wanyu/IteraTeR_v2 huggingface dataset:
Original:  By contrast, if the intrinsic heterogeneity of banks  is controlled for, the same properties undergo a slow and continuous transition , gradually connecting the crisisperiod to a much earlier stationary phase.
Revised:  By contrast, if the heterogeneity of banks is controlled for, the same properties undergo a slow and continuous transition , gradually connecting the crisisperiod to a much earlier stationary phase.
Edit intent: clarity
Original:  This early-warning signal begins in 2005 , and is preceded by an even earlier period of "risk autocatalysis" characterized by anomalous debt loops .
Revised:  This early-warning signal begins in 2005 and preceded by an even earlier period of "risk autocatalysis" characterized by anomalous debt loops .
Edit intent: fluency
Original:  This early-warning signal begins in 2005 , and is preceded by an even earlier period of "risk autocatalysis" characterized by anomalous debt loops .
Revised:  This early-warning signal begins in 2005 , and is preceded by an even earlier period during which anomalous debt loops .
Edit intent: clarity
Original: The financial crisis clearly illustrated the importance of characterizing the level of ` systemic' risk associated with an entire credit network, rather than with single institutions.
Revised: The financial crisis clearly illustrated the importance of characterizing the level of ' systemic' risk associated with an entire credit network, rather than with single institutions.
Edit intent: fluency
Original:  of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k  conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. A%DIFDELCMD < {\em %DIFDELCMD < %%% \kappa-deletion-minimal graph is one with maximum degree at most \kappa , and it has no acyclic edge coloring with \kappa colors, but{\em  \chiup'(G) > \kappa and }\chiup'(H) \leq \kappa for } every proper subgraph admits an acyclic edge coloring with \kappa colors .
Revised:  of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. %DIFDELCMD < {\em %DIFDELCMD < %%% \kappa-deletion-minimal graph is one with maximum degree at most \kappa , and it has no acyclic edge coloring with \kappa colors, but{\em \chiup'(G) > \kappa and }\chiup'(H) \leq \kappa for } every proper subgraph admits an acyclic edge coloring with \kappa colors .
Edit intent: fluency
Original:  of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k  conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. A%DIFDELCMD < {\em %DIFDELCMD < %%% \kappa-deletion-minimal graph is one with maximum degree at most \kappa , and it has no acyclic edge coloring with \kappa colors, but{\em  \chiup'(G) > \kappa and }\chiup'(H) \leq \kappa for } every proper subgraph admits an acyclic edge coloring with \kappa colors .
Revised:  of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. A%DIFDELCMD < {\em %DIFDELCMD < %%% \kappa-deletion-minimal graph is one with maximum degree at most \kappa is{\em \chiup'(G) > \kappa and }\chiup'(H) \leq \kappa for } every proper subgraph admits an acyclic edge coloring with \kappa colors .
Edit intent: coherence
Original:  of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k  conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. A%DIFDELCMD < {\em %DIFDELCMD < %%% \kappa-deletion-minimal graph is one with maximum degree at most \kappa , and it has no acyclic edge coloring with \kappa colors, but{\em  \chiup'(G) > \kappa and }\chiup'(H) \leq \kappa for } every proper subgraph admits an acyclic edge coloring with \kappa colors .
Revised:  of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. A%DIFDELCMD < {\em %DIFDELCMD < %%% \kappa-deletion-minimal graph is one with maximum degree at most \kappa , and it has no acyclic edge coloring with \kappa colors, but{\em \kappa-deletion-minimal \chiup'(G) > \kappa and }\chiup'(H) \leq \kappa for } every proper subgraph admits an acyclic edge coloring with \kappa colors .
Edit intent: fluency
Original:  of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k  conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. A%DIFDELCMD < {\em %DIFDELCMD < %%% \kappa-deletion-minimal graph is one with maximum degree at most \kappa , and it has no acyclic edge coloring with \kappa colors, but{\em  \chiup'(G) > \kappa and }\chiup'(H) \leq \kappa for } every proper subgraph admits an acyclic edge coloring with \kappa colors .
Revised:  of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. A%DIFDELCMD < {\em %DIFDELCMD < %%% \kappa-deletion-minimal graph is one with maximum degree at most \kappa , and it has no acyclic edge coloring with \kappa colors, but{\em \chiup'(G) > \kappa and }\chiup'(H) \leq \kappa for } every proper subgraph H of G .
Edit intent: clarity
Original:  In this paper, we give some structure lemmas on the \kappa-deletion-minimal graphs.
Revised:  In this paper, we present some structural lemmas on \kappa-deletion-minimal graphs.
Edit intent: clarity
Original:  We hope the structural lemmas will shed some light } on the acyclic edge coloring problem .
Revised:  We hope the structural lemmas will shed some light } on the acyclic edge coloring problems .
Edit intent: fluency
Original:  A graph G with maximum degree at most \kappa is {\em \kappa-deletion-minimal} if a'(G) > \kappa and a'(H) \leq \kappa for every proper subgraph H of G. In this paper , we present some structural lemmas on \kappa-deletion-minimal graphs.
Revised:  A graph G with maximum degree at most \kappa is {\em \kappa-deletion-minimal} if a'(G) > \kappa and a'(H) \leq \kappa for every proper subgraph H of G. The purpose of this paper is to provide many structural lemmas on \kappa-deletion-minimal graphs.
Edit intent: clarity
Original:  The {\em acyclic chromatic index} a'(G) of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k (1978) conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. This conjecture is well-known as Acyclic Edge Coloring Conjecture (AECC).
Revised:  The {\em acyclic chromatic index} a'(G) of a graph G is the least number of colors needed in an acyclic edge coloring of G. Fiamc\'{i}k (1978) conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. This conjecture is well-known as Acyclic Edge Coloring Conjecture (AECC).
Edit intent: fluency
Original:  The {\em acyclic chromatic index} a'(G) of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k (1978) conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. This conjecture is well-known as Acyclic Edge Coloring Conjecture (AECC).
Revised:  The {\em acyclic chromatic index} a'(G) of a graph G is the least number of colors needed in any acyclic edge coloring of G. Fiamc\'{i}k (1978) conjectured that a'(G) \leq \Delta(G) + 2, where \Delta(G) is the maximum degree of G. This conjecture is well known as Acyclic Edge Coloring Conjecture (AECC).
Edit intent: fluency
Original:  By using the structural lemmas, we firstly prove that AECC is true for the graphs with maximum average degree less than four ( Theorem 4.3 ).
Revised:  By using the structural lemmas, we firstly prove that AECC is true for the graphs with maximum average degree less than four ( ).
Edit intent: clarity
Original:  We secondly prove that AECC is true for the planar graphs without triangles adjacent to cycles of length at most four, with an additional condition that every 5-cycle has at most three edges contained in triangles ( Theorem 4.4 ), from which we can conclude some known results as corollaries.
Revised:  We secondly prove that AECC is true for the planar graphs without triangles adjacent to cycles of length at most four, with an additional condition that every 5-cycle has at most three edges contained in triangles ( ), from which we can conclude some known results as corollaries.
Edit intent: coherence
Original:  We thirdly prove that every planar graph G without intersecting triangles satisfies a'(G) \leq \Delta(G) + 3 ( Theorem 4.6 ).
Revised:  We thirdly prove that every planar graph G without intersecting triangles satisfies a'(G) \leq \Delta(G) + 3 ( ).
Edit intent: clarity
Original: Implicit-explicit  time stepping methods have proved useful for efficiently solving problems with both stiff and nonstiff components.
Revised: Implicit-explicit time stepping methods can efficiently solve differential equa- tions with both stiff and nonstiff components.
Edit intent: clarity
Original:  The new algorithms have great potential for practical use . Numerical results indicate the observed order of accuracy matches the theoretical order .
Revised:  The new algorithms have great potential for practical use . Numerical results confirm the theoretical findings .
Edit intent: clarity
Original:  This definition allows to compute the  non-termination precondition if either (i) the transition relation is deterministic, (ii) the descending Kleene sequence overapproximating the greatest fixpoint converges in finitely many steps, or (iii) the transition relation is well-founded .
Revised:  This definition allows to compute the non-termination precondition if at least one of the following holds: (i) the transition relation is deterministic, (ii) the descending Kleene sequence overapproximating the greatest fixpoint converges in finitely many steps, or (iii) the transition relation is well-founded .
Edit intent: clarity
Original:  This definition allows to compute the  non-termination precondition if either (i) the transition relation is deterministic, (ii) the descending Kleene sequence overapproximating the greatest fixpoint converges in finitely many steps, or (iii) the transition relation is well-founded .
Revised:  This definition allows to compute the non-termination precondition if either (i) the transition relation is deterministic, (ii) the descending Kleene sequence overapproximating the greatest fixpoint converges in finitely many steps, or (iii) the transition relation is well founded .
Edit intent: fluency
Original:  We  also improve estimates in the normal homogeneous-form of an arithmetic circuit obtained by Raz in Raz2009  . Our methods yield non-trivial lower bounds for the circuit size of several classes of multivariate homogeneous polynomials ( Examples 4.6, 4.9 ).
Revised:  We also improve estimates in the normal homogeneous-form of an arithmetic circuit obtained by Raz in Raz2009 . Our methods yield non-trivial lower bound for the circuit size of several classes of multivariate homogeneous polynomials ( Examples 4.6, 4.9 ).
Edit intent: fluency
Original: In this paper we associate to each partially homogeneous multivariate polynomial f over any field a series of polynomial families P_\lambda (f) of m-tuples of homogeneous polynomials of equal degree such that the circuit size of any member in P_\lambda (f) is bounded from above by the circuit size of f.
Revised: In this paper we associate to each multivariate polynomial f over any field a series of polynomial families P_\lambda (f) of m-tuples of homogeneous polynomials of equal degree such that the circuit size of any member in P_\lambda (f) is bounded from above by the circuit size of f.
Edit intent: clarity
Original:  At last, we evaluate the SPCP-TFC method by abundant simulations, and show it has  superior performance than other traffic baseline methods such as RBL and PCA.
Revised:  At last, we evaluate the SPCP-TFC method by abundant simulations, and show it has a superior performance than other traffic baseline methods such as RBL and PCA.
Edit intent: fluency
Original: In this letter, we develop a novel network-wide traffic analysis methodology , named Stable Principal Component Pursuit with Time-Frequency Constraints (SPCP-TFC), for extracting the baseline of a traffic matrix.
Revised: In this letter, we develop a novel baseline scheme , named Stable Principal Component Pursuit with Time-Frequency Constraints (SPCP-TFC), for extracting the baseline of a traffic matrix.
Edit intent: clarity
Original:  At last, we evaluate the SPCP-TFC method by abundant simulations, and show it has a superior performance than other traffic baseline methods such as RBL and PCA.
Revised:  At last, we evaluate this baseline scheme through simulations, and show it has a superior performance than other traffic baseline methods such as RBL and PCA.
Edit intent: clarity
Original:  At last, we evaluate the SPCP-TFC method by abundant simulations, and show it has a superior performance than other traffic baseline methods such as RBL and PCA.
Revised:  At last, we evaluate the SPCP-TFC method by abundant simulations, and show it has superior performance than other traffic baseline methods such as RBL and PCA.
Edit intent: fluency
Original:  At last, we evaluate the SPCP-TFC method by abundant simulations, and show it has a superior performance than other traffic baseline methods such as RBL and PCA.
Revised:  At last, we evaluate the SPCP-TFC method by abundant simulations, and show it has a superior performance than the existing baseline schemes RBL and PCA.
Edit intent: clarity
Original:  Additionally, we show numerically that the formulation with overlapping generations leads to similar results as the standard model with non-overlapping generations and the diffusion approximation in the regime where the ratchet clicks frequently.
Revised:  Additionally, we confirm numerically that the formulation with overlapping generations leads to similar results as the standard model with non-overlapping generations and the diffusion approximation in the regime where the ratchet clicks frequently.
Edit intent: clarity
Original:  Additionally, we show numerically that the formulation with overlapping generations leads to similar results as the standard model with non-overlapping generations and the diffusion approximation in the regime where the ratchet clicks frequently.
Revised:  Additionally, we show numerically that the formulation with overlapping generations leads to the same results as the standard model with non-overlapping generations and the diffusion approximation in the regime where the ratchet clicks frequently.
Edit intent: fluency
Original: Message-passing algorithms based on Belief-Propagation (BP) are successfully used for many applications including decoding error correcting codes and solving constraint satisfaction and inference problems.
Revised: Message-passing algorithms based on belief-propagation (BP) are successfully used for many applications including decoding error correcting codes and solving constraint satisfaction and inference problems.
Edit intent: fluency
Original: Message-passing algorithms based on Belief-Propagation (BP) are successfully used for many applications including decoding error correcting codes and solving constraint satisfaction and inference problems.
Revised: Message-passing algorithms based on Belief-Propagation (BP) are successfully used in many applications including decoding error correcting codes and solving constraint satisfaction and inference problems.
Edit intent: clarity
Original:  BP-based algorithms operate over graphs representations, called factor graphs, that are used to model the input.
Revised:  BP-based algorithms operate over graph representations, called factor graphs, that are used to model the input.
Edit intent: fluency
Original:  We study the performance of the Min-Sum algorithm when applied to the corresponding factor graph models of packing and covering LPs.
Revised:  We study the performance of the min-sum algorithm when applied to the corresponding factor graph models of packing and covering LPs.
Edit intent: fluency
Original:  This implies that the Min-Sum algorithm computes the optimal integral solution only if the LP has a unique integral optimal solution.
Revised:  This implies that the min-sum algorithm computes the optimal integral solution only if the LP has a unique integral optimal solution.
Edit intent: fluency
Original:  Our result unifies and extends recent results for the maximum weighted matching problem by [Sanghavi et al.,'2011] and [Bayati et al., 2011] and for the maximum weight independent set problem [Sanghavi et al.'2009].
Revised:  Our result unifies and extends recent results for the maximum weight matching problem by [Sanghavi et al.,'2011] and [Bayati et al., 2011] and for the maximum weight independent set problem [Sanghavi et al.'2009].
Edit intent: fluency
Original: RNA sequencing (RNA-seq) has been rapidly adopted for the multilayered profiling of transcriptomes in many areas of biology, including studies into gene regulation, development and disease.
Revised: RNA sequencing (RNA-seq) has been rapidly adopted for the profiling of transcriptomes in many areas of biology, including studies into gene regulation, development and disease.
Edit intent: clarity
Original:  Several variations have been presented in the literature, thus there is a need for guidance on current best practices.
Revised:  Several variations have been presented in the literature, and there is a need for guidance on current best practices.
Edit intent: coherence
Original:  Therefore, this study aims to set up standards for the use of bibliometrics in the evaluation of individual researchers working in the natural  sciences.
Revised:  Therefore, this study aims to set up proposals how to evaluate individual researchers working in the natural sciences.
Edit intent: clarity
Original:  Our standards relate to the selection of data on which an evaluation is based, the analysis of the data and the presentation of the results.
Revised:  Our proposals relate to the selection of data on which an evaluation is based, the analysis of the data and the presentation of the results.
Edit intent: clarity
Original: In this paper, we extend the work of our previous paper "Bounds on monotone switching networks for directed connectivity" by further analyzing the monotone space complexity of directed connectivity .
Revised: In this paper, we analyze the monotone space of complexity of directed connectivity .
Edit intent: clarity
Original:  By using this extra information, they can reduce the duration of exchanging a single bit and in this way they achieve not only higher speed but also an enhanced security because Eve's information will significantly be reduced due to smaller statistics.
Edit intent: coherence
Original:  The first is syntactic complexity of a regular language , that is, the cardinality of the syntactic semigroup of the language.
Revised:  The first is syntactic complexity , that is, the cardinality of the syntactic semigroup of the language.
Edit intent: clarity
Original:  That semigroup is isomorphic to the semigroup of transformations of the set of states performed by non-empty words in the minimal deterministic finite automaton accepting the language.
Revised:  That semigroup is isomorphic to the semigroup of transformations of states induced by non-empty words in the minimal deterministic finite automaton accepting the language.
Edit intent: clarity
Original:  In the worst case, a regular language has  2^n atoms  .
Revised:  In the worst case, a regular language has at most 2^n atoms .
Edit intent: clarity
Original:  The maximal quotient complexity of any atom with r complemented quotients is 2^n-1  if r=0 or r=n, and 1+k=1^{r} h=k+1^{k+n-r} C_{h^{n} \cdot C_{k}^{h} otherwise, where C_j^i is the binomial coefficient}  .
Revised:  The maximal quotient complexity of any atom with r complemented quotients is 2^n-1 , if r=0 or r=n, and 1+k=1^{r} h=k+1^{k+n-r} C_{h^{n} \cdot C_{k}^{h} otherwise, where C_j^i is the binomial coefficient} .
Edit intent: fluency
Original:  The maximal quotient complexity of any atom with r complemented quotients is 2^n-1  if r=0 or r=n, and 1+k=1^{r} h=k+1^{k+n-r} C_{h^{n} \cdot C_{k}^{h} otherwise, where C_j^i is the binomial coefficient}  .
Revised:  The maximal quotient complexity of any atom with r complemented quotients is 2^n-1 if r=0 or r=n, and 1+k=1^{r} h=k+1^{k+n-r} C_{h^{n} \cdot C_{k}^{h} otherwise, where C_j^i is the binomial coefficient} , otherwise .
Edit intent: coherence
Original:  Second, we show that there is no model-checking algorithm with elementary parameter dependence for MSO logic even restricted to paths (or equivalently to unary strings), unless EXP = NEXP . As a corollary, we resolve an open problem on the complexity of MSO model-checking on graphs of bounded max-leaf number.
Revised:  Second, we show that there is no model-checking algorithm with elementary parameter dependence for MSO logic even restricted to paths (or equivalently to unary strings), unless E = NEXP . As a corollary, we resolve an open problem on the complexity of MSO model-checking on graphs of bounded max-leaf number.
Edit intent: clarity
Original:  We show that, assuming the ETH, for every fixed d\ge 1 at least d+1 levels of exponentiation are necessary for this problem, thus showing that the (d+1)-fold exponential algorithm recently given by Gajarsk\'y and Hline n\`y is essentially optimal.
Revised:  We show that, assuming the ETH, for every fixed d\ge 1 at least d+1 levels of exponentiation are necessary for this problem, thus showing that the (d+1)-fold exponential algorithm recently given by Gajarsk\'y and Hline n\'y is essentially optimal.
Edit intent: fluency
Original: Biological systems show two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur;
Revised: Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur;
Edit intent: fluency
Original:  and modularity : the near decomposability of the system into modules with distinct functionality.
Revised:  and modularity - the near decomposability of the system into modules with distinct functionality.
Edit intent: fluency
Original:  We find that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for  special situations.
Revised:  We found that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for special situations.
Edit intent: fluency
Original:  We find that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for  special situations.
Revised:  We find that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for in special situations.
Edit intent: fluency
Original:  In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers , a better model for the effects of biological mutations , lead to sparseness naturally.
Revised:  In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers - a better model for the effects of biological mutations , lead to sparseness naturally.
Edit intent: fluency
Original:  In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers , a better model for the effects of biological mutations , lead to sparseness naturally.
Revised:  In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers , a better model for the effects of biological mutations - led to sparseness naturally.
Edit intent: fluency