With the rapid expansion of graphs and networks and the growing magnitude of data from all areas of science, effective treatment and compression schemes of context-dependent data is extremely desirable. A particularly interesting direction is to compress the data while keeping the “structural information” only and ignoring the concrete labelings. Under this direction, Choi and Szpankowski introduced the structures (unlabeled graphs) which allowed them to compute the structural entropy of the Erdős–Rényi random graph model. Moreover, they also provided an asymptotically optimal compression algorithm that (asymptotically) achieves this entropy limit and runs in expectation in linear time. In this paper, we consider the stochastic block models with an arbitrary number of parts. Indeed, we define a partitioned structural entropy for stochastic block models, which generalizes the structural entropy for unlabeled graphs and encodes the partition information as well. We then compute the partitioned structural entropy of the stochastic block models, and provide a compression scheme that asymptotically achieves this entropy limit. 相似文献
In rolling production, the foil flatness quality is judged by detecting the lateral distribution of the front tension stress. Currently, because of the inaccuracy of the tension control model, there are still many flatness defects in foil rolling production. For the tension stress model of foil rolling, the primary problem is the inaccuracy of the metal lateral flow model. Therefore, based on Fleck’s foil rolling theory, a new model of the lateral displacement in the foil deformation region is established by using the principle of minimum potential energy. Next, a tension stress model is established, which takes the effect of the metal lateral flow into account. Last, using a laboratory 20-high rolling mill as the research object, the finite element model of foil rolling is established, and the accuracy of the new model is demonstrated by comparing the theoretical calculations with the simulation results.
Shear damage may occur in the process of metal machining such as blanking and cutting, where localized shear deformation is developed. Experimental findings indicate that microscopic shear damage evolution in aluminium alloy 2024T3 (A1 2024T3) is a multi-stage mechanism, including particle cracking, micro-shear banding, matrix microcracking and coalescence of microcracks. This study is an attempt to use a set of equations to describe the multi-stage shear damage evolution in Al 2024T3. The shear damage variables in terms of multi-couple parameters of a power-law hardening material have been defined. An evolution curve of shearing damage has been calculated from experimental data. The values of the shear damage variable at different stages of damage have also been calculated. By making use of the findings, the relation between the microscopic shear damage evolution and the macroscopic shear response of the material has been discussed. 相似文献
The ring-polymer molecular dynamics (RPMD) was used to calculate the thermal rate coefficients and kinetic isotope effects of the heavy-light-heavy abstract reaction Cl+XCl\begin{document}$ \rightarrow $\end{document}XCl+Cl (X = H, D, Mu). For the Cl+HCl reaction, the excellent agreement between the RPMD and experimental values provides a strong proof for the accuracy of the RPMD theory. And the RPMD results are also consistent with results from other theoretical methods including improved-canonical-variational-theory and quantum dynamics. The most novel finding is that there is a double peak in Cl+MuCl reaction near the transition state, leaving a free energy well. It comes from the mode softening of the reaction system at the peak of the potential energy surface. Such an explicit free energy well suggests strongly there is an observable resonance. And for the Cl+DCl reaction, the RPMD rate coefficient again gives very accurate results compared with experimental values. The only exception is at the temperature of 312.5 K, results from RPMD and all other theoretical methods are close to each other but slightly lower than the experimental value, which indicates experimental or potential energy surface deficiency. 相似文献
Finding a seed set to propagate more information within a specific budget is defined as the influence maximization (IM) problem. The traditional IM model contains two cardinal aspects: (i) the influence propagation model and (ii) effective/efficient seed-seeking algorithms. However, most of models only consider one kind of node (i.e., influential nodes), ignoring the role of other nodes (e.g., boosting nodes) in the spreading process, which are irrational. Specifically, in the real-world propagation scenario, the boosting nodes always improve the spread of influence from the initial activated seeds, which is an efficient and cost-economic measure. In this paper, we consider the realistic budgeted influence maximization (RBIM) problem, which contains two kind of nodes to improve the diffusion of influence. Facing the newly modified objective function, we propose a novel B-degree discount algorithm to solve it. The novel B-degree discount algorithm which adopts the cost-economic boosting nodes to retweet the influence from the predecessor nodes can greatly reduce the cost, and performs better than other state-of-the-art algorithms in both effect and efficiency on RBIM problem solving. 相似文献