: Our data suggest that the Golgi may play an underappreciated role in modulating organic acid titres during industrial applications, and that this is SecG, GeaB and AgeB dependent in A. niger. These data may lead to novel avenues for strain optimization in filamentous fungi for improved protein and organic acid titres.TU Berlin, Open-Access-Mittel - 201