wanyu/IteraTeR_v2 huggingface dataset:
Original:  This naturally motivates the following important question to understand their limitations and empirical successes : the Bethe equation is computationally easy to solve?
Revised:  This naturally motivates the following important question to understand their limitations and empirical successes : the Bethe equation computationally easy to solve?
Edit intent: clarity
Original:  We present a message passing algorithm solving the Bethe equation in  polynomial number of operations for arbitrary binary graphical models of n variables where the maximum degree in the underlying graph is O(log n).
Revised:  We present a message-passing algorithm solving the Bethe equation in polynomial number of operations for arbitrary binary graphical models of n variables where the maximum degree in the underlying graph is O(log n).
Edit intent: fluency
Original:  We present a message passing algorithm solving the Bethe equation in  polynomial number of operations for arbitrary binary graphical models of n variables where the maximum degree in the underlying graph is O(log n).
Revised:  We present a message passing algorithm solving the Bethe equation in a polynomial number of operations for arbitrary binary graphical models of n variables where the maximum degree in the underlying graph is O(log n).
Edit intent: fluency
Original:  Our algorithm , an alternative to BP fixing its convergence issue , is the first fully polynomial-time approximation scheme for the BP fixed point computation in such a large class of graphical models, while the approximate fixed point computation is known to be (PPAD-)hard in general.
Revised:  Our algorithm , an alternative to BP fixing its convergence issue and is the first fully polynomial-time approximation scheme for the BP fixed point computation in such a large class of graphical models, while the approximate fixed point computation is known to be (PPAD-)hard in general.
Edit intent: coherence
Original:  Our algorithm , an alternative to BP fixing its convergence issue , is the first fully polynomial-time approximation scheme for the BP fixed point computation in such a large class of graphical models, while the approximate fixed point computation is known to be (PPAD-)hard in general.
Revised:  Our algorithm , an alternative to BP fixing its convergence issue , is the first fully polynomial-time approximation scheme for the BP fixed-point computation in such a large class of graphical models, while the approximate fixed point computation is known to be (PPAD-)hard in general.
Edit intent: fluency
Original:  Our algorithm , an alternative to BP fixing its convergence issue , is the first fully polynomial-time approximation scheme for the BP fixed point computation in such a large class of graphical models, while the approximate fixed point computation is known to be (PPAD-)hard in general.
Revised:  Our algorithm , an alternative to BP fixing its convergence issue , is the first fully polynomial-time approximation scheme for the BP fixed point computation in such a large class of graphical models, while the approximate fixed-point computation is known to be (PPAD-)hard in general.
Edit intent: fluency
Original:  We construct tolerant identifying codes in this network that are robust if the radius of the sensors may vary from r to r+Delta .
Revised:  We construct tolerant identifying codes in this network that are robust against some changes in the neighbourhood monitored by each sensor .
Edit intent: clarity
Original:  ] The NP-complete Permutation Pattern Matching problem asks whether a permutation P (the pattern) can be matched into a permutation T (the text).
Revised:  1] The NP-complete Permutation Pattern Matching problem asks whether a permutation P (the pattern) can be matched into a permutation T (the text).
Edit intent: fluency
Original: The following proof claiming that the Permutation Pattern Matching problem is W 1%DIFDELCMD < ]%%% -complete with respect to the length of the pattern is incorrect since it contains a flaw in Claim 3.
Revised:  1%DIFDELCMD < ]%%% -complete with respect to the length of the pattern is incorrect since it contains a flaw in Claim 3.
Edit intent: coherence
Original: The following proof claiming that the Permutation Pattern Matching problem is W 1%DIFDELCMD < ]%%% -complete with respect to the length of the pattern is incorrect since it contains a flaw in Claim 3.
Revised: The following proof claiming that the Permutation Pattern Matching problem is W %DIFDELCMD < ]%%% -complete with respect to the length of the pattern is incorrect since it contains a flaw in Claim 3.
Edit intent: fluency
Original:  We show that this problem is W[1] -complete with respect to the length of the pattern P.
Revised:  We show W[1] -complete with respect to the length of the pattern P.
Edit intent: clarity
Original:  We show that this problem is W[1] -complete with respect to the length of the pattern P.
Revised:  We show that this problem is W[1] -completeness with respect to the length of the pattern P.
Edit intent: clarity
Original:  Instead of taking into account three sites and beyond, we propose a novel excitable-wave mean-field approximation .
Revised:  We propose an excitable-wave mean-field approximation .
Edit intent: clarity
Original: Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision  and many others.
Revised: Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision , and many others.
Edit intent: fluency
Original:  On the other hand, many useful applications in computer vision and machine learning applications are defined over a special subclasses of submodular functions in which that can be written as the sum of many submodular cost functions defined over cliques containing few variables.
Revised:  On the other hand, many computer vision and machine learning applications are defined over a special subclasses of submodular functions in which that can be written as the sum of many submodular cost functions defined over cliques containing few variables.
Edit intent: clarity
Original:  On the other hand, many useful applications in computer vision and machine learning applications are defined over a special subclasses of submodular functions in which that can be written as the sum of many submodular cost functions defined over cliques containing few variables.
Revised:  On the other hand, many useful applications in computer vision and machine learning problems are defined over a special subclasses of submodular functions in which that can be written as the sum of many submodular cost functions defined over cliques containing few variables.
Edit intent: clarity
Original:  On the other hand, many useful applications in computer vision and machine learning applications are defined over a special subclasses of submodular functions in which that can be written as the sum of many submodular cost functions defined over cliques containing few variables.
Revised:  On the other hand, many useful applications in computer vision and machine learning applications are defined over special subclasses of submodular functions in which that can be written as the sum of many submodular cost functions defined over cliques containing few variables.
Edit intent: fluency
Original:  On the other hand, many useful applications in computer vision and machine learning applications are defined over a special subclasses of submodular functions in which that can be written as the sum of many submodular cost functions defined over cliques containing few variables.
Revised:  On the other hand, many useful applications in computer vision and machine learning applications are defined over a special subclasses of submodular functions that can be written as the sum of many submodular cost functions defined over cliques containing few variables.
Edit intent: clarity
Original:  To do this, we define novel mapping that transform submodular functions of order k into quadratic ones , which can be efficiently minimized in O(n^3) time using a max-flow algorithm .
Revised:  To do this, we define novel mapping that transform submodular functions of order k into quadratic ones .
Edit intent: coherence
Original:  Models with finitely-many alleles are considered in this paper, and approximate closed-form sampling formulas are derived for an arbitrary  recurrent mutation model or for a reversible recurrent mutation model, depending on whether the number of distinct observed allele types is at most three or four, respectively .
Revised:  In this paper, models with finitely-many alleles are considered in this paper, and approximate closed-form sampling formulas are derived for an arbitrary recurrent mutation model or for a reversible recurrent mutation model, depending on whether the number of distinct observed allele types is at most three or four, respectively .
Edit intent: coherence
Original:  Models with finitely-many alleles are considered in this paper, and approximate closed-form sampling formulas are derived for an arbitrary  recurrent mutation model or for a reversible recurrent mutation model, depending on whether the number of distinct observed allele types is at most three or four, respectively .
Revised:  Models with finitely-many alleles are considered in this paper, and approximate closed-form sampling formulas for an arbitrary recurrent mutation model or for a reversible recurrent mutation model, depending on whether the number of distinct observed allele types is at most three or four, respectively .
Edit intent: clarity
Original: Probabilistic B\"{uchi Automata (}%DIFDELCMD < \PBA%%%  ) are randomized, finite state automata that process input strings of infinite length.
Revised: Probabilistic chi Automata (}%DIFDELCMD < \PBA%%% ) are randomized, finite state automata that process input strings of infinite length.
Edit intent: fluency
Original:  It is often assumed that all nodes within a network perform coding operations , for minimal centralized control while maximizing the throughput .
Revised:  It is often assumed that all nodes within a network perform coding operations .
Edit intent: clarity
Original:  In energy-constrained systems, however, coding subgraphs should be chosen to minimize the number of coding nodes while maintaining the achievable throughput.
Revised:  In energy-constrained systems, however, coding subgraphs should be chosen to control the number of coding nodes while maintaining the achievable throughput.
Edit intent: clarity
Original:  In energy-constrained systems, however, coding subgraphs should be chosen to minimize the number of coding nodes while maintaining the achievable throughput.
Revised:  In energy-constrained systems, however, coding subgraphs should be chosen to minimize the number of coding nodes while maintaining throughput.
Edit intent: clarity
Original:  In this paper, we explore the  use of network coding in the wireless relay channel, where a single source communicates to a single sink through the aid of a relay in half-duplex mode.
Revised:  In this paper, we explore the use of network coding in the wireless relay channel, where a single source communicates to a single sink through the aid of a half-duplex mode.
Edit intent: clarity
Original:  Markov chain models are used to describe the evolution of innovative packets at different nodes within the network, and numerical solutions are determined to find how much time the relay should participate in the transmission .
Revised:  Markov chain models are proposed to describe packet evolution if only the source or only the relay is coding. In addition to transmission energy, we take into account coding and reception energies .
Edit intent: clarity
Original:  There are many ways to achieve this, however, and we analyze the relationship between topology and signaling in contrasting classes of such topologies.
Revised:  We analyze the relationship between topology and signaling in contrasting classes of such topologies.
Edit intent: coherence
Original:  They also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise.
Revised:  Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise.
Edit intent: clarity
Original: Unveiling the mechanisms by which the somitogenesis regulatory network exerts spatiotemporal control of the somitic patterning has required a combination of experimental and mathematical modeling strategies.
Revised: Unveiling the mechanisms through which the somitogenesis regulatory network exerts spatiotemporal control of the somitic patterning has required a combination of experimental and mathematical modeling strategies.
Edit intent: fluency
Original:  Although significant progress has been made for the zebrafish clockwork , the complexity of the amniote segmentation regulatory network makes it difficult to explain some dynamical features of this process .
Revised:  Significant progress has been made for the zebrafish clockwork , the complexity of the amniote segmentation regulatory network makes it difficult to explain some dynamical features of this process .
Edit intent: clarity
Original:  Although significant progress has been made for the zebrafish clockwork , the complexity of the amniote segmentation regulatory network makes it difficult to explain some dynamical features of this process .
Revised:  Although significant progress has been made for the zebrafish clockwork . However, due to its complexity, the clockwork of the amniote segmentation regulatory network makes it difficult to explain some dynamical features of this process .
Edit intent: coherence
Original:  Although significant progress has been made for the zebrafish clockwork , the complexity of the amniote segmentation regulatory network makes it difficult to explain some dynamical features of this process .
Revised:  Although significant progress has been made for the zebrafish clockwork , the complexity of the amniote segmentation regulatory network has not been fully elucidated .
Edit intent: clarity
Original:  We do this by constructing a minimal model of the regulatory network  which privileges architectural information over molecular details.
Revised:  We do this by constructing a minimal model of the regulatory network , which privileges architectural information over molecular details.
Edit intent: fluency
Original:  With a suitable choice of parameters, our model predicts an oscillatory behavior of the Wnt, Notch and FGF signaling pathways in presomitic mesoderm (PSM) cells.
Revised:  With a suitable choice of parameters, our model is able to reproduce the oscillatory behavior of the Wnt, Notch and FGF signaling pathways in presomitic mesoderm (PSM) cells.
Edit intent: clarity
Original:  Notably , the oscillations increase their amplitude as cells approach the anterior PSM and remain in an upregulated state when arrested .
Revised:  Notably : the oscillations increase their amplitude as cells approach the anterior PSM and remain in an upregulated state when arrested .
Edit intent: fluency
Original:  Moreover, the model also predicts an opposing distribution of the Fgf8 and RA gradients in the PSM . We hipothesize that the interaction between a limit cycle (originated by the Notch delayed-negative feedback loop) and a bistable switch (originated by the Wnt-Notch positive feedback loop ) is responsible for the observed segmentation patterning.
Revised:  Moreover, the model also predicts an opposing distribution of the Fgf8 and RA gradients in the PSM . We hipothesize that the interaction between a limit cycle (originated by the Notch delayed-negative feedback loop) and a bistable switch (originated by the Wnt-Notch positive cross-regulation ) is responsible for the observed segmentation patterning.
Edit intent: clarity
Original:  Our results agree with important experimental observations and suggest a simple plausible mechanism for spatiotemporal control of somitogenesis in amniotes.
Revised:  Our results agree with previously unexplained experimental observations and suggest a simple plausible mechanism for spatiotemporal control of somitogenesis in amniotes.
Edit intent: clarity
Original:  Building upon recent results on fault-tolerant spanners, we show how to build p-multipath spanners of constant stretch and of \tO(n^{1+1/k}) edges (Tilde-O notation is similar to Big-O up to poly-logarithmic factors in n.) , for fixed parameters p and k, n being the number of nodes of the graph.
Revised:  Building upon recent results on fault-tolerant spanners, we show how to build p-multipath spanners of constant stretch and of \tO(n^{1+1/k}) edges , for fixed parameters p and k, n being the number of nodes of the graph.
Edit intent: coherence
Original:  The method is essentially derived by making effective use of the random time change representation of Kurtz, and is no harder to implement than any standard continuous time Markov chain algorithm, such as "Gillespie's algorithm  " or the next reaction method.
Revised:  The method is essentially derived by making effective use of the random time change representation of Kurtz, and is no harder to implement than any standard continuous time Markov chain algorithm, such as "Gillespie's algorithm . " or the next reaction method.
Edit intent: fluency
Original:  Moreover, to the best of our knowledge, there is no analytic result on the performance of the mobile user at an arbitrary location considering the mobile user density.
Edit intent: coherence
Original:  In this paper, we use the stochastic geometry approach  and derive useful distributions and probabilities for cellular networks.
Revised:  In this paper, we use the stochastic geometry approach , and derive useful distributions and probabilities for cellular networks.
Edit intent: fluency
Original:  Using those , we analyze the  performance of the mobile user, e.g., outage probability at an arbitrary location considering the mobile user density.
Revised:  Using these results , we analyze the performance of the mobile user, e.g., outage probability at an arbitrary location considering the mobile user density.
Edit intent: clarity
Original:  Under some assumptions, those can be expressed by closed form formulas.
Revised:  Under some assumptions, we can express these by closed form formulas.
Edit intent: fluency
Original:  Our analytic results will provide a fundamental framework for the performance analysis of cellular networks , which will significantly reduce the burden of network-level simulations.
Revised:  Our results will provide a fundamental framework for the performance analysis of cellular networks , which will significantly reduce the burden of network-level simulations.
Edit intent: clarity
Original:  Our analytic results will provide a fundamental framework for the performance analysis of cellular networks , which will significantly reduce the burden of network-level simulations.
Revised:  Our analytic results will provide a framework for performance analysis of cellular networks , which will significantly reduce the burden of network-level simulations.
Edit intent: clarity
Original: The cellular network is one of the most useful networks for wireless communications and now universally used.
Edit intent: coherence
Original:  There have been a lot of analytic results about the performance of the mobile user at a specific location such as the cell center or edge , whereas very few results about the performance of the mobile userat an arbitrary location .
Revised:  There have been a bulk of analytic results about the performance of the mobile user at a specific location such as the cell center or edge , whereas very few results about the performance of the mobile userat an arbitrary location .
Edit intent: clarity
Original:  There have been a lot of analytic results about the performance of the mobile user at a specific location such as the cell center or edge , whereas very few results about the performance of the mobile userat an arbitrary location .
Revised:  There have been a lot of analytic results about the performance of the mobile user at a specific location such as the cell center or edge user) .
Edit intent: clarity
Original: Portfolio managers are often constrained by turnover limits, minimum and maximum stock positions, cardinality, a target market capitalization and sometimes the need to hew to a style (  growth or value).
Revised: Portfolio managers are typically constrained by turnover limits, minimum and maximum stock positions, cardinality, a target market capitalization and sometimes the need to hew to a style ( growth or value).
Edit intent: clarity
Original: Portfolio managers are often constrained by turnover limits, minimum and maximum stock positions, cardinality, a target market capitalization and sometimes the need to hew to a style (  growth or value).
Revised: Portfolio managers are often constrained by turnover limits, minimum and maximum stock positions, cardinality, a target market capitalization and sometimes the need to hew to a style ( such as growth or value).
Edit intent: clarity
Original:  We use MOEAs to satisfy the above real-world constraints and consistently outperform typical performance benchmarks .
Revised:  We use MOEAs to satisfy the above real-world constraints . The portfolios generated consistently outperform typical performance benchmarks .
Edit intent: clarity
Original: Roulette-wheel selection is a frequently used method in genetic or evolutionary algorithms . Existing routines select one of N individuals using search algorithms of O(N) or O( \log N) complexity.
Revised: Roulette-wheel selection is a frequently used method in genetic or evolutionary algorithms . Existing routines select one of N individuals using search algorithms of O(N) or O( log(N)) complexity.
Edit intent: fluency
Original:  We present a simple roulette-wheel selection algorithm that typically has O(1) complexity and is based on stochastic acceptance instead of searching.
Revised:  We present a simple roulette-wheel selection algorithm , which typically has O(1) complexity and is based on stochastic acceptance instead of searching.
Edit intent: fluency
Original:   With minor modifications  the algorithm might be also used for sampling with fitness being cut-off at a certain value or for sampling without replacement.
Revised:  With minor modifications , the algorithm might be also used for sampling with fitness being cut-off at a certain value or for sampling without replacement.
Edit intent: fluency
Original:   With minor modifications  the algorithm might be also used for sampling with fitness being cut-off at a certain value or for sampling without replacement.
Revised:  With minor modifications the algorithm might also be used for sampling with fitness being cut-off at a certain value or for sampling without replacement.
Edit intent: fluency
Original:   With minor modifications  the algorithm might be also used for sampling with fitness being cut-off at a certain value or for sampling without replacement.
Revised:  With minor modifications the algorithm might be also used for sampling with fitness cut-off at a certain value or for sampling without replacement.
Edit intent: clarity
Original:  Given a an n by n matrix A over R, we show how to compute the Hermite form H of A and a unimodular matrix U such that UA=H.
Revised:  Given a an m by n matrix A over R, we show how to compute the Hermite form H of A and a unimodular matrix U such that UA=H.
Edit intent: fluency
Original:  To accomplish our algorithm, we develop the Dieudonne determinant and quasideterminant theory for Ore polynomial rings to get explicit bounds on the degrees and sizes of entries in H and U.
Revised:  To accomplish our algorithm, we apply the Dieudonne determinant and quasideterminant theory for Ore polynomial rings to get explicit bounds on the degrees and sizes of entries in H and U.
Edit intent: clarity
Original:  This algorithm is the first to yield increasing speedup to an unbounded number of processors;
Revised:  This algorithm is the first to yield increasing speedup on an unbounded number of processors;
Edit intent: fluency