wanyu/IteraTeR_v2 huggingface dataset:
Original:  Although binary-state dynamics occurring in a broad class of complex networked systems in natureand society and has been intensively investigated, a general framework for reconstructing complex networks from binary states, the inverse problem, is lacking.
Revised:  Although binary-state dynamics that are ubiquitous in nature, technology and society still present an outstanding challenge in this field. Here we offer a framework for reconstructing complex networks from binary states, the inverse problem, is lacking.
Edit intent: coherence
Original:  Here we offer a general solution to the reconstruction problem by developing a  data-based linearization approach for binary-state dynamics with linear, nonlinear, discrete and stochastic switching functions.
Revised:  Here we offer a general solution to the reconstruction problem by developing a data-based linearization approach that is applicable to systems with linear, nonlinear, discrete and stochastic switching functions.
Edit intent: clarity
Original:  The linearization allows us to convert the network reconstruction problem into a sparse signal reconstruction problem that can be resolved efficiently and credibly by convex optimizationbased on compressed sensing.
Revised:  The linearization procedure enables us to convert the network reconstruction problem into a sparse signal reconstruction problem that can be resolved efficiently and credibly by convex optimizationbased on compressed sensing.
Edit intent: clarity
Original:  The linearization allows us to convert the network reconstruction problem into a sparse signal reconstruction problem that can be resolved efficiently and credibly by convex optimizationbased on compressed sensing.
Revised:  The linearization allows us to convert the network reconstruction into a sparse signal reconstruction problem that can be resolved efficiently and credibly by convex optimizationbased on compressed sensing.
Edit intent: fluency
Original:  Our approach opens a new route to the inverse problem in complex networked systems with binary-state dynamics and improves our ability to fully understand and control their emergent dynamics in a comprehensive way .
Revised:  Our approach opens a new route to the inverse problem in complex networked systems with binary-state dynamics .
Edit intent: coherence
Original:  Yet, mechanization of Galois connections has remained limited to certain restricted modes of use, preventing their fully general application in mechanized metatheory and certified programming.
Revised:  Yet, mechanization of Galois connections remains limited to restricted modes of use, preventing their fully general application in mechanized metatheory and certified programming.
Edit intent: clarity
Original:  Yet, mechanization of Galois connections has remained limited to certain restricted modes of use, preventing their fully general application in mechanized metatheory and certified programming.
Revised:  Yet, mechanization of Galois connections has remained limited to certain restricted modes of use, preventing their general application in mechanized metatheory and certified programming.
Edit intent: clarity
Original:  This paper presents constructive Galois connections, a framework for Galois connections that is effective both on paper and in proof assistants;
Revised:  This paper presents constructive Galois connections, a variant of Galois connections that is effective both on paper and in proof assistants;
Edit intent: clarity
Original:   Crucial to our technical approach is the addition of monadic structure to Galois connections to control a "specification effect . "  Effectful calculations may reason classically, while pure calculations have extractable computational content.
Revised:  Crucial to our metatheory is the addition of monadic structure to Galois connections to control a "specification effect . " Effectful calculations may reason classically, while pure calculations have extractable computational content.
Edit intent: clarity
Original:   Crucial to our technical approach is the addition of monadic structure to Galois connections to control a "specification effect . "  Effectful calculations may reason classically, while pure calculations have extractable computational content.
Revised:  Crucial to our technical approach is the addition of monadic structure to Galois connections to control a "specification effect " Effectful calculations may reason classically, while pure calculations have extractable computational content.
Edit intent: fluency
Original:   Crucial to our technical approach is the addition of monadic structure to Galois connections to control a "specification effect . "  Effectful calculations may reason classically, while pure calculations have extractable computational content.
Revised:  Crucial to our technical approach is the addition of monadic structure to Galois connections to control a "specification effect . " . Effectful calculations may reason classically, while pure calculations have extractable computational content.
Edit intent: fluency
Original: This paper introduces both a two-grid and a bootstrap multigrid finite element approximation to the Laplace-Beltrami (surface Laplacian) eigen-problem on a closed surface.
Revised: This paper introduces bootstrap two-grid and a bootstrap multigrid finite element approximation to the Laplace-Beltrami (surface Laplacian) eigen-problem on a closed surface.
Edit intent: clarity
Original: This paper introduces both a two-grid and a bootstrap multigrid finite element approximation to the Laplace-Beltrami (surface Laplacian) eigen-problem on a closed surface.
Revised: This paper introduces both a two-grid and multigrid finite element approximation to the Laplace-Beltrami (surface Laplacian) eigen-problem on a closed surface.
Edit intent: clarity
Original: This paper introduces both a two-grid and a bootstrap multigrid finite element approximation to the Laplace-Beltrami (surface Laplacian) eigen-problem on a closed surface.
Revised: This paper introduces both a two-grid and a bootstrap multigrid finite element approximations to the Laplace-Beltrami (surface Laplacian) eigen-problem on a closed surface.
Edit intent: clarity
Original:  The proposed multigrid method is suitable for solving problems with eigenvalues having large multiplicity, computing interior eigenvalues, and solving the shifted indefinite eigen-problem.
Revised:  The proposed multigrid method is suitable for recovering eigenvalues having large multiplicity, computing interior eigenvalues, and solving the shifted indefinite eigen-problem.
Edit intent: clarity
Original:  The proposed multigrid method is suitable for solving problems with eigenvalues having large multiplicity, computing interior eigenvalues, and solving the shifted indefinite eigen-problem.
Revised:  The proposed multigrid method is suitable for solving problems with eigenvalues having large multiplicity, computing interior eigenvalues, and approximating the shifted indefinite eigen-problem.
Edit intent: clarity
Original:  In particular, regular expression matching is a widely used computational primitive, employed in many programming languages and text processing utilities.
Edit intent: clarity
Original:  A classic algorithm for regular expressionmatching runs in O(m n) time (where m is the length of the pattern and n is the length of the text).
Revised:  A classic algorithm for these problems constructs and simulates a non-deterministic finite automaton corresponding to the expression, resulting in an O(mn) running time (where m is the length of the pattern and n is the length of the text).
Edit intent: clarity
Original:  In this paper, we show that the complexity of regular expression matching can be characterized based on its depth {\em  (when interpreted as a formula).
Revised:  In this paper, we show that the complexity of regular expression matching can be characterized based on its {\em (when interpreted as a formula).
Edit intent: coherence
Original:  Very roughly, our results state that for expressions involving concatenation, OR  and Kleene plus , the following dichotomy holds: * Matching regular expressions of depth two (involving any combination of the above operators)  can be solved in near-linear time .
Revised:  Our results hold for expressions involving concatenation, OR and Kleene plus , the following dichotomy holds: * Matching regular expressions of depth two (involving any combination of the above operators) can be solved in near-linear time .
Edit intent: clarity
Original:  Very roughly, our results state that for expressions involving concatenation, OR  and Kleene plus , the following dichotomy holds: * Matching regular expressions of depth two (involving any combination of the above operators)  can be solved in near-linear time .
Revised:  Very roughly, our results state that for expressions involving concatenation, OR and Kleene plus . For regular expressions of depth two (involving any combination of the above operators) can be solved in near-linear time .
Edit intent: coherence
Original:  * Matching regular expressions of depth three (involving any combination of the above operators) that are not reducible to some depth-two expressions cannot be solved in  sub-quadratic time unless the Strong Exponential Time Hypothesis (SETH) is false.
Revised:  * Matching regular expressions of depth three (involving any combination of the above operators) that are not reducible to some depth-two expressions cannot be solved in strongly sub-quadratic time unless the Strong Exponential Time Hypothesis (SETH) is false.
Edit intent: clarity
Original:  * Matching regular expressions of depth three (involving any combination of the above operators) that are not reducible to some depth-two expressions cannot be solved in  sub-quadratic time unless the Strong Exponential Time Hypothesis (SETH) is false.
Revised:  * Matching regular expressions of depth three (involving any combination of the above operators) that are not reducible to some depth-two expressions cannot be solved in sub-quadratic time assuming the Strong Exponential Time Hypothesis (SETH) is false.
Edit intent: clarity
Original:  Finally, a special multi-marginal case is studied, where we construct a Markov martingale and compute its explicit generator .
Revised:  Finally, a special multi-marginal case is studied, where we construct a Markov martingale and compute its generator explicitly .
Edit intent: fluency
Original:  In particular, we provide a new example of fake Brownian motion.
Revised:  In particular, this provides a new example of fake Brownian motion.
Edit intent: clarity
Original:  By using the stochastic control approach initiated in Galichon, Henry-Labord\`ere and Touzi, we identify the optimal hedging strategies and the corresponding prices in the one-marginal case .
Revised:  By using the stochastic control approach , in order to identify the optimal hedging strategies and the corresponding prices in the one-marginal case .
Edit intent: coherence
Original:  Finally, a special multi-marginal case is studied, where the stopping times given by Vallois are well-ordered .
Revised:  Finally, in a full-marginal setting where the stopping times given by Vallois are well-ordered .
Edit intent: clarity
Original: Separation Logic (SL) brought an advance to program verification of data structures by interpreting (recursively defined) predicates as implicit heaps, and using a separating conjoin operator to construct heaps from disjoint subheaps .
Revised: Separation Logic (SL) was a significant advance in program verification of data structures by interpreting (recursively defined) predicates as implicit heaps, and using a separating conjoin operator to construct heaps from disjoint subheaps .
Edit intent: clarity
Original: Separation Logic (SL) brought an advance to program verification of data structures by interpreting (recursively defined) predicates as implicit heaps, and using a separating conjoin operator to construct heaps from disjoint subheaps .
Revised: Separation Logic (SL) brought an advance to program verification of data structures . It used a "separating" conjoin operator in data structure specifications to construct heaps from disjoint subheaps .
Edit intent: clarity
Original:  Finally we demonstrate our framework to automatically prove two significant example programs, one concerning a summary of a program fragments, and one exhibiting structure sharing in data structures\emph{   .
Revised:  Finally we demonstrate our framework to automatically prove two significant example programs, one concerning a summary of a program fragments, and one exhibiting structure sharing in data structures\emph{ with .
Edit intent: clarity
Original:  Finally we demonstrate our framework to automatically prove two significant example programs, one concerning a summary of a program fragments, and one exhibiting structure sharing in data structures\emph{   .
Revised:  Finally we demonstrate our framework to automatically prove two significant example programs, one concerning a summary of a program fragments, and one exhibiting structure sharing in data structures\emph{ sharing .
Edit intent: clarity
Original:  Finally we demonstrate our framework to automatically prove two significant example programs, one concerning a summary of a program fragments, and one exhibiting structure sharing in data structures\emph{   .
Revised:  Finally we demonstrate our framework to automatically prove two significant example programs, one concerning a summary of a program fragments, and one exhibiting structure sharing in data structures\emph{ automation .
Edit intent: fluency
Original: This paper introduces  an environment for simple 2D maze games, designed as a sandbox for machine learning approaches to reasoning and planning.
Revised: This paper introduces an environment for simple 2D games, designed as a sandbox for machine learning approaches to reasoning and planning.
Edit intent: clarity
Original:  Within it, we create 10 simple games based on algorithmic tasks (e.g. embodying simple if-then statements ).
Revised:  Within it, we create 10 simple games embodying a range of algorithmic tasks (e.g. embodying simple if-then statements ).
Edit intent: clarity
Original:  Within it, we create 10 simple games based on algorithmic tasks (e.g. embodying simple if-then statements ).
Revised:  Within it, we create 10 simple games based on algorithmic tasks (e.g. if-then statements ).
Edit intent: clarity
Original:  We show that these architectures can be trained with reinforcement to respectable performance on these tasks, but are still far from optimal, despite their simplicity .
Revised:  Despite the tasks' simplicity, the performance of the models is far from optimal, despite their simplicity .
Edit intent: clarity
Original:  We show that these architectures can be trained with reinforcement to respectable performance on these tasks, but are still far from optimal, despite their simplicity .
Revised:  We show that these architectures can be trained with reinforcement to respectable performance on these tasks, but are still far from optimal, suggesting directions for future development .
Edit intent: clarity
Original:  Exact closed-form expressions of secondary outage probability are derived under a constraint on the quality of service of primary transmissions in terms of the required primary outage probability.
Revised:  Exact closed-form expressions for secondary outage probability are derived under a constraint on the quality of service of primary transmissions in terms of the required primary outage probability.
Edit intent: fluency
Original:  To better understand the impact of primary user interference on secondary transmissions, we further investigate the asymptotic behavior of the secondary relay network  when the primary signal-to-noise ratio goes to infinity , including power allocation and outage probability .
Revised:  To better understand the impact of primary user interference on secondary transmissions, we further investigate the asymptotic behaviors of the secondary relay network when the primary signal-to-noise ratio goes to infinity , including power allocation and outage probability .
Edit intent: fluency
Original:  To better understand the impact of primary user interference on secondary transmissions, we further investigate the asymptotic behavior of the secondary relay network  when the primary signal-to-noise ratio goes to infinity , including power allocation and outage probability .
Revised:  To better understand the impact of primary user interference on secondary transmissions, we further investigate the asymptotic behavior of the secondary relay network when the primary signal-to-noise ratio goes to infinity .
Edit intent: clarity
Original:  Then we introduce  a new lower bound on the unrooted SPR distance called the replug distance that is amenable to MAF methods, and give an efficient fixed-parameter algorithm for calculating it.
Revised:  Then we introduce the replug distance, a new lower bound on the unrooted SPR distance called the replug distance that is amenable to MAF methods, and give an efficient fixed-parameter algorithm for calculating it.
Edit intent: fluency
Original:  Then we introduce  a new lower bound on the unrooted SPR distance called the replug distance that is amenable to MAF methods, and give an efficient fixed-parameter algorithm for calculating it.
Revised:  Then we introduce a new lower bound on the unrooted SPR distance that is amenable to MAF methods, and give an efficient fixed-parameter algorithm for calculating it.
Edit intent: clarity
Original: This study demonstrates that incorrect values are entered into  pairwise comparisons matrix for processing .
Revised: This study demonstrates that incorrect data are entered into pairwise comparisons matrix for processing .
Edit intent: clarity
Original: This study demonstrates that incorrect values are entered into  pairwise comparisons matrix for processing .
Revised: This study demonstrates that incorrect values are entered into a pairwise comparisons matrix for processing .
Edit intent: fluency
Original:  A solution  , based on normalization, is proposed  .
Revised:  A solution to it , based on normalization, is proposed .
Edit intent: clarity
Original:  Such research is difficult because it requires making sense of non-linear computations performed by millions of learned parameters, but valuable because it increases our ability to understand current models and training algorithms and thus create improved versions of them.
Revised:  Such research is difficult because it requires making sense of non-linear computations performed by millions of parameters, but valuable because it increases our ability to understand current models and training algorithms and thus create improved versions of them.
Edit intent: clarity
Original:  Such research is difficult because it requires making sense of non-linear computations performed by millions of learned parameters, but valuable because it increases our ability to understand current models and training algorithms and thus create improved versions of them.
Revised:  Such research is difficult because it requires making sense of non-linear computations performed by millions of learned parameters, but valuable because it increases our ability to understand current models and create improved versions of them.
Edit intent: clarity
Original:  (3) that the representation codes are a mix between a local code and slightly, but not fully, distributed codes across multiple units.
Revised:  (3) that the representation codes show evidence of being a mix between a local code and slightly, but not fully, distributed codes across multiple units.
Edit intent: clarity
Original: Many real-world relations can be represented by signed networks with positive and negative links, and signed network analysis has attracted increasing attention from multiple disciplines.
Revised: Many real-world relations can be represented by signed networks with positive and negative links, as a result of which signed network analysis has attracted increasing attention from multiple disciplines.
Edit intent: coherence
Original:  With the evolution of data from offline to social media networks, signed network analysis has evolved from developing and measuring theories to mining tasks.
Revised:  With the increasing prevalence of social media networks, signed network analysis has evolved from developing and measuring theories to mining tasks.
Edit intent: clarity
Original:  We also delineate some tasks that have not been extensively studied with formal definitions and  research directions to expand the boundaries of signed network mining.
Revised:  We also delineate some tasks that have not been extensively studied with formal definitions and also propose research directions to expand the boundaries of signed network mining.
Edit intent: clarity
Original:  We also delineate some tasks that have not been extensively studied with formal definitions and  research directions to expand the boundaries of signed network mining.
Revised:  We also delineate some tasks that have not been extensively studied with formal definitions and research directions to expand the field of signed network mining.
Edit intent: clarity
Original:  Furthermore, it sets a new state-of-the-art on PASCAL VOC2012 test set achieving mAP of 74.8\%.
Edit intent: coherence
Original:  Finally, we demonstrate that our detection approach can achieve high detection accuracy even when it is given as input a set of sliding windows, thus proving that it is independent of bounding box proposal methods.
Revised:  Finally, we demonstrate that our detection approach can achieve high detection accuracy even when it is given as input a set of sliding windows, thus proving that it is independent of box proposal methods.
Edit intent: clarity
Original: We introduce a new information-theoretic complexity measure IC_\infty for 2-party functions which is a lower-bound on communication complexity, and has the two leading lower-bounds on communication complexity as its natural relaxations: (external) information complexity (IC) and logarithm of partition complexity (prt)  which have so far appeared conceptually quite different from each other.
Revised: We introduce a new information-theoretic complexity measure IC_\infty for 2-party functions which is a lower-bound on communication complexity, and has the two leading lower-bounds on communication complexity as its natural relaxations: (external) information complexity (IC) and logarithm of partition complexity (prt) , which have so far appeared conceptually quite different from each other.
Edit intent: fluency
Original:  IC_\infty is an external information complexity  based on R\'enyi mutual information of order infinity.
Revised:  IC_\infty is an external information complexity measure based on R\'enyi mutual information of order infinity.
Edit intent: clarity
Original: We give an introduction to some of the recent ideas that go under the name `` geometric complexity theory '' . We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent.
Revised: We give an introduction to some of the recent ideas that go under the name " geometric complexity theory '' . We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent.
Edit intent: fluency
Original: We give an introduction to some of the recent ideas that go under the name `` geometric complexity theory '' . We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent.
Revised: We give an introduction to some of the recent ideas that go under the name `` geometric complexity theory " . We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent.
Edit intent: fluency
Original: We show that the ]  Graph Automorphism problem is ZPP-reducible to MKTP, the problem of minimizing time-bounded Kolmogorov complexity.
Revised: It is well-known ] Graph Automorphism problem is ZPP-reducible to MKTP, the problem of minimizing time-bounded Kolmogorov complexity.
Edit intent: coherence