wanyu/IteraTeR_v2 huggingface dataset:
Original:  In this paper, we break the nearly 50 years old quadratic time bound for computing DTW or GED between two sequences of n points in R, by presenting a deterministic algorithms that run in O\left( n^2 \log\log\log n / \log\log n \right) time.
Revised:  In this paper, we break the nearly 50 years old quadratic time bound for computing DTW or GED between two sequences of n points in R, by presenting deterministic algorithms that run in O\left( n^2 \log\log\log n / \log\log n \right) time.
Edit intent: fluency
Original:  In this paper, we break the nearly 50 years old quadratic time bound for computing DTW or GED between two sequences of n points in R, by presenting a deterministic algorithms that run in O\left( n^2 \log\log\log n / \log\log n \right) time.
Revised:  In this paper, we break the nearly 50 years old quadratic time bound for computing DTW or GED between two sequences of n points in R, by presenting a deterministic algorithms that run in O\left( n^2 / \log\log n \right) time.
Edit intent: fluency
Original:  Our algorithms can be extended to work also for higher dimensional spaces X = R^d, for any constant d, when the underlying distance-metric \mathsf{dist is polyhedral (e.g., L_1, L_\infty).
Revised:  Our algorithms can be extended to work also for higher dimensional spaces R^d, for any constant d, when the underlying distance-metric \mathsf{dist is polyhedral (e.g., L_1, L_\infty).
Edit intent: clarity
Original:  In this paper, we propose several text generative neural networks for constructing Natural Language Inference datasets suitable for training classifiers .
Revised:  In this paper, we propose several text generative neural networks for constructing Natural Language Inference datasets .
Edit intent: clarity
Original:  To evaluate the models, we propose a new metric - the accuracy of the classifier trained on the generated dataset.
Revised:  To evaluate the models, we propose a new metric -- the accuracy of the classifier trained on the generated dataset.
Edit intent: fluency
Original:  The accuracy obtained with our best generative model is only 2.7\% lower than the accuracy of the classifier trained on the original, manually constructed dataset.
Revised:  The accuracy obtained by our best generative model is only 2.7\% lower than the accuracy of the classifier trained on the original, manually constructed dataset.
Edit intent: clarity
Original:  We prove that the problem of determining whether A(E) equals the number |E| of equivalence classes of E is NP-complete .
Revised:  We prove that the problem of determining whether A(E) equals the number |E| of equivalence classes of E is \mathsf{NP .
Edit intent: clarity
Original: For integers n\ge s\ge 2 let e(n,s) denote the maximum of |\mathcal F|  where \mathcal F is a family of subsets of an n-element set and \mathcal F contains no s pairwise disjoint members.
Revised: For integers n\ge s\ge 2 let e(n,s) denote the maximum of |\mathcal F| , where \mathcal F is a family of subsets of an n-element set and \mathcal F contains no s pairwise disjoint members.
Edit intent: fluency
Original: The families \mathcal F_1,\ldots, \mathcal F_s\subset 2^{[n]} are called q-dependent if there are no pairwise disjoint F _i \in \mathcal F _i,\ i=1,\ldots, s, satisfying |F_1\cup\ldots\cup F_s|\le q. We determine \max |\mathcal F_1|+\ldots +|\mathcal F_s| for all values n\ge q,s\ge 2.
Revised: The families \mathcal F_1,\ldots, \mathcal F_s\subset 2^{[n]} are called q-dependent if there are no pairwise disjoint F _i \in \mathcal F _i,\ i=1,\ldots, s, satisfying |F_1\cup\ldots\cup F_s|\le q. We determine \max |\mathcal F_1|+\ldots +|\mathcal F_s| for all values n\ge q,s\ge 2.
Edit intent: fluency
Original: The families \mathcal F_1,\ldots, \mathcal F_s\subset 2^{[n]} are called q-dependent if there are no pairwise disjoint F _i \in \mathcal F _i,\ i=1,\ldots, s, satisfying |F_1\cup\ldots\cup F_s|\le q. We determine \max |\mathcal F_1|+\ldots +|\mathcal F_s| for all values n\ge q,s\ge 2.
Revised: The families \mathcal F_1,\ldots, \mathcal F_s\subset 2^{[n]} are called q-dependent if there are no pairwise disjoint F _1 \in \mathcal F _i,\ i=1,\ldots, s, satisfying |F_1\cup\ldots\cup F_s|\le q. We determine \max |\mathcal F_1|+\ldots +|\mathcal F_s| for all values n\ge q,s\ge 2.
Edit intent: fluency
Original: The families \mathcal F_1,\ldots, \mathcal F_s\subset 2^{[n]} are called q-dependent if there are no pairwise disjoint F _i \in \mathcal F _i,\ i=1,\ldots, s, satisfying |F_1\cup\ldots\cup F_s|\le q. We determine \max |\mathcal F_1|+\ldots +|\mathcal F_s| for all values n\ge q,s\ge 2.
Revised: The families \mathcal F_1,\ldots, \mathcal F_s\subset 2^{[n]} are called q-dependent if there are no pairwise disjoint F _i \in \mathcal F _1,\ldots, F_s\in\mathcal F_s satisfying |F_1\cup\ldots\cup F_s|\le q. We determine \max |\mathcal F_1|+\ldots +|\mathcal F_s| for all values n\ge q,s\ge 2.
Edit intent: clarity
Original:  In the present paper  we provide a Hilton-Milner-type stability theorem for it in a relatively wide range, in particular, for n\ge (2+o(1))sk with o(1) depending on s  . This is a considerable improvement of a  result due to Bollob\'as, Daykin and Erd \H os .
Revised:  In the present paper , we provide a Hilton-Milner-type stability theorem for it in a relatively wide range, in particular, for n\ge (2+o(1))sk with o(1) depending on s . This is a considerable improvement of a result due to Bollob\'as, Daykin and Erd \H os .
Edit intent: fluency
Original:  In the present paper  we provide a Hilton-Milner-type stability theorem for it in a relatively wide range, in particular, for n\ge (2+o(1))sk with o(1) depending on s  . This is a considerable improvement of a  result due to Bollob\'as, Daykin and Erd \H os .
Revised:  In the present paper we provide a Hilton-Milner-type stability theorem for it in a relatively wide range, in particular, for n\ge (2+o(1))sk with o(1) depending on s only . This is a considerable improvement of a result due to Bollob\'as, Daykin and Erd \H os .
Edit intent: clarity
Original:  In the present paper  we provide a Hilton-Milner-type stability theorem for it in a relatively wide range, in particular, for n\ge (2+o(1))sk with o(1) depending on s  . This is a considerable improvement of a  result due to Bollob\'as, Daykin and Erd \H os .
Revised:  In the present paper we provide a Hilton-Milner-type stability theorem for it in a relatively wide range, in particular, for n\ge (2+o(1))sk with o(1) depending on s . This is a considerable improvement of a classical result due to Bollob\'as, Daykin and Erd \H os .
Edit intent: clarity
Original:  In the present paper  we provide a Hilton-Milner-type stability theorem for it in a relatively wide range, in particular, for n\ge (2+o(1))sk with o(1) depending on s  . This is a considerable improvement of a  result due to Bollob\'as, Daykin and Erd \H os .
Revised:  In the present paper we provide a Hilton-Milner-type stability theorem for it in a relatively wide range, in particular, for n\ge (2+o(1))sk with o(1) depending on s . This is a considerable improvement of a result due to Bollob\'as, Daykin and Erd \H{o .
Edit intent: fluency
Original:  We apply our results to advance in an anti-Ramsey-type problem, proposed by \"Ozkahya and Young.
Revised:  We apply our results to advance in the following anti-Ramsey-type problem, proposed by \"Ozkahya and Young.
Edit intent: clarity
Original:  They asked for the minimum number ar(n,k,s) of colors in the coloring of the k-element subsets of [n] that do not contain a \textit{rainbow matching} of size s, that is, s sets of different colors that are pairwise disjoint.
Revised:  Let ar(n,k,s) of colors in the coloring of the k-element subsets of [n] that do not contain a \textit{rainbow matching} of size s, that is, s sets of different colors that are pairwise disjoint.
Edit intent: clarity
Original: Given n non-vertical pairwise disjoint triangles in 3-space, their vertical depth (above/below) relation may contain cycles.
Revised: Given n non-vertical pairwise disjoint triangles in 3-space, their vertical depth relation may contain cycles.
Edit intent: clarity
Original:  We show that, for any \varepsilon>0, the triangles can be cut into O(n^{3/2+\varepsilon}) pieces, where each piece is a connected semi-algebraic set whose description complexity depends only on the choice of \varepsilon, such that the depth relation among these pieces is now a proper partial order.
Revised:  We show that, for any \varepsilon>0, the triangles can be cut into O(n^{3/2+\varepsilon}) connected semi-algebraic set whose description complexity depends only on the choice of \varepsilon, such that the depth relation among these pieces is now a proper partial order.
Edit intent: clarity
Original:  We show that, for any \varepsilon>0, the triangles can be cut into O(n^{3/2+\varepsilon}) pieces, where each piece is a connected semi-algebraic set whose description complexity depends only on the choice of \varepsilon, such that the depth relation among these pieces is now a proper partial order.
Revised:  We show that, for any \varepsilon>0, the triangles can be cut into O(n^{3/2+\varepsilon}) pieces, where each piece is a connected semi-algebraic pieces, whose description complexity depends only on the choice of \varepsilon, such that the depth relation among these pieces is now a proper partial order.
Edit intent: clarity
Original: In this work we study the likelihood of survival of single-species in the context of hostile and fluctuating environments.
Revised: In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments.
Edit intent: clarity
Original:  We perform a finite-size scaling and we obtain the associated critical exponents.
Revised:  We perform a finite-size scaling and we obtain the associated scaling exponents.
Edit intent: clarity
Original:  For  d \in \{2,3\}, let \rho^1_d(G) denote the minimum number of lines in R^d that together can accommodate all edges of a drawing of G , where \rho^1_2(G ) is defined for planargraphs .
Revised:  For d \in \{2,3\}, let \rho^1_d(G) denote the minimum number of lines in R^d that together can cover all edges of a drawing of G , where \rho^1_2(G ) is defined for planargraphs .
Edit intent: clarity
Original:  The result concerning \rho^1_3 holds even if G is restricted to be planar.  - Since NP \subseteq\exists\mathbb{R , deciding \rho^1_d(G)\le k is NP-hard for d\in\{2,3\}.
Revised:  The result concerning \rho^1_3 holds even if G is restricted to be planar. - Since NP \subseteq{\exists\mathbb{R , deciding \rho^1_d(G)\le k is NP-hard for d\in\{2,3\}.
Edit intent: fluency
Original:  On the positive side, we show that the problem is fixed-parameter tractable with respect to k. - Since \exists\mathbb{R \subseteq\mathrm{PSPACE}, both \rho^1_2(G) and \rho^1_3(G) are computable in polynomial space.
Revised:  On the positive side, we show that the problem is fixed-parameter tractable with respect to k. - Since \exists\mathbb{R \subseteq\mathrm{PSPACE}, both \rho^1_2(G) and \rho^1_3(G) are computable in polynomial space.
Edit intent: fluency
Original:  On the negative side, we show that constructing a drawing optimal with respect to \rho^1_2 or \rho^1_3 requires exponential space in the worst case, if the vertices are drawn at points with rational coordinates. -
Revised:  On the negative side, we show that drawings that are optimal with respect to \rho^1_2 or \rho^1_3 requires exponential space in the worst case, if the vertices are drawn at points with rational coordinates. -
Edit intent: clarity
Original:  On the negative side, we show that constructing a drawing optimal with respect to \rho^1_2 or \rho^1_3 requires exponential space in the worst case, if the vertices are drawn at points with rational coordinates. -
Revised:  On the negative side, we show that constructing a drawing optimal with respect to \rho^1_2 or \rho^1_3 sometimes require irrational coordinates. -
Edit intent: clarity
Original:  Let \rho^2_3(G) be the minimum number of planes in \mathbb{R}^3 needed to accommodate a straight-line drawing of a graph G. We prove that deciding whether \rho^2_3(G)\le k is NP-hard for any fixed k . \ge  Hence, the problem is not fixed-parameter tractable with respect to k unless \mathrm{P}=\mathrm{NP}.
Revised:  Let \rho^2_3(G) be the minimum number of planes in \mathbb{R}^3 needed to cover a straight-line drawing of a graph G. We prove that deciding whether \rho^2_3(G)\le k is NP-hard for any fixed k . \ge Hence, the problem is not fixed-parameter tractable with respect to k unless \mathrm{P}=\mathrm{NP}.
Edit intent: clarity
Original:  Let \rho^2_3(G) be the minimum number of planes in \mathbb{R}^3 needed to accommodate a straight-line drawing of a graph G. We prove that deciding whether \rho^2_3(G)\le k is NP-hard for any fixed k . \ge  Hence, the problem is not fixed-parameter tractable with respect to k unless \mathrm{P}=\mathrm{NP}.
Revised:  Let \rho^2_3(G) be the minimum number of planes in \mathbb{R}^3 needed to accommodate a straight-line drawing of a graph G. We prove that deciding whether \rho^2_3(G)\le k is NP-hard for any fixed k \ge Hence, the problem is not fixed-parameter tractable with respect to k unless \mathrm{P}=\mathrm{NP}.
Edit intent: fluency
Original:  We numerically demonstrate that our optimal nonadiabatic bang-bang protocols can outperform quantum annealing by orders of magnitude within the same running time.
Edit intent: coherence
Original:  The optimality of the bang-bang protocols and the characteristic time scale of the pulses  inform the search for effective hybrid (classical and quantum) machine learning schemes for tackling combinatorial optimization problems  .
Revised:  The optimality of the bang-bang protocols and the characteristic time scale of the pulses inform the search for effective hybrid (classical and quantum) schemes for tackling combinatorial optimization problems .
Edit intent: clarity
Original:  Focusing on the Sherrington-Kirkpatrick spin glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian.
Revised:  Focusing on the Sherrington-Kirkpatrick spin-glass as an example, we find a system-size independent distribution of the duration of pulses, with characteristic time scale set by the inverse of the coupling constants in the Hamiltonian.
Edit intent: fluency
Original:  As we numerically demonstrate, our optimal nonadiabatic bang-bang protocols can significantly outperform quantum annealing, favoring gate-model quantum computation for quantum enhanced optimization.
Revised:  For the particular systems we study, we find numerically that the optimal nonadiabatic bang-bang protocols can significantly outperform quantum annealing, favoring gate-model quantum computation for quantum enhanced optimization.
Edit intent: clarity
Original:  Several recent works on algorithmizations of the Lov\'{a}sz Local Lemma have established sufficient conditions for such an agent to succeed.
Revised:  Several recent works on algorithmizations of the Lov\'{a}sz Local Lemma have established sufficient conditions for the agent to succeed.
Edit intent: clarity
Original:  Motivated by the paradigm of Partially Observable Markov Decision Processes (POMDPs) we study whether such stochastic control is also possible in a noisy environment, where both the process of state-observation and the process of state-evolution are subject to adversarial perturbation (noise).
Revised:  Here we study whether such stochastic control is also possible in a noisy environment, where both the process of state-observation and the process of state-evolution are subject to adversarial perturbation (noise).
Edit intent: coherence
Original:  To overcome this challenge we develop a new analysis where entropy plays a central role, both to measure the rate at which progress towards an acceptable state is made and the rate at which the noise undoes this progress.
Revised:  To overcome this challenge we develop a new analysis where entropy plays a central role, both to measure the rate at which progress towards an acceptable state is made and the rate at which noise undoes this progress.
Edit intent: fluency
Original: We consider an agent trying to bring a system to an acceptable state by repeated \mbox{probabilistic action.
Revised: We consider an agent trying to bring a system to an acceptable state by repeated probabilistic action.
Edit intent: fluency
Original: We study the  problem of assigning resources in order to maximize the probability of resource utilization.
Revised: We study the fundamental problem of assigning resources in order to maximize the probability of resource utilization.
Edit intent: clarity
Original: We study the  problem of assigning resources in order to maximize the probability of resource utilization.
Revised: We study the problem of assigning resources to maximize their expected utilization.
Edit intent: clarity
Original: This is a sensible design goal in many settings with shared resources . Each agent has private information about its value distribution for different assignments.
Revised: This kind of problem arises in many settings with shared resources . Each agent has private information about its value distribution for different assignments.
Edit intent: clarity
Original: This is a sensible design goal in many settings with shared resources . Each agent has private information about its value distribution for different assignments.
Revised: This is a sensible design goal in many settings , where it is in the interest of a group, the general public, or a principal, that assigned resources be used and not wasted. At the time of assigning resources, each agent privately holds information about her distribution on future values for different assignments.
Edit intent: clarity
Original:  A mechanism elicits information about value distributions, using this information to determine an assignment along with payments , including payments that are contingent on utilization .
Revised:  Subsequently, we allow for payments to be contingent on ex post utilization decisions. The objective is to maximize expected utilization .
Edit intent: clarity
Original:  For allocating a single resource, we prove that a contingent second-price (CSP) mechanism  is unique under these criteria and optimal across a larger class of mechanisms  .
Revised:  For allocating a single resource, we prove that a contingent second-price (CSP) mechanism , is unique under these criteria and optimal across a larger class of mechanisms .
Edit intent: fluency
Original:  For allocating a single resource, we prove that a contingent second-price (CSP) mechanism  is unique under these criteria and optimal across a larger class of mechanisms  .
Revised:  For allocating a single resource, we prove that a contingent second-price (CSP) mechanism is unique under these criteria and optimal for a larger class of mechanisms .
Edit intent: clarity
Original:  For allocating a single resource, we prove that a contingent second-price (CSP) mechanism  is unique under these criteria and optimal across a larger class of mechanisms  .
Revised:  For allocating a single resource, we prove that a contingent second-price (CSP) mechanism is unique under these criteria and optimal across a larger class of mechanisms for assigning a single resource .
Edit intent: clarity
Original: We study the fundamental problem of assigning resources to maximize their expected utilization.
Revised: We introduce the problem of assigning resources to maximize their expected utilization.
Edit intent: coherence
Original:  This kind of problem arises in many settings , where it is in the interest of a group , the general public, or a principal, that assigned resources be used and not wasted.
Revised:  This kind of problem arises in many settings , where it is in the interest of a group that resources be used and not wasted.
Edit intent: clarity
Original:  We show that the natural, contingent second-price (CSP) mechanism, is unique under these criteria and optimal for a larger class of mechanisms for assigning a single resource .
Revised:  We show that the natural, contingent second-price mechanism, maximizes utilization .
Edit intent: clarity
Original:  We extend the CSP mechanism to assign multiple, heterogeneous resources (making a technical connection with assignment problems under non quasi-linear utility functions), showing that this generalized mechanism outperforms other methods such as first-come-first-serve and the VCG mechanism .
Revised:  We extend the mechanisms to assign multiple, heterogeneous resources (making a technical connection with assignment problems under non quasi-linear utility functions), showing that this generalized mechanism outperforms other methods such as first-come-first-serve and the VCG mechanism .
Edit intent: clarity
Original:  We extend the CSP mechanism to assign multiple, heterogeneous resources (making a technical connection with assignment problems under non quasi-linear utility functions), showing that this generalized mechanism outperforms other methods such as first-come-first-serve and the VCG mechanism .
Revised:  We extend the CSP mechanism to assign multiple, heterogeneous resources , and present a simulation study of the welfare properties of these mechanisms .
Edit intent: clarity
Original:  Our aim here is to develop a framework to leverage these structures and their existing implementations to approximate other fundamental statistics of the key frequency distribution.
Revised:  We present a framework that leverages these structures and their existing implementations to approximate other fundamental statistics of the key frequency distribution.
Edit intent: clarity
Original:  We present a  framework that leverages these structures and their existing implementations to approximate other fundamental statistics of the key frequency distribution .
Revised:  We present a novel framework that leverages these structures and their existing implementations to approximate other fundamental statistics of the key frequency distribution .
Edit intent: clarity
Original:  We present a  framework that leverages these structures and their existing implementations to approximate other fundamental statistics of the key frequency distribution .
Revised:  We present a framework that leverages these structures and their existing implementations to approximate any frequency statistics of the key frequency distribution .
Edit intent: clarity
Original:  We define transforms of the frequencies which can be approximated using%DIFDELCMD < {\em %%% count measurements . Each count measurement is obtained by applying a distinct counter to processed dataelements.
Revised:  We define transforms of the frequencies which can be approximated using%DIFDELCMD < {\em %%% . Each count measurement is obtained by applying a distinct counter to processed dataelements.
Edit intent: clarity
Original:  A thread of research pioneered by Flajolet and Martin three decades ago initiated the design of highly effective approximate counting structures, which with size that is double logarithmic in the number of  keys provides estimates with a small relative error.
Revised:  A thread of research pioneered by Flajolet and Martin three decades ago initiated the design of highly effective approximate counting structures, which with size that is double logarithmic in the number of distinct keys provides estimates with a small relative error.
Edit intent: clarity
Original:  These fundamental aggregations are very common in text, graphs, and logs analysis and include logarithms, low frequency moments, and capping statistics common in online advertising .
Revised:  These fundamental aggregations are very common in text, graphs, and logs analysis and include logarithms, low frequency moments, and capping statistics .
Edit intent: clarity
Original:  Our scheme is powerful but very simple to apply: We specify tailored mapping functions of data elements to output elements.
Revised:  Our scheme is powerful yet very simple to apply: We specify tailored mapping functions of data elements to output elements.
Edit intent: fluency