wanyu/IteraTeR_v2 huggingface dataset:
Original:  The method is based upon a reformulation of the classical real-valued Green's function integral expression for the far field amplitude to an  integral over a complex contour.
Revised:  The new technique is based upon a reformulation of the classical real-valued Green's function integral expression for the far field amplitude to an integral over a complex contour.
Edit intent: clarity
Original:  The method is based upon a reformulation of the classical real-valued Green's function integral expression for the far field amplitude to an  integral over a complex contour.
Revised:  The method is based upon a reformulation of the classical real-valued Green's function integral for the far field amplitude to an integral over a complex contour.
Edit intent: clarity
Original:  On this complex contour (or manifold, in multiple dimensions) the scattered wave can be calculated very efficiently using an iterative multigrid method as a solver for the discretized  scattered wave system, resulting in a fast and scalable calculation of the far field map.
Revised:  On this complex contour (or manifold, in multiple dimensions) . Using the iterative multigrid method as a solver for the discretized scattered wave system, resulting in a fast and scalable calculation of the far field map.
Edit intent: clarity
Original:  On this complex contour (or manifold, in multiple dimensions) the scattered wave can be calculated very efficiently using an iterative multigrid method as a solver for the discretized  scattered wave system, resulting in a fast and scalable calculation of the far field map.
Revised:  On this complex contour (or manifold, in multiple dimensions) the scattered wave can be calculated very efficiently using an iterative multigrid method as a solver for the discretized scattered wave system, the proposed approach results in a fast and scalable calculation of the far field map.
Edit intent: coherence
Original:  On this complex contour (or manifold, in multiple dimensions) the scattered wave can be calculated very efficiently using an iterative multigrid method as a solver for the discretized  scattered wave system, resulting in a fast and scalable calculation of the far field map.
Revised:  On this complex contour (or manifold, in multiple dimensions) the scattered wave can be calculated very efficiently using an iterative multigrid method as a solver for the discretized scattered wave system, resulting in a fast and scalable calculation method for the far field map.
Edit intent: clarity
Original:  The so-called `full complex contour ' approach is successfully validated on  model problems in two and three spatial dimensions, and multigrid convergence results are provided to demonstrate the wavenumber scalability and overall performance of the proposed method.
Revised:  The complex contour method is successfully validated on model problems in two and three spatial dimensions, and multigrid convergence results are provided to demonstrate the wavenumber scalability and overall performance of the proposed method.
Edit intent: clarity
Original:  The so-called `full complex contour ' approach is successfully validated on  model problems in two and three spatial dimensions, and multigrid convergence results are provided to demonstrate the wavenumber scalability and overall performance of the proposed method.
Revised:  The so-called `full complex contour ' approach is successfully validated on model problems in two and three spatial dimensions, and multigrid convergence results are provided to substantiate the wavenumber scalability and overall performance of the proposed method.
Edit intent: clarity
Original:  The so-called `full complex contour ' approach is successfully validated on  model problems in two and three spatial dimensions, and multigrid convergence results are provided to demonstrate the wavenumber scalability and overall performance of the proposed method.
Revised:  The so-called `full complex contour ' approach is successfully validated on model problems in two and three spatial dimensions, and multigrid convergence results are provided to demonstrate the wavenumber scalability and overall performance of the method.
Edit intent: clarity
Original: Microgrids represent an emerging paradigm of future electric power systems that integrate both distributed and centralized generation .
Revised: Microgrids represent an emerging paradigm of future electric power systems that can utilize both distributed and centralized generation .
Edit intent: clarity
Original: Microgrids represent an emerging paradigm of future electric power systems that integrate both distributed and centralized generation .
Revised: Microgrids represent an emerging paradigm of future electric power systems that integrate both distributed and centralized generations .
Edit intent: clarity
Original:  However, these trends also bring unprecedented challenges to the design of intelligent control strategies for the microgrids.
Revised:  However, these trends also bring unprecedented challenges to the design of intelligent control strategies for microgrids.
Edit intent: fluency
Original:  In this paper, we study online algorithms for the micro-grid generation scheduling problem with intermittent renewable energy sources and co-generation, in order to maximize the cost-savings with local generation.
Revised:  In this paper, we study online algorithms for the microgrid generation scheduling problem with intermittent renewable energy sources and co-generation, in order to maximize the cost-savings with local generation.
Edit intent: fluency
Original:  In this paper, we study online algorithms for the micro-grid generation scheduling problem with intermittent renewable energy sources and co-generation, in order to maximize the cost-savings with local generation.
Revised:  In this paper, we study online algorithms for the micro-grid generation scheduling problem with intermittent renewable energy sources and co-generation, with the goal of maximizing the cost-savings with local generation.
Edit intent: clarity
Original:  Under certain settings, we show that CHASE achieves the best competitive ratio of all deterministic online algorithms .
Revised:  Under typical settings, we show that CHASE achieves the best competitive ratio of all deterministic online algorithms .
Edit intent: clarity
Original:  Under certain settings, we show that CHASE achieves the best competitive ratio of all deterministic online algorithms .
Revised:  Under certain settings, we show that CHASE achieves the best competitive ratio among all deterministic online algorithms .
Edit intent: clarity
Original: The storage of binary cycles in continuous-time Hopfield-type networks is investigated.
Revised: Cyclic patterns of neuronal activity are ubiquitous in animal nervous systems, and partially responsible for generating and controlling rhythmic movements such as locomotion, respiration, swallowing and so on. Clarifying the role of the network connectivities for generating cyclic patterns is fundamental for understanding the generation of rhythmic movements. In this paper, the storage of binary cycles in continuous-time Hopfield-type networks is investigated.
Edit intent: coherence
Original: The storage of binary cycles in continuous-time Hopfield-type networks is investigated.
Revised: The storage of binary cycles in neural networks is investigated.
Edit intent: clarity
Original:  We call a cycle defined by a binary matrix \Sigma admissible if a connectivity matrix satisfying the cycle's transition conditions exists, and if so construct it using the pseudoinverse learning rule.
Revised:  We call a cycle \Sigma admissible if a connectivity matrix satisfying the cycle's transition conditions exists, and if so construct it using the pseudoinverse learning rule.
Edit intent: clarity
Original:  We call a cycle defined by a binary matrix \Sigma admissible if a connectivity matrix satisfying the cycle's transition conditions exists, and if so construct it using the pseudoinverse learning rule.
Revised:  We call a cycle defined by a binary matrix \Sigma admissible if a connectivity matrix satisfying the cycle's transition conditions exists, and construct it using the pseudoinverse learning rule.
Edit intent: coherence
Original:  Our main focus is on the structural features of admissible cycles and the topology of the corresponding networks .
Revised:  Our main focus is on the structural features of admissible cycles and corresponding network topology .
Edit intent: fluency
Original:  Based on the decomposition of the rows of \Sigma into disjoint subsets corresponding to loops, where a loop is defined by the set of all cyclic permutations of a row, cycles are classified as simple cycles, and separable or inseparable composite cycles.
Revised:  Based on the decomposition of the rows of \Sigma into loops, where a loop is defined by the set of all cyclic permutations of a row, cycles are classified as simple cycles, and separable or inseparable composite cycles.
Edit intent: clarity
Original:  Based on the decomposition of the rows of \Sigma into disjoint subsets corresponding to loops, where a loop is defined by the set of all cyclic permutations of a row, cycles are classified as simple cycles, and separable or inseparable composite cycles.
Revised:  Based on the decomposition of the rows of \Sigma into disjoint subsets corresponding to loops, where a loop is the set of all cyclic permutations of a row, cycles are classified as simple cycles, and separable or inseparable composite cycles.
Edit intent: clarity
Original:  Based on the decomposition of the rows of \Sigma into disjoint subsets corresponding to loops, where a loop is defined by the set of all cyclic permutations of a row, cycles are classified as simple cycles, and separable or inseparable composite cycles.
Revised:  Based on the decomposition of the rows of \Sigma into disjoint subsets corresponding to loops, where a loop is defined by the set of all cyclic permutations of a row, cycles are classified as simple cycles, separable or inseparable composite cycles.
Edit intent: fluency
Original:  For special cases this topology simplifies to a ring with only one feedback.
Edit intent: coherence
Original:  Composite cycles contain rows from at least two disjoint loops, and the neurons corresponding to the loop-vectors in \Sigma from the same loop are identified with a cluster.
Revised:  Composite cycles contain rows from at least two disjoint loops, and the neurons corresponding to the rows in \Sigma from the same loop are identified with a cluster.
Edit intent: clarity
Original:  The latter fact can be interpreted as a sort of weak form of market's viability, while this equivalence is established with a much less technical approach.
Edit intent: coherence
Original:  Furthermore, the obtained equivalent probability can be chosen as close to the real-world probability measure as we want (but might not be equal) {\it   .
Revised:  Furthermore, the obtained equivalent probability can be chosen as close to the real-world probability measure as we want (but might not be equal) {\it local .
Edit intent: fluency
Original:  Our lemma corresponds to the non-systematic encoding of affine variety codes, and can be stated by giving a canonical linear map as the composition of an extension through linear feedback shift registers from a Gr\"obner basis and a generalized inverse discrete Fourier transform.
Revised:  Our lemma corresponds to the non-systematic encoding of affine variety codes, and can be stated by giving a canonical linear map as the composition of an extension through linear feedback shift registers from a Grobner basis and a generalized inverse discrete Fourier transform.
Edit intent: fluency
Original: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Revised: We provide a novel approach to numerically approximate the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Edit intent: clarity
Original: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Revised: We show that the Kolmogorov-Chaitin complexity K(s) of a string s using a Coding Theorem Method with associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Edit intent: clarity
Original: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Revised: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) , as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Edit intent: coherence
Original: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Revised: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Edit intent: clarity
Original: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Revised: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) . We also show that the complexity values correlate with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Edit intent: clarity
Original: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, in agreement with strict integer-value program-size complexity.
Revised: We show that the Kolmogorov-Chaitin complexity K(s) of a string s numerically approximated using Levin's coding theorem with the associated measure K_m(s) (a method we have therefore named the Coding Theorem Method) as calculated from the frequency of production of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) correlates with the number of instructions used by the Turing machines, which is consistent with strict integer-value program-size complexity.
Edit intent: coherence
Original:  Nevertheless, K_m proves to be a finer-grained measure and a better approach for distinguishing K for short strings from non-integer evaluations .
Revised:  Nevertheless, K_m proves to be a finer-grained measure and an alternative approach for distinguishing K for short strings from non-integer evaluations .
Edit intent: clarity
Original:  Nevertheless, K_m proves to be a finer-grained measure and a better approach for distinguishing K for short strings from non-integer evaluations .
Revised:  Nevertheless, K_m proves to be a finer-grained measure and a better approach for distinguishing K for short strings .
Edit intent: clarity
Original:  We also show that neither K_m nor the number of instructions used suggests any correlation with Bennett's concept of Logical Depth ( the shortest runtime of the shortest computer program producing s).
Revised:  We also show that neither K_m nor the number of instructions used suggests any correlation with Bennett's concept of Logical Depth ( the shortest runtime of the smallest computer program producing s).
Edit intent: clarity
Original:  And we announce a first version of an online complexity calculator based on a combination of theoretical concepts as an implementation of our Coding Theorem Method.
Revised:  We also announce a first version of an online complexity calculator based on a combination of theoretical concepts as an implementation of our Coding Theorem Method.
Edit intent: clarity
Original:  And we announce a first version of an online complexity calculator based on a combination of theoretical concepts as an implementation of our Coding Theorem Method.
Revised:  And we announce a first version of an on-line algorithmic complexity calculator, based on a combination of theoretical concepts as an implementation of our Coding Theorem Method.
Edit intent: clarity
Original: We provide a novel approach to numerically approximate the Kolmogorov-Chaitin complexity K(s) of a string s using a Coding Theorem Method with associated measure K_m(s) , as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) .
Revised: We show that real-value approximations of Kolmogorov-Chaitin complexity K(s) of a string s using a Coding Theorem Method with associated measure K_m(s) , as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) .
Edit intent: clarity
Original: We provide a novel approach to numerically approximate the Kolmogorov-Chaitin complexity K(s) of a string s using a Coding Theorem Method with associated measure K_m(s) , as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) .
Revised: We provide a novel approach to numerically approximate the Kolmogorov-Chaitin (K_m) using the algorithmic Coding theorem as calculated from the output frequency of a large set of small deterministic Turing machines with up to 5 states (and 2 symbols) .
Edit intent: clarity
Original:  We also show that neither K_m nor the number of instructions used suggests any correlation with Bennett's concept of Logical Depth LD(s) (roughly the shortest runtime of the smallest computer program producing s) .
Revised:  We also show that neither K_m nor the number of instructions used shows any correlation with Bennett's concept of Logical Depth LD(s) (roughly the shortest runtime of the smallest computer program producing s) .
Edit intent: clarity
Original:  We also show that neither K_m nor the number of instructions used suggests any correlation with Bennett's concept of Logical Depth LD(s) (roughly the shortest runtime of the smallest computer program producing s) .
Revised:  We also show that neither K_m nor the number of instructions used suggests any correlation with Bennett's Logical Depth LD(s) (roughly the shortest runtime of the smallest computer program producing s) .
Edit intent: clarity
Original: Forward Automatic Differentiation (AD) is a technique for augmenting programs to both perform their original calculation and also compute its directional derivative .
Revised: Forward Automatic Differentiation (AD) is a technique for augmenting programs to compute derivatives .
Edit intent: clarity
Original:  When derivatives are nested, the distinct derivative calculations, and their associated attached values , must be distinguished.
Revised:  When derivatives are nested, the distinct derivative calculations, and their associated perturbations , must be distinguished.
Edit intent: clarity
Original:  In dynamic languages this is typically accomplished by creating a unique tag for each application of the derivative operator , tagging the attached values , and overloading the arithmetic operators.
Revised:  This is typically accomplished by creating a unique tag for each application of the derivative operator , tagging the attached values , and overloading the arithmetic operators.
Edit intent: clarity
Original:  In dynamic languages this is typically accomplished by creating a unique tag for each application of the derivative operator , tagging the attached values , and overloading the arithmetic operators.
Revised:  In dynamic languages this is typically accomplished by creating a unique tag for each derivative calculation , tagging the attached values , and overloading the arithmetic operators.
Edit intent: clarity
Original:  In dynamic languages this is typically accomplished by creating a unique tag for each application of the derivative operator , tagging the attached values , and overloading the arithmetic operators.
Revised:  In dynamic languages this is typically accomplished by creating a unique tag for each application of the derivative operator , tagging the perturbations , and overloading the arithmetic operators.
Edit intent: clarity
Original: As the Internet faces scalability, mobility, and security issues, new network architectures are being proposed to better accommodate the needs of modern  applications.
Revised: As the Internet struggles to cope with scalability, mobility, and security issues, new network architectures are being proposed to better accommodate the needs of modern applications.
Edit intent: clarity