wanyu/IteraTeR_v2 huggingface dataset:
Original:  However, almost all existing algorithms and applications have a strong assumption that the parameters are mutually independent or Gaussian correlated .
Revised:  However, almost all existing techniques assume that the parameters are mutually independent or Gaussian correlated .
Edit intent: clarity
Original:  This paper presents a new framework to solve high-dimensional uncertainty quantification problems with  non-Gaussian correlated uncertainties.
Revised:  We present a new framework to solve high-dimensional uncertainty quantification problems with non-Gaussian correlated uncertainties.
Edit intent: coherence
Original:  This paper presents a new framework to solve high-dimensional uncertainty quantification problems with  non-Gaussian correlated uncertainties.
Revised:  This paper presents a new framework to solve uncertainty quantification problems with non-Gaussian correlated uncertainties.
Edit intent: clarity
Original:  Firstly, we propose a class of smooth basis functions that can well capture the impact of non-Gaussian correlated process variations.
Revised:  Firstly, we propose a set of smooth basis functions that can well capture the impact of non-Gaussian correlated process variations.
Edit intent: clarity
Original:  Firstly, we propose a class of smooth basis functions that can well capture the impact of non-Gaussian correlated process variations.
Revised:  Firstly, we propose a class of smooth basis functions to well capture the impact of non-Gaussian correlated process variations.
Edit intent: clarity
Original:  Additionally, we present three approaches for adaptive sampling : D-optimal, R-optimal, and E-optimal methods, which can improve the performance of the sparse solver significantly .
Revised:  We present three adaptive sampling approaches to improve the performance of the sparse solver significantly .
Edit intent: coherence
Original:  Additionally, we present three approaches for adaptive sampling : D-optimal, R-optimal, and E-optimal methods, which can improve the performance of the sparse solver significantly .
Revised:  Additionally, we present three approaches for adaptive sampling : D-optimal, R-optimal, and E-optimal methods, which can improve the performance of the sparse solver .
Edit intent: clarity
Original:  Finally, we validate our theory and algorithms by a synthetic example and three electronic and  photonic ICs with 19 to 57 non-Gaussian correlated variation parameters.
Revised:  Finally, we validate our methods by synthetic and photonic ICs with 19 to 57 non-Gaussian correlated variation parameters.
Edit intent: clarity
Original:  Our approach outperforms Monte Carlo by thousands of times in terms of efficiency on these examples .
Revised:  Our approach outperforms Monte Carlo by thousands of times in terms of efficiency .
Edit intent: clarity
Original: A \lambda-fold r-packing in a Hamming metric space is a code C such that the radius-r balls centered in C cover each vertex of the space by not more than \lambda -times .
Revised: A \lambda-fold r-packing in a Hamming metric space is a code C such that the radius-r balls centered in C cover each vertex of the space by not more than \lambda times .
Edit intent: fluency
Original:  We propose asymptotic bounds for  q-ary 2-fold 1-packings as q grows ,\ge  find that the maximum size of a binary 2-fold 1-packing of length 9 is 96 , and derive upper bounds for the size of a binary \lambda-fold 1-packing  .
Revised:  We propose asymptotic bounds for the maximum size of a q-ary 2-fold 1-packings as q grows ,\ge find that the maximum size of a binary 2-fold 1-packing of length 9 is 96 , and derive upper bounds for the size of a binary \lambda-fold 1-packing .
Edit intent: fluency
Original:  We propose asymptotic bounds for  q-ary 2-fold 1-packings as q grows ,\ge  find that the maximum size of a binary 2-fold 1-packing of length 9 is 96 , and derive upper bounds for the size of a binary \lambda-fold 1-packing  .
Revised:  We propose asymptotic bounds for q-ary 2-fold 1-packing as q grows ,\ge find that the maximum size of a binary 2-fold 1-packing of length 9 is 96 , and derive upper bounds for the size of a binary \lambda-fold 1-packing .
Edit intent: clarity
Original:  We propose asymptotic bounds for  q-ary 2-fold 1-packings as q grows ,\ge  find that the maximum size of a binary 2-fold 1-packing of length 9 is 96 , and derive upper bounds for the size of a binary \lambda-fold 1-packing  .
Revised:  We propose asymptotic bounds for q-ary 2-fold 1-packings as q grows ,\ge find that the maximum size of a binary 2-fold 1-packing of length 9 is 96 ; and derive upper bounds for the size of a binary \lambda-fold 1-packing .
Edit intent: fluency
Original:  find that the maximum size of a binary 2-fold 1-packing of length 9 is 96 ;
Revised:  (c) derive an upper bound for the size of a binary 2-fold 1-packing of length 9 is 96 ;
Edit intent: clarity
Original:  find that the maximum size of a binary 2-fold 1-packing of length 9 is 96 ;
Revised:  find that the maximum size of a binary 2-fold 1-packing of length 9 , in particular, establish the maximum size 96 ;
Edit intent: clarity
Original:  We prove some properties of 1-perfect unitrades, which are a special case of two-fold 1-packings.
Revised:  We prove some properties of 1-perfect unitrades, which are a special case of 2-fold 1-packings.
Edit intent: fluency
Original:  Keywords: Hamming graph, multifold ball packings, two-fold ball packings, l-list decodable codes,  completely regular codes, linear programming bound , unitrades, bitrades.
Revised:  Keywords: Hamming graph, multifold ball packings, two-fold ball packings, list decodable codes, completely regular codes, linear programming bound , unitrades, bitrades.
Edit intent: fluency
Original:  Keywords: Hamming graph, multifold ball packings, two-fold ball packings, l-list decodable codes,  completely regular codes, linear programming bound , unitrades, bitrades.
Revised:  Keywords: Hamming graph, multifold ball packings, two-fold ball packings, l-list decodable codes, completely regular codes, linear programming bound 
Edit intent: coherence
Original: In computer vision, the gradient and Laplacian of an image are used in many different applications, such as edge detection, feature extraction  and seamless image cloning.
Revised: In computer vision, the gradient and Laplacian of an image are used in different applications, such as edge detection, feature extraction and seamless image cloning.
Edit intent: clarity
Original: In computer vision, the gradient and Laplacian of an image are used in many different applications, such as edge detection, feature extraction  and seamless image cloning.
Revised: In computer vision, the gradient and Laplacian of an image are used in many different applications, such as edge detection, feature extraction , and seamless image cloning.
Edit intent: fluency
Original:  To obtain the gradient of an image , it requires the use of numerical derivatives , which are available in most computer vision toolboxes.
Revised:  Computing the gradient of an image , it requires the use of numerical derivatives , which are available in most computer vision toolboxes.
Edit intent: fluency
Original:  To obtain the gradient of an image , it requires the use of numerical derivatives , which are available in most computer vision toolboxes.
Revised:  To obtain the gradient of an image is straightforward since numerical derivatives are available in most computer vision toolboxes.
Edit intent: clarity
Original:  The objective of this paper is to present a novel fast and robust method of computing the image from its gradient or Laplacian with minimal error, which can be used for gradient-domain editing.
Revised:  The objective of this paper is to present a novel fast and robust method of solving the image gradient or Laplacian with minimal error, which can be used for gradient-domain editing.
Edit intent: clarity
Original:  The objective of this paper is to present a novel fast and robust method of computing the image from its gradient or Laplacian with minimal error, which can be used for gradient-domain editing.
Revised:  The objective of this paper is to present a novel fast and robust method of computing the image from its gradient or Laplacian with minimal error, which can be used for gradient domain editing.
Edit intent: fluency
Original:  It can also be optimized on a GPU using fast Fourier transforms and can easily be generalized for an n-dimension image.
Revised:  It can also be optimized on a GPU using fast Fourier transforms and can easily be generalized for an n dimension image.
Edit intent: fluency
Original:  The tests show that the gradient solver takes around 2 milliseconds (ms) to reconstruct an image of 801x1200 pixels compared to between 6ms and 3000ms for competing methods .
Revised:  The tests show that , for images of resolution 801x1200 pixels compared to between 6ms and 3000ms for competing methods .
Edit intent: clarity
Original:  Finally, the developed method is  validated with examples of Poisson blending, gradient removal, edge preserving blurring and edge-preserving painting effect .
Revised:  Finally, the developed method is also validated with examples of Poisson blending, gradient removal, edge preserving blurring and edge-preserving painting effect .
Edit intent: clarity
Original:  We present two constructions of finite semantics for  second-order Multiplicative-Additive Linear Logic (MALL2) and study their properties.
Revised:  We exhibit such a finite semantics for second-order Multiplicative-Additive Linear Logic (MALL2) and study their properties.
Edit intent: clarity
Original: Monte Carlo (MC) permutation testing is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail.
Revised: Monte Carlo (MC) permutation test is considered the gold standard for statistical hypothesis testing, especially when standard parametric assumptions are not clear or likely to fail.
Edit intent: fluency
Original:  In genome-wide association studies, for example, the number of hypothesis tests m is around 10^6 while the number of MC samples n for each test could be greater than 10^8, totaling more than nm=10 ^14 samples.
Revised:  In genome-wide association studies, for example, the number of hypothesis tests m is around 10^6 while the number of MC samples n for each test could be greater than 10^8, totaling more than nm=10 ^{14 samples.
Edit intent: fluency
Original:  The algorithm outputs the same result as the standard full MC approach with high probability while requiring only O (nm) samples.
Revised:  The algorithm outputs the same result as the standard full MC approach with high probability while requiring only (nm) samples.
Edit intent: clarity
Original: In this paper, we propose a new indexing structure for parameterized strings, called parameterized linear-size suffix tries , by generalizing linear-size suffix tries for ordinary strings .
Revised: In this paper, we discuss a possible generalization of linear-size suffix tries for parameterized strings, called parameterized linear-size suffix tries , by generalizing linear-size suffix tries for ordinary strings .
Edit intent: clarity
Original: In this paper, we propose a new indexing structure for parameterized strings, called parameterized linear-size suffix tries , by generalizing linear-size suffix tries for ordinary strings .
Revised: In this paper, we propose a new indexing structure for parameterized strings, which we call parameterized linear-size suffix tries , by generalizing linear-size suffix tries for ordinary strings .
Edit intent: clarity
Original: In this paper, we propose a new indexing structure for parameterized strings, called parameterized linear-size suffix tries , by generalizing linear-size suffix tries for ordinary strings .
Revised: In this paper, we propose a new indexing structure for parameterized strings, called parameterized linear-size suffix tries (PLSTs) .
Edit intent: clarity
Original:  Two parameterized strings are said to match if there is a bijection between symbols that makes the two coincide.
Revised:  Two parameterized strings are said to match if there is a bijection on the symbol set that makes the two coincide.
Edit intent: clarity
Original:  Parameterized linear-size suffix tries are applicable to the parameterized pattern matching problem, which is to decide whether the input  text has a substring that matches the input  pattern.
Revised:  PLSTs are applicable to the parameterized pattern matching problem, which is to decide whether the input text has a substring that matches the input pattern.
Edit intent: clarity
Original:  The size of our proposed structure is linear in the text size , with which our algorithm solves the problem in linear time in the pattern size .
Revised:  The size of our proposed PLST is linear in the text size , with which our algorithm solves the problem in linear time in the pattern size .
Edit intent: clarity
Original:  Our proposed data structure can be seen as a compacted version of a parameterized suffix trie and an alternative of a parameterized suffix tree .
Revised:  Our proposed data structure .
Edit intent: clarity
Original: In this paper, we discuss a possible generalization of linear-size suffix tries for parameterized strings , which we call parameterized linear-size suffix tries (PLSTs) .
Revised: In this paper, we discuss a possible generalization of linear-size suffix tries for parameterized strings which we call parameterized linear-size suffix tries (PLSTs) .
Edit intent: fluency
Original: In this paper, we discuss a possible generalization of linear-size suffix tries for parameterized strings , which we call parameterized linear-size suffix tries (PLSTs) .
Revised: In this paper, we discuss a possible generalization of linear-size suffix tries for parameterized strings , which we call PLSTs, by generalizing linear-size suffix tries (PLSTs) .
Edit intent: clarity
Original:  The size of our proposed PLST is linear in the text size .
Revised:  The size of PLSTs is linear in the text size .
Edit intent: clarity
Original:  In particular, motivated by error correction and reconstruction problems in DNA-based data storage applications, we determine the size of "balls" of radius one in the TDRL metric, as well as the cardinality of the maximum intersection of two balls .
Revised:  In particular, the cardinality of `balls' of radius one in the TDRL metric, as well as the cardinality of the maximum intersection of two balls .
Edit intent: clarity
Original: We study descriptive complexity of counting complexity classes in the range from \#P to \# \cdotNP.
Revised: We study descriptive complexity of counting complexity classes in the range from #P to \cdotNP.
Edit intent: fluency
Original:  A corollary of Fagin's characterization of NP by existential second-order logic is that \# P can be logically described as the class of functions counting satisfying assignments to free relation variables in first-order formulae.
Revised:  A corollary of Fagin's characterization of NP by existential second-order logic is that P can be logically described as the class of functions counting satisfying assignments to free relation variables in first-order formulae.
Edit intent: fluency
Original:  In this paper we extend this study to classes beyond \# P and extensions of first-order logic with team semantics.
Revised:  In this paper we extend this study to classes beyond P and extensions of first-order logic with team semantics.
Edit intent: fluency
Original:  Our results show that the class \# \cdotNP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of \# \cdotNP and \# P , respectively.
Revised:  Our results show that the class \cdotNP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of \# \cdotNP and \# P , respectively.
Edit intent: fluency
Original:  Our results show that the class \# \cdotNP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of \# \cdotNP and \# P , respectively.
Revised:  Our results show that the class \# \cdotNP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of \cdotNP and \# P , respectively.
Edit intent: fluency
Original:  Our results show that the class \# \cdotNP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of \# \cdotNP and \# P , respectively.
Revised:  Our results show that the class \# \cdotNP can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of \# \cdotNP and P , respectively.
Edit intent: fluency
Original:  Our main technical result shows that the problem of counting satisfying assignments for monotone Boolean \Sigma_1-formulae is \# \cdotNP-complete as well as complete for the function class generated by dependence logic.
Revised:  Our main technical result shows that the problem of counting satisfying assignments for monotone Boolean \Sigma_1-formulae is \cdotNP-complete as well as complete for the function class generated by dependence logic.
Edit intent: coherence
Original: In this paper, we prove that the simplest Stochastic Gradient Descent (SGD) algorithm is able to efficiently escape from saddle points and find an (\epsilon, O(\epsilon^{0.5}))-approximate second-order stationary point in O(\epsilon^{-3.5}) stochastic gradient computations for generic nonconvex optimization problems, under both gradient-Lipschitz and Hessian-Lipschitz  assumptions.
Revised: In this paper, we prove that the simplest Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an (\epsilon, O(\epsilon^{0.5}))-approximate second-order stationary point in O(\epsilon^{-3.5}) stochastic gradient computations for generic nonconvex optimization problems, under both gradient-Lipschitz and Hessian-Lipschitz assumptions.
Edit intent: clarity
Original: In this paper, we prove that the simplest Stochastic Gradient Descent (SGD) algorithm is able to efficiently escape from saddle points and find an (\epsilon, O(\epsilon^{0.5}))-approximate second-order stationary point in O(\epsilon^{-3.5}) stochastic gradient computations for generic nonconvex optimization problems, under both gradient-Lipschitz and Hessian-Lipschitz  assumptions.
Revised: In this paper, we prove that the simplest Stochastic Gradient Descent (SGD) algorithm is able to efficiently escape from saddle points and find an (\epsilon, O(\epsilon^{0.5}))-approximate second-order stationary point in O(\epsilon^{-3.5}) stochastic gradient computations for generic nonconvex optimization problems, under both gradient-Lipschitz , Hessian-Lipschitz assumptions.
Edit intent: fluency
Original:  This unexpected result subverts the classical belief that SGD requires at least O(\epsilon^{-4}) stochastic gradient computations for obtaining an (\epsilon,O(\epsilon^{0.5}))-approximate second-order stationary point.
Revised:  This result subverts the classical belief that SGD requires at least O(\epsilon^{-4}) stochastic gradient computations for obtaining an (\epsilon,O(\epsilon^{0.5}))-approximate second-order stationary point.
Edit intent: clarity
Original:  The agents act in the plane and are identical and indistinguishable, oblivious and lack any means of direct communication.
Revised:  The agents act in the plane and are identical and indistinguishable, oblivious , and lack the capacity of direct communication.
Edit intent: clarity
Original:  The second algorithm assumes agents with continuous sensing and motion , and in this case we can prove gathering into a very small circular region in finite expected time  .
Revised:  The second algorithm assumes agents with continuous sensing and motion we can prove gathering into a very small circular region in finite expected time .
Edit intent: coherence
Original: Connected vehicles may produce gigabytes of data per hour, which makes centralized data processing impractical at the fleet level .
Revised: A fleet of connected vehicles easily produces many gigabytes of data per hour, which makes centralized data processing impractical at the fleet level .
Edit intent: clarity
Original: Connected vehicles may produce gigabytes of data per hour, which makes centralized data processing impractical at the fleet level .
Revised: Connected vehicles may produce gigabytes of data per hour, which makes centralized data processing impractical .
Edit intent: clarity
Original:  In addition, there are the problems of distributing tasks to edge devices and processing them efficiently.
Revised:  In addition, there is the issue of distributing tasks to edge devices and processing them efficiently.
Edit intent: clarity
Original:  In addition, there are the problems of distributing tasks to edge devices and processing them efficiently.
Revised:  In addition, there are the problems of distributing tasks to on-board units in vehicles and processing them efficiently.
Edit intent: clarity
Original:  Our solution to this problem is OODIDA (On-board/ off-board Distributed Data Analytics), which is a platform that tackles both task distribution to connected vehicles as well as concurrent execution of large-scale tasks on arbitrary subsets of  clients.
Revised:  Our solution to this problem is OODIDA (On-board/ Off-board Distributed Data Analytics), which is a platform that tackles both task distribution to connected vehicles as well as concurrent execution of large-scale tasks on arbitrary subsets of clients.
Edit intent: fluency
Original:  Our solution to this problem is OODIDA (On-board/ off-board Distributed Data Analytics), which is a platform that tackles both task distribution to connected vehicles as well as concurrent execution of large-scale tasks on arbitrary subsets of  clients.
Revised:  Our solution to this problem is OODIDA (On-board/ off-board Distributed Data Analytics), which is a platform that tackles both task distribution to connected vehicles as well as concurrent execution of tasks on arbitrary subsets of clients.
Edit intent: clarity
Original:  OODIDA is highly scalable and able to process a significant volume of data on resource-constrained clients .
Revised:  OODIDA is highly scalable , facilitating the execution of large numbers of concurrent tasks .
Edit intent: clarity
Original:  The deep factor suggests that beneath these potentials for attachment there exist any number of important latent variables describing the nodes.
Revised:  A `depth' factor suggests that beneath these potentials for attachment there exist any number of important latent variables describing the nodes.
Edit intent: fluency
Original:  We also demonstrate how inverting an estimated surface factor of a complete weighted world city network provides  more plausible clusters of nodes than the original network based on geometric and cultural considerations.
Revised:  We also demonstrate how inverting an estimated surface factor of a complete weighted world city network provides much more plausible clusters of nodes than the original network based on geometric and cultural considerations.
Edit intent: clarity
Original: Our world is abundant with interdependent interactions occurring at all levels-- be it in the global ecology, human social institutions, within the human brain, or right down to micro-scale protein interactions.
Revised: Our world is abundant with interdependent interactions occurring at all levels-- be it in the global ecology, human social institutions, within the human brain, or in micro-scale protein interactions.
Edit intent: clarity