wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our result is a sparse analog of Gordon's theorem, which was concerned with a dense \Phi having i.i.d. gaussian entries.
Revised:  Our result is a sparse analog of Gordon's theorem, which was concerned with a dense \Phi having i.i.d. Gaussian entries.
Edit intent: fluency
Original:  In this paper we give the first near-linear time algorithm for edit distance computation to Dyck(s) that achieves an approximation factor of O(1{\epsilon} (\log{OPT (n)^{1{\epsilon}}) in O(n^{1+\epsilon}n) time.
Revised:  In this paper we give the first near-linear time algorithm for edit distance computation to Dyck(s) that achieves an approximation factor of O(1{\epsilon} \log{OPT (n)^{1{\epsilon}}) in O(n^{1+\epsilon}n) time.
Edit intent: coherence
Original:  In fact, given there exists an algorithm for computing string edit distance on input of size n in \alpha(n) time with \beta(n)-approximation factor, we can devise an algorithm for edit distance problem to Dyck(s) running in O(n^{1+\epsilon}+\alpha(n)) and achieving an approximation factor of O( {\epsilon}} \beta(n) (\log{OPT ).
Revised:  In fact, given there exists an algorithm for computing string edit distance on input of size n in \alpha(n) time with \beta(n)-approximation factor, we can devise an algorithm for edit distance problem to Dyck(s) running in O(n^{1+\epsilon}+\alpha(n)) and achieving an approximation factor of O( {\epsilon}} \beta(n) \log{OPT ).
Edit intent: fluency
Original:  A thorough study of this receptor contributes to a better understanding of calcium oscillations and waves.
Revised:  A thorough study of the IPR channel contributes to a better understanding of calcium oscillations and waves.
Edit intent: clarity
Original:  Based on the patch-clamp experimental data obtained from the outer membranes of isolated nuclei of theXenopus oocyte, we construct an allosteric competition model of single IPR channels on their native ER membrane environment.
Revised:  Xenopus oocyte, we construct an allosteric competition model of single IPR channels on their native ER membrane environment.
Edit intent: clarity
Original: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Revised: Given a simplicial complex K, we consider several notions of thickness and distortionfor complexes in Euclidean spaces } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Edit intent: clarity
Original: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Revised: We consider several notions of geometric complexity of embeddings of K in a Euclidean space } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Edit intent: clarity
Original: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Revised: We consider several notions of thickness and distortionfor complexes in Euclidean spaces \mathbb R} } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Edit intent: clarity
Original: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Revised: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } }^{2n } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Edit intent: fluency
Original: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Revised: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } } }^{2n with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Edit intent: fluency
Original: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has exponentially small thickness as a function of the number of simplices of K.
Revised: We consider several notions of thickness and distortionfor complexes in Euclidean spaces } } } with refinement complexity O(e^{N^{4+{\epsilon}}})} . Families of simplicial n-complexes K are constructed such that any embedding of K into {\mathbb R}^{2n} has an exponential lower bound on thickness and refinement complexity as a function of the number of simplices of K.
Edit intent: clarity
Original:  As the required computations are extensive, we also obtain simple expressions for the expected value \mathrm{E ]   . Finally, we calculate the asymptotic limit of the average speed of the packet.
Revised:  As the required computations are extensive, we also obtain simple expressions for the expected value \mathrm{E ] . Finally, we calculate the asymptotic limit of the average speed of the packet.
Edit intent: fluency
Original:  In particularly , we show that, with respect to the independent interference case, \mathrm{E ]   increase, whereas the packet speed decreases.
Revised:  In particular , we show that, with respect to the independent interference case, \mathrm{E ] increase, whereas the packet speed decreases.
Edit intent: fluency
Original:  In particularly , we show that, with respect to the independent interference case, \mathrm{E ]   increase, whereas the packet speed decreases.
Revised:  In particularly , we show that, with respect to the independent interference case, \mathrm{E ] increase, whereas the packet speed decreases.
Edit intent: fluency
Original:  Our assumption is that offering means of digital, structured aggregation and annotation of the objects of an experiment will provide enough meta-data for a scientist to understand and recreate the results of an experiment.
Revised:  Our assumption is that offering means of digital, structured aggregation and annotation of the objects of an experiment will provide necessary meta-data for a scientist to understand and recreate the results of an experiment.
Edit intent: clarity
Original:  To support this we used a model for the semantic description of a workflow-centric Research Object (RO), where a RO is defined as a resource that aggregates other resources, e.g., datasets, software, spreadsheets, text, etc.
Revised:  To support this we explored a model for the semantic description of a workflow-centric Research Object (RO), where a RO is defined as a resource that aggregates other resources, e.g., datasets, software, spreadsheets, text, etc.
Edit intent: clarity
Original:  To support this we used a model for the semantic description of a workflow-centric Research Object (RO), where a RO is defined as a resource that aggregates other resources, e.g., datasets, software, spreadsheets, text, etc.
Revised:  To support this we used a model for the semantic description of a workflow-centric Research Object (RO), where an RO is defined as a resource that aggregates other resources, e.g., datasets, software, spreadsheets, text, etc.
Edit intent: fluency
Original:  We applied this model to a genomics case study where we analysed human metabolite variation by workflows . A set of workflows was produced conform recently defined Best Practices for workflow design.
Revised:  We applied this model to a case study where we analysed human metabolite variation by workflows . A set of workflows was produced conform recently defined Best Practices for workflow design.
Edit intent: clarity
Original: Spectral clustering is arguably one of the most important algorithms in data mining and machine intelligence;
Revised: Spectral clustering is one of the most important algorithms in data mining and machine intelligence;
Edit intent: clarity
Original:  however, its computational complexity makes challenging to use in large scale data analysis.
Revised:  however, its computational complexity limits its application to truly large scale data analysis.
Edit intent: clarity
Original:  Such determinisation constructions are notoriously difficult and cumbersome to implement.
Edit intent: coherence
Original:  In this paper we argue that applying this step in full generality is only required in some places, and can often be circumvented by subset and breakpoint constructions  .
Revised:  In this paper , we show that full determinisation can be avoided: subset and breakpoint constructions .
Edit intent: clarity
Original:  In this paper we argue that applying this step in full generality is only required in some places, and can often be circumvented by subset and breakpoint constructions  .
Revised:  In this paper we argue that applying this step in full generality is only required in some places, and can often be circumvented by subset and breakpoint constructions suffice .
Edit intent: fluency
Original:  In this paper, we propose an efficient polynomial time non-convex approximation deflation approach for solving the problem.
Revised:  In this paper, we propose an effective polynomial time non-convex approximation deflation approach for solving the problem.
Edit intent: clarity
Original:  Our reductionsshow that k-SUM on "small" numbers (in the range -n^{f(k),n^{f(k)}}%DIFDELCMD < ] %%% for any computable function f) is W[1] -complete, and that k-SUM (in general) is W[1]-complete under a common derandomization assumption.
Revised:  Our reductionsshow that k-SUM on "small" numbers (in the range ,n^{f(k)}}%DIFDELCMD < ] %%% for any computable function f) is W[1] -complete, and that k-SUM (in general) is W[1]-complete under a common derandomization assumption.
Edit intent: fluency
Original:  Our reductionsshow that k-SUM on "small" numbers (in the range -n^{f(k),n^{f(k)}}%DIFDELCMD < ] %%% for any computable function f) is W[1] -complete, and that k-SUM (in general) is W[1]-complete under a common derandomization assumption.
Revised:  Our reductionsshow that k-SUM on "small" numbers (in the range -n^{f(k),n^{f(k)}}%DIFDELCMD < ] %%% remains W[1] -complete, and that k-SUM (in general) is W[1]-complete under a common derandomization assumption.
Edit intent: clarity
Original:  Our reductionsshow that k-SUM on "small" numbers (in the range -n^{f(k),n^{f(k)}}%DIFDELCMD < ] %%% for any computable function f) is W[1] -complete, and that k-SUM (in general) is W[1]-complete under a common derandomization assumption.
Revised:  Our reductionsshow that k-SUM on "small" numbers (in the range -n^{f(k),n^{f(k)}}%DIFDELCMD < ] %%% for any computable function f) is W[1] -hard, and is in fact W[1]-complete under a common derandomization assumption.
Edit intent: clarity
Original:  This, and the fact that researchers are keen on promoting their work, has contributed to increasing popularity of online scientific communities  .
Revised:  This, together with growing popularity of online scientific communities .
Edit intent: clarity
Original:  The algorithm is evaluated on artificially-generated data as well as on real data from the Econophysics Forum community to determine its best-performing variants.
Revised:  The algorithm is evaluated on artificially-generated data and real data from the Econophysics Forum community to determine its best-performing variants.
Edit intent: coherence
Original:  The algorithm is evaluated on artificially-generated data as well as on real data from the Econophysics Forum community to determine its best-performing variants.
Revised:  The algorithm is evaluated on artificially-generated data as well as on real data from the Econophysics Forum is used to determine the method's best-performing variants.
Edit intent: clarity
Original:  We show that when the algorithm is extended by considering author credit, its performance improves on multiple levels.
Revised:  We show that when the method is extended by considering author credit, its performance improves on multiple levels.
Edit intent: clarity
Original: Motivated by the challenges in the design and implementation of wireless cloud networks and the complex optimization of Physical Layer Network Coding (PNC) in Compute-and-Forward (C \& F) relaying, we propose a cooperative network management scheme for Cloud C \& F networks, employing Coalitional Game Theory.
Revised: Motivated by the challenges in the design and implementation of wireless cloud networks and the complex optimization of Physical Layer Network Coding (PNC) in Compute-and-Forward (C F) relaying, we propose a cooperative network management scheme for Cloud C \& F networks, employing Coalitional Game Theory.
Edit intent: fluency
Original: Motivated by the challenges in the design and implementation of wireless cloud networks and the complex optimization of Physical Layer Network Coding (PNC) in Compute-and-Forward (C \& F) relaying, we propose a cooperative network management scheme for Cloud C \& F networks, employing Coalitional Game Theory.
Revised: Motivated by the challenges in the design and implementation of wireless cloud networks and the complex optimization of Physical Layer Network Coding (PNC) in Compute-and-Forward (C \& F) relaying, we propose a cooperative network management scheme for Cloud C F networks, employing Coalitional Game Theory.
Edit intent: fluency
Original:  The proposed scheme is an efficient PNC technique for the uplink of cloud C \& F networks, which jointly optimizes the sum and the minimum transmission rates, while minimizing the total transmitting power.
Revised:  The proposed scheme is an efficient PNC technique for the uplink of cloud C F networks, which jointly optimizes the sum and the minimum transmission rates, while minimizing the total transmitting power.
Edit intent: fluency
Original:  In the proposed network architecture, C \& F Relays are considered as rational players which form coalitions, in order to optimize the achievable rates via relay selection and PNC, while the tradeoff between the minimum and the sum rate is investigated by utilizing the concept of Pareto frontier and Pareto optimal point.
Revised:  In the proposed network architecture, C F Relays are considered as rational players which form coalitions, in order to optimize the achievable rates via relay selection and PNC, while the tradeoff between the minimum and the sum rate is investigated by utilizing the concept of Pareto frontier and Pareto optimal point.
Edit intent: fluency
Original: Motivated by the challenges in the design and implementation of wireless cloud networks and the complex optimization of Physical Layer Network Coding (PNC)in Compute-and-Forward (C F) relaying, we propose a cooperative network management scheme for Cloud C%DIFDELCMD < &%%% F networks, employing Coalitional Game Theory.
Revised: Motivated by the challenges in the design and implementation of wireless cloud networks and the complex optimization of Physical Layer Network Coding (PNC)in Compute-and-Forward F) relaying, we propose a cooperative network management scheme for Cloud C%DIFDELCMD < &%%% F networks, employing Coalitional Game Theory.
Edit intent: fluency
Original: Motivated by the challenges in the design and implementation of wireless cloud networks and the complex optimization of Physical Layer Network Coding (PNC)in Compute-and-Forward (C F) relaying, we propose a cooperative network management scheme for Cloud C%DIFDELCMD < &%%% F networks, employing Coalitional Game Theory.
Revised: Motivated by the challenges in the design and implementation of wireless cloud networks and the complex optimization of Physical Layer Network Coding (PNC)in Compute-and-Forward (C %DIFDELCMD < &%%% F networks, employing Coalitional Game Theory.
Edit intent: clarity
Original:  The proposed algorithms eliminate the dominated strategies and converge to the optimal solution with respect to three criteria: maximization of the minimum rate , maximization of the sum rate with simultaneous maximization of the minimum rate, and maximization of the sum rate for specific minimum rate requirements.
Revised:  The proposed algorithms eliminate the dominated strategies and converge to the optimal solution with respect to the maximization of the minimum rate , maximization of the sum rate with simultaneous maximization of the minimum rate, and maximization of the sum rate for specific minimum rate requirements.
Edit intent: clarity
Original: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex  of G is replaced by k vertices  and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Revised: A k-lift of an n-vertex base graph G is a graph H on n\times k vertices, where each vertex of G is replaced by k vertices and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Edit intent: clarity
Original: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex  of G is replaced by k vertices  and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Revised: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex v of G is replaced by k vertices and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Edit intent: fluency
Original: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex  of G is replaced by k vertices  and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Revised: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex of G is replaced by k vertices and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ %DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Edit intent: coherence
Original: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex  of G is replaced by k vertices  and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Revised: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex of G is replaced by k vertices and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% %DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Edit intent: coherence
Original: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex  of G is replaced by k vertices  and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% . H s a (uniformly) random lift of G if for every edge (u,v) the bijection \pi _{uv} is chosen uniformly and independently at random.
Revised: A k-lift of an n-vertex base-graph G is a graph H on n\times k vertices, where each vertex of G is replaced by k vertices and each edge (u,v) in G is replaced by a matching representing a bijection uv so that the edges of H are of the form %DIFDELCMD < \big (%%% (u,i),(v,\pi _{ uv%DIFDELCMD < \MBLOCKRIGHTBRACE%%% (i))%DIFDELCMD < \big )%%% \pi _{uv} is chosen uniformly and independently at random.
Edit intent: clarity
Original:  Lately, there has been an increased interest in lifts and their close relation to the notorious Unique Games Conjecture \mbox{ Kho02  .
Revised:  Lately, there has been an increased interest in lifts and their close relation to the notorious Unique Games Conjecture \mbox{ Kho02 ) .
Edit intent: fluency
Original:  On our way to obtain the result on perfect matching polytopes we improve on a result of Padberg and Rao's on the adjacency structures of those polytopes  .
Revised:  On our way to obtain the result on perfect matching polytopes we generalize a result of Padberg and Rao's on the adjacency structures of those polytopes .
Edit intent: clarity