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The Practical Byzantine Fault Tolerance (PBFT) protocol-supported blockchain can provide decentralized security and trust mechanisms for the Internet of Things (IoT). However, the PBFT protocol is not specifically designed for IoT applications. Consequently, adapting PBFT to the dynamic changes of an IoT environment with incomplete information represents a challenge that urgently needs to be addressed. To this end, we introduce DA-PBFT, a PBFT dynamic adaptive framework based on a multi-agent architecture. DA-PBFT divides the dynamic adaptive process into two sub-processes: optimality-seeking and optimization decision-making. During the optimality-seeking process, a PBFT optimization model is constructed based on deep reinforcement learning. This model is designed to generate PBFT optimization strategies for consensus nodes. In the optimization decision-making process, a PBFT optimization decision consensus mechanism is constructed based on the Borda count method. This mechanism ensures consistency in PBFT optimization decisions within an environment characterized by incomplete information. Furthermore, we designed a dynamic adaptive incentive mechanism to explore the Nash equilibrium conditions and security aspects of DA-PBFT. The experimental results demonstrate that DA-PBFT is capable of achieving consistency in PBFT optimization decisions within an environment of incomplete information, thereby offering robust and efficient transaction throughput for IoT applications.

Molecular fingerprints are significant cheminformatics tools to map molecules into vectorial space according to their characteristics in diverse functional groups, atom sequences, and other topological structures. In this paper, we investigate a novel molecular fingerprint Anonymous-FP that possesses abundant perception about the underlying interactions shaped in small, medium, and large-scale atom chains. In detail, the possible atom chains from each molecule are sampled and extended as anonymous atom chains using an anonymous encoding manner. After that, the molecular fingerprint Anonymous-FP is embedded into vectorial space in virtue of the Natural Language Processing technique PV-DBOW. Anonymous-FP is studied on molecular property identification via molecule classification experiments on a series of molecule databases and has shown valuable advantages such as less dependence on prior knowledge, rich information content, full structural significance, and high experimental performance. During the experimental verification, the scale of the atom chain or its anonymous pattern is found significant to the overall representation ability of Anonymous-FP. Generally, the typical scale $r = 8$r=8 could enhance the molecule classification performance, and specifically, Anonymous-FP gains the classification accuracy to above 93% on all NCI datasets.

Smoothing the discretized toolpaths generated by CAM systems is vital for CNC options in improving the quality of machined surfaces. One discretized toolpath from CAM is commonly represented in the form of a series of linear and arc segments. The linear segment smoothing method has been extensively investigated. However, for linear and arc joint segments, which are in the form of G01 and G02/03 mixing modes, efficient smoothing strategies are still lacking. In this study, an integrated toolpath smoothing method based on motion overlapping strategy is proposed to improve the continuities of the mixture of G01 and G02/03 codes. To satisfy the requests of the kinematic limitations and high efficiency, heuristic algorithms are used to seek optimum kinematic parameters. Meanwhile, we also introduce a variable jerk-limited feedrate profile in the motion overlapping strategy to further reduce the machining time. Simulations on various toolpaths are performed to validate the effectiveness of the proposed method compared with the classical FIR and B-spline methods. The machining experiment executed on a 3-axis machine tool with a real-time CNC system also demonstrates the applicability of the proposed method.

Feed rate scheduling is a critical step in computer numerical control machining, as it has a close relationship with machining time and surface quality. It has now become a hot issue in both industry and academia. In this article, we present a novel and complete S-shape-based feed rate scheduling method for three-axis non-uniform rational B-spline (NURBS) tool paths, which can reduce high chord errors and round-off errors, and generate continuous velocity, acceleration, and jerk profile. The proposed feed rate scheduling method consists of three modules: a bidirectional scanning module, a velocity scheduling module, and a round-off error elimination module. The bidirectional scanning module aims to guarantee the continuity of the feed rate at the junctions between successive NURBS blocks, where the chord error, tangential acceleration, and tangential jerk limitations are considered. After the NURBS blocks have been classified into two cases by the previous module, the velocity scheduling module first calculates the actual maximum feed rate. It then generates the feed rate profiles of all NURBS blocks according to the proposed velocity profile. Later, the round-off error elimination module is applied to adjust the actual maximum feed rate so that the total interpolation time becomes an integer multiple of the interpolation period, which leads to the elimination of round-off errors. Finally, benchmarks are conducted to verify the applicability of the proposed method. Compared with the traditional method, the proposed method can save the interpolation time by $4.67$to $14.26\% $.Graphical Abstract

Federated learning is a promising learning paradigm that allows collaborative training of models across multiple data owners without sharing their raw datasets. To enhance privacy in federated learning, multi-party computation can be leveraged for secure communication and computation during model training. This survey provides a comprehensive review on how to integrate mainstream multi-party computation techniques into diverse federated learning setups for guaranteed privacy, as well as the corresponding optimization techniques to improve model accuracy and training efficiency. We also pinpoint future directions to deploy federated learning to a wider range of applications.

Enhancing capacities of cathodes is critical to developing high energy density potassium-based batteries. Here, we explore a conversion-type carbon fluoride material that can deliver capacity of >250 mAh g−1and reveal the underlying reaction mechanism.

Since the beginning of the 21st century, the geoscience research has been entering a significant transitional period with the establishment of a new knowledge system as the core and with the drive of big data as the means. It is a revolutionary leap in the research of geoscience knowledge discovery from the traditional encyclopedic discipline knowledge system to the computer-understandable and operable knowledge graph. Based on adopting the graph pattern of general knowledge representation, the geoscience knowledge graph expands the unique spatiotemporal features to the Geoscience knowledge, and integrates geoscience knowledge elements such as map, text, number, to establish an all-domain geoscience knowledge representation model. A federated, crowd intelligence-based collaborative method of constructing the geoscience knowledge graph is developed here, which realizes the construction of high-quality professional knowledge graph in collaboration with global geoscientists. We also develop a method for constructing a dynamic knowledge graph of multi-modal geoscience data based on in-depth text analysis, which extracts geoscience knowledge from massive geoscience literature to construct the latest and most complete dynamic geoscience knowledge graph. A comprehensive and systematic geoscience knowledge graph can not only deepen the existing geoscience big data analysis, but also advance the construction of the high-precision geological time scale driven by big data, the compilation of intelligent maps driven by rules and data, and the geoscience knowledge evolution and reasoning analysis, and others. It will further expand the new directions of geoscience research driven by both data and knowledge, break new ground where geoscience, information science, and data science intersect, and realize the original innovation of the geoscience research and achieve major theoretical breakthroughs in the spatiotemporal big data research.

Conversion-type transition-metal phosphide anode materials with high theoretical capacity usually suffer from low-rate capability and severe capacity decay, which are mainly caused by their inferior electronic conductivities and large volumetric variations together with the poor reversibility of discharge product (Li3P), impeding their practical applications. Herein, guided by density functional theory calculations, these obstacles are simultaneously mitigated by confining amorphous FeP nanoparticles into ultrathin 3D interconnected P-doped porous carbon nanosheets (denoted as FeP@CNs) viaa facile approach, forming an intriguing 3D flake-CNs-like configuration. As an anode for lithium-ion batteries (LIBs), the resulting FeP@CNs electrode not only reaches a high reversible capacity (837 mA h g–1after 300 cycles at 0.2 A g–1) and an exceptional rate capability (403 mA h g–1at 16 A g–1) but also exhibits extraordinary durability (2500 cycles, 563 mA h g–1at 4 A g–1, 98% capacity retention). By combining DFT calculations, in situtransmission electron microscopy, and a suite of ex situmicroscopic and spectroscopic techniques, we show that the superior performances of FeP@CNs anode originate from its prominent structural and compositional merits, which render fast electron/ion-transport kinetics and abundant active sites (amorphous FeP nanoparticles and structural defects in P-doped CNs) for charge storage, promote the reversibility of conversion reactions, and buffer the volume variations while preventing pulverization/aggregation of FeP during cycling, thus enabling a high rate and highly durable lithium storage. Furthermore, a full cell composed of the prelithiated FeP@CNs anode and commercial LiFePO4cathode exhibits impressive rate performance while maintaining superior cycling stability. This work fundamentally and experimentally presents a facile and effective structural engineering strategy for markedly improving the performance of conversion-type anodes for advanced LIBs.

Conversion-type reaction anode materials with high specific capacity are attractive candidates to improve lithium ion batteries (LIBs), yet the rapid capacity fading and poor rate capability caused by drastic volume change and low electronic conductivity greatly hinder their practical applications. To circumvent these issues, the successful design of yolk@shell Fe2O3@C hybrid composed of a columnar-like Fe2O3core within a hollow cavity completely surrounded by a thin, self-supported carbon (C) shell is presented as an anode for high-performance LIBs. This yolk@shell structure allows each Fe2O3core to swell upon lithiation without deforming the carbon shell. This preserves the structural and electrical integrity against pulverization, as revealed by in situ transmission electron microscopy (TEM) measurement. Benefiting from these structural advantages, the resulting electrode exhibits a high reversible capacity (1013 mAh g−1after 80 cycles at 0.2 A g−1), outstanding rate capability (710 mAh g−1at 8 A g−1) and superior cycling stability (800 mAh g−1after 300 cycles at 4 A g−1). A Li-ion full cell using prelithiated yolk@shell Fe2O3@C hybrid as the anode and commercial LiCoO2(LCO) as the cathode demonstrates impressive cycling stability with a capacity retention of 84.5% after 100 cycles at 1 C rate, holding great promise for future practical applications.

Bioaerosol, an important constituent of the atmosphere, can directly affect light radiation characteristics due to absorption and scattering effects. Current research lacks a reasonable explanation for the extinction abilities of bioaerosols in a broadband. Herein, we measured the reflectance spectra of 12 common biomaterials and calculated their complex refractive indexes. The peaks of the imaginary part of the complex refractive indexes are located at wavelengths of approximately 0.7, 2.7, 6.1 and 9.5 μm. Based on photographs of the floating structures of bioaerosols, we constructed a model for calculating the extinction abilities of bioaerosols in the wavelength range of 240 nm to 14 μm. Taking AN02 spores as an example, absorption was found to account for more than 90% of the total extinction. In addition, the theoretical calculations and experimental data of transmittance corresponding to the smoke box show that bioaerosol exhibits significant broadband extinction ability from UV to IR bands, which provides new directions for the development of broadband light attenuation materials. 生物气溶胶是大气的重要组成部分, 因其吸收和散射效应, 可直接影响光辐射特性. 当前对于生物气溶胶是否具有宽波段消光特性 的研究还不够充分. 本文中, 我们测量了12种常见生物材料在240 nm–14 μm波段内的反射光谱, 并结合K-K算法计算了不同生物气溶胶材 料的复折射率. 我们发现, 不同种质生物气溶胶的吸收峰具有共性, 位于约0.7, 2.7, 6.1和9.5 μm处. 基于烟幕箱中生物气溶胶漂浮状态实际 结构的照片, 我们构建了模型计算240 nm–14 μm波长范围内生物气溶胶的消光能力. 以AN02孢子为例, 我们发现吸收作用占AN02孢子群 消光总量的90%以上. 此外, 我们对比了生物气溶胶理论计算透过率与大型烟幕箱实测透射率数据, 理论计算和实验验证都显示生物气溶 胶在紫外到红外波段具有显著的宽波段消光能力. 这一发现为宽波段消光材料的发展提供了新的研究方向.

High-performance lithium-ion batteries are commonly built with heterogeneous composite electrodes that combine multiple active components for serving various electrochemical and structural functions. Engineering these heterogeneous composite electrodes toward drastically improved battery performance is hinged on a fundamental understanding of the mechanisms of multiple active components and their synergy or trade-off effects. Herein, we report a rational design, fabrication, and understanding of yolk@shell Bi2S3@N-doped mesoporous carbon (C) composite anode, consisting of a Bi2S3nanowire (NW) core within a hollow space surrounded by a thin shell of N-doped mesoporous C. This composite anode exhibits desirable rate performance and long cycle stability (700 cycles, 501 mAhg–1at 1.0 Ag–1, 85% capacity retention). By in situtransmission electron microscopy (TEM), X-ray diffraction, and NMR experiments and computational modeling, we elucidate the dominant mechanisms of the phase transformation, structural evolution, and lithiation kinetics of the Bi2S3NWs anode. Our combined in situTEM experiments and finite element simulations reveal that the hollow space between the Bi2S3NWs core and carbon shell can effectively accommodate the lithiation-induced expansion of Bi2S3NWs without cracking C shells. This work demonstrates an effective strategy of engineering the yolk@shell-architectured anodes and also sheds light onto harnessing the complex multistep reactions in metal sulfides to enable high-performance lithium-ion batteries.

We investigate the effects of the frequency-degree correlation on local synchronization in complex networks with Kuramoto oscillators. We find that a discontinuous synchronization transition occurs in the local patterns for heterogenous networks while for homogenous networks, the local synchronization transition remains continuous. Then, we extend our study to a general frequency-degree correlation case and conclude that the positive correlation does not change the local synchronization patterns while in the case of a negative correlation, the local synchronization transition degenerates to second order. Moreover, the correlation parameter αis verified to have a strong influence on the synchronization level. In particular, smaller |α| results in higher synchronization ability and faster speed to a synchronized state. Our study provides a deeper understanding of the effects of the frequency-degree correlation on network synchronization.

Synchronization phenomenon plays an important role in the dynamic process on complex networks. In this letter, we consider synchronization under multiplex structures and explore the effect of external parts on the multilayered Kuramoto model with positive correlation between frequencies and degree. We show that large and strong mixing parts of the external layer may put off synchronization while the coupling strength of external layers has an accelerating, but limited, influence on synchronization. In particular, an explosive synchronization can be obtained by weakening the co-evolution coupling strength. The transition tends to be smooth when the co-evolution coupling strength increases. Our findings indicate that externality from multiplex networks, especially the mixing parts, and the co-evolution coupling strength should be of importance for synchronization on one certain layer.

The voter model has served to address the emergence of consensus within populations of individuals. However, the dynamics based on the classic voter model has usually been analyzed based on the assumption that the two states in the model are simply equivalent. In this paper, we discuss a mathematical description of the weighted voter model and obtain a series of results for the evolutionary process on complex networks. For homogeneous networks, we study the active link density analytically and find that the opinion strength plays a crucial role in determining whether the system can reach consensus. We also extend our research to heterogeneous networks and discover that the network structure can affect the convergence time but has less influence on the positive proportion. The results can be applied to various pervasive cases in which two conflicting opinions interact with each other.

Abstract: Software trustworthiness has become one of the key restrictions for software service quality and the development of the software industry. However, trustworthiness attributes interlace structured and dynamical coupling relations, which causes great barriers for trustworthiness measurements of large-scale software. According to the dynamical evolutionary characteristics of software trustworthiness attributes, this paper proposes a new approach for optimizing the trustworthiness measurement in terms the kernel trustworthiness attributes, and improves a downsize-optimized statistical analysis method for software trustworthiness attributes based on their nonlinear relations. The improved method considerably simplifies the trustworthiness assessment of largescale software. Using theoretical analysis and numerical simulations, the feasibility of this method is verified using two typical examples that illustrate the realization of the trustworthiness measurement.

Cyclophanes based on 2,2′biimidazole and 2,2′bibenzimidazole were synthesized as receptors. UV spectroscopic titration in chloroform at 25°C showed 1:1 complexes between the cyclophanes and the guests, and the binding constants K and Gibbs free energy changes −ΔG0 were calculated according to the modified BenesiHildebrand equation. J. Heterocyclic Chem., 00, 00 2009.

This paper deals with the problem of computing Lyapunov functions for asymptotic stability analysis of autonomous polynomial systems of differential equations. We propose a new semi-algebraic approach by making advantage of the local property of the Lyapunov function as well as its derivative. This is done by first constructing a semi-algebraic system and then solving this semi-algebraic system in an adaptive way. Experiment results show that our semi-algebraic approach is more efficient in practice, especially for low-order systems.

Abstract: Nitrogen (N) supply from organic sources to the potato (Solanum tuberosum L.) crop is difficult to predict and to synchronize with crop demand. In this study, Plant Root Simulator™ (PRS™) probes were evaluated as a tool for prediction of N supply from two rates (300 vs. 600 kg N ha−1) of either a hog manure-sawdust compost (HMC) or a pelletized dehydrated poultry manure (NW) in Atlantic Canada. The cumulative PRS mineral N supply rate (PRS-N) measured for the period of 31 days after planting (DAP), soil mineral N at 10 DAP and soil NO3-N at 31 DAP were closely related to plant N uptake (PNU) (r = 0.77, 0.71 and 0.73, respectively; P < 0.001) and PNU plus soil mineral N to 30 cm depth at tuber harvest (PNU + SMNh) (r = 0.77, 0.81 and 0.74, respectively; P < 0.001). The supply of N from organic sources to a potato crop can be predicted by PRS-N early in the growing season.

In this paper, we first generalize reachability constraints for linear differential equations, then tighten them by using the information of multiplicity of the eigenvalues and eigenvectors of such equations and put them into our constraint based approach for safety verification of hybrid systems that employs recursive reasoning to improve the method of constraint propagation based abstraction refinement.

Knowledge of phosphorus (P) dynamics in soil is essential for predicting its bioavailability and the risk of P transfer from soil to bodies of water. A comparative study was conducted to assess the changes in P fractions and pathways of P transformation in soil measured after 10 annual applications of mineral fertilizers (MIN) and liquid dairy manure (LDM). Fractionation and path analyses were performed to quantify inorganic P (Pi) and organic P (Po) forms and the relationships between P pools in the 0 to 15-cm layer of a Labarre silty clay (fine, mixed, frigid, Humic Cryaquept) under barley monoculture. The MIN additions resulted in larger increases in Pifractions and smaller increases in the NaOH-Pocompared with the LDM applications. The LDM, however, produced 1.9 times more total soil labile P than the MIN plot. Path analysis indicated that path coefficients between the source and recipient P pools were P-source dependent. The NaOH-Piwas a primary sink of added Piand a source of NaHCO3-Pi. The roles of Popools were more important than the Pipools for P transformations. The NaHCO3-Powas sensitive to P sources and likely acted as a transitory pool rather than as a sink or source of soil P. The NaOH-Poconstituted a sink for added Poand immobilized labile Piin the MIN plot; it was conversely mineralized and contributed to labile Piin the LDM plot. The results of this study stress that the pathways of P transformation in this Cryaquept can be revealed by the descriptive path analysis.

Most previous studies have limited the assessments of soil phosphorus (P) status within the plow layer. This study was to assess the impacts of crop sequences and nutrient sources on P status of a Labarre silty clay (Humic Cryaquept) profile in a frigid continental climate. Soil of the 0- to 15-, 15- to 30-, 30- to 60-, and 60- to 90-cm layers was sampled from a split-plot experiment comprising a barley ( Hordeum vulgare L.) monoculture and a 3-year barley-forage rotation as main plots, and receiving mineral fertilizers (MIN) or liquid dairy manure (LDM) as subplots. A modified Hedley sequential fractionation was used to characterize soil P status. Labile P pools were more affected than stable ones by the investigated treatments. After 10 years, the MIN resulted in larger resin-P and NaHCO 3-P i, and lower NaHCO 3-P o and NaOH-P o pools than the LDM in the top 30 cm of soil. The rotation resulted in larger labile P i and P opools than the monoculture in the 30- to 60-cm layer. The rotation associated with LDM produced the largest total labile P pool, whereas the LDM resulted in an about 20% higher degree of soil P saturation as expressed by the P ox/(Fe ox + Al ox) molar ratio than the MIN in the 0- to 30-cm layer. Our observations stressed that the impacts of crop sequences and nutrient sources on soil labile P extended deeper into the profile than the disturbance caused by primary tillage.

Soil‐test P is not only used for fertilizer recommendations but also as a component to predict risk of P transfer from soils to surface waters. The changes in soil‐test P following P application are often related to soil texture. This study assessed the changes in anion‐exchange membrane P (AEM‐P) and Mehlich‐III extractable P (M3P) in Humaquepts varying in clay content. Five soils from loamy sand to “heavy” clay received 0 (P0), 10 (P10), 20 (P20), or 40 (P40) mg P kg−1per each simulated growth season were successively cropped with barley (Hordeum vulgareL.) and soybean (Glycine maxL. Merr.) in a growth chamber experiment. There were clay content mineral fertilizer P (MFP) interactive effects on soil AEM‐P, M3P contents and plant P uptake. The AEM‐P paralleled clay content and MFP rate. The average increase in M3P at P10 and P20 over P0 was smaller on clayey than on coarse‐textured soils. The converse trend was true at P40 over P10 and P20. The increase in M3P per unit MFP addition in excess of plant uptake decreased linearly with the increase in clay at P10 and P20 but not at P40. There was a quadratic plateau relationship between AEM‐P and M3P contents with a turning point at 4.2 μg AEM‐P cm−2or 93.0 mg M3P kg−1Plant P uptake was more closely related to AEM‐P than M3P in all soils, suggesting AEM‐P is a more reliable indicator of labile P than M3P in Humaquepts for the tested crops, particularly in fine‐textured soils. Clay content has a large influence on changes in AEM‐P and M3P following MFP additions to Humaquepts.

The knowledge of P transformations is essential to understand the P behaviour in soils. Organic (Po) and inorganic (Pi) P fractions were obtained from the 0‐ to 30‐ and 30‐ to 90‐cm layers of a Labarre silty clay (fine, mixed, frigid, Humic Cryaquept) by a sequential extraction. Barley (Hordeum vulgareL.) monoculture and 3‐yr barley‐forage rotation as main plots, and two nutrient sources (mineral fertilizer and liquid dairy manure) as subplots were studied. Path analysis was used to describe soil P transformations between the falls of 1989 and 1997. Nutrient source was the main factor affecting P transformations in the 0‐ to 30‐cm soil layer, whereas crop rotation predominated in the subsoil. Pathways differed more for Pothan for Pipools. In the 0‐ to 30‐cm soil layer, 86 to 97% of the variation in resin‐P was the direct effect of added PiThe NaHCO3‐Piand Powere sensitive to crop rotations and nutrient sources, and were transitory pools of soil P. The NaOH‐Piwas a sink for added Piand a source of NaHCO3‐PiLabile Pitended to store as NaOH‐Po, which was the sink for added Poand immobilized soil Piin the mineral fertilizer systems. Conversely, the NaOH‐Powas mineralized and contributed to labile Piin dairy manure systems. The NaOH‐Poacted as store of subsoil Poin the monoculture but was the main source of labile P in the rotation systems. The P transformations in this Cryaquept were strongly influenced by nutrient sources and crop rotations.

In E.M. James and N.G. Lloyd's paper A Cubic System with Eight Small-Amplitude Limit Cycles[1], a set of conditions is given that ensures the origin to be a fine focus of order eight and eight limit cycles to bifurcate from the origin by perturbing parameters. We find that one of the conditions, a9= σ*a7, where 666/97 < σ*< 103/15, can be weakened as a9= σ*a7or a9= σ1a7, where 283/125 < σ1< 284/125. In [1], deriving above conditions is reduced to finding the real solutions of a system of some algebraic equations and inequalities. When verifying these conditions by solving this system in a different ordering, we find another real solution to the system, which is leading to above improvement of the conditions.

Despite the high specific capacity of silicon as a promising anode material for the next-generation high-capacity Li-ion batteries (LIBs), its practical applications are impeded by the rapid capacity decay during cycling. To tackle the issue, herein, a binder-grafting strategy is proposed to construct a covalently cross-linked binder [carboxymethyl cellulose/phytic acid (CMC/PA)], which builds a robust branched network with more contact points, allowing stronger bonds with Si nanoparticles by hydrogen bonding. Benefitting from the enhanced mechanical reliability, the resulting Si-CMC/PA electrodes exhibit a high reversible capacity with improved long-term cycling stability. Moreover, an assembled full cell consisting of the as-obtained Si-CMC/PA anode and commercial LiFePO4cathode also exhibits excellent cycling performance (120.4 mA h g–1at 1 C for over 100 cycles with 88.4% capacity retention). In situ transmission electron microscopy was employed to visualize the binding effect of CMC/PA, which, unlike the conventional CMC binder, can effectively prevent the lithiated Si anodes from cracking. Furthermore, the combined ex situ microscopy and X-ray photoelectron spectroscopy analysis unveils the origin of the superior Li-ion storage performance of the Si-CMC/PA electrode, which arises from its excellent structural integrity and the stabilized solid–electrolyte interphase films during cycling. This work presents a facile and efficient binder-engineering strategy for significantly improving the performance of Si anodes for next-generation LIBs.

T-spline has been recently developed to represent objects of arbitrary shapes in computer-aided design, computer graphics, and reverse engineering. In fact, fitting a T-spline over a point cloud is usually ineffective by using traditional iterative fit-and-refine paradigm. In traditional T-spline least-square fitting method, all control points are recomputed in each iteration, which costs large amount of calculations. In this paper, we propose a fast T-spline fitting method based on T-mesh segmentation. The segmentation technology is introduced to identify the inactive and active region of T-mesh. Computational costs can be largely reduced since only the control points in the active part need to be recalculated in the upcoming process, while those in inactive part are kept invariant once the fitting accuracy is achieved. Classical datasets are used to validate the proposed fast fitting method, and the experimental results yield that a total running time is reduced to 34%of the traditional T-spline fitting method. We argue this method is particularly useful in the reconstruction of scanned scatter data of which the parameter distribution is not uniform.

Community detection is a fundamental and important problem in network science, as community structures often reveal both topological and functional relationships between different components of the complex system. In this paper, we first propose a gradient descent framework of modularity optimization called vector-label propagation algorithm (VLPA), where a node is associated with a vector of continuous community labels instead of one label. Retaining weak structural information in vector-label, VLPA outperforms some well-known community detection methods, and particularly improves the performance in networks with weak community structures. Further, we incorporate stochastic gradient strategies into VLPA to avoid stuck in the local optima, leading to the stochastic vector-label propagation algorithm (sVLPA). We show that sVLPA performs better than Louvain Method, a widely used community detection algorithm, on both artificial benchmarks and real-world networks. Our theoretical scheme based on vector-label propagation can be directly applied to high-dimensional networks where each node has multiple features, and can also be used for optimizing other partition measures such as modularity with resolution parameters. • We propose a gradient descent frame of modularity optimization to detect communities. • Our vector-label propagation algorithm (VLPA) retains weak structural information. • VLPA obtains better performance particularly when the community structure is weak. • sVLPA is further proposed via equipping stochastic strategies to avoid local optima. • sVLPA outperforms the classic Louvain Method on both artificial and real networks. [ABSTRACT FROM AUTHOR]

• Such a mechanism could promote cooperation even at high temptation values. • It has good robustness for random initial distributions. • Dynamic aspiration model is more in line with psychology so it has a wider application in practical problems. In recent years, Win-Stay-Lose-Learn rule has attracted wide attention as an effective strategy updating rule, and voluntary participation is proposed by introducing a third strategy in Prisoner's dilemma game. Some researches show that combining Win-Stay-Lose-Learn rule with voluntary participation could promote cooperation more significantly under moderate temptation values, however, cooperators' survival under high aspiration levels and high temptation values is still a challenging problem. In this paper, inspired by Achievement Motivation Theory, a Dynamic-Win-Stay-Lose-Learn rule with voluntary participation is investigated, where a dynamic aspiration process is introduced to describe the co-evolution of individuals' strategies and aspirations. It is found that cooperation is extremely promoted and defection is almost extinct in our model, even when the initial aspiration levels and temptation values are high. The combination of dynamic aspiration and voluntary participation plays an active role since loners could survive under high initial aspiration levels and they will expand stably because of their fixed payoffs. The robustness of our model is also discussed and some adverse structures are found which should be alerted in the evolutionary process. Our work provides a more rational model and shows that cooperators may prevail defectors in an unfavorable initial environment. [ABSTRACT FROM AUTHOR]