Covering matroid

In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions, coverings are more natural combinatorial objects and can sometimes be more efficient to deal with problems in the real world. Through extending partitions to coverings, we propose a new type of matroids called covering matroids and prove them to be an extension of partition matroids. Secondly, since some researchers have successfully applied partition matroids to classical rough sets, we study the relationships between covering matroids and covering-based rough sets which are an extension of classical rough sets. Thirdly, in matroid theory, there are many special matroids, such as transversal matroids, partition matroids, 2-circuit matroid and partition-circuit matroids. The relationships among several special matroids and covering matroids are studied.Comment: 15 page

Parametric matroid of rough set

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.Comment: 15 page

Characteristic of partition-circuit matroid through approximation number

Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence in vector spaces, and has a variety of applications in many fields. In this paper, we propose a new type of matroids, namely, partition-circuit matroids, which are induced by partitions. Firstly, a partition satisfies circuit axioms in matroid theory, then it can induce a matroid which is called a partition-circuit matroid. A partition and an equivalence relation on the same universe are one-to-one corresponding, then some characteristics of partition-circuit matroids are studied through rough sets. Secondly, similar to the upper approximation number which is proposed by Wang and Zhu, we define the lower approximation number. Some characteristics of partition-circuit matroids and the dual matroids of them are investigated through the lower approximation number and the upper approximation number.Comment: 12 page

Deterministic and statistical methods for inverse problems with partial data

Inverse problems with partial data have many applications in science and engineering. They are more challenging than the complete data cases since the lack of data increases ill-posedness and nonlinearity. The use of only deterministic or statistical methods might not provide satisfactory results. We propose to combine the deterministic and statistical methods to treat such inverse problems. The thesis is organized as follows. In Chapter 1, we briefly introduce the inverse problems and their applications. The classical deterministic methods and Bayesian inversion are discussed. The chapter is concluded with a summary of contributions. Chapter 2 considers the reconstruction of the unknown acoustic sources using partial data. First, we extend the direct sampling method to approximate the source locations. Second, the inverse problem is formulated as a statistical inference problem using the Bayes\u27 formula. The source locations obtained in the first step are coded in the priors. Then a Metropolis-Hastings algorithm is used to explore the posterior density. In Chapter 3, a two-step deterministic-statistical approach is proposed to recover the trajectories of moving sources using partial measured data. In the first step, an approximate direct sampling method is developed to obtain the locations of the sources at different times. Such information is coded in the priors, which is critical for the success of the Bayesian method in the second step. The combined approach inherits the merits of the deterministic method and Bayesian inversion as demonstrated by the numerical examples. Chapter 4 studies the reconstruction of Stekloff eigenvalues and the index of refraction of an inhomogeneous medium from Cauchy data. The inverse spectrum problem of Stekloff eigenvalues is investigated by the reciprocity gap method. Then a Bayesian approach is proposed to estimate the index of refraction using a few reconstructed eigenvalues. In Chapter 5, we consider the inverse spectral problem to determine the material properties given a few transmission eigenvalues. The lack of theoretical results motivates us to propose a Bayesian approach to formulate a statistical inference problem. The MCMC algorithm is used to explore the posterior density. Due to the non-uniqueness nature of the problem, we adopt the local conditional means (LCM) to characterize the posterior density function

On generalized LDPC codes for ultra reliable communication

Ultra reliable low latency communication (URLLC) is an important feature in future mobile communication systems, as they will require high data rates, large system capacity and massive device connectivity [11]. To meet such stringent requirements, many error-correction codes (ECC)s are being investigated; turbo codes, low density parity check (LDPC) codes, polar codes and convolutional codes [70, 92, 38], among many others. In this work, we present generalized low density parity check (GLDPC) codes as a promising candidate for URLLC. Our proposal is based on a novel class of GLDPC code ensembles, for which new analysis tools are proposed. We analyze the trade-o_ between coding rate and asymptotic performance of a class of GLDPC codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. To incorporate both bounded distance (BD) and maximum likelihood (ML) decoding at GC nodes into our analysis without resorting to multi-edge type of degree distribution (DD)s, we propose the probabilistic peeling decoding (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a successful decoding probability that depends on both the GC block code as well as its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as Density evolution (DE) or the differential equation method. We demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code under ML decoding at GC nodes. We illustrate our analysis for GLDPC code ensembles with regular and irregular DDs. This design methodology is applied to construct practical codes for URLLC. To this end, we incorporate to our analysis the use of quasi-cyclic (QC) structures, to mitigate the code error floor and facilitate the code very large scale integration (VLSI) implementation. Furthermore, for the additive white Gaussian noise (AWGN) channel, we analyze the complexity and performance of the message passing decoder with various update rules (including standard full-precision sum product and min-sum algorithms) and quantization schemes. The block error rate (BLER) performance of the proposed GLDPC codes, combined with a complementary outer code, is shown to outperform a variety of state-of-the-art codes, for URLLC, including LDPC codes, polar codes, turbo codes and convolutional codes, at similar complexity rates.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Matilde Pilar Sánchez Fernández.- Vocal: Javier Valls Coquilla

Application of Value Stream Mapping in E-Commerce: A Case Study on an Amazon Retailer

In recent years, the e-commerce market has grown significantly, and the online retail market has become very competitive. Online retailers strive to improve their supply chain operations to reduce costs and to improve customer satisfaction. Value stream mapping (VSM), a tool created by the lean production movement to identify and reduce errors, losses, and lead time and to improve value-added activities, has been proven to be effective in many manufacturing processes. In this study, we investigate the application of value stream mapping (VSM) in the supply chain of an e-commerce retailer on Amazon. By visualizing the entire supply chain with VSM, the waste that is produced during the delivery process from the retailer to the customer was identified. The five whys method was then applied to find the root cause of the waste. Furthermore, a scoring method was developed to evaluate and compare two different supply chain logistic models to identify a strategy for improvement. This study provides a systematic methodology to understand, evaluate, and improve the entire e-commerce supply chain process utilizing VSM. It was demonstrated that the methodology could improve supply chain management efficiency, customer satisfaction, and cost reduction

Gradient Ultra-fine Grained Surface Layer in 6063 Aluminum Alloy Obtained by Means of Rotational Accelerated Shot Peening

Gradient ultra-fine grained surface layer in 6063 aluminum alloy was obtained by means of a novel surface self-nanocrystallization technique, namely rotational accelerated shot peening (RASP) treatment. The average grain sizes along the vertical section vary from hundreds of nanometers in the top surface to micrometers in the matrix. By using orthogonal experimental design to compare roughness values and hardness values, we synthesized the processing parameters to obtain sample of smaller roughness values and higher hardness

Dynamic Analysis and Control of the Clutch Filling Process in Clutch-to-Clutch Transmissions

Clutch fill control in clutch-to-clutch transmissions influences shift quality considerably. An oncoming clutch should be applied synchronously with the release of an offgoing clutch to shift gear smoothly; therefore, the gap between the piston and clutch plates should be eliminated when the torque capacity is near zero at the end of the clutch fill phase. Open-loop control is typically implemented for the clutch fill because of the cost of pressure sensor. Low control precision causes underfill or overfill to occur, deteriorating shift quality. In this paper, a mathematical model of an electrohydraulic clutch shift control system is presented. Special dynamic characteristic parameters for optimal clutch fill control are subsequently proposed. An automatic method for predicting initial fill control parameters is proposed to eliminate distinct discrepancies among transmissions caused by manufacturing or assembling errors. To prevent underfill and overfill, a fuzzy adaptive control method is proposed, in which clutch fill control parameters are adjusted self-adaptively and continually. Road vehicle test results proved that applying the fuzzy adaptive method ensures the consistency of shift quality even after the transmission’s status is changed

Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data

We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a disc such that it contains the compact support of the source. The Dirichlet eigenfunctions of the disc are used to expand the source function. Then the inverse problem is recast as a statistical inference problem for the expansion coefficients and the Bayesian inversion is employed to reconstruct the coefficients. The stability of the statistical inverse problem with respect to the measured data is justified in the sense of Hellinger distance. A preconditioned Crank-Nicolson (pCN) Metropolis-Hastings (MH) algorithm is implemented to explore the posterior density function of the unknowns. Numerical examples show that the proposed method is effective for both smooth and non-smooth sources given limited-aperture data

On LDPC Code Ensembles with Generalized Constraints

Proceeding of: 2017 IEEE International Symposium on Information Theory, Aachen, Germany, 25-30 June, 2017In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the graph. The rate of the GLDPC ensemble is bounded using classical results on linear block codes, namely Hamming bound and Varshamov bound. We also study the impact of the decoding method used at GC nodes. To incorporate both bounded-distance (BD) and Maximum Likelihood (ML) decoding at GC nodes into our analysis without having to resort on multi-edge type of degree distributions (DDs), we propose the probabilistic peeling decoder (P-PD) algorithm, which models the decoding step at every GC node as an instance of a Bernoulli random variable with a success probability that depends on the GC block code and its decoding algorithm. The P-PD asymptotic performance over the BEC can be efficiently predicted using standard techniques for LDPC codes such as density evolution (DE) or the differential equation method. Furthermore, for a class of GLDPC ensembles, we demonstrate that the simulated P-PD performance accurately predicts the actual performance of the GLPDC code. We illustrate our analysis for GLDPC code ensembles using (2, 6) and (2,15) base DDs. In all cases, we show that a large fraction of GC nodes is required to reduce the original gap to capacity.This work has been funded in part by the Spanish Ministerio de Economía y Competitividad and the Agencia Española de Investigación under Grant TEC2016-78434-C3-3-R (AEI/FEDER, EU) and by the Comunidad de Madrid in Spain under Grant S2103/ICE-2845. T. Koch has further received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 714161), from the 7th European Union Framework Programme under Grant 333680, and from the Spanish Ministerio de Economía y Competitividad under Grants TEC2013-41718-R and RYC-2014-16332. Pablo M. Olmos has further received funding from the Spanish Ministerio de Economía y Competitividad under Grant IJCI-2014-19150