In this work we give two new constructions of ε-biased generators. Our first construction significantly extends a result of
Mossel et al. (Random Structures and Algorithms 2006, pages 56-81), and our second construction answers an open question of
Dodis and Smith (STOC 2005, pages 654-663). In particular we obtain the following results:
1.
For every k = o(log n) we construct an ε-biased generator G : {0, 1}m ? {0, 1}nG : \{0, 1\}^{m} \rightarrow \{0, 1\}^n that is implementable by degree k polynomials (namely, every output bit of the generator is a degree k polynomial in the input bits). For any constant k we get that n = W(m/log(1/ e))kn = \Omega(m/{\rm log}(1/ \epsilon))^k, which is nearly optimal. Our result also separates degree k generators from generators in NC0k, showing that the stretch of the former can be much larger than the stretch of the latter. The problem of constructing degree
k generators was introduced by Mossel et al. who gave a construction only for the case of k = 2.
2.
We construct a family of asymptotically good binary codes such that the codes in our family are also ε-biased sets for an
exponentially small ε. Our encoding algorithm runs in polynomial time in the block length of the code. Moreover, these codes
have a polynomial time decoding algorithm. This answers an open question of Dodis and Smith.
The paper also contains an appendix by Venkatesan Guruswami that provides an explicit construction of a family of error correcting
codes of rate 1/2 that has efficient encoding and decoding algorithms and whose dual codes are also good codes. 相似文献
This paper presents a robust adaptive fuzzy control algorithm for controlling unknown chaotic systems. The control approach encompasses a fuzzy system and a robust controller. The fuzzy system is designed to mimic an ideal controller, based on sliding-mode control. The robust controller is designed to compensate for the difference between the fuzzy controller and the ideal controller. The parameters of the fuzzy system, as well as uncertainty bound of the robust controller, are tuned adaptively. The adaptive laws are derived in the Lyapunov sense to guarantee the stability of the controlled system. Numerical simulations show the effectiveness of the proposed approach. 相似文献
Calcium cobaltite Ca3Co4−xO9+δ (CCO) is a promising p-type thermoelectric (TE) material for high-temperature applications in air. The grains of the material exhibit strong anisotropic properties, making texturing and nanostructuring mostly favored to improve thermoelectric performance. On the one hand multitude of interfaces are needed within the bulk material to create reflecting surfaces that can lower the thermal conductivity. On the other hand, low residual porosity is needed to improve the contact between grains and raise the electrical conductivity. In this study, CCO fibers with 100% flat cross sections in a stacked, compact form are electrospun. Then the grains within the nanoribbons in the plane of the fibers are grown. Finally, the nanoribbons are electrospun into a textured ceramic that features simultaneously a high electrical conductivity of 177 S cm−1 and an immensely enhanced Seebeck coefficient of 200 µV K−1 at 1073 K are assembled. The power factor of 4.68 µW cm−1 K−2 at 1073 K in air surpasses all previous CCO TE performances of nanofiber ceramics by a factor of two. Given the relatively high power factor combined with low thermal conductivity, a relatively large figure-of-merit of 0.3 at 873 K in the air for the textured nanoribbon ceramic is obtained. 相似文献
Engineering with Computers - This work addresses a hybrid scheme for the numerical solutions of time fractional Tricomi and Keldysh type equations. In proposed methodology, Haar wavelets are used... 相似文献
Cloud computing is becoming a very popular form of distributed computing, in which digital resources are shared via the Internet. The user is provided with an overview of many available resources. Cloud providers want to get the most out of their resources, and users are inclined to pay less for better performance. Task scheduling is one of the most important aspects of cloud computing. In order to achieve high performance from cloud computing systems, tasks need to be scheduled for processing by appropriate computing resources. The large search space of this issue makes it an NP-hard problem, and more random search methods are required to solve this problem. Multiple solutions have been proposed with several algorithms to solve this problem until now. This paper presents a hybrid algorithm called GSAGA to solve the Task Scheduling Problem (TSP) in cloud computing. Although it has a high ability to search the problem space, the Genetic Algorithm (GA) performs poorly in terms of stability and local search. It is therefore possible to create a stable algorithm by combining the general search capacities of the GA with the Gravitational Search Algorithm (GSA). Our experimental results indicate that the proposed algorithm can solve the problem with higher efficiency compared with the state-of-the-art.
The exposition of any nature-inspired optimization technique relies firmly upon its executed organized framework. Since the regularly utilized backtracking search algorithm (BSA) is a fixed framework, it is not always appropriate for all difficulty levels of problems and, in this manner, probably does not search the entire search space proficiently. To address this limitation, we propose a modified BSA framework, called gQR-BSA, based on the quasi reflection-based initialization, quantum Gaussian mutations, adaptive parameter execution, and quasi-reflection-based jumping to change the coordinate structure of the BSA. In gQR-BSA, a quantum Gaussian mechanism was developed based on the best population information mechanism to boost the population distribution information. As population distribution data can represent characteristics of a function landscape, gQR-BSA has the ability to distinguish the methodology of the landscape in the quasi-reflection-based jumping. The updated automatically managed parameter control framework is also connected to the proposed algorithm. In every iteration, the quasi-reflection-based jumps aim to jump from local optima and are adaptively modified based on knowledge obtained from offspring to global optimum. Herein, the proposed gQR-BSA was utilized to solve three sets of well-known standards of functions, including unimodal, multimodal, and multimodal fixed dimensions, and to solve three well-known engineering optimization problems. The numerical and experimental results reveal that the algorithm can obtain highly efficient solutions to both benchmark and real-life optimization problems.
The world has been challenged since late 2019 by COVID-19. Higher education institutions have faced various challenges in adapting online education to control the pandemic spread of COVID-19. The present study aims to conduct a survey study through the interview and scrutinizing the literature to find the key challenges. Subsequently, an integrated MCDM framework, including Stepwise Weight Assessment Ratio Analysis (SWARA) and Multiple Objective Optimization based on Ratio Analysis plus Full Multiplicative Form (MULTIMOORA), is developed. The SWARA procedure is applied to the analysis and assesses the challenges to adapt the online education during the COVID-19 outbreak, and the MULTIMOORA approach is utilized to rank the higher education institutions on hesitant fuzzy sets. Further, an illustrative case study is considered to express the proposed idea's feasibility and efficacy in real-world decision-making. Finally, the obtained result is compared with other existing approaches, confirming the proposed framework's strength and steadiness. The identified challenges were systemic, pedagogical, and psychological challenges, while the analysis results found that the pedagogical challenges, including the lack of experience and student engagement, were the main essential challenges to adapting online education in higher education institutions during the COVID-19 outbreak.
In this study, Y3+ ion-substituted M-type barium hexaferrites (BaM; BaFe12O19) were fabricated via facile ceramic route. As-prepared powders were characterized by X-ray powder diffractometry (XRD), Fourier transform infrared (FT-IR) spectroscopy, and impedance spectroscopy. XRD (Rietveld) analyses confirmed the presence of a single characterization of all samples (except x = 0.0 and 0.1 samples). The crystallite sizes of products are found in the range of 47.2–63.2 nm. Spectral analysis (FT-IR) also presented the formation of spinel structure for all products. The ac conductivity of the substituted samples was found to initially decrease slightly with increase in Y3+ compared with unsubstituted, and then variation tendency changes at the medium substitution ranges are observed with a different attitude against temperature. In the end, the lower conductivity for high substitutions is recorded and increases as functions of frequency while it also increases with the elevation of temperature. It was observed that ac conductivities of products increased by increasing frequency which indicate that observed ac conductivity is due to both electronic and polaron hopping mechanism. 相似文献
