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This paper studies early-stopped mirror descent applied to noisy sparse phase retrieval, which is the problem of recovering a $k$ -sparse signal $\textbf{x}^\star \in{\mathbb{R}}^n$ from a set of quadratic Gaussian measurements...
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This paper studies early-stopped mirror descent applied to noisy sparse phase retrieval, which is the problem of recovering a $k$ -sparse signal $\textbf{x}^\star \in{\mathbb{R}}^n$ from a set of quadratic Gaussian measurements corrupted by sub-exponential noise. We consider the (non-convex) unregularized empirical risk minimization problem and show that early-stopped mirror descent, when equipped with the hypentropy mirror map and proper initialization, achieves a nearly minimax-optimal rate of convergence, provided the sample size is at least of order $k^2$ (modulo logarithmic term) and the minimum (in modulus) non-zero entry of the signal is on the order of $\|\textbf{x}^\star \|_2/\sqrt{k}$ . Our theory leads to a simple algorithm that does not rely on explicit regularization or thresholding steps to promote sparsity. More generally, our results establish a connection between mirror descent and sparsity in the non-convex problem of noisy sparse phase retrieval, adding to the literature on early stopping that has mostly focused on non-sparse, Euclidean and convex settings via gradient descent. Our proof combines a potential-based analysis of mirror descent with a quantitative control on a variational coherence property that we establish along the path of mirror descent, up to a prescribed stopping time.
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In recent years, solid-state lithium batteries (SSLBs) using solid electrolytes CSEs) have been widely recognized as the key next-generation energy storage technology due to its high safety, high energy density, long cycle life, g...
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In recent years, solid-state lithium batteries (SSLBs) using solid electrolytes CSEs) have been widely recognized as the key next-generation energy storage technology due to its high safety, high energy density, long cycle life, good rate performance and wide operating temperature range. However, SSLBs still suffer from many obstacles that hinder their practical application. This review discusses typical lithium-ion conductors and their in-depth lithium-ion conduction mechanism. The key interfacial problems of electrolytes and electrodes for SSLBs are comprehensively elaborated and several possible solution methods are proposed. Furthermore, three viable manufacturing strategies for free-standing thin SE membranes are discussed in details. Moreover, for the first time, the government policies and latest company industrialization process relative to SSLBs worldwide are systematically summarized. Finally, several potential strategies are identified for the future development of high-energy-density SSLBs.
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A higher-order function takes one or more functions as inputs or outputs to support the generality of function definitions. In modern programming languages,higher-order functions are designed as a feature to enhance usability and ...
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A higher-order function takes one or more functions as inputs or outputs to support the generality of function definitions. In modern programming languages,higher-order functions are designed as a feature to enhance usability and scalability. Abstracting higher-order functions from existing functions decreases the number of similar functions and improves the code reuse. However,due to the complexity,defining and calling higher-order functions are not widely used in practice. In this paper,we investigate the use of higher-order functions in Scala programs. We collected 8,285 higher-order functions from 35 Scala projects in GitHub with the most stars and conducted an exploratory study via answering five research questions of using higher-order functions,including the data scale,the definition types,the definition distribution,the factor that correlates with the function calls,and the developer contribution. Our study mainly shows five empirical results about the common use of higher-order functions in Scala programs. Our findings are listed as follows. (1) Among 35 Scala projects,6.84% of functions are defined as higher-order functions on average and the average calls per function show that higher-order functions are called more frequently than first-order functions. (2) In all higher-order functions in the study,87.35% of definitions of higher-order functions and 90.66% of calls belong to the type that only takes functions as parameters. (3) Three measurements (including lines of executable code,Cyclomatic complexity,and warnings in the code style) in higher-order functions are lower than those of first-order functions. (4) Regression analysis on all projects suggests that the number of calling higher-order functions highly correlates with the Cyclomatic complexity. (5) In all projects in the study,43.82% calls of higher-order functions are written by the same developers who have defined the functions and results show that top 20% authors of higher-order functions favor defining or calling higher-order functions than first-order functions. This study can be viewed as a preliminary result to understand the use of higher-order functions and to motivate further investigation in Scala programs.
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In this paper, we study an optimal management problem for a general insurance company which holds shares of an insurance company and a reinsurance company. The general company aims to derive the equilibrium reinsurance-investment ...
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In this paper, we study an optimal management problem for a general insurance company which holds shares of an insurance company and a reinsurance company. The general company aims to derive the equilibrium reinsurance-investment strategy under the mean-variance criterion. The claim process described by a generalized compound dynamic contagion process introduced by [18] which allows for self-exciting and externally-exciting clustering effect for the claim arrivals and the processes of the risky assets are described by the jump-diffusion models. Based on practical considerations, we suppose that the externally-exciting clustering effect will simultaneously affect both the price of risky assets and the intensity of claims. To overcome the inconsistency issue caused by the mean-variance criterion, we formulate the optimization problem as an embedded game and solve it via a corresponding extended Hamilton-Jacobi-Bellman equation. The equilibrium reinsurance-investment strategy is obtained, which depends on a solution to an ordinary differential equation. In addition, we demonstrate the derived equilibrium strategy and the economic implications behind it through a large number of mathematical analysis and numerical examples.
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Nonuniform linear arrays (NLAs) have attracted considerable attention owing to their capability to enhance the degrees of freedom (DOF) and increase the array aperture, which is essential for improving performance in terms of both...
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Nonuniform linear arrays (NLAs) have attracted considerable attention owing to their capability to enhance the degrees of freedom (DOF) and increase the array aperture, which is essential for improving performance in terms of both the direction of arrival estimation and adaptive beamforming. This paper presents two new NLAs, namely interleaved coprime array (ICA) and augmented interleaved array (AIA). The ICA consists of two uniform linear subarrays, whose inter-element spacings are coprime integers. The ICA can obtain more uniform degrees of freedom (uDOF), while maintaining weak mutual coupling effects, because its configuration includes only minority sensors interleaved. The optimal configuration of the ICA is deduced using the principle of maximizing the uDOF. Moreover, the AIA geometry is obtained by removing a redundant element in the ICA and appropriately designing the location of the additional element. For a fixed total number of sensors, the AIA can gain more uDOF and DOF than the ICA, while exhibiting lower mutual coupling effects. The closed-form expressions for the properties of the proposed array structures involving an arbitrary number of sensors are also derived. Numerical simulations are performed to verify the superiority of the proposed arrays over other sparse arrays.
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Abstract In this paper, we first study the problem of Correlation-aware Task computation offloading (CoTask) in mobile edge computing. Specifically, considering the correlation among multiple computation tasks, we study how to det...
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Abstract In this paper, we first study the problem of Correlation-aware Task computation offloading (CoTask) in mobile edge computing. Specifically, considering the correlation among multiple computation tasks, we study how to determine a joint task offloading decision and resource allocation strategy under the constraints of feasible offloading decisions and edge servers’ computation capacity, such that the overall task latency is minimized. Before addressing the challenging CoTask problem, we first investigate the case without considering task correlation, namely, NonCoTask. We prove that, NonCoTask with two combinatorial integer-continuous optimization variables (i.e., integral offloading decision variable and continuous resource allocation variable) can be equivalently solved by solving a 0-1 integer programming problem with respect to the offloading decision variable only, while the closed-form optimal resource allocation can be efficiently obtained under any given offloading decision. The 0-1 integer programming problem further falls into the realm of minimizing a supermodular set function with a matroid base constraint. We then propose a performance-guaranteed algorithm for NonCoTask. Next, we rigorously analyze the performance gap between CoTask and NonCoTask, and develop a correlation-aware offloading decision and resource allocation algorithm with theoretic performance guarantee for CoTask, via a correlation-aware exchange search based on the solution to NonCoTask. Extensive evaluation results show that our proposed algorithm outperforms several state-of-the-art algorithms as well as their enhanced counterparts with correlation in terms of overall task latency.
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Dielectric materials with higher energy storage and electromagnetic (EM)
energy conversion are in high demand to advance electronic devices, military
stealth, and mitigate EM wave pollution. Existing dielectric materials for hig...
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Dielectric materials with higher energy storage and electromagnetic (EM)
energy conversion are in high demand to advance electronic devices, military
stealth, and mitigate EM wave pollution. Existing dielectric materials for highenergy-
storage electronics and dielectric loss electromagnetic wave absorbers
are studied toward realizing these goals, each aligned with the current global
grand challenges. Libraries of dielectric materials with desirable permittivity,
dielectric loss, and/or dielectric breakdown strength potentially meeting the
device requirements are reviewed here. Regardless, aimed at translating
these into energy storage devices, the oft-encountered shortcomings can be
caused by either of two confluences: a) low permittivity, high dielectric loss,
and low breakdown strength; b) low permittivity, low dielectric loss, and process
complexity. Contextualizing these aspects and the overarching objectives
of enabling high-efficiency energy storage and EM energy conversion, recent
advances in by-design inorganic–organic hybrid materials are reviewed here,
with a focus on design approaches, preparation methods, and characterization
techniques. In light of their strengths and weaknesses, potential strategies
to foster their commercial adoption are critically interrogated.
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2D transition metal chalcogenide (TMDC) materials, such as MoS_2, have recently attracted considerable research interest in the context of their use in ultrascaled devices owing to their excellent electronic properties. Microproce...
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2D transition metal chalcogenide (TMDC) materials, such as MoS_2, have recently attracted considerable research interest in the context of their use in ultrascaled devices owing to their excellent electronic properties. Microprocessors and neural network circuits based on MoS_2 have been developed at a large scale but still do not have an advantage over silicon in terms of their integrated density. In this study, the current structures, contact engineering, and doping methods for 2D TMDC materials for the scaling-down process and performance optimization are reviewed. Devices are introduced according to a new mechanism to provide the comprehensive prospects for the use of MoS_2 beyond the traditional complementary-metal-oxide semiconductor in order to summarize obstacles to the goal of developing high-density and low-power integrated circuits (ICs). Finally, prospects for the use of MoS_2 in large-scale ICs from the perspectives of the material, system performance, and application to nonlogic functionalities such as sensor circuits and analogous circuits, are briefly analyzed. The latter issue is along the direction of “more than Moore” research.
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Background Osmanthus fragrans (Oleaceae) is one of the most important ornamental plant species in China. Many cultivars with different leaf color phenotypes and good ornamental value have recently been developed. For example, a ne...
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Background Osmanthus fragrans (Oleaceae) is one of the most important ornamental plant species in China. Many cultivars with different leaf color phenotypes and good ornamental value have recently been developed. For example, a new cultivar ‘Qiannan Guifei’, presents a rich variety of leaf colors, which change from red to yellow-green and ultimately to green as leaves develop, making this cultivar valuable for landscaping. However, the biochemical characteristics and molecular mechanisms underlying leaf color changes of these phenotypes have not been elucidated. It has been hypothesized that the biosynthesis of different pigments in O. fragrans might change during leaf coloration. Here, we analyzed transcriptional changes in genes involved in chlorophyll (Chl), flavonoid, and carotenoid metabolic pathways and identified candidate genes responsible for leaf coloration in the new cultivar ‘Qiannan Guifei’. Methods Leaf samples were collected from ‘Qiannan Guifei’ plants at the red (R), yellow-green (YG) and green (G) leaf stages. We compared the different-colored leaves via leaf pigment concentrations, chloroplast ultrastructure, and transcriptomic data. We further analyzed differentially expressed genes (DEGs) involved in the Chl, flavonoid, and carotenoid metabolic pathways. In addition, we used qRT-PCR to validate expression patterns of the DEGs at the three stages. Results We found that, compared with those at the G stage, chloroplasts at the R and YG stages were less abundant and presented abnormal morphologies. Pigment analyses revealed that the leaves had higher flavonoid and anthocyanin levels at the R stage but lower Chl and carotenoid concentrations. Similarly, Chl and carotenoid concentrations were lower at the YG stage than at the G stage. By using transcriptomic sequencing, we further identified 61 DEGs involved in the three pigment metabolic pathways. Among these DEGs, seven structural genes (OfCHS, OfCHI, OfF3H, OfDFR, OfANS, OfUGT andOf3AT) involved in the flavonoid biosynthesis pathway were expressed at the highest level at the R stage, thereby increasing the biosynthesis of flavonoids, especially anthocyanins. Six putativeOfMYB genes, including three flavonoid-related activators and three repressors, were also highly expressed at the R stage, suggesting that they might coordinately regulate the accumulation of flavonoids, including anthocyanins. Additionally, expressions of the Chl biosynthesis-related genes OfHEMA, OfCHLG and OfCAO and the carotenoid biosynthesis-related genes OfHYB and OfZEP were upregulated from the R stage to the G stage, which increased the accumulation of Chl and carotenoids throughout leaf development. In summary, we screened the candidate genes responsible for the leaf color changes of ‘Qiannan Guifei’, improved current understanding of the regulatory mechanisms underlying leaf coloration and provided potential targets for future leaf color improvement in O. fragrans.
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To address the problems of strong coupling and large hysteresis in the temperature control of a continuously stirred tank reactor (CSTR) process, an improved sparrow search algorithm (ISSA) is proposed to optimize the PID paramete...
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To address the problems of strong coupling and large hysteresis in the temperature control of a continuously stirred tank reactor (CSTR) process, an improved sparrow search algorithm (ISSA) is proposed to optimize the PID parameters. The improvement aims to solve the problems of population diversity reduction and easy-to-fall-into local optimal solutions when the traditional sparrow algorithm is close to the global optimum. This differs from other improved algorithms by adding a new Gauss Cauchy mutation strategy at the end of each iteration without increasing the time complexity of the algorithm. By introducing tent mapping in the sparrow algorithm to initialize the population, the population diversity and global search ability are improved; the golden partition coefficient is introduced in the explorer position update process to expand the search space and balance the relationship between search and exploitation; the Gauss Cauchy mutation strategy is used to enhance the ability of local minimum value search and jumping out of local optimum. Compared with the four existing classical algorithms, ISSA has improved the convergence speed, global search ability and the ability to jump out of local optimum. The proposed algorithm is combined with PID control to design an ISSA-PID temperature controller, which is simulated on a continuous reactor temperature model identified by modeling. The results show that the proposed method improves the transient and steady-state performance of the reactor temperature control with good control accuracy and robustness. Finally, the proposed algorithm is applied to a semi-physical experimental platform to verify its feasibility.
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