wanyu/IteraTeR_v2 huggingface dataset:
Original:  The result nicely compliments existing contracts that enforce partial correctness to obtain the first contracts for total correctness.
Revised:  The result nicely compliments existing contracts that enforce partial correctness specifications to obtain contracts for total correctness.
Edit intent: clarity
Original:  We apply higher-order symbolic execution to obtain a novel terminationanalysis that is competitive with  existing, purpose-built termination analyzers.
Revised:  We apply higher-order symbolic execution to obtain a novel terminationanalysis that is competitive with with existing, purpose-built termination analyzers.
Edit intent: fluency
Original:  We apply higher-order symbolic execution to obtain a novel terminationanalysis that is competitive with  existing, purpose-built termination analyzers.
Revised:  We apply higher-order symbolic execution to obtain a novel terminationanalysis that is competitive with existing, purpose-built analyzers.
Edit intent: fluency
Original:  Our bounds hold for a class of phase-type file size distributions;
Revised:  Our bounds hold for a class of phase-type file-size distributions;
Edit intent: fluency
Original:  Furthermore, our state-space collapse result implies an interchange of limits as a by-product for the diffusion approximation by Vlasiou, Zhang and Zwart (2014) .
Revised:  Furthermore, this state-space collapse result implies an interchange of limits as a by-product for the diffusion approximation by Vlasiou, Zhang and Zwart (2014) .
Edit intent: clarity
Original:  Furthermore, our state-space collapse result implies an interchange of limits as a by-product for the diffusion approximation by Vlasiou, Zhang and Zwart (2014) .
Revised:  Furthermore, our state-space collapse result implies the interchange of limits as a by-product for the diffusion approximation by Vlasiou, Zhang and Zwart (2014) .
Edit intent: fluency
Original: Mastering the dynamics of social influence requires separating, in a database of information propagation traces, the genuine causal processes from temporal correlation,  homophily and other spurious causes.
Revised: Mastering the dynamics of social influence requires separating, in a database of information propagation traces, the genuine causal processes from temporal correlation, i.e., homophily and other spurious causes.
Edit intent: coherence
Original:  However, most of the studies to characterize social influence  and, in general, most data-science analyses focus on correlations, statistical independence, conditional independence etc. ;
Revised:  However, most studies to characterize social influence and, in general, most data-science analyses focus on correlations, statistical independence, conditional independence etc. ;
Edit intent: coherence
Original:  However, most of the studies to characterize social influence  and, in general, most data-science analyses focus on correlations, statistical independence, conditional independence etc. ;
Revised:  However, most of the studies to characterize social influence , and, in general, most data-science analyses focus on correlations, statistical independence, conditional independence etc. ;
Edit intent: fluency
Original:  In this paper we adopt a principled causal approach to the analysis of social influence from information-propagation data, rooted in probabilistic causal theory .
Revised:  In this paper we adopt a principled causal approach to the analysis of social influence from information-propagation data, rooted in the theory of probabilistic causation .
Edit intent: fluency
Original:  Our approach develops around two phases.
Revised:  Our approach consists of two phases.
Edit intent: clarity
Original:  In the first step , in order to avoid the pitfalls of misinterpreting causation when the data spans a mixture of several subtypes ("Simpson's paradox"), we partition the set of propagation traces in groups, in such a way that each group is as less contradictory as possible in terms of the hierarchical structure of information propagation.
Revised:  In the first one , in order to avoid the pitfalls of misinterpreting causation when the data spans a mixture of several subtypes ("Simpson's paradox"), we partition the set of propagation traces in groups, in such a way that each group is as less contradictory as possible in terms of the hierarchical structure of information propagation.
Edit intent: clarity
Original:  In the first step , in order to avoid the pitfalls of misinterpreting causation when the data spans a mixture of several subtypes ("Simpson's paradox"), we partition the set of propagation traces in groups, in such a way that each group is as less contradictory as possible in terms of the hierarchical structure of information propagation.
Revised:  In the first step , in order to avoid the pitfalls of misinterpreting causation when the data spans a mixture of several subtypes ("Simpson's paradox"), we partition the set of propagation traces into groups, in such a way that each group is as less contradictory as possible in terms of the hierarchical structure of information propagation.
Edit intent: fluency
Original:  For this goalwe borrow from the literature the notion of "agony" and define the Agony-bounded Partitioning problem, which we prove being hard, and for which we develop two efficient algorithms with approximation guarantees.
Revised:  To achieve this goal, we borrow the notion of "agony" and define the Agony-bounded Partitioning problem, which we prove being hard, and for which we develop two efficient algorithms with approximation guarantees.
Edit intent: clarity
Original:  In the second step , for each group from the first phase, we apply a constrained MLE approach to ultimately learn a minimal causal topology.
Revised:  In the second phase , for each group from the first phase, we apply a constrained MLE approach to ultimately learn a minimal causal topology.
Edit intent: fluency
Original:  Experiments on synthetic data show that our method is able to retrieve the genuine causal arcs w.r.t. a known ground-truth generative model.
Revised:  Experiments on synthetic data show that our method is able to retrieve the genuine causal arcs w.r.t. a ground-truth generative model.
Edit intent: clarity
Original:  Experiments on real data show that, by focusing only on the extracted causal structures instead of the whole social network, we can improve the effectiveness of predicting influence spread  .
Revised:  Experiments on real data show that, by focusing only on the extracted causal structures instead of the whole social graph, the effectiveness of predicting influence spread .
Edit intent: clarity
Original: Despite great advances, molecular cancer pathology is often limited to use a small number of biomarkers rather than the whole transcriptome, partly due to the computational challenges.
Revised: Despite great advances, molecular cancer pathology is often limited to the use of a small number of biomarkers rather than the whole transcriptome, partly due to the computational challenges.
Edit intent: fluency
Original: Despite great advances, molecular cancer pathology is often limited to use a small number of biomarkers rather than the whole transcriptome, partly due to the computational challenges.
Revised: Despite great advances, molecular cancer pathology is often limited to use a small number of biomarkers rather than the whole transcriptome, partly due to computational challenges.
Edit intent: fluency
Original:  Our system significantly outperforms prior works and classical machine learning approaches in predicting tissue-of-origin, normal or disease state and cancer type of each sample.
Revised:  Our method significantly outperforms prior works and classical machine learning approaches in predicting tissue-of-origin, normal or disease state and cancer type of each sample.
Edit intent: clarity
Original: For a given graph G, each partition of the vertices has a modularity score, with higher values taken to indicate that the partition better captures community structure in G. The modularity q* (G) (where 0\leq q*(G)\leq 1) of the graph G is defined to be the maximum over all vertex partitions of the modularity score .
Revised: For a given graph G, each partition of the vertices has a modularity score, with higher values indicating that the partition better captures community structure in G. The modularity q* (G) (where 0\leq q*(G)\leq 1) of the graph G is defined to be the maximum over all vertex partitions of the modularity score .
Edit intent: clarity
Original: For a given graph G, each partition of the vertices has a modularity score, with higher values taken to indicate that the partition better captures community structure in G. The modularity q* (G) (where 0\leq q*(G)\leq 1) of the graph G is defined to be the maximum over all vertex partitions of the modularity score .
Revised: For a given graph G, each partition of the vertices has a modularity score, with higher values taken to indicate that the partition better captures community structure in G. The modularity q* (G) of the graph G is defined to be the maximum over all vertex partitions of the modularity score .
Edit intent: coherence
Original:  In particular, we may want to understand the behaviour of modularity for the Erdos-R\'enyi random graph G_{n,p} with n vertices and edge-probability p.
Revised:  In particular, we may want to understand the behaviour of the modularity of the Erdos-R\'enyi random graph G_{n,p} with n vertices and edge-probability p.
Edit intent: fluency
Original:  Two key features which we find are that the modularity is 1+o(1) with high probability (whp) for np up to 1+o(1) ( and no further ) ;
Revised:  Two key findings are that the modularity is 1+o(1) with high probability (whp) for np up to 1+o(1) ( and no further ) ;
Edit intent: clarity
Original:  Two key features which we find are that the modularity is 1+o(1) with high probability (whp) for np up to 1+o(1) ( and no further ) ;
Revised:  Two key features which we find are that the modularity is 1+o(1) with high probability (whp) for np up to 1+o(1) and no further ) ;
Edit intent: fluency
Original:  Two key features which we find are that the modularity is 1+o(1) with high probability (whp) for np up to 1+o(1) ( and no further ) ;
Revised:  Two key features which we find are that the modularity is 1+o(1) with high probability (whp) for np up to 1+o(1) ( and no further ;
Edit intent: fluency
Original: An oriented graph is a directed graph with no loops or digons.
Revised: A vertex in a directed graph with no loops or digons.
Edit intent: clarity
Original:  The second out-neighbors of a vertex u in an oriented graph are the vertices to which there exist directed paths of length 2 from u, but are not out-neighbors of u .
Revised:  The second out-neighbors as out-neighbors of u .
Edit intent: clarity
Original:  The second out-neighbors of a vertex u in an oriented graph are the vertices to which there exist directed paths of length 2 from u, but are not out-neighbors of u .
Revised:  The second out-neighbors of a vertex u in an oriented graph are the vertices to which there exist directed paths of length 2 from u, but are not out-neighbors .
Edit intent: clarity
Original:  The Second Neighborhood Conjecture, first stated by Seymour, asserts that in every oriented graph, there is a vertex which has at least as many second out-neighbors as out-neighbors .
Revised:  The Second Neighborhood Conjecture, first stated by Seymour, asserts that there is a vertex which has at least as many second out-neighbors as out-neighbors .
Edit intent: clarity
Original:  Using this model , we examine connected components of observable nodes and of unobservable nodes in random clustered networks, which generalize random graphs to include triangles.
Revised:  For the observability model on random clustered networks, which generalize random graphs to include triangles.
Edit intent: clarity
Original: In the trace reconstruction problem, an unknown bit string {\bf x}\in\{0,1 \}^n is sent through a deletion channel where each bit is deleted independently with some probability q\in(0,1), yielding a contracted string \bf x. How many i.i.d.  samples of \bf x are needed to reconstruct \bf x with high probability?
Revised: In the trace reconstruction problem, an unknown bit string {\bf x}\in\{0,1 \}^n is sent through a deletion channel where each bit is deleted independently with some probability q\in(0,1), yielding a contracted string \bf x. How many i.i.d. \ samples of \bf x are needed to reconstruct \bf x with high probability?
Edit intent: fluency
Original:  We prove that there exist {\bf x},{\bf y} \in\{0,1 \}^n such that we need at least c\, n^{5/4}/\log n traces  to distinguish between {\bf x} and {\bf y} for some absolute constant c, improving the previous lower bound of c\,n.
Revised:  We prove that there exist {\bf x},{\bf y} \in\{0,1 \}^n such that at least c\, n^{5/4}/\log n traces to distinguish between {\bf x} and {\bf y} for some absolute constant c, improving the previous lower bound of c\,n.
Edit intent: coherence
Original:  The main idea of the method is to boost standard linear regression algorithms in each backward induction step by adding new basis functions based on previously estimated continuation values.
Revised:  The main idea of the method is to reinforce standard linear regression algorithms in each backward induction step by adding new basis functions based on previously estimated continuation values.
Edit intent: clarity
Original:  The proposed methodology is illustrated by several numerical examples from finance.
Revised:  The proposed methodology is illustrated by a numerical example from mathematical finance.
Edit intent: clarity
Original: We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each n \geq 2 we present a convex optimization problem whose optimal value is the largest possible ratio between the value of an optimal rank-n solution to the relaxation and the value of an optimal cut.
Revised: We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite-programming relaxation: for each n \geq 2 we present a convex optimization problem whose optimal value is the largest possible ratio between the value of an optimal rank-n solution to the relaxation and the value of an optimal cut.
Edit intent: fluency
Original: We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite-programming relaxation: for each n \geq 2 we present a convex optimization problem whose optimal value is the largest possible ratio between the value of an optimal rank-n solution to the relaxation and the value of an optimal cut.
Revised: We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each n \geq 2 we present a convex optimization problem whose optimal value is the largest possible ratio between the value of an optimal rank-n solution to the relaxation and the value of an optimal cut.
Edit intent: fluency
Original:  In this work, we study the task of finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident with the path.
Revised:  In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident with the path.
Edit intent: clarity
Original:  Herein, we consider short and long path on the one side, and small and large neighborhoods on the other side---yielding four decision problems.
Revised:  Herein, we consider short and long paths on the one side, and small and large neighborhoods on the other side---yielding four decision problems.
Edit intent: fluency
Original:  Moreover, we study all four variant when parameterized by the bound k on the length of the path, by the bound \ell on the size of neighborhood, and by k + \ell.
Revised:  Moreover, we study all four variants when parameterized by the bound k on the length of the path, by the bound \ell on the size of neighborhood, and by k + \ell.
Edit intent: fluency
Original:  Moreover, we study all four variant when parameterized by the bound k on the length of the path, by the bound \ell on the size of neighborhood, and by k + \ell.
Revised:  Moreover, we study all four variant when parameterized by a bound k on the length of the path, by the bound \ell on the size of neighborhood, and by k + \ell.
Edit intent: fluency
Original:  Moreover, we study all four variant when parameterized by the bound k on the length of the path, by the bound \ell on the size of neighborhood, and by k + \ell.
Revised:  Moreover, we study all four variant when parameterized by the bound k on the length of the path, by a bound \ell on the size of neighborhood, and by k + \ell.
Edit intent: fluency
Original:  In appendix 1, I point to its possible generalization 
Revised:  In appendix 1, I point to its possible generalization .
Edit intent: fluency
Original: Recently Dzhafarov and Kon published the paper advertising the possibility to use the coupling technique of classical probability theory to model incompatible observables in quantum physics and quantum-like models of cognition, and psychology.
Revised: Recently Dzhafarov and Kon published the paper advertising the possibility to use the coupling technique of classical probability theory to model incompatible observables in quantum physics and quantum-like models of psychology.
Edit intent: coherence
Original:  Our algorithms are width-independent, i.e. , their running time depends only poly-logarithmically on the largest entry of the constraint matrix, and closely matches the state-of-the-art guarantees for distributed algorithms for packing linear programs , i.e., for the case \alpha = 0.
Revised:  Our algorithms are width-independent, that is , their running time depends only poly-logarithmically on the largest entry of the constraint matrix, and closely matches the state-of-the-art guarantees for distributed algorithms for packing linear programs , i.e., for the case \alpha = 0.
Edit intent: fluency
Original:  Our algorithms are width-independent, i.e. , their running time depends only poly-logarithmically on the largest entry of the constraint matrix, and closely matches the state-of-the-art guarantees for distributed algorithms for packing linear programs , i.e., for the case \alpha = 0.
Revised:  Our algorithms are width-independent, i.e. , their running times depend only poly-logarithmically on the largest entry of the constraint matrix, and closely matches the state-of-the-art guarantees for distributed algorithms for packing linear programs , i.e., for the case \alpha = 0.
Edit intent: fluency
Original:  Our algorithms are width-independent, i.e. , their running time depends only poly-logarithmically on the largest entry of the constraint matrix, and closely matches the state-of-the-art guarantees for distributed algorithms for packing linear programs , i.e., for the case \alpha = 0.
Revised:  Our algorithms are width-independent, i.e. , their running time depends only poly-logarithmically on the largest entry of the constraint matrix, and closely match the state-of-the-art guarantees for distributed algorithms for packing linear programs , i.e., for the case \alpha = 0.
Edit intent: fluency
Original:  Our algorithms are width-independent, i.e. , their running time depends only poly-logarithmically on the largest entry of the constraint matrix, and closely matches the state-of-the-art guarantees for distributed algorithms for packing linear programs , i.e., for the case \alpha = 0.
Revised:  Our algorithms are width-independent, i.e. , their running time depends only poly-logarithmically on the largest entry of the constraint matrix, and closely matches the state-of-the-art guarantees for distributed algorithms for packing linear programs -- the case \alpha = 0.
Edit intent: coherence
Original:  The only previously known width-independent algorithms for \alpha-fair resource allocation , by Marasevic, Stein, and Zussman, obtained convergence times that exhibited much worse dependence on \epsilon and \alpha and relied on a less principled analysis.
Revised:  Previously known width-independent algorithms for \alpha-fair resource allocation , by Marasevic, Stein, and Zussman, obtained convergence times that exhibited much worse dependence on \epsilon and \alpha and relied on a less principled analysis.
Edit intent: clarity
Original:  The only previously known width-independent algorithms for \alpha-fair resource allocation , by Marasevic, Stein, and Zussman, obtained convergence times that exhibited much worse dependence on \epsilon and \alpha and relied on a less principled analysis.
Revised:  The only previously known width-independent algorithms for \alpha-fair resource allocation have convergence times with much worse dependence on \epsilon and \alpha and relied on a less principled analysis.
Edit intent: clarity
Original:  By contrast, our analysis leverages the Approximate Duality Gap framework of Diakonikolas and Orecchia to obtain better algorithms with a (slightly) simpler analysis.
Revised:  By contrast, our analysis leverages the Approximate Duality Gap framework of Diakonikolas and Orecchia to obtain better algorithms with a more streamlined analysis.
Edit intent: clarity
Original: Fair allocation of resources has deep roots in early philosophy, and has been broadly studied in political science, economic theory, operations research, and networking.
Revised: Fair resource allocation is a fundamental optimization problem with applications in operations research, and networking.
Edit intent: clarity
Original:  Over the past decades, an axiomatic approach to fair resource allocation has led to the general acceptance of a class of \alpha-fair utility functions parametrized by a single inequality aversion parameter \alpha \in [0, \infty].
Revised:  Over the past decades, an axiomatic approach to fair resource allocation has led to the general acceptance of a class of \alpha-fair utility functions parameterized by \alpha \in [0, \infty].
Edit intent: clarity
Original:  In this work, we consider general \alpha-fair resource allocation problems, defined as the maximization of \alpha-fair utility functions under packing constraints .
Revised:  In this work, we consider general \alpha-fair packing -- the problem of maximizing \alpha-fair utility functions under packing constraints .
Edit intent: clarity
Original: We present a data structure that  given a graph G of n vertices and m edges, and a suitable pair of  r-divisions of G, preprocesses G in O(m+n) time and handles any series of edge-deletions in O(m) total time while answering queries to pairwise biconnectivity in  O(1) time.
Revised: We present a data structure that , given a graph G of n vertices and m edges, and a suitable pair of r-divisions of G, preprocesses G in O(m+n) time and handles any series of edge-deletions in O(m) total time while answering queries to pairwise biconnectivity in O(1) time.
Edit intent: fluency
Original:  In case the vertices are not biconnected, the data structure can return a cut-vertex separating them in  O(1) time.
Revised:  In case the vertices are not biconnected, the data structure can return a cutvertex separating them in O(1) time.
Edit intent: fluency
Original:  As an immediate consequence, this gives optimal amortised decremental biconnectivity, 2-edge connectivity, and connectivity for large classes of graphs, such as planar graphs , minor free graphs , and more .
Revised:  As an immediate consequence, this gives optimal amortized decremental biconnectivity, 2-edge connectivity, and connectivity for large classes of graphs, such as planar graphs , minor free graphs , and more .
Edit intent: fluency