wanyu/IteraTeR_v2 huggingface dataset:
Original:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation.
Revised:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation.
Edit intent: fluency
Original:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation.
Revised:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) %DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation.
Edit intent: fluency
Original:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation.
Revised:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% matrix is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation.
Edit intent: clarity
Original:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation.
Revised:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by quantum circuits acting on O(k(n)) space and performs all quantum measurements at the end of the computation.
Edit intent: clarity
Original:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) space and performs all quantum measurements at the end of the computation.
Revised:  We show that given the size-n efficient encoding of a 2^{ \mathcal{O k(n) ) }\times 2^{ \mathcal{O k(n) )%DIFDELCMD < \MBLOCKRIGHTBRACE %%% well-conditioned matrix H, approximating a particular entry of H^{-1 is complete for the class of problems solvable by a quantum algorithm that uses O(k(n)) qubits with all measurements at the end of the computation.
Edit intent: clarity
Original:  In particular, the problem of computing entries of H^{-1 for an explicit well-conditioned n \times n matrix H is complete for unitary quantum logspace.
Revised:  for an explicit well-conditioned n \times n matrix H is complete for unitary quantum logspace.
Edit intent: clarity
Original:  In the logspace case, our results improve on previous results of Ta-Shma }[  QMA with exponentially small completeness-soundness gap is equal to PSPACE , that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian .
Revised:  In the logspace case, our results improve on previous results of Ta-Shma }[ QMA with exponentially small completeness-soundess gap, is equal to PSPACE , that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian .
Edit intent: fluency
Original:  In the logspace case, our results improve on previous results of Ta-Shma }[  QMA with exponentially small completeness-soundness gap is equal to PSPACE , that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian .
Revised:  In the logspace case, our results improve on previous results of Ta-Shma }[ QMA with exponentially small completeness-soundness gap is equal to PSPACE . Thus, the problem of estimating the minimum eigenvalue of a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian .
Edit intent: clarity
Original:  In the logspace case, our results improve on previous results of Ta-Shma }[  QMA with exponentially small completeness-soundness gap is equal to PSPACE , that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare PEPS states gives less computational power than the ability to prepare the ground state of a generic local Hamiltonian .
Revised:  In the logspace case, our results improve on previous results of Ta-Shma }[ QMA with exponentially small completeness-soundness gap is equal to PSPACE , that determining whether a local Hamiltonian is frustration-free is PSPACE-complete, and give a provable setting in which the ability to prepare the ground state of a generic local Hamiltonian .
Edit intent: clarity
Original:  No existing O(p( n)m ^{1-\epsilon}) time (1-{1\over e})-approximation algorithm for the maximum coverage has been found for any function p( n ) that only depends on the number of sets, where m =\max(|A_1|,\cdots,| A _n |) (the largest size of input sets).
Revised:  No existing O(p( m)n ^{1-\epsilon}) time (1-{1\over e})-approximation algorithm for the maximum coverage has been found for any function p( n ) that only depends on the number of sets, where m =\max(|A_1|,\cdots,| A _n |) (the largest size of input sets).
Edit intent: fluency
Original:  No existing O(p( n)m ^{1-\epsilon}) time (1-{1\over e})-approximation algorithm for the maximum coverage has been found for any function p( n ) that only depends on the number of sets, where m =\max(|A_1|,\cdots,| A _n |) (the largest size of input sets).
Revised:  No existing O(p( n)m ^{1-\epsilon}) time (1-{1\over e})-approximation algorithm for the maximum coverage has been found for any function p( m ) that only depends on the number of sets, where m =\max(|A_1|,\cdots,| A _n |) (the largest size of input sets).
Edit intent: fluency
Original:  No existing O(p( n)m ^{1-\epsilon}) time (1-{1\over e})-approximation algorithm for the maximum coverage has been found for any function p( n ) that only depends on the number of sets, where m =\max(|A_1|,\cdots,| A _n |) (the largest size of input sets).
Revised:  No existing O(p( n)m ^{1-\epsilon}) time (1-{1\over e})-approximation algorithm for the maximum coverage has been found for any function p( n ) that only depends on the number of sets, where n =\max(|A_1|,\cdots,| A _n |) (the largest size of input sets).
Edit intent: fluency
Original:  No existing O(p( n)m ^{1-\epsilon}) time (1-{1\over e})-approximation algorithm for the maximum coverage has been found for any function p( n ) that only depends on the number of sets, where m =\max(|A_1|,\cdots,| A _n |) (the largest size of input sets).
Revised:  No existing O(p( n)m ^{1-\epsilon}) time (1-{1\over e})-approximation algorithm for the maximum coverage has been found for any function p( n ) that only depends on the number of sets, where m =\max(|A_1|,\cdots,| A _m |) (the largest size of input sets).
Edit intent: fluency
Original:  For a computational problem with input size controlled by two parameters n and m, a partial sublinear time algorithm for it runs in a O(p( n)m ^{1-\epsilon}) time or O(q( m)n ^{1-\epsilon}) time.
Revised:  For a computational problem with input size controlled by two parameters n and m, a partial sublinear time algorithm for it runs in a O(p( m)n ^{1-\epsilon}) time or O(q( m)n ^{1-\epsilon}) time.
Edit intent: fluency
Original:  For a computational problem with input size controlled by two parameters n and m, a partial sublinear time algorithm for it runs in a O(p( n)m ^{1-\epsilon}) time or O(q( m)n ^{1-\epsilon}) time.
Revised:  For a computational problem with input size controlled by two parameters n and m, a partial sublinear time algorithm for it runs in a O(p( n)m ^{1-\epsilon}) time or O(q( n)m ^{1-\epsilon}) time.
Edit intent: fluency
Original:  On the other hand, we show that the maximum coverage problem has no partial sublinear O(q( m)n ^{1-\epsilon}) time constant factor approximation algorithm.
Revised:  On the other hand, we show that the maximum coverage problem has no partial sublinear O(q( n)m ^{1-\epsilon}) time constant factor approximation algorithm.
Edit intent: fluency
Original:  A D-secting family F' of F, where D=\{-1,0,1\}, is a bisecting family ensuring  existence of a subset A' \in F' such that |A \cap A'| \in \{\lceil |A|{2}\rceil,\lfloor |A|{2}\rfloor\}, for each A \in F.
Revised:  A D-secting family F' of F, where D=\{-1,0,1\}, is a bisecting family ensuring the existence of a subset A' \in F' such that |A \cap A'| \in \{\lceil |A|{2}\rceil,\lfloor |A|{2}\rfloor\}, for each A \in F.
Edit intent: fluency
Original:  In this paper, we study D-secting families for F with restrictions on D, cardinality and sizes of subsets of \mathcal{F}.
Revised:  In this paper, we study D-secting families for F with restrictions on D, and the cardinalities of \mathcal{F subsets of \mathcal{F}.
Edit intent: clarity
Original:  We show that committee scoring rules are characterized by the set of four standard axioms, anonymity, neutrality, consistency and continuity, and by two axioms specific to multiwinner rules , committee neutrality and committee dominance.
Revised:  We show that committee scoring rules are characterized by the set of four standard axioms, anonymity, neutrality, consistency and continuity, and by two axioms specific to multiwinner rules which we call committee dominance.
Edit intent: clarity
Original:  In the course of our proof, we develop several new notions  .
Revised:  In the course of our proof, we develop several new notions and techniques .
Edit intent: clarity
Original: In this paper we establish an exponential lower bound on the size of syntactic non-deterministic read d-times branching programs (d-NBPs) for d \leq \log n /10^5 computing a class of monotone CNFs with a linear number of clauses.
Revised: In this paper we establish an exponential lower bound on the size of syntactic non-deterministic read d-times branching programs for d \leq \log n /10^5 computing a class of monotone CNFs with a linear number of clauses.
Edit intent: clarity
Original:  It is thus desirable to identify structural properties of networks such that random graphs having these properties are guaranteed to be latent-geometric, that is, to be typical elements in a latent-space ensemble.
Revised:  It is thus desirable to identify structural properties of networks that guarantee that random graphs having these properties are guaranteed to be latent-geometric, that is, to be typical elements in a latent-space ensemble.
Edit intent: clarity
Original:  Here we show that random graphs in which expected degrees and clustering of every node are fixed to the same values, are equivalent to random geometric graphs on the real line  if clustering is sufficiently strong.
Revised:  Here we show that random graphs in which expected degree and clustering of every node are fixed to the same values, are equivalent to random geometric graphs on the real line if clustering is sufficiently strong.
Edit intent: fluency
Original:  Here we show that random graphs in which expected degrees and clustering of every node are fixed to the same values, are equivalent to random geometric graphs on the real line  if clustering is sufficiently strong.
Revised:  Here we show that random graphs in which expected degrees and clustering of every node are fixed to the same values, are equivalent to random geometric graphs on the real line , if clustering is sufficiently strong.
Edit intent: fluency
Original:  Large numbers of triangles, homogeneously distributed across all nodes as in real networks, are thus a signature of their latent geometry .
Revised:  Large numbers of triangles, homogeneously distributed across all nodes as in real networks, are thus a consequence of network geometricity .
Edit intent: clarity
Original: Heuristic algorithms are able to optimize objective functions efficiently because they use intelligently the information of the objective functions.
Revised: Heuristic algorithms are able to optimize objective functions efficiently because they use intelligently the information about the objective functions.
Edit intent: clarity
Original:  Thus  information utilization is vital to the performance of heuristics.
Revised:  Thus , information utilization is vital to the performance of heuristics.
Edit intent: coherence
Original:  Thus  information utilization is vital to the performance of heuristics.
Revised:  Thus information utilization is critical to the performance of heuristics.
Edit intent: clarity
Original:  However, the concept of information utilization has remained vague and abstract because there is no reliable metric to reflect the extent to which the information of the objective function is utilized in heuristic algorithms.
Revised:  However, the concept of information utilization has remained vague and abstract because there is no reliable metric to reflect the extent to which the information about the objective function is utilized in heuristic algorithms.
Edit intent: clarity
Original:  However, the concept of information utilization has remained vague and abstract because there is no reliable metric to reflect the extent to which the information of the objective function is utilized in heuristic algorithms.
Revised:  However, the concept of information utilization has remained vague and abstract because there is no reliable metric to reflect the extent to which the information of the objective function is utilized by heuristic algorithms.
Edit intent: coherence
Original:  In this paper, the metric of information utilization ratio (IUR) is defined, which is the ratio between the utilized information quantity and the acquired information quantity in the searching process.
Revised:  In this paper, the metric of information utilization ratio (IUR) is defined, which is the ratio of the utilized information quantity and the acquired information quantity in the searching process.
Edit intent: clarity
Original:  In this paper, the metric of information utilization ratio (IUR) is defined, which is the ratio between the utilized information quantity and the acquired information quantity in the searching process.
Revised:  In this paper, the metric of information utilization ratio (IUR) is defined, which is the ratio between the utilized information quantity over the acquired information quantity in the searching process.
Edit intent: clarity
Original:  In this paper, the metric of information utilization ratio (IUR) is defined, which is the ratio between the utilized information quantity and the acquired information quantity in the searching process.
Revised:  In this paper, the metric of information utilization ratio (IUR) is defined, which is the ratio between the utilized information quantity and the acquired information quantity in the search process. The
Edit intent: fluency
Original:  IUR can be an index of how exquisite an algorithm is designed and guide the design of new heuristics and the improvement of existing ones.
Revised:  IUR can be an index of how finely an algorithm is designed and guide the design of new heuristics and the improvement of existing ones.
Edit intent: clarity
Original:  IUR can be an index of how exquisite an algorithm is designed and guide the design of new heuristics and the improvement of existing ones.
Revised:  IUR can be an index of how exquisite an algorithm is designed and guide the invention of new heuristics and the improvement of existing ones.
Edit intent: clarity
Original:  We apply the method to a typical problem in chemical kinetics: the reaction mechanism of hydrogen combustion.
Revised:  We apply the method to a typical problem in chemical kinetics---the reaction mechanism of hydrogen combustion.
Edit intent: fluency
Original:  The complete weighted networks (CWNs) derived from functional connectivity analyses are fundamentally different to the sparse binary networks studied in other research areas.
Revised:  The complete weighted networks derived from functional connectivity analyses are fundamentally different to the sparse binary networks studied in other research areas.
Edit intent: clarity
Original:  We offer an alternative framework for  brain networks designed specifically for CWN analysis, generalising widely used binary network models to CWN form and analysing at different densities using straightforward metrics related to the main topological features of brain networks: integration, regularity and modularity .
Revised:  We offer an alternative framework for brain networks designed specifically for CWN analysis, generalising widely used binary network models to CWN form and analysing the main topological features of brain networks: integration, regularity and modularity .
Edit intent: coherence
Original:  We offer an alternative framework for  brain networks designed specifically for CWN analysis, generalising widely used binary network models to CWN form and analysing at different densities using straightforward metrics related to the main topological features of brain networks: integration, regularity and modularity .
Revised:  We offer an alternative framework for brain networks designed specifically for CWN analysis, generalising widely used binary network models to CWN form and analysing at different densities using straightforward metrics related to the main topological features of brain networks- integration, regularity and modularity .
Edit intent: fluency
Original:  Importantly, we introduce two techniques to probe the hierarchical complexity of topologies which complement and enhance this framework .
Revised:  Importantly, we introduce two techniques to probe the hierarchical complexity of topologies .
Edit intent: coherence
Original:  Firstly, a new metric to measure hierarchical complexity , secondly, a Weighted Complex Hierarchy (WCH) null modelfor EEG functional connectivity.
Revised:  Firstly, a new metric to measure hierarchical complexity ; secondly, a Weighted Complex Hierarchy (WCH) null modelfor EEG functional connectivity.
Edit intent: fluency
Original:  By controlling the parameters of the model, the highest complexity is found to arises between a random topology and a strict 'class-based' topology.
Revised:  By controlling the parameters of our model, the highest complexity is found to arises between a random topology and a strict 'class-based' topology.
Edit intent: fluency
Original:  By controlling the parameters of the model, the highest complexity is found to arises between a random topology and a strict 'class-based' topology.
Revised:  By controlling the parameters of the model, the highest complexity is found to arise between a random topology and a strict 'class-based' topology.
Edit intent: fluency
Original:  Our metric and model provide a full characterisation of hierarchical complexity.
Revised:  Our metric and model provide a rigorous characterisation of hierarchical complexity.
Edit intent: clarity
Original:  Importantly, our framework shows a scale of complexity arising between random and regular topologies at one extreme and star and strict ' class-based' topologies at the other.
Revised:  Importantly, our framework shows a scale of complexity arising between random and regular topologies at one extreme and 'strict class-based' topologies at the other.
Edit intent: fluency
Original:  We also anticipate that the model can be used to guide developing regions in the construction of new citiesand major transport links .
Revised:  We also anticipate that the model can be used to estimate the risk associated with actions such as the merging of cities, construction of transportation infrastructure, or interventions in trade or migration patterns .
Edit intent: clarity
Original:  Unfortunately, high throughput DNA sequencing (HTS) technologies generate  excessive number of small DNA segments -called short reads- that incur significant computational burden.
Revised:  Unfortunately, high throughput DNA sequencing (HTS) technologies generate an excessive number of small DNA segments -called short reads- that incur significant computational burden.
Edit intent: fluency
Original:  Unfortunately, high throughput DNA sequencing (HTS) technologies generate  excessive number of small DNA segments -called short reads- that incur significant computational burden.
Revised:  Unfortunately, high throughput DNA sequencing (HTS) technologies generate excessive number of small DNA segments -called short reads- that cause significant computational burden.
Edit intent: clarity
Original:  Due to sequencing errors and genomic variants, the similarity measurement between a read and "candidate" locations in the reference genome , called alignment, is formulated as an approximate string-matching problem, which is solved using quadratic-time dynamic programming algorithms .
Revised:  Due to sequencing errors and genomic variants, the similarity measurement between a read and "candidate" locations in that reference genome. The similarity measurement , called alignment, is formulated as an approximate string-matching problem, which is solved using quadratic-time dynamic programming algorithms .
Edit intent: fluency
Original:  Due to sequencing errors and genomic variants, the similarity measurement between a read and "candidate" locations in the reference genome , called alignment, is formulated as an approximate string-matching problem, which is solved using quadratic-time dynamic programming algorithms .
Revised:  Due to sequencing errors and genomic variants, the similarity measurement between a read and "candidate" locations in the reference genome , called alignment, formulated as an approximate string-matching problem, which is solved using quadratic-time dynamic programming algorithms .
Edit intent: fluency
Original:  The verification process of such candidate locations occupies most of a modern read mapper's execution time.
Revised:  Calculating the alignment of such incorrect candidate locations consumes an overwhelming majority of a modern read mapper's execution time.
Edit intent: clarity