This paper studies a single machine scheduling problem with time-dependent learning and setup times. Time-dependent learning means that the actual processing time of a job is a function of the sum of the normal proces...This paper studies a single machine scheduling problem with time-dependent learning and setup times. Time-dependent learning means that the actual processing time of a job is a function of the sum of the normal processing times of the jobs already scheduled. The setup time of a job is proportional to the length of the already processed jobs, that is, past-sequence-dependent (psd) setup time. We show that the addressed problem remains polynomially solvable for the objectives, i.e., minimization of the total completion time and minimization of the total weighted completion time. We also show that the smallest processing time (SPT) rule provides the optimum sequence for the addressed problem.展开更多
Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme ...Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme are developed including the dominance rules where the objective is to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.展开更多
In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequal...In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequalities, we extends this result to W 1 H inequalities.展开更多
This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random...This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random variables with long-tailed and dominatedly varying tailed distributions, and the shot noise function has both positive lower and upper bounds, a uniform asymptotic formula for the tail probability of the process has been established.Furthermore, when the shocks have continuous and consistently varying tailed distributions, the positive lower-bound condition on the shot noise function can be removed. For the case that the shot noise function is not necessarily upper-bounded, a uniform asymptotic result is also obtained when the shocks follow a pairwise negatively quadrant dependence structure.展开更多
This work aims to give a systematic construction of the two families of mixed-integer-linear-programming (MILP) formulations, which are graph-<span style="font-family:;" "=""> </span&...This work aims to give a systematic construction of the two families of mixed-integer-linear-programming (MILP) formulations, which are graph-<span style="font-family:;" "=""> </span><span style="font-family:Verdana;">based and sequence-based, of the well-known scheduling problem<img src="Edit_41010f25-7ca5-482c-89be-790fad4616e1.png" alt="" /></span><span style="font-family:Verdana;text-align:justify;">. Two upper bounds of job completion times are introduced. A numerical test result analysis is conducted with a two-fold objective 1) testing the performance of each solving methods, and 2) identifying and analyzing the tractability of an instance according to the instance structure in terms of the number of machines, of the jobs setup time lengths and of the jobs release date distribution over the scheduling horizon.</span> <div> <span style="font-family:Verdana;text-align:justify;"><br /> </span> </div>展开更多
In this study, we consider the problem of scheduling a set of jobs with sequence-dependent setup times on a set of parallel production cells. The objective of this study is to minimize the total completion time. We no...In this study, we consider the problem of scheduling a set of jobs with sequence-dependent setup times on a set of parallel production cells. The objective of this study is to minimize the total completion time. We note that total customer demands for each type should be satisfied, and total required production time in each cell cannot exceed the capacity of the cell. This problem is formulated as an integer programming model and an interface is designed to provide integrity between data and software. Mathematical model is tested by both randomly generated data set and real-world data set from a factory that produce automotive components. As a result of this study, the solution which gives the best alternative production schedule is obtained.展开更多
Saccharina is one of the most important cold-water living marine brown algal genera. In this study we ana-lyzed the transcriptome of S. japonica, which belongs to the 1 000 Plants （OneKP） Project, by using a next-ge...Saccharina is one of the most important cold-water living marine brown algal genera. In this study we ana-lyzed the transcriptome of S. japonica, which belongs to the 1 000 Plants （OneKP） Project, by using a next-generation high-throughput DNA sequencing technique. About 5.16 GB of raw data were generated, and 65 536 scaffolds with an average length of 454 bp were assembled with SOAP de novo assembly method. In total, 19 040 unigenes were identified by BLAST;25 734 scaffolds were clustered into 37 Gene ontology functional groups;6 760 scaffolds were classified into 25 COG categories, as well as 2 665 scaffolds that were assigned to 306 KEGG pathways. Majority of the unigenes exhibited more similarities to algae including brown algae and diatom than other cyanobacteria, marine diatom, and plant. Saccharina japonica has the outstanding capability to accumulate halogen such as Br and I via halogenation processes from seawater. We acquired 42 different vanadium-dependent haloperoxidases （vHPO） in S. japonica transcriptome data, including 5 segments of vanadium-dependent iodoperoxidase （vIPO） and 37 segments of vanadium-de-pendent bromoperoxidase （vBPO）. Complicated analyses of identified fulllength S. japonica vBPO1 and S. japonica vBPO2 revealed the importance of vBPO among species of brown algae and the strong relationship between marine algal vBPOs and vIPOs. This study will enhance our understanding of the biological charac-teristics and economic values of S. japonica species.展开更多
Let {Xkl,…, Xkp, k≥ 1} be a p-dimensional standard （zero-means, unit-variances）non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maximaof {Xkl,…, Xkp, k 〉 1}, the incompl...Let {Xkl,…, Xkp, k≥ 1} be a p-dimensional standard （zero-means, unit-variances）non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maximaof {Xkl,…, Xkp, k 〉 1}, the incomplete maxima of those sequences subject to random failureand the partial sums of those sequences are obtained.展开更多
Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequal...Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50(2): 419-428). We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.展开更多
Evidential Reasoning(ER)rule,which can combine multiple pieces of independent evidence conjunctively,is widely applied in multiple attribute decision analysis.However,the assumption of independence among evidence is o...Evidential Reasoning(ER)rule,which can combine multiple pieces of independent evidence conjunctively,is widely applied in multiple attribute decision analysis.However,the assumption of independence among evidence is often not satisfied,resulting in ER rule inapplicable.In this paper,an Evidential Reasoning rule for Dependent Evidence combination(ERr-DE)is developed.Firstly,the aggregation sequence of multiple pieces of evidence is determined according to evidence reliability.On this basis,a calculation method of evidence Relative Total Dependence Coefficient(RTDC)is proposed using the distance correlation method.Secondly,as a discounting factor,RTDC is introduced into the ER rule framework,and the ERr-DE model is formulated.The aggregation process of two pieces of dependent evidence by ERr-DE is investigated,which is then generalized to aggregate multiple pieces of non-independent evidence.Thirdly,sensitivity analysis is carried out to investigate the relationship between the model output and the RTDC.The properties of sensitivity coefficient are explored and mathematically proofed.The conjunctive probabilistic reasoning process of ERr-DE and the properties of sensitivity coefficient are verified by two numerical examples respectively.Finally,the practical application of the ERr-DE is validated by a case study on the performance assessment of satellite turntable system.展开更多
Under the conditions on covariances of the original random variables, a Glivenko-Cantelli theorem for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, ...Under the conditions on covariances of the original random variables, a Glivenko-Cantelli theorem for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, assuming the random variables to be discrete.展开更多
In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences a...In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.展开更多
Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables a...Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables are given, which extend the corresponding known results.展开更多
A double helix model of charge transport in DNA molecule is given and the transmission spectra of four DNA sequences are obtained.The calculated results show that the transmission characteristics of DNA are not only r...A double helix model of charge transport in DNA molecule is given and the transmission spectra of four DNA sequences are obtained.The calculated results show that the transmission characteristics of DNA are not only related to the longitudinal transport but also to the transverse transport of molecule.The periodic sequence with the same composition has stronger conduction ability.With the increasing of bases composition,the conductive ability reduces,but the weight of θ direction rises in charge transfer.展开更多
In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)a...In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences.展开更多
Stochastic dynamic job shop scheduling pro- blem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatchin...Stochastic dynamic job shop scheduling pro- blem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under due date tightness factor of 3, shop utilization percentage of 90 % and setup times less than processing times. Results indicate that shortest setup time （SIMSET） rule provides the best performance for mean flow time and number of tardy jobs measures. The job with similar setup and modified earliest due date （JMEDD） rule provides the best performance for make- span, maximum flow time, mean tardiness, maximum tardiness, total setups and mean setup time measures.展开更多
Let X and Y be positive weakly negatively dependent （WND） random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail o...Let X and Y be positive weakly negatively dependent （WND） random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on F（x） = 1-F（x） and G（x） = of XY when X and Y are WND random variables 1- G（x） are provided. Moreover, subexponentiality is derived.展开更多
Over the past few years, many researchers have attempted to develop non-invasive prenatal testing methods in order to investigate the genetic status of the fetus. The aim is to avoid invasive procedures such as chorio...Over the past few years, many researchers have attempted to develop non-invasive prenatal testing methods in order to investigate the genetic status of the fetus. The aim is to avoid invasive procedures such as chorionic villus and amniotic fluid sampling, which result in a significant risk for pregnancy loss. The discovery of cell free fetal DNA circulating in the maternal blood has great potential for the development of non-invasive prenatal testing(NIPT) methodologies. Such strategies have been successfully applied for the determination of the fetal rhesus status and inherited monogenic disease but the field of fetal aneuploidy investigation seems to be more challenging. The main reason for this is that the maternal cell free DNA in the mother's plasma is far more abundant, and because it is identical to half of the corresponding fetal DNA. Approaches developed are mainly based on next generation sequencing(NGS) technologies and epigenetic genetic modifications, such as fetal-maternal DNA differential methylation. At present, genetic services for non-invasive fetal aneuploidy detection are offered using NGS-based approaches but, for reasons that are presented herein, they still serve as screening tests which are not readily accessed by the majority of couples. Here we discuss the limitations of both strategies for NIPT and the future potential of the methods developed.展开更多
文摘This paper studies a single machine scheduling problem with time-dependent learning and setup times. Time-dependent learning means that the actual processing time of a job is a function of the sum of the normal processing times of the jobs already scheduled. The setup time of a job is proportional to the length of the already processed jobs, that is, past-sequence-dependent (psd) setup time. We show that the addressed problem remains polynomially solvable for the objectives, i.e., minimization of the total completion time and minimization of the total weighted completion time. We also show that the smallest processing time (SPT) rule provides the optimum sequence for the addressed problem.
文摘Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme are developed including the dominance rules where the objective is to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.
文摘In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequalities, we extends this result to W 1 H inequalities.
基金Supported by the National Social Science Fund of China (Grant No.22BTJ060)the Humanities and Social Sciences Foundation of the Ministry of Education of China (Grant No.20YJA910006)+3 种基金the Natural Science Foundation of Jiangsu Province (Grant No.BK20201396)the Natural Science Foundation of the Jiangsu Higher Education Institutions (Grant No.19KJA180003)the Grant from the Research Grants Council of the Hong Kong Special Administrative Region,China (Grant No.HKU17306220)the 333 High Level Talent Training Project of Jiangsu Province。
文摘This paper considers the uniform asymptotic tail behavior of a Poisson shot noise process with some dependent and heavy-tailed shocks. When the shocks are bivariate upper tail asymptotic independent nonnegative random variables with long-tailed and dominatedly varying tailed distributions, and the shot noise function has both positive lower and upper bounds, a uniform asymptotic formula for the tail probability of the process has been established.Furthermore, when the shocks have continuous and consistently varying tailed distributions, the positive lower-bound condition on the shot noise function can be removed. For the case that the shot noise function is not necessarily upper-bounded, a uniform asymptotic result is also obtained when the shocks follow a pairwise negatively quadrant dependence structure.
文摘This work aims to give a systematic construction of the two families of mixed-integer-linear-programming (MILP) formulations, which are graph-<span style="font-family:;" "=""> </span><span style="font-family:Verdana;">based and sequence-based, of the well-known scheduling problem<img src="Edit_41010f25-7ca5-482c-89be-790fad4616e1.png" alt="" /></span><span style="font-family:Verdana;text-align:justify;">. Two upper bounds of job completion times are introduced. A numerical test result analysis is conducted with a two-fold objective 1) testing the performance of each solving methods, and 2) identifying and analyzing the tractability of an instance according to the instance structure in terms of the number of machines, of the jobs setup time lengths and of the jobs release date distribution over the scheduling horizon.</span> <div> <span style="font-family:Verdana;text-align:justify;"><br /> </span> </div>
文摘In this study, we consider the problem of scheduling a set of jobs with sequence-dependent setup times on a set of parallel production cells. The objective of this study is to minimize the total completion time. We note that total customer demands for each type should be satisfied, and total required production time in each cell cannot exceed the capacity of the cell. This problem is formulated as an integer programming model and an interface is designed to provide integrity between data and software. Mathematical model is tested by both randomly generated data set and real-world data set from a factory that produce automotive components. As a result of this study, the solution which gives the best alternative production schedule is obtained.
基金The National Natural Science Foundation of China under contract Nos 41206116,31140070 and 31271397Technology Project of Ocean and Fisheries of Guangdong Province under contract No.A201201E03+1 种基金the Fundamental Research Funds for the Central Universities under contract No.201262003the algal transcriptome sequencing was supported by OneKP Project(www.onekp.com)
文摘Saccharina is one of the most important cold-water living marine brown algal genera. In this study we ana-lyzed the transcriptome of S. japonica, which belongs to the 1 000 Plants （OneKP） Project, by using a next-generation high-throughput DNA sequencing technique. About 5.16 GB of raw data were generated, and 65 536 scaffolds with an average length of 454 bp were assembled with SOAP de novo assembly method. In total, 19 040 unigenes were identified by BLAST;25 734 scaffolds were clustered into 37 Gene ontology functional groups;6 760 scaffolds were classified into 25 COG categories, as well as 2 665 scaffolds that were assigned to 306 KEGG pathways. Majority of the unigenes exhibited more similarities to algae including brown algae and diatom than other cyanobacteria, marine diatom, and plant. Saccharina japonica has the outstanding capability to accumulate halogen such as Br and I via halogenation processes from seawater. We acquired 42 different vanadium-dependent haloperoxidases （vHPO） in S. japonica transcriptome data, including 5 segments of vanadium-dependent iodoperoxidase （vIPO） and 37 segments of vanadium-de-pendent bromoperoxidase （vBPO）. Complicated analyses of identified fulllength S. japonica vBPO1 and S. japonica vBPO2 revealed the importance of vBPO among species of brown algae and the strong relationship between marine algal vBPOs and vIPOs. This study will enhance our understanding of the biological charac-teristics and economic values of S. japonica species.
基金Supported by the National Natural Science Foundation of China(11326175,71471090)the Zhejiang Natural Science Foundation of China(LQ14A010012)
文摘Let {Xkl,…, Xkp, k≥ 1} be a p-dimensional standard （zero-means, unit-variances）non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maximaof {Xkl,…, Xkp, k 〉 1}, the incomplete maxima of those sequences subject to random failureand the partial sums of those sequences are obtained.
基金Supported by the NSF of Anhui Province(1308085QA03,1408085QA02,1208085QA03)Supported by the Youth Science Research Fund of Anhui University+1 种基金Supported by the Students Innovative Training Project of Anhui University(201410357118)Supported by the Students Science Research Training Program of Anhui University(kyxl2013003)
文摘Some exponential inequalities and complete convergence are established for extended negatively dependent(END) random variables. The inequalities extend and improve the results of Kim and Kim(On the exponential inequality for negative dependent sequence.Communications of the Korean Mathematical Society, 2007, 22(2): 315-321) and Nooghabi and Azarnoosh(Exponential inequality for negatively associated random variables. Statistical Papers, 2009, 50(2): 419-428). We also obtain the convergence rate O(n-1/2ln1/2n) for the strong law of large numbers, which improves the corresponding ones of Kim and Kim,and Nooghabi and Azarnoosh.
基金co-supported by the National Natural Science Foundation of China (No. 61833016)the Shaanxi Outstanding Youth Science Foundation,China (No. 2020JC-34)the Shaanxi Science and Technology Innovation Team,China(No. 2022TD-24)
文摘Evidential Reasoning(ER)rule,which can combine multiple pieces of independent evidence conjunctively,is widely applied in multiple attribute decision analysis.However,the assumption of independence among evidence is often not satisfied,resulting in ER rule inapplicable.In this paper,an Evidential Reasoning rule for Dependent Evidence combination(ERr-DE)is developed.Firstly,the aggregation sequence of multiple pieces of evidence is determined according to evidence reliability.On this basis,a calculation method of evidence Relative Total Dependence Coefficient(RTDC)is proposed using the distance correlation method.Secondly,as a discounting factor,RTDC is introduced into the ER rule framework,and the ERr-DE model is formulated.The aggregation process of two pieces of dependent evidence by ERr-DE is investigated,which is then generalized to aggregate multiple pieces of non-independent evidence.Thirdly,sensitivity analysis is carried out to investigate the relationship between the model output and the RTDC.The properties of sensitivity coefficient are explored and mathematically proofed.The conjunctive probabilistic reasoning process of ERr-DE and the properties of sensitivity coefficient are verified by two numerical examples respectively.Finally,the practical application of the ERr-DE is validated by a case study on the performance assessment of satellite turntable system.
文摘Under the conditions on covariances of the original random variables, a Glivenko-Cantelli theorem for associated sequences and weak convergence for empirical processes of stationary associated sequences are obtained, assuming the random variables to be discrete.
基金The NSF(10871001,60803059) of ChinaTalents Youth Fund(2010SQRL016ZD) of Anhi Province Universities+2 种基金Youth Science Research Fund(2009QN011A) of Anhui UniversityProvincial Natural Science Research Project of Anhui Colleges(KJ2010A005)Academic innovation team of Anhui University (KJTD001B)
文摘In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.
基金Supported by the National Natural Science Foundation of China (10671149,60574002)
文摘Rosenthal inequality for NOD （negatively＇ orthant dependent） random variable sequences is established. As its applications, two theorems of complete convergence of weighted sums for arrays of NOD random variables are given, which extend the corresponding known results.
基金supported by National Natural Science Foundation of China under Grant No.60571062the Natural Science Foundation of Shandong Province under Grant No.Y2004G09
文摘A double helix model of charge transport in DNA molecule is given and the transmission spectra of four DNA sequences are obtained.The calculated results show that the transmission characteristics of DNA are not only related to the longitudinal transport but also to the transverse transport of molecule.The periodic sequence with the same composition has stronger conduction ability.With the increasing of bases composition,the conductive ability reduces,but the weight of θ direction rises in charge transfer.
基金Foundation of Anhui Educational Committee(No.KJ2013Z225)
文摘In the paper,we get the precise results of Hájek-Rényi type inequalities for the partial sums of negatively orthant dependent sequences,which improve the results of Theorem 3.1and Corollary 3.2 in Kim(2006)and the strong law of large numbers and strong growth rate for negatively orthant dependent sequences.
文摘Stochastic dynamic job shop scheduling pro- blem with consideration of sequence-dependent setup times are among the most difficult classes of scheduling problems. This paper assesses the performance of nine dispatching rules in such shop from makespan, mean flow time, maximum flow time, mean tardiness, maximum tardiness, number of tardy jobs, total setups and mean setup time performance measures viewpoint. A discrete event simulation model of a stochastic dynamic job shop manufacturing system is developed for investigation purpose. Nine dispatching rules identified from literature are incorporated in the simulation model. The simulation experiments are conducted under due date tightness factor of 3, shop utilization percentage of 90 % and setup times less than processing times. Results indicate that shortest setup time （SIMSET） rule provides the best performance for mean flow time and number of tardy jobs measures. The job with similar setup and modified earliest due date （JMEDD） rule provides the best performance for make- span, maximum flow time, mean tardiness, maximum tardiness, total setups and mean setup time measures.
基金Supported by Ferdowsi University of Mashhad(Grant No.MS88076AMI)
文摘Let X and Y be positive weakly negatively dependent （WND） random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on F（x） = 1-F（x） and G（x） = of XY when X and Y are WND random variables 1- G（x） are provided. Moreover, subexponentiality is derived.
文摘Over the past few years, many researchers have attempted to develop non-invasive prenatal testing methods in order to investigate the genetic status of the fetus. The aim is to avoid invasive procedures such as chorionic villus and amniotic fluid sampling, which result in a significant risk for pregnancy loss. The discovery of cell free fetal DNA circulating in the maternal blood has great potential for the development of non-invasive prenatal testing(NIPT) methodologies. Such strategies have been successfully applied for the determination of the fetal rhesus status and inherited monogenic disease but the field of fetal aneuploidy investigation seems to be more challenging. The main reason for this is that the maternal cell free DNA in the mother's plasma is far more abundant, and because it is identical to half of the corresponding fetal DNA. Approaches developed are mainly based on next generation sequencing(NGS) technologies and epigenetic genetic modifications, such as fetal-maternal DNA differential methylation. At present, genetic services for non-invasive fetal aneuploidy detection are offered using NGS-based approaches but, for reasons that are presented herein, they still serve as screening tests which are not readily accessed by the majority of couples. Here we discuss the limitations of both strategies for NIPT and the future potential of the methods developed.
