Context-aware Adaptive Surgery

Deep Neural Networks (DNNs) have made massive progress in many fields and deploying DNNs on end devices has become an emerging trend to make intelligence closer to users. However, it is challenging to deploy large-scale and computation-intensive DNNs on resource-constrained end devices due to their small size and lightweight. To this end, model partition, which aims to partition DNNs into multiple parts to realize the collaborative computing of multiple devices, has received extensive research attention. To find the optimal partition, most existing approaches need to run from scratch under given resource constraints. However, they ignore that resources of devices (e.g., storage, battery power), and performance requirements (e.g., inference latency), are often continuously changing, making the optimal partition solution change constantly during processing. Therefore, it is very important to reduce the tuning latency of model partition to realize the real-time adaption under the changing processing context. To address these problems, we propose the Context-aware Adaptive Surgery (CAS) framework to actively perceive the changing processing context, and adaptively find the appropriate partition solution in real-time. Specifically, we construct the partition state graph to comprehensively model different partition solutions of DNNs by import context resources. Then "the neighbor effect" is proposed, which provides the heuristic rule for the search process. When the processing context changes, CAS adopts the runtime search algorithm, Graph-based Adaptive DNN Surgery (GADS), to quickly find the appropriate partition that satisfies resource constraints under the guidance of the neighbor effect. The experimental results show that CAS realizes adaptively rapid tuning of the model partition solutions in 10ms scale even for large DNNs (2.25x to 221.7x search time improvement than the state-of-the-art researches), and the total inference latency still keeps the same level with baselines.

Optimized Partition Scheme for Prefabricated Underpass with Large Cross Section

With the acceleration of urbanization in China, more underpasses will be constructed in big cities to alleviate the great traffic pressure. The prefabricated and assembly construction method has been introduced to replace the traditional cast-in-place method to achieve quick construction. However, for a fully prefabricated and assembled underground structure (PAUS) with large cross section, the structure must be cut into segments in transverse direction to reduce the size and weight for easy transportation and assembly. Therefore, how to develop an optimal partition scheme is a new problem to be studied. Firstly, three preliminary partition schemes were proposed based on the internal force distribution and completed engineering practices. Then, the three schemes were compared in terms of bending moment, shear force, and axial force. The construction efficiencies were also compared with special emphasis on difference of the build period. Finally, an optimal partition scheme was determined and successfully applied in the real project. Furthermore, the construction period of this partition scheme was 1/3 of the traditional cast-in-place method. The results of the current paper can provide some design guidance to large cross-sectional underpasses and other underground structures in the partition stage.

Linear Optimization in Uncertain Environment: Sensitivity of the Solution to the Belief Degree

Uncertainty theory has been initiated in 2007 by Liu, as an axiomatically developed notion, which considers the uncertainty on data as a belief degree on the domain expert’s opinion. Uncertain linear optimization is devised to model linear programs in an uncertain environment. In this paper, we investigate the relation between uncertain linear optimization and parametric programming. It is denoted that the problem can be converted to parametric linear optimization problem, at which belief degrees play the role of parameters, and parametric linear optimization with its rich literature provides insightful interpretations. In a point of view, a strictly complementary optimal solution of problem is known for the belief degree [Formula: see text], as well as the associated optimal partition. One may be interested in knowing the region of belief degrees (parameters) where this optimal partition remains invariant for all parameter values (belief degrees) in this region. We consider the linear optimization problem with uncertain rim data, i.e., the right-hand side and the objective function data. The known results in the literature are translated to the language of uncertainty theory, and managerial interpretations are provided. The methodology is illustrated via concrete examples.

Critical polyharmonic systems and optimal partitions

<p style='text-indent:20px;'>We establish the existence of solutions to a weakly-coupled competitive system of polyharmonic equations in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula> which are invariant under a group of conformal diffeomorphisms, and study the behavior of least energy solutions as the coupling parameters tend to <inline-formula><tex-math id="M2">\begin{document}$ -\infty $\end{document}</tex-math></inline-formula>. We show that the supports of the limiting profiles of their components are pairwise disjoint smooth domains and solve a nonlinear optimal partition problem of <inline-formula><tex-math id="M3">\begin{document}$ \mathbb R^N $\end{document}</tex-math></inline-formula>. We give a detailed description of the shape of these domains.</p>

Yamabe systems and optimal partitions on manifolds with symmetries

<p style='text-indent:20px;'>We prove the existence of regular optimal <inline-formula><tex-math id="M1">\begin{document}$ G $\end{document}</tex-math></inline-formula>-invariant partitions, with an arbitrary number <inline-formula><tex-math id="M2">\begin{document}$ \ell\geq 2 $\end{document}</tex-math></inline-formula> of components, for the Yamabe equation on a closed Riemannian manifold <inline-formula><tex-math id="M3">\begin{document}$ (M,g) $\end{document}</tex-math></inline-formula> when <inline-formula><tex-math id="M4">\begin{document}$ G $\end{document}</tex-math></inline-formula> is a compact group of isometries of <inline-formula><tex-math id="M5">\begin{document}$ M $\end{document}</tex-math></inline-formula> with infinite orbits. To this aim, we study a weakly coupled competitive elliptic system of <inline-formula><tex-math id="M6">\begin{document}$ \ell $\end{document}</tex-math></inline-formula> equations, related to the Yamabe equation. We show that this system has a least energy <inline-formula><tex-math id="M7">\begin{document}$ G $\end{document}</tex-math></inline-formula>-invariant solution with nontrivial components and we show that the limit profiles of its components separate spatially as the competition parameter goes to <inline-formula><tex-math id="M8">\begin{document}$ -\infty $\end{document}</tex-math></inline-formula>, giving rise to an optimal partition. For <inline-formula><tex-math id="M9">\begin{document}$ \ell = 2 $\end{document}</tex-math></inline-formula> the optimal partition obtained yields a least energy sign-changing <inline-formula><tex-math id="M10">\begin{document}$ G $\end{document}</tex-math></inline-formula>-invariant solution to the Yamabe equation with precisely two nodal domains.</p>

A Fast CU Size Decision Optimal Algorithm based on Coding Bits for HEVC

HEVC (High Efficiency Video Codng) employs quadtree CTU (Coding Tree Unit) structure to improve its coding efficiency, but at the same time, it also requires a very high computational complexity due to its exhaustive search process for an optimal partition mode for the current CU(Coding Unit). Aiming to solve the problem, a fast CU size decision optimal algorithm based on coding bits is presented for HEVC in this paper. The contribution of this paper lies that we successfully use the coding bits technology to quickly determine the optimal partition mode for the current CU. Specially, in our scheme, firstly we carefully observe and statistically analyze the relationship among the texture complexity and partition size and coding bits in the CUs of video image; Secondly we find the correlation between coding bits and partition size based on the relationship above; Thirdly, we build the corresponding threshold of coding bits for partition size under different CU size and QP value based on the correlation above to reduce many unnecessary prediction and partition operations for the current CU. As a result, our proposed algorithm can effectively saving lots of computational complexity for HEVC. The simulation results show that our proposed fast CU size decision algorithm based on coding bits in this paper can save about 34.67% coding time, and only at a cost of 0.61% BDBR increase and 0.043db BDPSNR decline compared with the standard reference of HM16.1, thus improving the coding performance of HEVC.