wanyu/IteraTeR_v2 huggingface dataset:
Original:  This dissemination, however, may expose sensitive patterns that model confidential knowledge (e. g., trips to mental health clinics from a string representing a user's location history).
Revised:  This dissemination, however, may expose sensitive patterns that model confidential knowledge .
Edit intent: clarity
Original:  First, we propose a time-optimal algorithm, TFS-ALGO, to construct the shortest string preserving the order of appearance and the frequency of all non-sensitive patterns.
Revised:  First, we propose a time-optimal algorithm, TFS-ALGO, to construct the shortest string preserving the order of appearance and frequency of all non-sensitive patterns.
Edit intent: fluency
Original:  Second , we propose a time-optimal algorithm,  PFS-ALGO, which preserves a partial order of appearance of non-sensitive patterns but produces a much shorter string that can be analyzed more efficiently.
Revised:  To construct such a string , we propose a time-optimal algorithm, PFS-ALGO, which preserves a partial order of appearance of non-sensitive patterns but produces a much shorter string that can be analyzed more efficiently.
Edit intent: clarity
Original:  In response, we propose a heuristic, MCSR-ALGO, which replaces letters in these strings with carefully selected letters, so that sensitive patterns are not reinstated  and occurrences of spurious patterns are prevented.
Revised:  In response, we propose a heuristic, MCSR-ALGO, which replaces letters in the strings output by the algorithms with carefully selected letters, so that sensitive patterns are not reinstated and occurrences of spurious patterns are prevented.
Edit intent: clarity
Original: In the following we discuss the history and  evolution of encodings .
Revised: In the following we discuss the history and evolution of the encoding schemes .
Edit intent: clarity
Original: Golumbic, Lipshteyn  and Stern defined in 2009 the class of EPG graphs, as the intersection graph  of edge paths on a grid.
Revised: Golumbic, Lipshteyn , and Stern defined in 2009 the class of EPG graphs, as the intersection graph of edge paths on a grid.
Edit intent: fluency
Original: Golumbic, Lipshteyn  and Stern defined in 2009 the class of EPG graphs, as the intersection graph  of edge paths on a grid.
Revised: Golumbic, Lipshteyn and Stern defined in 2009 the class of EPG graphs, the intersection graph of edge paths on a grid.
Edit intent: coherence
Original:  If the paths in the representation have at most k changes of direction (bends) , we say that it is a B_k-EPG representation.
Revised:  If the paths in the representation have at most k bends , we say that it is a B_k-EPG representation.
Edit intent: clarity
Original:  In this paper  we show that  the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial  of |V(G)|.
Revised:  In this paper , we show that the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial of |V(G)|.
Edit intent: fluency
Original:  In this paper  we show that  the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial  of |V(G)|.
Revised:  In this paper we show that the problem of recognizing B_k-EPG representation whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial of |V(G)|.
Edit intent: clarity
Original:  In this paper  we show that  the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial  of |V(G)|.
Revised:  In this paper we show that the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial of |V(G)|.
Edit intent: clarity
Original:  In this paper  we show that  the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial  of |V(G)|.
Revised:  In this paper we show that the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k -EPG representation , is in \mathcal{NP , for every k bounded by a polynomial of |V(G)|.
Edit intent: clarity
Original:  In this paper  we show that  the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial  of |V(G)|.
Revised:  In this paper we show that the problem of recognizing B_k-EPG graphs G=(V,E) whose edge-intersections of paths in a grid satisfy the Helly property, so-called Helly-B_k EPG graphs , is in \mathcal{NP , for every k bounded by a polynomial function of |V(G)|.
Edit intent: clarity
Original:  In addition , we show that  recognizing Helly-B_1 EPG graphs is NP-complete, and it remains NP-complete even when restricted to 2-apex and 3-degenerate graphs.
Revised:  Moreover , we show that recognizing Helly-B_1 EPG graphs is NP-complete, and it remains NP-complete even when restricted to 2-apex and 3-degenerate graphs.
Edit intent: coherence
Original:  In addition , we show that  recognizing Helly-B_1 EPG graphs is NP-complete, and it remains NP-complete even when restricted to 2-apex and 3-degenerate graphs.
Revised:  In addition , we show that the problem of recognizing Helly-B_1 EPG graphs is NP-complete, and it remains NP-complete even when restricted to 2-apex and 3-degenerate graphs.
Edit intent: clarity
Original:  Here, we show that local spatial patterns of cell growth within tissue spheroids  are strongly influenced by cell-cell adhesion.
Revised:  Here, we show that local spatial patterns of cell growth within tissue spheroids , are strongly influenced by cell-cell adhesion.
Edit intent: fluency
Original:  In this article , we provide an explicit formula to the problem of computing correlators, that is, computing the expected value of moments of the process at different time points along its path.
Revised:  In this article , we provide a formula for computing correlators, that is, computing the expected value of moments of the process at different time points along its path.
Edit intent: clarity
Original:  In this article , we provide an explicit formula to the problem of computing correlators, that is, computing the expected value of moments of the process at different time points along its path.
Revised:  In this article , we provide an explicit formula to the problem of computing correlators, namely, cross-moments of the process at different time points along its path.
Edit intent: clarity
Original:  The strength of our formula is that it only involves linear combinations of the exponential of the  generator matrix, as in the one-dimensional case.
Revised:  The formula involves only linear combinations of the exponential of the generator matrix, as in the one-dimensional case.
Edit intent: coherence
Original:  The strength of our formula is that it only involves linear combinations of the exponential of the  generator matrix, as in the one-dimensional case.
Revised:  The strength of our formula is that it only involves linear combinations of the exponential of the so-called generator matrix, as in the one-dimensional case.
Edit intent: clarity
Original: In the setting of polynomial jump-diffusion dynamics, we provide a formula for computing correlators, namely, cross-moments of the process at different time points along its path.
Revised: In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path.
Edit intent: clarity
Original:  The formula involves only linear combinations of the exponential of the so-called generator matrix, extending the well-known moment formula for polynomial processes.
Revised:  The formula appears as a linear combination of exponentials of the generator matrix, extending the well-known moment formula for polynomial processes.
Edit intent: clarity
Original:  The developed framework allows to replace costly simulations with more accurate estimates, and it may be used for increasing the accuracy in financial pricing, such as for path-dependent options or in a stochastic volatility models context  .
Revised:  The developed framework can, for example, be applied in financial pricing, such as for path-dependent options or in a stochastic volatility models context .
Edit intent: clarity
Original: Recommender systems are a critical tool to match listings and travelers in two-sided vacation rental marketplaces.
Revised: Recommender systems are critical tools to match listings and travelers in two-sided vacation rental marketplaces.
Edit intent: fluency
Original:  This approach is computationally efficient and scalable, and allows us to capture non-linear dependencies.
Revised:  Deployed in the production environment, this approach is computationally efficient and scalable, and allows us to capture non-linear dependencies.
Edit intent: clarity
Original:  Our offline evaluation indicates that traveler embeddings created using a Deep Average Network can improve the precision of a downstream conversion prediction model by seven percent, outperforming more complex benchmark methods for  shopping experience personalization.
Revised:  Our offline evaluation indicates that traveler embeddings created using a Deep Average Network can improve the precision of a downstream conversion prediction model by seven percent, outperforming more complex benchmark methods for online shopping experience personalization.
Edit intent: clarity
Original:  We then use this result to study metric features of plane curves, including the medial axis, curvature, evolute, bottlenecks, and reach.
Revised:  We use this result to study metric features of plane curves, including the medial axis, curvature, evolute, bottlenecks, and reach.
Edit intent: coherence
Original:  We then show how to identify the desired metric feature from Voronoi or Delaunay cells, and therefore how to approximate it by a finite point sample from the variety.
Revised:  We show how to identify the desired metric feature from Voronoi or Delaunay cells, and therefore how to approximate it by a finite point sample from the variety.
Edit intent: coherence
Original:  Among the existing approaches based on nonlinear histogram transformations, contrast limited adaptive histogram equalization (CLAHE) is a popular choice when dealing with 2D images obtained in natural and scientific settings.
Revised:  Among the existing approaches based on nonlinear histogram transformations, contrast limited adaptive histogram equalization (CLAHE) is a popular choice for dealing with 2D images obtained in natural and scientific settings.
Edit intent: fluency
Original:  We show both qualitatively and quantitatively that using our multidimensional extension of CLAHE (MCLAHE) acting simultaneously on all dimensions of the datasets allows better visualization and discernment of multidimensional image features, as demonstrated using cases from 4D photoemission spectroscopy and fluorescence microscopy.
Revised:  We show both qualitatively and quantitatively that using our multidimensional extension of CLAHE (MCLAHE) simultaneously on all dimensions of the datasets allows better visualization and discernment of multidimensional image features, as demonstrated using cases from 4D photoemission spectroscopy and fluorescence microscopy.
Edit intent: clarity
Original:  The greedy algorithm's O(\log n) approximation ratio is the best known, but the largest approximation ratio known to be NP-hard is 4-\varepsilon.
Revised:  The greedy algorithm's O(\log n) approximation ratio was the best known, but the largest approximation ratio known to be NP-hard is 4-\varepsilon.
Edit intent: fluency
Original:  As a corollary, this resolves a conjecture of Kosaraju, Przytycka, and Borgstrom.
Revised:  As a corollary, we resolve a conjecture of Kosaraju, Przytycka, and Borgstrom.
Edit intent: coherence
Original:  Our results also hold for instances of Decision Tree whose weights are not too far from uniform.
Edit intent: coherence
Original:  Leveraging this result,  we exhibit a subexponential algorithm that yields an O(1/\alpha) approximation{\alpha} approximation algorithm } to Uniform Decision Tree in time 2^{ \tilde O(n^\alpha)}.
Revised:  Leveraging this result, we exhibit a subexponential algorithm that yields an O(1/\alpha) approximation{\alpha} approximation algorithm } to Uniform Decision Tree running in subexponential time 2^{ \tilde O(n^\alpha)}.
Edit intent: clarity
Original:  This work therefore adds approximating Uniform Decision Tree to a small list of natural problems that have subexponential  algorithms but no known polynomial time algorithms.
Revised:  This work therefore adds approximating Uniform Decision Tree to a small list of natural problems that have subexponential time algorithms but no known polynomial time algorithms.
Edit intent: fluency
Original:  Like the greedy algorithm, our subexponential algorithm gives similar guarantees even for slightly nonuniform weights .
Revised:  All our results hold for Decision Tree with weights not too far from uniform. A key technical contribution of our work is showing a connection between greedy algorithms for Uniform Decision Tree and for Min Sum Set Cover .
Edit intent: coherence
Original: A d-dimensional polycube is a facet-connected set of cells (cubes) on the d-dimensional cubical lattice ~ Z^d.
Revised: A d-dimensional polycube is a facet-connected set of cells (cubes) on the d-dimensional cubical lattice Z^d.
Edit intent: fluency
Original:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and ~ \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Revised:  Let A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and ~ \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Edit intent: fluency
Original:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and ~ \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Revised:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with n cubes, and ~ \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Edit intent: fluency
Original:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and ~ \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Revised:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Edit intent: fluency
Original:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and ~ \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Revised:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and ~ \lambda_d denote the limit of the ratio A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Edit intent: fluency
Original:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and ~ \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as ~ n \to \infty.
Revised:  Let ~ A_d(n) denote the number of d-dimensional polycubes (distinct up to translations) with ~ n cubes, and ~ \lambda_d denote the limit of the ratio ~ A_d(n{+}1)/A_d(n) as n \to \infty.
Edit intent: fluency
Original:  The exact value of ~ \lambda_d is still unknown rigorously for any dimension ~ d \geq 2;
Revised:  The exact value of \lambda_d is still unknown rigorously for any dimension ~ d \geq 2;
Edit intent: fluency
Original:  The exact value of ~ \lambda_d is still unknown rigorously for any dimension ~ d \geq 2;
Revised:  The exact value of ~ \lambda_d is still unknown rigorously for any dimension d \geq 2;
Edit intent: fluency
Original:  the asymptotics of ~ \lambda_d, as ~ d \to \infty, also remained elusive as of today.
Revised:  the asymptotics of \lambda_d, as ~ d \to \infty, also remained elusive as of today.
Edit intent: fluency
Original:  the asymptotics of ~ \lambda_d, as ~ d \to \infty, also remained elusive as of today.
Revised:  the asymptotics of ~ \lambda_d, as d \to \infty, also remained elusive as of today.
Edit intent: fluency
Original:  In this paper, we revisit and extend the approach presented by Klarner and Rivest in ~ 1973 to bound A_2(n) from above.
Revised:  In this paper, we revisit and extend the approach presented by Klarner and Rivest in 1973 to bound A_2(n) from above.
Edit intent: fluency
Original:  Our contributions are: Using available computing power, we prove that ~ \lambda_2 \leq 4.5252.
Revised:  Our contributions are: Using available computing power, we prove that \lambda_2 \leq 4.5252.
Edit intent: clarity
Original:  This is the first improvement of the upper bound on ~ \lambda_2 in almost half a century;
Revised:  This is the first improvement of the upper bound on \lambda_2 in almost half a century;
Edit intent: clarity
Original:  We prove that ~ \lambda_d \leq (2d-2)e+o(1) for any value of ~ d \geq 2, using a novel construction of a rational generating function which dominates that of the sequence ~ \left(A_d(n)\right);
Revised:  We prove that \lambda_d \leq (2d-2)e+o(1) for any value of ~ d \geq 2, using a novel construction of a rational generating function which dominates that of the sequence ~ \left(A_d(n)\right);
Edit intent: fluency
Original:  We prove that ~ \lambda_d \leq (2d-2)e+o(1) for any value of ~ d \geq 2, using a novel construction of a rational generating function which dominates that of the sequence ~ \left(A_d(n)\right);
Revised:  We prove that ~ \lambda_d \leq (2d-2)e+o(1) for any value of d \geq 2, using a novel construction of a rational generating function which dominates that of the sequence ~ \left(A_d(n)\right);
Edit intent: fluency
Original:  We prove that ~ \lambda_d \leq (2d-2)e+o(1) for any value of ~ d \geq 2, using a novel construction of a rational generating function which dominates that of the sequence ~ \left(A_d(n)\right);
Revised:  We prove that ~ \lambda_d \leq (2d-2)e+o(1) for any value of ~ d \geq 2, using a novel construction of a rational generating function which dominates that of the sequence \left(A_d(n)\right);
Edit intent: fluency
Original:  For d=3, this provides a subtantial improvement of the upper bound on ~ \lambda_3 from ~ 12.2071 to ~ 9.8073;
Revised:  For d=3, this provides a subtantial improvement of the upper bound on \lambda_3 from ~ 12.2071 to ~ 9.8073;
Edit intent: fluency
Original:  For d=3, this provides a subtantial improvement of the upper bound on ~ \lambda_3 from ~ 12.2071 to ~ 9.8073;
Revised:  For d=3, this provides a subtantial improvement of the upper bound on ~ \lambda_3 from 12.2071 to ~ 9.8073;
Edit intent: fluency
Original:  For d=3, this provides a subtantial improvement of the upper bound on ~ \lambda_3 from ~ 12.2071 to ~ 9.8073;
Revised:  For d=3, this provides a subtantial improvement of the upper bound on ~ \lambda_3 from ~ 12.2071 to 9.8073;
Edit intent: fluency
Original:  However, we implement an iterative process in three dimensions, which improves further the upper bound on ~ \lambda_3to ~ 9.3835 ;
Revised:  However, we implement an iterative process in three dimensions, which improves further the upper bound on \lambda_3to ~ 9.3835 ;
Edit intent: coherence
Original:  However, we implement an iterative process in three dimensions, which improves further the upper bound on ~ \lambda_3to ~ 9.3835 ;
Revised:  However, we implement an iterative process in three dimensions, which improves further the upper bound on ~ \lambda_3to 9.3835 ;
Edit intent: fluency
Original:  However, we implement an iterative process in three dimensions, which improves further the upper bound on ~ \lambda_3to ~ 9.3835 ;
Revised:  However, we implement an iterative process in three dimensions, which improves further the upper bound on ~ \lambda_3to ~ 9.3835 .
Edit intent: coherence
Original:  RL-based recommender systems have two key advantages: (i) they can continuously update their recommendation strategies according to users' real-time feedback, and (ii) the optimal strategy maximizes the long-term reward from users, such as the total revenue of a recommendation session.
Edit intent: coherence
Original:  To be specific, we design the generator to capture the  underlining distribution of users' historical logs and generate realistic logs that can be considered as augmentations of real logs;
Revised:  To be specific, the underlining distribution of users' historical logs and generate realistic logs that can be considered as augmentations of real logs;
Edit intent: clarity
Original:  To be specific, we design the generator to capture the  underlining distribution of users' historical logs and generate realistic logs that can be considered as augmentations of real logs;
Revised:  To be specific, we design the generator to capture the underlining distribution of users' historical logs and generates realistic logs that can be considered as augmentations of real logs;
Edit intent: fluency
Original:  while the discriminator is developed to not only distinguish real and fake logs but also predict users' behaviors.
Revised:  while the discriminator not only distinguishes real and fake logs but also predict users' behaviors.
Edit intent: clarity
Original:  while the discriminator is developed to not only distinguish real and fake logs but also predict users' behaviors.
Revised:  while the discriminator is developed to not only distinguish real and fake logs but also predicts users' behaviors.
Edit intent: fluency
Original: The proliferation of Unmanned Aerial Vehicles (UAVs) embedded with vulnerable monolithic software , involving concurrency and fragile communication links, has recently raised serious concerns about their security .
Revised: The proliferation of Unmanned Aerial Vehicles (UAVs) embedded with vulnerable monolithic software has recently raised serious concerns about their security .
Edit intent: clarity
Original:  However, verifying security in UAV software based on traditional testing remains an open challenge mainly due to scalability and deployment issue .
Revised:  However, verifying security in UAV software based on traditional testing remains an open challenge mainly due to scalability and deployment issues .
Edit intent: fluency
Original:  Here we investigate the application of software verification techniques ;
Revised:  Here we investigate software verification techniques ;
Edit intent: clarity
Original:  in particular, existing software analyzers and verifiers, which implement fuzzing and bounded model checking  techniques, to detect security vulnerabilities in typical UAVs . We also investigate fragility aspects related to the UAV communication link since all remaining UAV components (e.g., position, velocity  and attitude control) heavily depend on it .
Revised:  in particular, existing software analyzers and verifiers, which implement fuzzing and bounded model checking (BMC) techniques, to detect security vulnerabilities in typical UAVs . We also investigate fragility aspects related to the UAV communication link since all remaining UAV components (e.g., position, velocity and attitude control) heavily depend on it .
Edit intent: clarity