wanyu/IteraTeR_full_sent huggingface dataset:
Original: We give the first ANN-data structure for time series under the continuous Fr\'echet distance , where ANN stands for approximate near neighbor . Given a parameter \epsilon \in (0,1], the data structure can be used to preprocess n curves in Euclidean R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance 2+\epsilon, or answering that there exists no curve in the input within distance 1.
Revised: We give the first ANN-data structure for time series under the continuous Fr\'echet distance . Given a parameter \epsilon \in (0,1], the data structure can be used to preprocess n curves in Euclidean R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance 2+\epsilon, or answering that there exists no curve in the input within distance 1.
Edit intent: coherence
Original: We give the first ANN-data structure for time series under the continuous Fr\'echet distance , where ANN stands for approximate near neighbor . Given a parameter \epsilon \in (0,1], the data structure can be used to preprocess n curves in Euclidean R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance 2+\epsilon, or answering that there exists no curve in the input within distance 1.
Revised: We give the first ANN-data structure for time series under the continuous Fr\'echet distance , where ANN stands for approximate near neighbor . Given a parameter \epsilon \in (0,1], the data structure can be used to preprocess n curves in R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance 2+\epsilon, or answering that there exists no curve in the input within distance 1.
Edit intent: clarity
Original:  Our data structure uses only a constant number of probes per query and does not have any dependency on L. We apply similar techniques for proving cell-probe lower bounds for the discrete Fr\'echet distance matching known upper bounds .
Revised:  Our data structure uses only a constant number of probes per query and does not have any dependency on L. In particular, this shows that our solution is optimal if only a constant number of probes is allowed. Our second positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in O(nm) and query time in O(k), and which answers queries with an approximation factor in O(k). Both of our data structures make use of the concept of signatures, which were originally introduced for the problem of clustering time series under the Fr\'echet distance matching known upper bounds .
Edit intent: meaning-changed
Original:  Our data structure uses only a constant number of probes per query and does not have any dependency on L. We apply similar techniques for proving cell-probe lower bounds for the discrete Fr\'echet distance matching known upper bounds .
Revised:  Our data structure uses only a constant number of probes per query and does not have any dependency on L. We apply similar techniques for proving cell-probe lower bounds for the discrete Fr\'echet distance .
Edit intent: clarity
Original:  Concretely, we show that for any data structure which achieves an approximation factor less than 2 and which supports curves of arclength at most L, uses a word size bounded by O (L^{1-\epsilon}) for some constant \epsilon>0, and answers the query using only a constant number of probes, the number of words used to store the data structure must be at least L^{\Omega(k)}.
Revised:  Concretely, we show that for any data structure which achieves an approximation factor less than 2 and which supports curves of arclength at most L, uses a word size bounded by \mathcal{O (L^{1-\epsilon}) for some constant \epsilon>0, and answers the query using only a constant number of probes, the number of words used to store the data structure must be at least L^{\Omega(k)}.
Edit intent: meaning-changed
Original:  Our second positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in O (nm) and query time in O (k), and which answers queries with an approximation factor in O (k).
Revised:  Our second positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in \mathcal{O (nm) and query time in O (k), and which answers queries with an approximation factor in O (k).
Edit intent: meaning-changed
Original:  Our second positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in O (nm) and query time in O (k), and which answers queries with an approximation factor in O (k).
Revised:  Our second positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in O (nm) and query time in \mathcal{O (k), and which answers queries with an approximation factor in O (k).
Edit intent: meaning-changed
Original:  Our second positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in O (nm) and query time in O (k), and which answers queries with an approximation factor in O (k).
Revised:  Our second positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in O (nm) and query time in O (k), and which answers queries with an approximation factor in \mathcal{O (k).
Edit intent: meaning-changed
Original:  For an attainable approximation factor c>1 , the data structure can be used to preprocess n curves in R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance c , or answering that there exists no curve in the input within distance 1.
Revised:  For an attainable approximation factor c>1 and a query radius r, an approximate-near-neighbor data structure can be used to preprocess n curves in R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance c , or answering that there exists no curve in the input within distance 1.
Edit intent: meaning-changed
Original:  For an attainable approximation factor c>1 , the data structure can be used to preprocess n curves in R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance c , or answering that there exists no curve in the input within distance 1.
Revised:  For an attainable approximation factor c>1 , the data structure can be used to preprocess n curves in R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance cr , or answering that there exists no curve in the input within distance 1.
Edit intent: fluency
Original:  For an attainable approximation factor c>1 , the data structure can be used to preprocess n curves in R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance c , or answering that there exists no curve in the input within distance 1.
Revised:  For an attainable approximation factor c>1 , the data structure can be used to preprocess n curves in R (aka time series), each of complexity m, to answer queries with a curve of complexity k by either returning a curve that lies within Fr\'echet distance c , or answering that there exists no curve in the input within distance r.
Edit intent: meaning-changed
Original:  As an indicator of hardness, we show that for any data structure which achieves an approximation factor less than 2 and which supports curves of arclength at most L, uses a word size bounded by \mathcal{O(L^{1-\epsilon}) for some constant \epsilon>0, and answers the query using only a constant number of probes, the number of words used to store the data structure must be at least L^{\Omega(k)}.
Revised:  (L^{1-\epsilon}) for some constant \epsilon>0, and answers the query using only a constant number of probes, the number of words used to store the data structure must be at least L^{\Omega(k)}.
Edit intent: coherence
Original:  } Our third positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in \mathcal{O}(  nm) and query time in \mathcal{O}(k  ), and which answers queries with an approximation factor in \mathcal{O}(k).
Revised:  } Our third positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in \mathcal{O}( n\log n+ nm) and query time in \mathcal{O}(k ), and which answers queries with an approximation factor in \mathcal{O}(k).
Edit intent: meaning-changed
Original:  } Our third positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in \mathcal{O}(  nm) and query time in \mathcal{O}(k  ), and which answers queries with an approximation factor in \mathcal{O}(k).
Revised:  } Our third positive result is a probabilistic data structure based on locality-sensitive hashing, which achieves space in \mathcal{O}( nm) and query time in \mathcal{O}(k \log n ), and which answers queries with an approximation factor in \mathcal{O}(k).
Edit intent: meaning-changed
Original:  All of our data structures make use of the concept of signatures, which were originally introduced for the problem of clustering time series under the Fr\'echet distance  .
Revised:  All of our data structures make use of the concept of signatures, which were originally introduced for the problem of clustering time series under the Fr\'echet distance . In addition, we show lower bounds for this problem. Consider any data structure which achieves an approximation factor less than 2 and which supports curves of arclength up to L and answers the query using only a constant number of probes. We show that under reasonable assumptions on the word size any such data structure needs space in L^{\Omega(k) .
Edit intent: meaning-changed
Original:  We map the problem of testing  the existence of such representations to the one of testing  the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time or pseudo-polynomial-time algorithms.
Revised:  We map the problem of testing for the existence of such representations to the one of testing the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time or pseudo-polynomial-time algorithms.
Edit intent: clarity
Original:  We map the problem of testing  the existence of such representations to the one of testing  the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time or pseudo-polynomial-time algorithms.
Revised:  We map the problem of testing the existence of such representations to the one of testing for the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time or pseudo-polynomial-time algorithms.
Edit intent: clarity
Original:  We map the problem of testing  the existence of such representations to the one of testing  the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time or pseudo-polynomial-time algorithms.
Revised:  We map the problem of testing the existence of such representations to the one of testing the existence of suitably constrained 1-page book-embeddings and propose several polynomial-time and pseudo-polynomial-time algorithms.
Edit intent: fluency
Original:  When the number of limiting profiles used to define each category is not restricted, ELECTRE TRI-nB is easy to characterize axiomatically and is found to be equivalent to several other methods proposed in the literature.
Revised:  When the number of limiting profiles used to define each category is not restricted, Electre Tri-nB is easy to characterize axiomatically and is found to be equivalent to several other methods proposed in the literature.
Edit intent: fluency
Original:  When the number of masses is two we find the optimal load analytically. For the case of three or more masses, we obtain conjectures for the globally optimal load that are strongly supported by extensive computational results .
Revised:  The stability constraint is nonconvex and nonsmooth, making the optimization problem quite challenging. We give a detailed analytical treatment for the case of three or more masses, we obtain conjectures for the globally optimal load that are strongly supported by extensive computational results .
Edit intent: meaning-changed
Original:  For the case of three or more masses, we obtain conjectures for the globally optimal load that are strongly supported by extensive computational results .
Revised:  For the case of two masses, arguing that the optimal parameter configuration approaches the flutter and divergence boundaries of the stability region simultaneously. Furthermore, we conjecture that this property holds for any number of masses, which in turn suggests a simple formula for the maximal load interval for n masses. This conjecture is strongly supported by extensive computational results .
Edit intent: meaning-changed
Original:  For the case of three or more masses, we obtain conjectures for the globally optimal load that are strongly supported by extensive computational results . To obtain these, we use techniques from nonsmooth optimization, employing the recently developed open-source software package GRANSO (GRadient-based Algorithm for Non-Smooth Optimization) to maximize the load subject to appropriate nonsmooth stability constraints .
Revised:  For the case of three or more masses, we obtain conjectures for the globally optimal load that are strongly supported by extensive computational results , obtained using the recently developed open-source software package GRANSO (GRadient-based Algorithm for Non-Smooth Optimization) to maximize the load subject to appropriate nonsmooth stability constraints .
Edit intent: clarity
Original:  To obtain these, we use techniques from nonsmooth optimization, employing the recently developed open-source software package GRANSO (GRadient-based Algorithm for Non-Smooth Optimization) to maximize the load subject to appropriate nonsmooth stability constraints .
Revised:  To obtain these, we use techniques from nonsmooth optimization, employing the recently developed open-source software package GRANSO (GRadient-based Algorithm for Non-Smooth Optimization) to maximize the load interval subject to an appropriate formulation of the nonsmooth stability constraint. We hope that our work will provide a foundation for new approaches to classical long-standing problems of stability optimization for nonconservative elastic systems arising in civil and mechanical engineering .
Edit intent: meaning-changed
Original:  We introduce a reinforcement learning approach to audio-visual navigation with two key novel elements  1) audio-visual waypoints that are dynamically set and learned end-to-end within the navigation policy, and 2) an acoustic memory that provides a structured, spatially grounded record of what the agent has heard as it moves.
Revised:  We introduce a reinforcement learning approach to audio-visual navigation with two key novel elements : 1) audio-visual waypoints that are dynamically set and learned end-to-end within the navigation policy, and 2) an acoustic memory that provides a structured, spatially grounded record of what the agent has heard as it moves.
Edit intent: fluency
Original:  We introduce a reinforcement learning approach to audio-visual navigation with two key novel elements  1) audio-visual waypoints that are dynamically set and learned end-to-end within the navigation policy, and 2) an acoustic memory that provides a structured, spatially grounded record of what the agent has heard as it moves.
Revised:  We introduce a reinforcement learning approach to audio-visual navigation with two key novel elements 1) waypoints that are dynamically set and learned end-to-end within the navigation policy, and 2) an acoustic memory that provides a structured, spatially grounded record of what the agent has heard as it moves.
Edit intent: fluency
Original: Analyzing graphs by representing them in a low dimensional space using Graph Neural Networks (GNNs) is a promising research problem, with a lot of ongoing research.
Revised: Learning feature space node embeddings that encode the position of a node within the context of a graph is useful in several graph prediction tasks. Majority of the existing graph neural networks (GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods would map to similar embeddings. This limitation may prevent accurate performance in predictive tasks that rely on position information.
Edit intent: coherence
Original:  The model incorporates the reachability of nodes from anchors and vice versa, captured through multiple random walks. We use random walk since it captures the locality better.
Revised:  The reachability estimations compute the frequency with which a node may visit an anchor through any possible path. The anchors are strategically selected so that the reachability estimations across all nodes are maximized. We show that this combinatorial anchor selection problem is NP-hard and consequently, develop a greedy (1-1/e) approximation.
Edit intent: meaning-changed
Original:  An extensive experimental evaluation comparing different variants of the model provides an insight into its ability to perform well on the downstream prediction tasks. GraphReach significantly outperforms the current state-of-the-art models and achieves an improvement of up to 31 and 11 percentage points, measured in ROC AUC, for the standard pairwise node classification and link prediction tasks, respectively .
Revised:  An extensive experimental evaluation covering six datasets and five state-of-the-art models and achieves an improvement of up to 31 and 11 percentage points, measured in ROC AUC, for the standard pairwise node classification and link prediction tasks, respectively .
Edit intent: meaning-changed
Original:  GraphReach significantly outperforms the current state-of-the-art models and achieves an improvement of up to 31 and 11 percentage points, measured in ROC AUC, for the standard pairwise node classification and link prediction tasks, respectively .
Revised:  GraphReach significantly outperforms the current state-of-the-art GNN architectures reveal that GraphReach is consistently superior and provides up to 40\% relative improvement in the predictive tasks of link prediction and pairwise node classification and link prediction tasks, respectively .
Edit intent: meaning-changed
Original:  GraphReach significantly outperforms the current state-of-the-art models and achieves an improvement of up to 31 and 11 percentage points, measured in ROC AUC, for the standard pairwise node classification and link prediction tasks, respectively .
Revised:  GraphReach significantly outperforms the current state-of-the-art models and achieves an improvement of up to 31 and 11 percentage points, measured in ROC AUC, for the standard pairwise node classification . In addition, GraphReach is more robust against adversarial attacks .
Edit intent: meaning-changed
Original:  In our experiments with several graphs, when we consider only minimal separators which are no larger than treewidth, we can significantly speed up the decomposition while still have an optimal treedepth decomposition. By the conjecture, we solve more instances than any algorithm submitted to PACE 2020. Theoretically, we prove that the conjecture for many classes of graphs. We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw +  1 when tw is the treewidth\le  .
Revised:  In those algorithms, although a number of minimal separators are enumerated, the minimal separators that are used for an optimal solution are empirically very small. Therefore, analyzing the upper bound on the size of minimal separators is an important problem because it has the potential to significantly reduce the computation time. A minimal separator S is called an optimal top separator if td(G) = |S| + 1 when tw is the treewidth\le .
Edit intent: meaning-changed
Original:  We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw +  1 when tw is the treewidth\le  .
Revised:  We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw + td(G \backslash S), where td(G) denotes the treedepth of G. Then, we have two theoretical results on the size of optimal top separators. ( 1 when tw is the treewidth\le .
Edit intent: meaning-changed
Original:  We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw +  1 when tw is the treewidth\le  .
Revised:  We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw + 1 ) For any G, there is an optimal top separator S such that |S|\le .
Edit intent: meaning-changed
Original:  We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw +  1 when tw is the treewidth\le  .
Revised:  We also prove a relaxed version of the conjecture that the size of the separators should not be larger than 2 \cdot tw + 1 when tw is the treewidth\le 2tw(G), where tw(G) is the treewidth of G. (2) For any c < 2, there exists a graph G such that any optimal top separator S of G have |S| > c \cdot tw(G), i.e., the first result gives a tight bound on the size of an optimal top separator .
Edit intent: meaning-changed
Original:  For proper functioning, particularly as sensors, the length of a specific protrusion must not cross a narrow band bounded by two thresholds. However, fluctuations may drive the length beyond these thresholds. We study generic stochastic models of length control of long cell protrusions; the special cases of this model correspond to specific examples of different types of cell appendages . Exploiting the techniques of level crossings developed for random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these protrusions.
Revised:  We develop here a stochastic model motivated by length fluctuations of a type of appendage of an eukaryotic cell called flagellum (also called cilium) . Exploiting the techniques of level crossings developed for random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these protrusions.
Edit intent: clarity
Original:  the special cases of this model correspond to specific examples of different types of cell appendages . Exploiting the techniques of level crossings developed for random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these protrusions.
Revised:  the special cases of this model correspond to specific examples of different types of cell appendages . Exploiting the techniques developed for the calculation of level-crossing statistics of random excursions of stochastic process, we have derived analytical expressions of passage times for hitting various thresholds, sojourn times of random excursions beyond the threshold and the extreme lengths attained during the lifetime of these protrusions.
Edit intent: clarity