wanyu/IteraTeR_v2 huggingface dataset:
Original:  the ultimate goal of mining D is not an analysis of the dataset per se , but the understanding of the underlying process that generated \mathcal{D . Specifically, in many applications D is a collection of samples obtained from an unknown probability distribution \pi on transactions, and by extracting the FIs in the dataset D one attempts to infer itemsets that are frequently  generated by \pi, which we call the True Frequent Itemsets (TFIs).
Revised:  the ultimate goal of mining D is not an analysis of the dataset per se , but the understanding of the underlying process that generated it . Specifically, in many applications D is a collection of samples obtained from an unknown probability distribution \pi on transactions, and by extracting the FIs in the dataset D one attempts to infer itemsets that are frequently generated by \pi, which we call the True Frequent Itemsets (TFIs).
Edit intent: clarity
Original:  the ultimate goal of mining D is not an analysis of the dataset per se , but the understanding of the underlying process that generated \mathcal{D . Specifically, in many applications D is a collection of samples obtained from an unknown probability distribution \pi on transactions, and by extracting the FIs in the dataset D one attempts to infer itemsets that are frequently  generated by \pi, which we call the True Frequent Itemsets (TFIs).
Revised:  the ultimate goal of mining D is not an analysis of the dataset per se , but the understanding of the underlying process that generated \mathcal{D . Specifically, in many applications D is a collection of samples obtained from an unknown probability distribution \pi on transactions, and by extracting the FIs in D one attempts to infer itemsets that are frequently generated by \pi, which we call the True Frequent Itemsets (TFIs).
Edit intent: fluency
Original:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets \emph{ , i.e.,  itemsets that are not among the TFIs.
Revised:  Due to the inherently stochastic nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets \emph{ , i.e., itemsets that are not among the TFIs.
Edit intent: clarity
Original:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets \emph{ , i.e.,  itemsets that are not among the TFIs.
Revised:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation of the set of TFIs, as it often contains a huge number of spurious itemsets \emph{ , i.e., itemsets that are not among the TFIs.
Edit intent: fluency
Original:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets \emph{ , i.e.,  itemsets that are not among the TFIs.
Revised:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of \emph{ , i.e., itemsets that are not among the TFIs.
Edit intent: clarity
Original:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets \emph{ , i.e.,  itemsets that are not among the TFIs.
Revised:  Due to the inherently random nature of the generative process, the set of FIs is only a rough approximation to the set of TFIs, as it often contains a huge number of spurious itemsets \emph{ , i.e., spurious itemsets that are not among the TFIs.
Edit intent: fluency
Original:  In this work we present two methods to identify a \hat{\theta}  collection of itemsets that\hat{\theta}  contains only TFIs with probability at least 1 - \delta(i.e., the methods have Family-Wise Error Rate bounded by \delta), for some user-specified \delta , without imposing any restriction on \pi.
Revised:  In this work we present two methods to identify a \hat{\theta} such that the collection of itemsets that\hat{\theta} contains only TFIs with probability at least 1 - \delta(i.e., the methods have Family-Wise Error Rate bounded by \delta), for some user-specified \delta , without imposing any restriction on \pi.
Edit intent: clarity
Original:  In this work we present two methods to identify a \hat{\theta}  collection of itemsets that\hat{\theta}  contains only TFIs with probability at least 1 - \delta(i.e., the methods have Family-Wise Error Rate bounded by \delta), for some user-specified \delta , without imposing any restriction on \pi.
Revised:  In this work we present two methods to identify a \hat{\theta} collection of itemsets that\hat{\theta} contains only TFIs with probability at least 1-\delta, for some user-specified \delta , without imposing any restriction on \pi.
Edit intent: coherence
Original:  In the experimental evaluation we compare our methods to established techniques (Bonferroni correction, holdout) and show that they return a very large subset of the TFIs, achieving a very high statistical power, while controlling the Family-Wise Error Rate .
Revised:  In the experimental evaluation we compare our methods to established techniques (Bonferroni correction, holdout) and show that our algorithm outperforms these methods and achieves even better results than what is guaranteed by the theoretical analysis .
Edit intent: clarity
Original:  Many important stochastic counting models can be written as general birth-death processes (BDPs) , which are continuous-time Markov chains on the non-negative integers in which only jumps to adjacent states are allowed, and there are no jumps down from zero.
Revised:  Many important stochastic counting models can be written as general birth-death processes (BDPs) . BDPs are continuous-time Markov chains on the non-negative integers in which only jumps to adjacent states are allowed, and there are no jumps down from zero.
Edit intent: fluency
Original:  Presented programs are based on Blitz++ (C++), NumPy (Python), and Fortran's built-in array containers.
Revised:  The presented programs are based on Blitz++ (C++), NumPy (Python), and Fortran's built-in array containers.
Edit intent: fluency
Original:  The introduced codes serve as a basis for discussion on the tradeoffs of the programming language choice  .
Revised:  A discussion on the tradeoffs of the programming language choice .
Edit intent: clarity
Original:  In  case of Python, a significant performance gain is observed when switching from the standard interpreter (CPython) to the PyPy implementation of Python.
Revised:  In the case of Python, a significant performance gain is observed when switching from the standard interpreter (CPython) to the PyPy implementation of Python.
Edit intent: fluency
Original: IFS Fractals - the attractors of Iterated Function Systems in Euclidean space - have motivated plenty of investigation to date,  due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas.
Revised: IFS fractals - the attractors of Iterated Function Systems in Euclidean space - have motivated plenty of investigation to date, due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas.
Edit intent: fluency
Original: IFS Fractals - the attractors of Iterated Function Systems in Euclidean space - have motivated plenty of investigation to date,  due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas.
Revised: IFS Fractals - the attractors of Iterated Function Systems - have motivated plenty of investigation to date, due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas.
Edit intent: coherence
Original: IFS Fractals - the attractors of Iterated Function Systems in Euclidean space - have motivated plenty of investigation to date,  due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas.
Revised: IFS Fractals - the attractors of Iterated Function Systems in Euclidean space - have motivated plenty of research to date, due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas.
Edit intent: clarity
Original: IFS Fractals - the attractors of Iterated Function Systems in Euclidean space - have motivated plenty of investigation to date,  due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas.
Revised: IFS Fractals - the attractors of Iterated Function Systems in Euclidean space - have motivated plenty of investigation to date, partly due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas.
Edit intent: coherence
Original:  The statement and resolution of the Fractal-Line Intersection Problem is imperative for a more efficient treatment of  applications.
Revised:  The statement and resolution of the Fractal-Line Intersection Problem is imperative for a more efficient treatment of certain applications.
Edit intent: clarity
Original:  We provide a verifiable condition guaranteeing intersection with any line passing through the convex hull of an IFS fractal , shownin%DIFDELCMD < \R%%%  ^d for hyperplanes.
Revised:  We provide a verifiable condition guaranteeing intersection with any line passing through the convex hull of %DIFDELCMD < \R%%% ^d for hyperplanes.
Edit intent: clarity
Original:  We give several numerical conditionsthat guarantee an infinite number of approximate intersections  if there is at least one.
Revised:  Under certain conditions, an infinite number of approximate intersections if there is at least one.
Edit intent: clarity
Original:  We give several numerical conditionsthat guarantee an infinite number of approximate intersections  if there is at least one.
Revised:  We give several numerical conditionsthat guarantee an infinite number of approximate intersections are guaranteed, if there is at least one.
Edit intent: clarity
Original:  In our effort to quantify the intersection , we provide an explicit formula for the well-known invariant measure of IFS.
Revised:  Quantification of the intersection is done via an explicit formula for the well-known invariant measure of IFS.
Edit intent: clarity
Original:  In our effort to quantify the intersection , we provide an explicit formula for the well-known invariant measure of IFS.
Revised:  In our effort to quantify the intersection , we provide an explicit formula for the invariant measure of IFS.
Edit intent: clarity
Original:  The aim of this paper is to investigate theoretically how SAT can be utilized for the efficient solution of problems that are harder than NP or co-NP.
Revised:  The aim of this paper is to investigate theoretically how Sat can be utilized for the efficient solution of problems that are harder than NP or co-NP.
Edit intent: fluency
Original:  We cannot transform these two reasoning problems to SAT in polynomial time, unless the Polynomial Hierarchy collapses.
Revised:  One cannot transform these two reasoning problems to SAT in polynomial time, unless the Polynomial Hierarchy collapses.
Edit intent: fluency
Original:  We cannot transform these two reasoning problems to SAT in polynomial time, unless the Polynomial Hierarchy collapses.
Revised:  We cannot transform these two reasoning problems into SAT in polynomial time, unless the Polynomial Hierarchy collapses.
Edit intent: fluency
Original:  Our basic numerical entity has three elements , then, for a given vector function f: R->Rm}\to  , its dual version will have the form f: R3 -> R3m^3}\to  .
Revised:  Our basic numerical entity has three elements . Then, for a given vector function f: R->Rm}\to , its dual version will have the form f: R3 -> R3m^3}\to .
Edit intent: fluency
Original: We contribute to the program of proving lower bounds on the size of branching programs solving the Tree Evaluation Problem introduced by Cook et  al. ( 2011 ).
Revised: We contribute to the program of proving lower bounds on the size of branching programs solving the Tree Evaluation Problem introduced by Cook et . al. ( 2011 ).
Edit intent: fluency
Original:  Proving an exponential lower bound for the size of the non-deterministic thrifty branching programs  would separate NL from P under the thrifty hypothesis.
Revised:  Proving an exponential lower bound for the size of nondeterministic thrifty branching programs would separate NL from P under the thrifty hypothesis.
Edit intent: clarity
Original:  Our lower bounds are also tight (up to a factor of k), since the known(Cook et al. , 2011 ) non-deterministic thrifty branching programs for this problem of size O(k^{h/2+1 . We prove our results by associating a fractional  pebbling strategy with any bitwise-independent non-deterministic thrifty branching program solving the Tree Evaluation Problem.
Revised:  Our lower bounds are also tight (up to a factor of k), since the known(Cook et al. , 2011 ) . We prove our results by associating a fractional pebbling strategy with any bitwise-independent non-deterministic thrifty branching program solving the Tree Evaluation Problem.
Edit intent: coherence
Original:  Our main technique is the entropy method introduced by Jukna and Zak } (2001) originally in the context of proving lower bounds for read-once branching programs.
Revised:  Our main technique is the entropy method introduced by Jukna and Z } (2001) originally in the context of proving lower bounds for read-once branching programs.
Edit intent: fluency
Original: We study the properties of adaptive walk performed by a maladapted asexual population in which beneficial mutations fix sequentially until a local fitness peak is reached.
Revised: We study the adaptation dynamics of a maladapted asexual population in which beneficial mutations fix sequentially until a local fitness peak is reached.
Edit intent: clarity
Original:  Interestingly, the fitness difference between successive steps shows a pattern of diminishing returns for bounded distributions and accelerating returns for fat-tailed distributions } . These trends are found to be robust with respect to fitness correlations  .
Revised:  Interestingly, the fitness difference between successive steps follows a pattern of diminishing returns for bounded distributions and accelerating returns for fat-tailed distributions } . These trends are found to be robust with respect to fitness correlations .
Edit intent: clarity
Original:  We capture the effects of mechanical tension F applied on the template DNA within the framework of a stochastic kinetic model of DNA replication .
Revised:  We develop a stochastic kinetic model of DNA replication .
Edit intent: clarity
Original:   Using the methods of first-passage times for same model , we also derive the exact analytical expressions for the probability distributions of nine distinct conditional dwell times of a DNAP .
Revised:  Using the methods of first-passage times , we also derive the exact analytical expressions for the probability distributions of nine distinct conditional dwell times of a DNAP .
Edit intent: clarity
Original:   Using the methods of first-passage times for same model , we also derive the exact analytical expressions for the probability distributions of nine distinct conditional dwell times of a DNAP .
Revised:  Using the methods of first-passage times for same model , we also derive the exact analytical expressions for the probability distributions of these conditional dwell times of a DNAP .
Edit intent: clarity
Original:   Using the methods of first-passage times for same model , we also derive the exact analytical expressions for the probability distributions of nine distinct conditional dwell times of a DNAP .
Revised:  Using the methods of first-passage times for same model , we also derive the exact analytical expressions for the probability distributions of nine distinct conditional dwell times .
Edit intent: clarity
Original:  But, whenever it commits an error by misincorporting an incorrect nucleotide, it can switch to an exonuclease mode.
Revised:  But, whenever it commits an error by misincorporating an incorrect nucleotide, it can switch to an exonuclease mode.
Edit intent: fluency
Original:  We further show that correlations decaying exponentially with  Hamming distance yield exponentially decaying spectra similar to those reported recently for a model of molecular signal transduction.
Revised:  We further show that correlations decaying exponentially with the Hamming distance yield exponentially decaying spectra similar to those reported recently for a model of molecular signal transduction.
Edit intent: fluency
Original: We present a block minimum residual (MINRES) algorithm for symmetric indefinite matrices based on an alternate methodfor constructing the block Lanczos vectors.
Revised: We develop a block minimum residual (MINRES) algorithm for symmetric indefinite matrices based on an alternate methodfor constructing the block Lanczos vectors.
Edit intent: clarity
Original:  We also present some experiments to show how the relationship between right-hand sides affects the performance of this method.
Revised:  We also present some experiments to show how the relationship between right-hand sides can affect the performance of this method.
Edit intent: clarity
Original:  This version is built upon the banded Lanczos method , which generates one basis vector of the block Krylov subspace per iteration rather than a whole block , as in the block Lanczos process.
Revised:  This version is built upon the band Lanczos method that generates one basis vector of the block Krylov subspace per iteration rather than a whole block , as in the block Lanczos process.
Edit intent: clarity
Original:  This version is built upon the banded Lanczos method , which generates one basis vector of the block Krylov subspace per iteration rather than a whole block , as in the block Lanczos process.
Revised:  This version is built upon the banded Lanczos method , which generates one basis vector of the block Krylov subspace per iteration rather than a whole block as in the block Lanczos process.
Edit intent: fluency
Original:  With the banded Lanczos method , one can detect breakdown from scalar values arising in the computation, allowing for a handling of breakdown which is straightforward to implement.
Revised:  The benefit of using the band Lanczos method is that one can detect breakdown from scalar values arising in the computation, allowing for a handling of breakdown which is straightforward to implement.
Edit intent: coherence
Original:  With the banded Lanczos method , one can detect breakdown from scalar values arising in the computation, allowing for a handling of breakdown which is straightforward to implement.
Revised:  With the banded Lanczos method , one can detect breakdowns from scalar values arising in the computation, allowing for a handling of breakdown which is straightforward to implement.
Edit intent: fluency
Original:  In this paper, we derive a progressive formulation of the MINRES method based on the banded Lanczos process and give some implementation details.
Revised:  We derive a progressive formulation of the MINRES method based on the banded Lanczos process and give some implementation details.
Edit intent: clarity
Original:  In this paper, we derive a progressive formulation of the MINRES method based on the banded Lanczos process and give some implementation details.
Revised:  In this paper, we derive a progressive formulation of the MINRES method based on the band Lanczos process and give some implementation details.
Edit intent: fluency
Original:  Specifically, a simple reordering of the steps allows us to perform many of the operations at the block level , in order take advantage of communication efficiencies offered by the block Lanczos process.
Revised:  Specifically, a simple reordering of the steps allows us to perform many of the operations at the block level in order to take advantage of communication efficiencies offered by the block Lanczos process.
Edit intent: fluency
Original:  This is an important concern in the context of next generation super computing applications.
Revised:  This is an important concern in the context of next-generation super computing applications.
Edit intent: fluency
Original:  We also present some experiments to show how the relationship between right-hand sides can affect the performance of this method.
Revised:  We present experiments that show how the relationship between right-hand sides can affect the performance of this method.
Edit intent: clarity
Original:  We also present some experiments to show how the relationship between right-hand sides can affect the performance of this method.
Revised:  We also present some experiments to show how the relationship between right-hand sides can effect the performance of this method.
Edit intent: fluency
Original:  We also present some experiments to show how the relationship between right-hand sides can affect the performance of this method.
Revised:  We also present some experiments to show how the relationship between right-hand sides can affect the performance of the method.
Edit intent: clarity
Original:  Yannakakis provided a quasi-polynomial CS-separator, i.e. of size O(n^log n), and address the problem of finding a polynomial CS-separator.
Revised:  Yannakakis provided a quasi-polynomial CS-separator, i.e. of size O(n^log n), and addresses the problem of finding a polynomial CS-separator.
Edit intent: fluency
Original:  This question is still open for general graphs (for which a negative answer is likely) and for perfect graphs.
Revised:  This question is still open even for perfect graphs.
Edit intent: coherence
Original:  The natural class of hard instances coming to mind for CL-IS is random graphs.
Edit intent: coherence
Original:  One of the main reason why  CL-IS  is fascinating is that it admits equivalent formulations.
Revised:  One of the main reason why CL-IS problem is fascinating is that it admits equivalent formulations.
Edit intent: clarity
Original:  A lower bound of O(k^6/5) was provided by Huang and Sudakov for this problem.
Edit intent: coherence
Original:  We also show that the classical approach to the stubborn problem (arising in CSP) which leads to a quasi-polynomial time algorithm by covering the set of all solutions by O(n^log n) instances of 2-SAT is again equivalent to the existence of a polynomial CS-separator.
Revised:  We also show that the classical approach to the stubborn problem (arising in CSP) which consists in covering the set of all solutions by O(n^log n) instances of 2-SAT is again equivalent to the existence of a polynomial CS-separator.
Edit intent: clarity
Original:  We also provide a O(n ^c_k ) CS-separator on the class of graphs without induced path of length k and its complement.
Revised:  We also provide a O(n ^{c_k ) CS-separator on the class of graphs without induced path of length k and its complement.
Edit intent: fluency
Original:  We also show that the classical approach to the stubborn problem (arising in CSP) which consists in covering the set of all solutions by O(n ^log n ) instances of 2-SAT is again equivalent to the existence of a polynomial CS-separator.
Revised:  We also show that the classical approach to the stubborn problem (arising in CSP) which consists in covering the set of all solutions by O(n ^{\log n ) instances of 2-SAT is again equivalent to the existence of a polynomial CS-separator.
Edit intent: fluency