wanyu/IteraTeR_v2 huggingface dataset:
Original: In a drawing of a clustered graph vertices and edges are drawn as points and curves,  while clusters are represented by simple closed regions.
Revised: In a drawing of a clustered graph vertices and edges are drawn as points and curves, respectively, while clusters are represented by simple closed regions.
Edit intent: clarity
Original:  However, planarity is not sufficient and the constraints imposed by the absence of edge-region and of region-region crossings make the family of c-planar graphs too small for some of the typical Graph Drawing application contexts.
Revised:  However, such a condition is not sufficient and the constraints imposed by the absence of edge-region and of region-region crossings make the family of c-planar graphs too small for some of the typical Graph Drawing application contexts.
Edit intent: clarity
Original:  However, planarity is not sufficient and the constraints imposed by the absence of edge-region and of region-region crossings make the family of c-planar graphs too small for some of the typical Graph Drawing application contexts.
Revised:  However, planarity is not sufficient and the constraints imposed by the absence of edge-region and region-region crossings make the family of c-planar graphs too small for some of the typical Graph Drawing application contexts.
Edit intent: fluency
Original:  The data from experiments in which circuits are stimulated by optogenetics presents the statistical challenge of modeling a high frequency point process (neuronal spikes) while the input is another high frequency point process (light flashes).
Revised:  The data from these experiments present a statistical challenge of modeling a high frequency point process (neuronal spikes) while the input is another high frequency point process (light flashes).
Edit intent: clarity
Original:  We propose a new simple probabilistic approach to model the relationships between two point processes which employs additive point-process response functions on the logit scale .
Revised:  We propose a new simple probabilistic approach to model the relationships between two point processes , employing additive point-process response functions on the logit scale .
Edit intent: coherence
Original:  We propose a new simple probabilistic approach to model the relationships between two point processes which employs additive point-process response functions on the logit scale .
Revised:  We propose a new simple probabilistic approach to model the relationships between two point processes which employs additive point-process response functions .
Edit intent: clarity
Original:  Such response functions may provide important and interpretable scientific insights into  properties of the biophysical process that govern neural spiking in response to optogenetics stimulation.
Revised:  Such response functions may provide important and interpretable scientific insights into the properties of the biophysical process that govern neural spiking in response to optogenetics stimulation.
Edit intent: fluency
Original:  Such response functions may provide important and interpretable scientific insights into  properties of the biophysical process that govern neural spiking in response to optogenetics stimulation.
Revised:  Such response functions may provide important and interpretable scientific insights into properties of the biophysical process that governs neural spiking in response to optogenetics stimulation.
Edit intent: fluency
Original:  Such response functions may provide important and interpretable scientific insights into  properties of the biophysical process that govern neural spiking in response to optogenetics stimulation.
Revised:  Such response functions may provide important and interpretable scientific insights into properties of the biophysical process that govern neural spiking in response to optogenetic stimulation.
Edit intent: fluency
Original:  Compared with other statistical and biophysical models, the PRO model yields a superior area-under-the-curve value as high as 93\% for predicting every future spike within a 5ms interval.
Revised:  Compared with other statistical and biophysical models, the PRO model yields a superior area-under-the- curve value as high as 93\% for predicting every future spike within a 5ms interval.
Edit intent: fluency
Original:  This leads to a naive lower bound log_{2}(n) + 1 for the number of  Lyndon factors that a Lyndon word of length n must have .
Revised:  This leads to a naive lower bound log_{2}(n) + 1 for the number of distinct Lyndon factors that a Lyndon word of length n must have .
Edit intent: clarity
Original:  In this paper we show that a much more accurate lower bound is log_{phi}(n)  , where phi = (1 + sqrt{5})/ 2, the golden ratio.
Revised:  In this paper we show that a much more accurate lower bound is log_{phi}(n) , where phi denotes the golden ratio (1 + sqrt{5})/ 2, the golden ratio.
Edit intent: clarity
Original:  In this paper we show that a much more accurate lower bound is log_{phi}(n)  , where phi = (1 + sqrt{5})/ 2, the golden ratio.
Revised:  In this paper we show that a much more accurate lower bound is log_{phi}(n) , where phi = (1 + sqrt{5})/ 2.
Edit intent: clarity
Original:  As an application, we introduce a mapping L _{x that counts the number of Lyndon factors of length at most n of an infinite word x.
Revised:  As an application, we introduce a mapping L _x that counts the number of Lyndon factors of length at most n of an infinite word x.
Edit intent: fluency
Original:  As an application, we introduce a mapping L _{x that counts the number of Lyndon factors of length at most n of an infinite word x.
Revised:  As an application, we introduce a mapping L _{x that counts the number of Lyndon factors of length at most n in an infinite word x.
Edit intent: clarity
Original:  We show that a recurrent infinite word x is aperiodic if and only if L_x >= L_f, where f is the Fibonacci infinite word, with equality if and only if x is in the shift orbit closure of f.
Revised:  We show that a recurrent infinite word x is aperiodic if and only if L_x >= L_f, where f is the Fibonacci infinite word, with equality if and only if f is in the shift orbit closure of f.
Edit intent: fluency
Original:  This leads to a family of probability distributions generalizing the Luria-Delbr\"uck family, and depending on 3 parameters: the expected number of mutations, the relative fitness of normal cells compared to mutants, and the death probability of mutants.
Revised:  This leads to a family of probability distributions generalizing the Luria-Delbr\"uck family, and depending on three parameters: the expected number of mutations, the relative fitness of normal cells compared to mutants, and the death probability of mutants.
Edit intent: fluency
Original:  simulation and computing algorithms are given .
Revised:  simulation and computing algorithms are provided .
Edit intent: clarity
Original:  Among others we prove that there is an online coloring method that colors N intervals on the line using \Theta(\log N/k) colors such that for every point p, contained in at least k intervals, there exist two intervals containing p and having different colors.
Revised:  We prove that there is an online coloring method that colors N intervals on the line using \Theta(\log N/k) colors such that for every point p, contained in at least k intervals, there exist two intervals containing p and having different colors.
Edit intent: coherence
Original:  Among others we prove that there is an online coloring method that colors N intervals on the line using \Theta(\log N/k) colors such that for every point p, contained in at least k intervals, there exist two intervals containing p and having different colors.
Revised:  Among others we prove that there is an online coloring algorithm that colors N intervals on the line using \Theta(\log N/k) colors such that for every point p, contained in at least k intervals, there exist two intervals containing p and having different colors.
Edit intent: clarity
Original:  Among others we prove that there is an online coloring method that colors N intervals on the line using \Theta(\log N/k) colors such that for every point p, contained in at least k intervals, there exist two intervals containing p and having different colors.
Revised:  Among others we prove that there is an online coloring method that colors N intervals on the line using \Theta(\log N/k) colors such that for every point p, contained in at least k intervals, not all the intervals containing p and having different colors.
Edit intent: clarity
Original:  We prove the corresponding (but not equivalent) result about online coloring quadrants in the plane that are parallel to a given fixed quadrant .
Revised:  We prove the corresponding result about online coloring quadrants in the plane that are parallel to a given fixed quadrant .
Edit intent: clarity
Original:  We prove the corresponding (but not equivalent) result about online coloring quadrants in the plane that are parallel to a given fixed quadrant .
Revised:  We prove the corresponding (but not equivalent) result about online coloring quadrants in the plane that are the translates of a given fixed quadrant .
Edit intent: clarity
Original:  We prove the corresponding (but not equivalent) result about online coloring quadrants in the plane that are parallel to a given fixed quadrant .
Revised:  We prove the corresponding (but not equivalent) result about online coloring quadrants in the plane that are parallel to a given fixed wedge .
Edit intent: clarity
Original:  These results contrast to recent results of the first and third author showing that in the quasi-online setting 12 colors are enough to color quadrants (independent of N and k).
Revised:  These results contrast the results of the first and third author showing that in the quasi-online setting 12 colors are enough to color quadrants (independent of N and k).
Edit intent: clarity
Original:  We also consider coloring intervals in the quasi-online setting .
Revised:  We also consider quasi-online coloring of intervals .
Edit intent: clarity
Original:  In all cases we present efficient coloring algorithms as well .
Revised:  In all cases we present efficient coloring algorithms .
Edit intent: clarity
Original:  Yet, most common techniques either adopt classical power control, in which users are received with the same Signal to Interference-plus-Noise Ratio(SINR) , or use centralized schemes, in which base stations coordinate their allocations.
Revised:  Yet, most common techniques either adopt classical power control, in which mobile stations are received with the same Signal to Interference-plus-Noise Ratio(SINR) , or use centralized schemes, in which base stations coordinate their allocations.
Edit intent: clarity
Original:  Yet, most common techniques either adopt classical power control, in which users are received with the same Signal to Interference-plus-Noise Ratio(SINR) , or use centralized schemes, in which base stations coordinate their allocations.
Revised:  Yet, most common techniques either adopt classical power control, in which users are received with the same Signal-to-Interference-plus-Noise Ratio , or use centralized schemes, in which base stations coordinate their allocations.
Edit intent: clarity
Original:  We suggest a novel scheduling approach in which each base station, besides allocating the time and frequency resources according to given constraints, also manages its uplink power budget such that the aggregate interference, "Noise Rise", caused by its subscribers at the neighboring cells is bounded.
Revised:  We suggest a novel scheduling approach in which each base station, besides allocating the time and frequency according to given constraints, also manages its uplink power budget such that the aggregate interference, "Noise Rise", caused by its subscribers at the neighboring cells is bounded.
Edit intent: clarity
Original:  Our suggested scheme is completely distributedbetween the cells , requiring neither coordination nor message exchange.
Revised:  Our suggested scheme is distributed , requiring neither coordination nor message exchange.
Edit intent: clarity
Original:  We rigorously define this allocation problem under noise rise constraints, give the optimal solution and derive an efficient iterative algorithm for it.
Revised:  We rigorously define the allocation problem under noise rise constraints, give the optimal solution and derive an efficient iterative algorithm for it.
Edit intent: fluency
Original:  We rigorously define this allocation problem under noise rise constraints, give the optimal solution and derive an efficient iterative algorithm for it.
Revised:  We rigorously define this allocation problem under noise rise constraints, give the optimal solution and derive an efficient iterative algorithm to achieve it.
Edit intent: clarity
Original:  We then discus a relaxed problem, where the noise rise is constraint separately for each sub-channel or resource unit.
Revised:  We then discuss a relaxed problem, where the noise rise is constraint separately for each sub-channel or resource unit.
Edit intent: fluency
Original:  We then discus a relaxed problem, where the noise rise is constraint separately for each sub-channel or resource unit.
Revised:  We then discus a relaxed problem, where the noise rise is constrained separately for each sub-channel or resource unit.
Edit intent: fluency
Original:  Via extensive simulations, we show that the suggested approach increases overall throughput dramatically, with the same level of fairness and power consumption.
Revised:  Via extensive simulations, we show that the suggested approach increases overall performance dramatically, with the same level of fairness and power consumption.
Edit intent: clarity
Original: The directed polymerization of dendritic actin networks is an essential element of many biological processes, including cell migration.
Revised: The directed polymerization of actin networks is an essential element of many biological processes, including cell migration.
Edit intent: clarity
Original:  Different theoretical models for the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions.
Revised:  Different theoretical models considering the interplay between the underlying processes of polymerization, capping and branching have resulted in conflicting predictions.
Edit intent: clarity
Original:  One of the main reasons for this discrepancy is the assumption of a branching reaction which is first (autocatalytic) versus zeroth order in filament density .
Revised:  One of the main reasons for this discrepancy is the assumption of a branching reaction that is either first order (autocatalytic) versus zeroth order in filament density .
Edit intent: style
Original:  One of the main reasons for this discrepancy is the assumption of a branching reaction which is first (autocatalytic) versus zeroth order in filament density .
Revised:  One of the main reasons for this discrepancy is the assumption of a branching reaction which is first (autocatalytic) or zeroth order in filament density .
Edit intent: fluency
Original:  One of the main reasons for this discrepancy is the assumption of a branching reaction which is first (autocatalytic) versus zeroth order in filament density .
Revised:  One of the main reasons for this discrepancy is the assumption of a branching reaction which is first (autocatalytic) versus zeroth order in the number of existing filaments .
Edit intent: clarity
Original:  Here we introduce a unifying framework from which these two models emerge as limiting cases for low and high filament density, respectively .
Revised:  Here we introduce a unifying framework from which the two established scenarios emerge as limiting cases for low and high filament density, respectively .
Edit intent: clarity
Original:  Here we introduce a unifying framework from which these two models emerge as limiting cases for low and high filament density, respectively .
Revised:  Here we introduce a unifying framework from which these two models emerge as limiting cases for low and high filament number .
Edit intent: clarity
Original:  A smooth transition between these cases is found at intermediate conditions.
Revised:  A smooth transition between the two cases is found at intermediate conditions.
Edit intent: clarity
Original: We present a new algorithm for calculating exact hypervolumes, QHV . Given a set of d-dimensional points this algorithm determines the hypervolume of the dominated space.
Revised: We present a new algorithm to calculate exact hypervolumes . Given a set of d-dimensional points this algorithm determines the hypervolume of the dominated space.
Edit intent: clarity
Original: We present a new algorithm for calculating exact hypervolumes, QHV . Given a set of d-dimensional points this algorithm determines the hypervolume of the dominated space.
Revised: We present a new algorithm for calculating exact hypervolumes, QHV . Given a set of d-dimensional points , it computes the hypervolume of the dominated space.
Edit intent: clarity
Original:  This value is useful for comparing the performance of multiobjective optimizers, a subroutine in Multiobjective Evolutionary Algorithms (MOEAs).
Revised:  Determining this value is an important subroutine of Multiobjective Evolutionary Algorithms (MOEAs).
Edit intent: clarity
Original:  We analyze QHV both theoretically and experimentally.
Revised:  We analyze the "Quick Hypervolume" (QHV) algorithm theoretically and experimentally.
Edit intent: clarity
Original:  It achieves state of the art performance , compared with other exact hypervolume algorithms.
Revised:  It achieves state of the art performance , compared with existing exact hypervolume algorithms.
Edit intent: clarity
Original:  We present an O(n^2) time and O(n) space algorithm for the computation of an exact minimizer of this non-convex optimization problem.
Revised:  We present an O(n^2) time and O(n) space algorithm to compute an exact minimizer of this non-convex optimization problem.
Edit intent: fluency
Original: The currently fastest exact algorithm for traveling salesman problem  in cubic graphs is due to Iwama and Nakashima Proc.
Revised: The currently fastest exact algorithm for traveling salesman problem in cubic graphs Proc.
Edit intent: coherence
Original:  The unique informational narrative of living systems suggests that life may be characterized by context-dependent causal influences, and in particular, that top-down (or downward) causation -- where higher-levels influence and constrain the dynamics of lower-levels in organizational hierarchies - may be a major contributor to the hierarchal structure of living systems.
Revised:  The unique informational narrative of living systems suggests that life may be characterized by context-dependent causal influences, and in particular, that top-down (or downward) causation -- where higher-levels influence and constrain the dynamics of lower-levels in organizational hierarchies -- may be a major contributor to the hierarchal structure of living systems.
Edit intent: fluency
Original:  Here we propose that the origin of life may correspond to a physical transition associated with a fundamental shift in causal structure .
Revised:  Here we propose that the origin of life may correspond to a physical transition associated with a shift in causal structure .
Edit intent: clarity
Original:  Such a transition may be akin to a thermodynamic phase transition , with the crucial distinction that determining which phase ( nonlife or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal relationships .
Revised:  Such a transition may be akin to a thermodynamic phase transition , with the crucial distinction that determining which phase ( non-life or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal relationships .
Edit intent: fluency
Original:  Such a transition may be akin to a thermodynamic phase transition , with the crucial distinction that determining which phase ( nonlife or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal relationships .
Revised:  Such a transition may be akin to a thermodynamic phase transition , with the crucial distinction that determining which phase ( nonlife or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal architecture .
Edit intent: clarity
Original:  We discuss one potential measure of such a transition , which is amenable to laboratory study, and how the proposed mechanism corresponds to the onset of the unique mode of (algorithmic) information processing characteristic of living systems.
Revised:  We discuss one potential measure of such a transition that may be amenable to laboratory study, and how the proposed mechanism corresponds to the onset of the unique mode of (algorithmic) information processing characteristic of living systems.
Edit intent: clarity
Original:  For this we introduce inter-agent channels modeled as 2-state automata, compute the overall system behavior, and then present an effective computational test for delay-robustness.
Revised:  For this we introduce inter-agent channels modeled as 2-state automata, compute the overall system behavior, and present an effective computational test for delay-robustness.
Edit intent: coherence
Original:  In previous work by Cai et al. a distributed supervisory control problem has been investigated on the assumption that inter-agent communications take place with negligible delay.
Revised:  In previous work a distributed supervisory control problem has been investigated on the assumption that inter-agent communications take place with negligible delay.
Edit intent: clarity
Original:  From the test it typically results that the given delay-free distributed control is delay-robust with respect to certain communicated events, but not for all, thus distinguishing events which are not delay-critical from those that are . Another test is proposed to identify whether or not an uncontrollable event, which cannot be re-transmitted until its communication channel becomes available, will be blocked .
Revised:  From the test it typically results that the given delay-free distributed control is delay-robust with respect to certain communicated events, but not for all, thus distinguishing events which are not delay-critical from those that are .
Edit intent: coherence
Original: We describe a family of quadrilateral meshes based on diamonds, rhombi with 60 degree and 120 degree angles, and kites with 60 degree , 90 degree , and 120 degree angles, that can be adapted to a local size function by local subdivision operations.
Revised: We describe a family of quadrilateral meshes based on diamonds, rhombi with 60 and 120 degree angles, and kites with 60 degree , 90 degree , and 120 degree angles, that can be adapted to a local size function by local subdivision operations.
Edit intent: fluency
Original: We describe a family of quadrilateral meshes based on diamonds, rhombi with 60 degree and 120 degree angles, and kites with 60 degree , 90 degree , and 120 degree angles, that can be adapted to a local size function by local subdivision operations.
Revised: We describe a family of quadrilateral meshes based on diamonds, rhombi with 60 degree and 120 degree angles, and kites with 60 , 90 degree , and 120 degree angles, that can be adapted to a local size function by local subdivision operations.
Edit intent: fluency
Original: We describe a family of quadrilateral meshes based on diamonds, rhombi with 60 degree and 120 degree angles, and kites with 60 degree , 90 degree , and 120 degree angles, that can be adapted to a local size function by local subdivision operations.
Revised: We describe a family of quadrilateral meshes based on diamonds, rhombi with 60 degree and 120 degree angles, and kites with 60 degree , 90 , and 120 degree angles, that can be adapted to a local size function by local subdivision operations.
Edit intent: fluency