wanyu/IteraTeR_v2 huggingface dataset:
Original: The irreducible information content of finite strings are considered with regard to universal representations.
Revised: The irreducible information content of finite strings is considered with regard to universal representations.
Edit intent: fluency
Original:  This machine-independent measure of first order logic may be used to test the reducibility of binary sequences with regard to first-order set membership.
Revised:  This machine-independent measure of first order logic may be used to test the quasi-randomness of binary sequences with regard to first-order set membership.
Edit intent: clarity
Original:  The intrinsic arithmetic complexity is given by a universal representation which recursively decodes the Godel number of the string  .
Revised:  The intrinsic numeric complexity is given by a universal representation which recursively decodes the Godel number of the string .
Edit intent: clarity
Original:  The design of generalized non-binary arithmetic circuits is discussed, including the use of optical repeaters for calculation in lieu of logic gates 
Revised:  The design of generalized non-binary circuits is discussed, including the use of optical repeaters for calculation in lieu of logic gates 
Edit intent: clarity
Original:  The design of generalized non-binary arithmetic circuits is discussed, including the use of optical repeaters for calculation in lieu of logic gates 
Revised:  The design of generalized non-binary arithmetic circuits is discussed, including the use of optical repeaters for calculation in lieu of logic gates .
Edit intent: fluency
Original:  The design of generalized non-binary circuits is discussed, including the use of optical repeaters for calculation in lieu of logic gates  .
Revised:  Corresponding arithmetic circuits using optical repeaters in place of logic gates .
Edit intent: clarity
Original:  The design of generalized non-binary circuits is discussed, including the use of optical repeaters for calculation in lieu of logic gates  .
Revised:  The design of generalized non-binary circuits is discussed, including the use of optical repeaters for calculation in lieu of logic gates are discussed .
Edit intent: clarity
Original: The computational complexity of finite strings is considered with regard to universal representations  .
Revised: We relate the computational complexity of finite strings is considered with regard to universal representations .
Edit intent: coherence
Original: The computational complexity of finite strings is considered with regard to universal representations  .
Revised: The computational complexity of finite strings to universal representations .
Edit intent: clarity
Original:  Finally , strings over general alphabets are considered.
Revised:  Next , strings over general alphabets are considered.
Edit intent: fluency
Original:  The intrinsic numeric complexity is given by a universal representation which recursively factors the codeword associated with the string.
Revised:  The intrinsic numeric complexity is given by a universal representation which recursively factors the codeword number associated with a string.
Edit intent: clarity
Original:  This is equivalent to recursively decoding the Godel number which has the value of the string;
Revised:  This is the complexity of the representation recursively decoding a Godel number having the value of the string;
Edit intent: clarity
Original:  We say that the relaxation is {\em totally half-integral} if \hat f( %DIFDELCMD < \bx%%%  ) is a polyhedral function with half-integral extreme points %DIFDELCMD < \bx%%%  , and this property is preserved after adding an arbitrary combination of constraints of the form x_i=x_j, x_i=1-x_j, and x_i=\gamma where \gamma\in\{0, 1, 1/2} is a constant.
Revised:  We say that the relaxation is {\em totally half-integral} if \hat f( %DIFDELCMD < \bx%%% x ) is a polyhedral function with half-integral extreme points %DIFDELCMD < \bx%%% , and this property is preserved after adding an arbitrary combination of constraints of the form x_i=x_j, x_i=1-x_j, and x_i=\gamma where \gamma\in\{0, 1, 1/2} is a constant.
Edit intent: clarity
Original:  We say that the relaxation is {\em totally half-integral} if \hat f( %DIFDELCMD < \bx%%%  ) is a polyhedral function with half-integral extreme points %DIFDELCMD < \bx%%%  , and this property is preserved after adding an arbitrary combination of constraints of the form x_i=x_j, x_i=1-x_j, and x_i=\gamma where \gamma\in\{0, 1, 1/2} is a constant.
Revised:  We say that the relaxation is {\em totally half-integral} if \hat f( %DIFDELCMD < \bx%%% ) is a polyhedral function with half-integral extreme points %DIFDELCMD < \bx%%% x , and this property is preserved after adding an arbitrary combination of constraints of the form x_i=x_j, x_i=1-x_j, and x_i=\gamma where \gamma\in\{0, 1, 1/2} is a constant.
Edit intent: clarity
Original: We generalize the class of split graphs to directed graphs and show these split digraphs can be identified from their degree sequences.
Revised: We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences.
Edit intent: clarity
Original:  Let A\RR^{n\times m} and B \in{\RR^{n \times p\RR be two matrices and \eps>0.
Revised:  Let A\RR^{n\times m} and B \in\RR be two matrices and \eps>0.
Edit intent: clarity
Original:  Let A\RR^{n\times m} and B \in{\RR^{n \times p\RR be two matrices and \eps>0.
Revised:  Let A\RR^{n\times m} and B \in{\RR^{n \times p\RR^{n \times p be two matrices and \eps>0.
Edit intent: fluency
Original:  We approximate the product A^\top B using two down-sampled sketches, A \in{\RR^{t\times m\RR and B \in{\RR^{t\times p\RR, where t\ll n } such that \tilde{A^\top B - A^\top B} \leq \eps AB with constant probability.
Revised:  We approximate the product A^\top B using two down-sampled sketches, A \in\RR and B \in{\RR^{t\times p\RR, where t\ll n } such that \tilde{A^\top B - A^\top B} \leq \eps AB with constant probability.
Edit intent: clarity
Original:  We approximate the product A^\top B using two down-sampled sketches, A \in{\RR^{t\times m\RR and B \in{\RR^{t\times p\RR, where t\ll n } such that \tilde{A^\top B - A^\top B} \leq \eps AB with constant probability.
Revised:  We approximate the product A^\top B using two down-sampled sketches, A \in{\RR^{t\times m\RR and B \in\RR, where t\ll n } such that \tilde{A^\top B - A^\top B} \leq \eps AB with constant probability.
Edit intent: clarity
Original:  We approximate the product A^\top B using two down-sampled sketches, A \in{\RR^{t\times m\RR and B \in{\RR^{t\times p\RR, where t\ll n } such that \tilde{A^\top B - A^\top B} \leq \eps AB with constant probability.
Revised:  We approximate the product A^\top B using two down-sampled sketches, A \in{\RR^{t\times m\RR and B \in{\RR^{t\times p\RR^{t\times p, where t\ll n } such that \tilde{A^\top B - A^\top B} \leq \eps AB with constant probability.
Edit intent: fluency
Original:  We approximate the product A^\top B using two down-sampled sketches, A \in{\RR^{t\times m\RR and B \in{\RR^{t\times p\RR, where t\ll n } such that \tilde{A^\top B - A^\top B} \leq \eps AB with constant probability.
Revised:  We approximate the product A^\top B using two down-sampled sketches, A \in{\RR^{t\times m\RR and B \in{\RR^{t\times p\RR, where t\ll n } such that \tilde{A^\top B - A^\top B} \leq \eps AB with high probability.
Edit intent: clarity
Original:  For achieving bounds that depend on rank we employ standard tools from high-dimensional geometry such as concentration of measure arguments combined with elaborate \eps-net arguments .
Revised:  For achieving bounds that depend on rank we employ standard tools from high-dimensional geometry such as concentration of measure arguments combined with elaborate \eps-net constructions .
Edit intent: clarity
Original:  To handle such bounds , we develop a novel matrix-valued Chernoff bound inequality which we call low rank matrix-valued Chernoff Bound .
Revised:  To handle such bounds , we develop a novel matrix-valued Chernoff bound inequality which we call low rank matrix-valued Chernoff bound .
Edit intent: fluency
Original:  Finally, we prove a comparison theorem for these obstacle problems when the generator is convex or concave on the z variable .
Revised:  Finally, we prove a comparison theorem for these obstacle problems when the generator is convex or concave in the z-variable .
Edit intent: clarity
Original: We present a Monte Carlo algorithm that allows efficient and unbiased sampling of polymer melts consisting of two chains of equal length that jointly visit all the sites of a cubic lattice  .
Revised: We present a Monte Carlo algorithm that provides efficient and unbiased sampling of polymer melts consisting of two chains of equal length that jointly visit all the sites of a cubic lattice .
Edit intent: clarity
Original:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case  d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound  .
Revised:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case n= d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound .
Edit intent: clarity
Original:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case  d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound  .
Revised:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case d + 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound .
Edit intent: clarity
Original:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case  d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound  .
Revised:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case d = n- 1. In this paper, we present optimal, explicit constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound .
Edit intent: clarity
Original:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case  d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound  .
Revised:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all n, k, d > = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound .
Edit intent: coherence
Original:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case  d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound  .
Revised:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = 2k-2 .
Edit intent: coherence
Original:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case  d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound  .
Revised:  Previous, explicit and general constructions of exact-regenerating codes have been confined to the case d = n- 1. In this paper, we present explicit, product-matrix constructions of MBR codes for all feasible values of [n, k, d] and MSR codes for all 2k - 2 <= d < = n - 1. In both instances, the (small) file size is as dictated by the cut-set bound , using a product-matrix framework .
Edit intent: clarity
Original:  Also contained in the paper , is a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies d = (n- 1 ) >= 2k - 1. 
Revised:  The paper also contains a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies d = (n- 1 ) >= 2k - 1. 
Edit intent: coherence
Original:  Also contained in the paper , is a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies d = (n- 1 ) >= 2k - 1. 
Revised:  Also contained in the paper , is a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies n = (n- 1 ) >= 2k - 1. 
Edit intent: fluency
Original:  Also contained in the paper , is a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies d = (n- 1 ) >= 2k - 1. 
Revised:  Also contained in the paper , is a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies d = (n- 1 ) >= 2k-1 
Edit intent: fluency
Original:  Also contained in the paper , is a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies d = (n- 1 ) >= 2k - 1. 
Revised:  Also contained in the paper , is a simpler description, in the product-matrix framework, of a previously constructed MSR code in which the parameter d satisfies d = (n- 1 ) >= 2k - 1. .
Edit intent: fluency
Original: We use Fourier Analysis and related techniques to investigate the question of periodicities in fossil biodiversity.
Revised: We use Fourier analysis and related techniques to investigate the question of periodicities in fossil biodiversity.
Edit intent: fluency
Original:  Joint time series analysis of various reductions of the Sepkoski Data, Paleobiology Database, and Fossil Record 2 indicate the same periodicity in biodiversity of marine animals at 62 Myr.
Revised:  Joint time-series analysis of various reductions of the Sepkoski Data, Paleobiology Database, and Fossil Record 2 indicate the same periodicity in biodiversity of marine animals at 62 Myr.
Edit intent: fluency
Original:  The existence of a 62 Myr periodicity despite very different treatment of systematic error, particularly sampling-strength biases, in all three major databases strongly argues for its reality in the fossil record.
Revised:  The existence of a 62-Myr periodicity despite very different treatment of systematic error, particularly sampling-strength biases, in all three major databases strongly argues for its reality in the fossil record.
Edit intent: fluency
Original:  We show that many pricing and hedging problems concerning structured products, participating products or variable annuities can be handled by this equations.
Edit intent: coherence
Original:  Time-delayed BSDEs may appear when we want to find a strategy and a portfolio which should replicate the liability whose pay-off depends on the applied investment strategy or the  values of the portfolio.
Revised:  Time-delayed BSDEs may arise when we want to find a strategy and a portfolio which should replicate the liability whose pay-off depends on the applied investment strategy or the values of the portfolio.
Edit intent: fluency
Original:  Time-delayed BSDEs may appear when we want to find a strategy and a portfolio which should replicate the liability whose pay-off depends on the applied investment strategy or the  values of the portfolio.
Revised:  Time-delayed BSDEs may appear when we want to find a strategy and a portfolio which should replicate the liability whose pay-off depends on the applied investment strategy or the past values of the portfolio.
Edit intent: clarity
Original:   This is usually the case for investment funds or life insurance investment contracts which have bonus distribution mechanisms or provide protection against low returns .
Revised:  This is usually the case for capital protected funds and performance linked pay-offs .
Edit intent: clarity
Original:  We investigate perfect hedging and quadratic hedging which is crucial for insurance applications .
Revised:  Perfect hedging and quadratic hedging which is crucial for insurance applications .
Edit intent: coherence
Original:  We investigate perfect hedging and quadratic hedging which is crucial for insurance applications .
Revised:  We investigate perfect hedging and quadratic hedging are investigated .
Edit intent: clarity
Original:  Time-delayed BSDEs may arise  when we want to find a strategy and a portfolio which should replicate the liability whose pay-off depends on the applied investment strategy or the past values of the portfolio.
Revised:  Time-delayed BSDEs may arise when we want to find a strategy and a portfolio which should replicate a liability or meet a target depending on the applied investment strategy or the past values of the portfolio.
Edit intent: clarity
Original:  Time-delayed BSDEs may arise  when we want to find a strategy and a portfolio which should replicate the liability whose pay-off depends on the applied investment strategy or the past values of the portfolio.
Revised:  Time-delayed BSDEs may arise when we want to find a strategy and a portfolio which should replicate the liability whose pay-off depends on the applied strategy or the past values of the portfolio.
Edit intent: clarity
Original:  In our setting, an investment portfolio serves simultaneously as the underlying security on which the liability  is contingent and as a hedge portfolio for the liability .
Revised:  In this setting, a managed investment portfolio serves simultaneously as the underlying security on which the liability is contingent and as a hedge portfolio for the liability .
Edit intent: clarity
Original:  This is usually the case for capital protected funds and performance linked pay-offs.
Revised:  This is usually the case for capital-protected investments and performance-linked pay-offs.
Edit intent: clarity
Original:  We study consequences and give an economic interpretation of the  fact that a time-delay BSDE may not have a solution or may have multiple solutions.
Revised:  We study consequences and give an economic interpretation of the fact that a time-delayed BSDE may not have a solution or may have multiple solutions.
Edit intent: fluency
Original: Functional dependencies - traditional, approximate and conditional are of critical importance in relational databases, as they inform us about the relationships between attributes.
Revised: Functional dependencies -- traditional, approximate and conditional are of critical importance in relational databases, as they inform us about the relationships between attributes.
Edit intent: fluency
Original:  In this paper , we define the logical extensions of various forms of functional dependencies for probabilistic databases .
Revised:  This paper defines the logical extensions of various forms of functional dependencies for probabilistic databases .
Edit intent: clarity
Original:  We believe that having these dependencies and algorithms available for probabilistic databases will further drive adoption of probabilistic data storage in the industry.
Revised:  We believe that having these dependencies and algorithms available for probabilistic databases will drive adoption of probabilistic data storage in the industry.
Edit intent: clarity
Original:  They support sequential and parallel languages without the space/time overheads associated with the Turing Machine and l-calculus , enabling massive programs to be simulated.
Revised:  They support sequential and parallel languages without the space/time overheads associated with the Turing Machine and lambda-calculus , enabling massive programs to be simulated.
Edit intent: fluency
Original:  The numerical results obtained by the new algorithm are compared with the already published QNM frequencies  .
Revised:  The numerical results obtained by our method are compared with the already published QNM frequencies .
Edit intent: clarity
Original: Central Force Optimization is a global search and optimization algorithm that searches a decision space be flying "probes" whose trajectories are deterministically computed using two equations of motion.
Revised: Central Force Optimization is a global search and optimization algorithm that searches a decision space by flying "probes" whose trajectories are deterministically computed using two equations of motion.
Edit intent: fluency
Original:  We introduce and study the list-coloring (or choice) version of this notion.
Revised:  We study the list-coloring (or choice) version of this notion.
Edit intent: coherence
Original:   List coloring arises naturally in the context of wireless networks  .
Revised:  In this version, each vertex is associated with a set of (admissible) colors and it is allowed to be colored only with colors from its set. List coloring arises naturally in the context of wireless networks .
Edit intent: coherence
Original: A graph G with a list of colors L(v) and weight \omega(v) for each vertex v is (L,\omega) -choosable if one can choose a subset of \omega(v) colors from L(v) for each vertex v, such that adjacent vertices receive disjoint color sets.
Revised: A graph G with a list of colors L(v) and weight \omega(v) for each vertex v is (L,\omega) -colorable if one can choose a subset of \omega(v) colors from L(v) for each vertex v, such that adjacent vertices receive disjoint color sets.
Edit intent: clarity
Original:  In this paper, we give a necessary and sufficient condition for a weighted path to be (L,\omega) -choosable for some lists L. Furthermore, we solve the problem of the free-choosability of a cycle.
Revised:  In this paper, we give necessary and sufficient condition for a weighted path to be (L,\omega) -choosable for some lists L. Furthermore, we solve the problem of the free-choosability of a cycle.
Edit intent: fluency
Original:  In this paper, we give a necessary and sufficient condition for a weighted path to be (L,\omega) -choosable for some lists L. Furthermore, we solve the problem of the free-choosability of a cycle.
Revised:  In this paper, we give a necessary and sufficient conditions for a weighted path to be (L,\omega) -choosable for some lists L. Furthermore, we solve the problem of the free-choosability of a cycle.
Edit intent: fluency
Original:  In this paper, we give a necessary and sufficient condition for a weighted path to be (L,\omega) -choosable for some lists L. Furthermore, we solve the problem of the free-choosability of a cycle.
Revised:  In this paper, we give a necessary and sufficient condition for a weighted path to be (L,\omega) -colorable for some list assignments L. Furthermore, we solve the problem of the free-choosability of a cycle.
Edit intent: clarity