wanyu/IteraTeR_v2 huggingface dataset:
Original:  and (5)  "road through bridges " is a sufficient condition for super linear scalability .
Revised:  and (5) The "road through bridges " is a sufficient condition for super linear scalability .
Edit intent: fluency
Original:  and (5)  "road through bridges " is a sufficient condition for super linear scalability .
Revised:  and (5) "road through bridge " is a sufficient condition for super linear scalability .
Edit intent: fluency
Original:  Population scalability describes the relationship between the performance of a population-based EA and its population size.
Revised:  The question of how the performance of a population-based EA and its population size.
Edit intent: clarity
Original:  This is called the problem of super linear population speedup under the hitting time .
Revised:  This is called the population scalability problem .
Edit intent: clarity
Original:  Although intuitively the performance of an EA may improve if its population size increases, currently there exist few theoretical answers and all are based on case studies.
Revised:  Although intuitively the performance of an EA may improve if its population size increases, currently there exist few theoretical answers to the question and all of these are based on case studies.
Edit intent: clarity
Original:  A novel approach is introduced to analyse population scalability using the spectral radius of the fundamental matrix.
Revised:  A novel approach is introduced to analyse population scalability using the notion of the fundamental matrix.
Edit intent: clarity
Original:  (2) No super linear speedup is available when elitist EAs are used to maximize any regular monotonic fitness function ;
Revised:  (2) No super linear speedup is possible in the case of regular monotonic ?tness functions ;
Edit intent: clarity
Original:  (3) Potential super linear speedup may happen when elitist EAs are used to maximize deceptive fitness functions;
Revised:  (3) Super linear speedup may happen when elitist EAs are used to maximize deceptive fitness functions;
Edit intent: clarity
Original:  (3) Potential super linear speedup may happen when elitist EAs are used to maximize deceptive fitness functions;
Revised:  (3) Potential super linear speedup may take place in the case of deceptive ?tness functions;
Edit intent: clarity
Original:  (4) \Bridgeable  " Bridgeable state" and "diversity\bridgeable  preservation" are two necessary conditions for a super linear speedup  ;
Revised:  (4) \Bridgeable point " Bridgeable state" and "diversity\bridgeable preservation" are two necessary conditions for a super linear speedup ;
Edit intent: clarity
Original:  (4) \Bridgeable  " Bridgeable state" and "diversity\bridgeable  preservation" are two necessary conditions for a super linear speedup  ;
Revised:  (4) \Bridgeable " and\bridgeable preservation" are two necessary conditions for a super linear speedup ;
Edit intent: clarity
Original:  (4) \Bridgeable  " Bridgeable state" and "diversity\bridgeable  preservation" are two necessary conditions for a super linear speedup  ;
Revised:  (4) \Bridgeable " Bridgeable state" and "diversity\bridgeable preservation" are both necessary conditions for a super linear speedup ;
Edit intent: fluency
Original:  (4) \Bridgeable  " Bridgeable state" and "diversity\bridgeable  preservation" are two necessary conditions for a super linear speedup  ;
Revised:  (4) \Bridgeable " Bridgeable state" and "diversity\bridgeable preservation" are two necessary conditions for a super linear speedup to take place ;
Edit intent: clarity
Original:  (5) The "road \road through bridge" condition is sufficient and also necessary for a super linear speedup  .
Revised:  (5) The \road through bridge" condition is sufficient and also necessary for a super linear speedup .
Edit intent: fluency
Original:  (5) The "road \road through bridge" condition is sufficient and also necessary for a super linear speedup  .
Revised:  (5) The "road \road through bridge" condition is su?cient and also necessary for a super linear speedup .
Edit intent: fluency
Original: Population-based evolutionary algorithms  have been widely applied to solving discrete optimization problems.
Revised: Population-based evolutionary algorithms (EAs) have been widely applied to solving discrete optimization problems.
Edit intent: clarity
Original: Population-based evolutionary algorithms  have been widely applied to solving discrete optimization problems.
Revised: Population-based evolutionary algorithms have been widely applied to solve various optimization problems.
Edit intent: clarity
Original:  The question of how the performance of a population-based EA varies depending on the population size arises naturally.
Revised:  The question of how the performance of a population-based EA depends on the population size arises naturally.
Edit intent: clarity
Original:  A novel approach is introduced to analyse population scalability using the notion of the fundamental matrix.
Revised:  A novel approach is introduced to analyse population scalability using the fundamental matrix.
Edit intent: clarity
Original:  (4)%DIFDELCMD < \Bridgeable %%% point" and%DIFDELCMD < \bridgeable %%% point preservation" are both necessary conditions for a super linear speedup to take place;
Revised:  (4)%DIFDELCMD < \Bridgeable %%% %DIFDELCMD < \bridgeable %%% point preservation" are both necessary conditions for a super linear speedup to take place;
Edit intent: coherence
Original: The spectral bound, s( \alpha A + \beta V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in \beta \in \Re.
Revised: The spectral bound, s( a A + \beta V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in \beta \in \Re.
Edit intent: fluency
Original: The spectral bound, s( \alpha A + \beta V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in \beta \in \Re.
Revised: The spectral bound, s( \alpha A + b V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in \beta \in \Re.
Edit intent: clarity
Original: The spectral bound, s( \alpha A + \beta V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in \beta \in \Re.
Revised: The spectral bound, s( \alpha A + \beta V), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in \in \Re.
Edit intent: clarity
Original:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Revised:  Using an elementary lemma, to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Edit intent: clarity
Original:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Revised:  Using an elementary lemma, this is here shown to imply that s( a A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Edit intent: fluency
Original:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Revised:  Using an elementary lemma, this is here shown to imply that s( \alpha A + b V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Edit intent: clarity
Original:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Revised:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in a > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Edit intent: fluency
Original:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Revised:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( a A + \beta V) / \partial \alpha \leq s(A) when it exists.
Edit intent: fluency
Original:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Revised:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + b V) / \partial \alpha \leq s(A) when it exists.
Edit intent: clarity
Original:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \alpha \leq s(A) when it exists.
Revised:  Using an elementary lemma, this is here shown to imply that s( \alpha A + \beta V) is also convex in \alpha > 0, and notably, \partial s( \alpha A + \beta V) / \partial \leq s(A) when it exists.
Edit intent: coherence
Original:  These cases are included under the general result here and shown to be part of a single  `reduction' phenomenon.
Revised:  These cases are shown here to be part of a single `reduction' phenomenon.
Edit intent: clarity
Original:  These cases are shown here to be part of a single, extremely general, `reduction' phenomenon.
Revised:  These cases are shown here to be part of a single, broadly general, `reduction' phenomenon.
Edit intent: clarity
Original:  The possibility of social behaviors affecting the migration strategies has been taken into exam, in the case anomalous diffusion is obtained by means of a continuous time random walk (CTRW).
Revised:  The possibility of social behaviors affecting the migration strategies has been taken into exam, in the case anomalous diffusion is produced by means of a continuous time random walk (CTRW).
Edit intent: clarity
Original:  In both limits, the growth rate of  fluctuations becomes independent of the Hurst exponent of the CTRW  .
Revised:  In both limits, the growth rate of the fluctuations becomes independent of the Hurst exponent of the CTRW .
Edit intent: fluency
Original: We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated to within better than a polynomial factor  in polynomial time unless P = NP.
Revised: We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial factor in polynomial time unless P = NP.
Edit intent: clarity
Original:  We also provide approximation algorithms that show that some of our lower bounds are tight, and a fixed-parameter-tractable algorithm for testing whether a drawing can be compacted to a small number of rows.
Revised:  We also provide a fixed-parameter-tractable algorithm for testing whether a drawing can be compacted to a small number of rows.
Edit intent: coherence
Original:  We also determine the complete differential spectra of x \mapsto x^7 by means of the value of some Kloosterman sums, and of x \mapsto x^{2^t-1} for t \in \{}\lfloor \rfloor\lceil \rceil
Revised:  We also determine the complete differential spectra of x \mapsto x^7 by means of the value of some Kloosterman sums, and of x \mapsto x^{2^t-1} for t \in \{}\lfloor \rfloor,\lceil \rceil
Edit intent: fluency
Original:  This expression relates these macroscopic variables to each other, generating commonly observed macroecological patterns . Since we do not require any details of the ecosystem function  to obtain these broad macroecological patterns this may explain why they are ubiquitous.
Revised:  This expression relates these macroscopic variables to each other, generating commonly observed macroecological patterns . Since we do not require any details of the ecosystem function are not required to obtain these broad macroecological patterns this may explain why they are ubiquitous.
Edit intent: clarity
Original:  Quite generally, a dimensionless control parameter for ecosystem complexity emerges from our dimensional analysis .
Revised:  A dimensionless control parameter for ecosystem complexity emerges from our dimensional analysis .
Edit intent: coherence
Original:  In the algorithm, holonomic distributions ( a generalized function in the sense of L. Schwartz) are inevitably involved even if the integrand is a usual function.
Revised:  In the algorithm, holonomic distributions ( generalized functions in the sense of L. Schwartz) are inevitably involved even if the integrand is a usual function.
Edit intent: fluency
Original:  In particular, we focus on the computational expense and  analytical work that needs to be done.
Revised:  In particular, we focus on the computational expense and the analytical work that needs to be done.
Edit intent: fluency
Original: The homology search process depends on the free energy of double stranded DNA (dsDNA) triplets bound to pre-synaptic filaments .
Revised: It has long been known that during homology recognition and strand exchange the double stranded DNA (dsDNA) triplets bound to pre-synaptic filaments .
Edit intent: coherence
Original: It has long been known that during homology recognition and strand exchange the double stranded DNA (dsDNA) in DNA/RecA filaments is highly extended, but the functional role of the extension has been unclear.
Revised: It is well known that during homology recognition and strand exchange the double stranded DNA (dsDNA) in DNA/RecA filaments is highly extended, but the functional role of the extension has been unclear.
Edit intent: clarity
Original:  We present an analytical model for the dsDNA tension .
Revised:  We present an analytical model that calculates the distribution of tension in the extended dsDNA during strand exchange .
Edit intent: clarity
Original:  The model suggests that the binding of additional dsDNA base pairs to the DNA/RecA filament alters the tension in the dsDNA that was already bound to the filament .
Revised:  The model suggests that the binding of additional dsDNA base pairs to the DNA/RecA filament alters the tension in dsDNA that was already bound to the filament .
Edit intent: fluency
Original:  We applied heat-bath cooling to 1,2-13C2-amino acids, using the \alpha\ protons to shift entropy from selected carbons to the environment.
Revised:  We applied heat-bath cooling to 1,2-13C2-amino acids, using the alpha protons to shift entropy from selected carbons to the environment.
Edit intent: fluency
Original: Chemical reaction networks taken with mass-action kinetics are dynamical systems that arise in chemical engineering and systems biology.
Revised: Chemical reaction systems are dynamical systems that arise in chemical engineering and systems biology.
Edit intent: clarity
Original:  Deciding whether a chemical reaction network admits multiple positive steady states is to determine existence of multiple positive solutions to a system of polynomials with unknown coefficients.
Edit intent: coherence
Original:  ] We consider the problem of finding the optimal coalition structure in Weighted Graph Games (WGGs) , a simple restricted representation of coalitional games%DIFDELCMD < [%%% Deng, Papadimitriou, Math.
Revised:  14] We consider the problem of finding the optimal coalition structure in Weighted Graph Games (WGGs) , a simple restricted representation of coalitional games%DIFDELCMD < [%%% Deng, Papadimitriou, Math.
Edit intent: coherence
Original:  ] We consider the problem of finding the optimal coalition structure in Weighted Graph Games (WGGs) , a simple restricted representation of coalitional games%DIFDELCMD < [%%% Deng, Papadimitriou, Math.
Revised:  ] We consider the problem of finding the optimal coalition structure in , a simple restricted representation of coalitional games%DIFDELCMD < [%%% Deng, Papadimitriou, Math.
Edit intent: clarity
Original:  ] We consider the problem of finding the optimal coalition structure in Weighted Graph Games (WGGs) , a simple restricted representation of coalitional games%DIFDELCMD < [%%% Deng, Papadimitriou, Math.
Revised:  ] We consider the problem of finding the optimal coalition structure in Weighted Graph Games (WGGs) %DIFDELCMD < [%%% Deng, Papadimitriou, Math.
Edit intent: clarity
Original:  OR 1994 . The agents in such games are vertices of the graph, and the value of a coalition is the sum of the weights of the edges present between coalition members.
Revised:  OR 1994 . The agents in such games are vertices in a graph, and the value of a coalition is the sum of the weights of the edges present between coalition members.
Edit intent: clarity
Original:  The \emph{optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions.
Revised:  The \emph{optimal coalition structure is a partition of the agents to coalitions, that maximizes the sum of utilities obtained by the coalitions.
Edit intent: fluency
Original:  Motivated by a desire to understand the computational complexity of counting constraint satisfaction problems (counting CSPs), particularly the complexity of approximation, we study functional clones of functions on the Boolean domain, which are analogous to the familiar relational clonesconstituting Post's lattice .
Revised:  Motivated by a desire to understand the computational complexity of (weighted) counting CSPs, we develop an analogous notion of functional clones and study the landscape of these clones .
Edit intent: clarity
Original:  Furthermore,  any non-trivial functional clone (in a sense that will be made precise below ) contains the binary function "implies".
Revised:  Furthermore, we show that any non-trivial functional clone (in a sense that will be made precise below ) contains the binary function "implies".
Edit intent: clarity
Original:  Furthermore,  any non-trivial functional clone (in a sense that will be made precise below ) contains the binary function "implies".
Revised:  Furthermore, any non-trivial functional clone (in a sense that will be made precise ) contains the binary function "implies".
Edit intent: coherence
Original:  As a consequence,  all non-trivial counting CSPs (with non-negative unary weights assumed to be available) are computationally at least as difficult as  #BIS, the problem of counting independent sets in a bipartite graph.
Revised:  As a consequence, all non-trivial counting CSPs are as #BIS, the problem of counting independent sets in a bipartite graph.
Edit intent: clarity
Original:  Finally, we investigate functional clones in which only restricted unary functions (either favouring 0 or 1) are available.
Revised:  Finally, we investigate functional clones in which only restricted classes of unary functions are available.
Edit intent: clarity
Original: Recovering a low rank matrix from  corrupted data, which is known as Robust PCA , has attracted considerable interests in recent years.
Revised: Recently, recovering a low rank matrix from corrupted data, which is known as Robust PCA , has attracted considerable interests in recent years.
Edit intent: coherence
Original:  In this paper, inspired by digital filtering idea in image processing, we propose a novel algorithm, named l_1 Filter, for solving Robust PCA with linear cost.
Revised:  In this paper, we propose a novel algorithm, named l_1 Filter, for solving Robust PCA with linear cost.
Edit intent: coherence
Original: Recently, recovering a low rank matrix from sparsely corrupted data , which is known as Robust Principal Component Analysis (RPCA), has attracted tremendous interest and also found many applications in computer vision society.
Revised: Recently, recovering a low rank matrix from sparsely corrupted data , which is known as robust principal component analysis (RPCA), has attracted tremendous interest and also found many applications in computer vision society.
Edit intent: fluency
Original: Recently, recovering a low rank matrix from sparsely corrupted data , which is known as Robust Principal Component Analysis (RPCA), has attracted tremendous interest and also found many applications in computer vision society.
Revised: Recently, recovering a low rank matrix from sparsely corrupted data , which is known as Robust Principal Component Analysis (RPCA), has attracted tremendous interests and found many applications in computer vision society.
Edit intent: coherence
Original:  The solution to RPCA can be exactly found by Principal Component Pursuit (PCP), i.e., minimizing a combination of nuclear norm and l_1 norm.
Revised:  The solution to RPCA can be exactly solved by principal component pursuit (PCP), i.e., minimizing a combination of nuclear norm and l_1 norm.
Edit intent: clarity
Original:  The existing methods for solving PCP all require singular value decompositions (SVD) of the data matrix, resulting in a high computational complexity, hence preventing the applications of RPCA to very large scale  problems.
Revised:  Most of the existing methods for solving PCP all require singular value decompositions (SVD) of the data matrix, resulting in a high computational complexity, hence preventing the applications of RPCA to very large scale problems.
Edit intent: clarity
Original:  The existing methods for solving PCP all require singular value decompositions (SVD) of the data matrix, resulting in a high computational complexity, hence preventing the applications of RPCA to very large scale  problems.
Revised:  The existing methods for solving PCP require singular value decompositions (SVD) of the data matrix, resulting in a high computational complexity, hence preventing the applications of RPCA to very large scale problems.
Edit intent: clarity
Original:  Numerical experiments testify to the great advantage of l_1 filtering in speed over state of the art algorithmsfor solving PCP .
Revised:  Numerical experiments testify to the great advantage of l_1 filtering in speed over state-of-the-art algorithms .
Edit intent: clarity
Original: Stochastic network calculus is an evolving theory which accounts for statistical multiplexing and uses  envelope approach for probabilistic delay and backlog analysis of networks.
Revised: Stochastic network calculus is an evolving theory which accounts for statistical multiplexing and uses an envelope approach for probabilistic delay and backlog analysis of networks.
Edit intent: fluency
Original:  The one of the key ideas of stochastic network calculus is the possibility to describe service offered at network node as  stochastic service envelope, which in turn can be used to describe the stochastic service available in a network of nodes and determine end-to-end probabilistic delay and backlog bounds.
Revised:  One of the key ideas of stochastic network calculus is the possibility to describe service offered at network node as stochastic service envelope, which in turn can be used to describe the stochastic service available in a network of nodes and determine end-to-end probabilistic delay and backlog bounds.
Edit intent: coherence