wanyu/IteraTeR_v2 huggingface dataset:
Original:  Let x be a set of n differential variables, f a finite family of differential polynomials in the ring %DIFDELCMD < \C%%%  \{x\} and f\in %DIFDELCMD < \C%%%  \{x\} another polynomial which vanishes at every solution of the differential equation system f=0 in any differentially closed field containing %DIFDELCMD < \C%%%  . Let d:=\max\{\deg(f), \deg(f)\} and \epsilon:=\max\{2,{ord}(f), {ord}(f)\}.
Revised:  Let x be a set of n differential variables, f a finite family of differential polynomials in the ring %DIFDELCMD < \C%%% \{x\} and f\in %DIFDELCMD < \C%%% K \{x\} another polynomial which vanishes at every solution of the differential equation system f=0 in any differentially closed field containing %DIFDELCMD < \C%%% . Let d:=\max\{\deg(f), \deg(f)\} and \epsilon:=\max\{2,{ord}(f), {ord}(f)\}.
Edit intent: clarity
Original:  Let x be a set of n differential variables, f a finite family of differential polynomials in the ring %DIFDELCMD < \C%%%  \{x\} and f\in %DIFDELCMD < \C%%%  \{x\} another polynomial which vanishes at every solution of the differential equation system f=0 in any differentially closed field containing %DIFDELCMD < \C%%%  . Let d:=\max\{\deg(f), \deg(f)\} and \epsilon:=\max\{2,{ord}(f), {ord}(f)\}.
Revised:  Let x be a set of n differential variables, f a finite family of differential polynomials in the ring %DIFDELCMD < \C%%% \{x\} and f\in %DIFDELCMD < \C%%% \{x\} another polynomial which vanishes at every solution of the differential equation system f=0 in any differentially closed field containing %DIFDELCMD < \C%%% K . Let d:=\max\{\deg(f), \deg(f)\} and \epsilon:=\max\{2,{ord}(f), {ord}(f)\}.
Edit intent: clarity
Original:  Then, f^M belongs to the algebraic ideal generated by the successive derivatives of f of order at most L = (n\epsilon d)^{2^{c(n\epsilon)^3}}, for a suitable universal constant c>0, and M=d^{n(\epsilon +L+1)}.
Revised:  We show that f^M belongs to the algebraic ideal generated by the successive derivatives of f of order at most L = (n\epsilon d)^{2^{c(n\epsilon)^3}}, for a suitable universal constant c>0, and M=d^{n(\epsilon +L+1)}.
Edit intent: coherence
Original:  The previously known bound for the number L of required differentiations is described in terms of the Ackermann function and , in particular, it is not primitive recursive.
Revised:  The previously known bounds for L and M are not elementary recursive.
Edit intent: clarity
Original: We present a novel approach allowing the accurate study of rare events in a broad class of evolutionary processes under fluctuating environments .
Revised: We present a novel approach allowing the study of rare events in a broad class of evolutionary processes under fluctuating environments .
Edit intent: clarity
Original:  Our approach consists of mapping these processes, not necessarily displaying metastability, onto auxiliary models characterized by metastability that can be analyzed semiclassically.
Revised:  Our approach consists of mapping the system onto an auxiliary model, exhibiting metastable species coexistence, that can be analyzed semiclassically.
Edit intent: clarity
Original:  This  enables us to study the interplay between extrinsic (environmental) noise and intrinsic (demographic ) fluctuations on the statistics of interest.
Revised:  This approach enables us to study the interplay between extrinsic (environmental) noise and intrinsic (demographic ) fluctuations on the statistics of interest.
Edit intent: clarity
Original:  This  enables us to study the interplay between extrinsic (environmental) noise and intrinsic (demographic ) fluctuations on the statistics of interest.
Revised:  This enables us to study the interplay between extrinsic and demographic noise on the statistics of interest.
Edit intent: clarity
Original:  We illustrate our theory for the paradigmatic prisoner's dilemma game whose evolution is described by the probability that cooperators take over and fixate the entire population .
Revised:  We illustrate our theory by considering the paradigmatic prisoner's dilemma game whose evolution is described by the probability that cooperators take over and fixate the entire population .
Edit intent: clarity
Original: Motivation: Transcriptome sequencing has long been the favored method for quickly and inexpensively obtaining the sequences of many (but not all) of the genes from an organism with no reference genome.
Revised: Motivation: Transcriptome sequencing has long been the favored method for quickly and inexpensively obtaining the sequences for a large number of genes from an organism with no reference genome.
Edit intent: clarity
Original:  With the rapidly increasing throughputs and decreasing costs of next generation sequencing, RNA-Seq has gained in popu-larity ;
Revised:  With the rapidly increasing throughputs and decreasing costs of next generation sequencing, RNA-Seq has gained in popularity ;
Edit intent: fluency
Original:  but given the  short reads (e.g. 2 * 90 bp paired ends)  , de novo assembly to recover complete full length gene sequences remains an algorithmic challenge.
Revised:  but given the short reads (e.g. 2 x 90 bp paired ends) , de novo assembly to recover complete full length gene sequences remains an algorithmic challenge.
Edit intent: fluency
Original:  but given the  short reads (e.g. 2 * 90 bp paired ends)  , de novo assembly to recover complete full length gene sequences remains an algorithmic challenge.
Revised:  but given the short reads (e.g. 2 * 90 bp paired ends) , de novo assembly to recover complete or full-length transcript sequences remains an algorithmic challenge.
Edit intent: clarity
Original:  Its performance was evaluated on 2Gb and 5Gb of transcriptome data from mouse and rice . Using the known transcripts from these two well-annotated genomes as a benchmark, we assessed how SOAPdenovo-Trans and other competing software handle the practical issues of alterna-tive splicing and variable expression levels.
Revised:  Its performance was evaluated on transcriptome datasets from rice and mouse . Using the known transcripts from these two well-annotated genomes as a benchmark, we assessed how SOAPdenovo-Trans and other competing software handle the practical issues of alterna-tive splicing and variable expression levels.
Edit intent: clarity
Original:  Its performance was evaluated on 2Gb and 5Gb of transcriptome data from mouse and rice . Using the known transcripts from these two well-annotated genomes as a benchmark, we assessed how SOAPdenovo-Trans and other competing software handle the practical issues of alterna-tive splicing and variable expression levels.
Revised:  Its performance was evaluated on 2Gb and 5Gb of transcriptome data from mouse and rice . Using the known transcripts from these well-annotated genomes as a benchmark, we assessed how SOAPdenovo-Trans and other competing software handle the practical issues of alterna-tive splicing and variable expression levels.
Edit intent: clarity
Original:  Its performance was evaluated on 2Gb and 5Gb of transcriptome data from mouse and rice . Using the known transcripts from these two well-annotated genomes as a benchmark, we assessed how SOAPdenovo-Trans and other competing software handle the practical issues of alterna-tive splicing and variable expression levels.
Revised:  Its performance was evaluated on 2Gb and 5Gb of transcriptome data from mouse and rice . Using the known transcripts from these two well-annotated genomes as a benchmark, we assessed how SOAPdenovo- Trans and two other popular software handle the practical issues of alterna-tive splicing and variable expression levels.
Edit intent: clarity
Original:  Its performance was evaluated on 2Gb and 5Gb of transcriptome data from mouse and rice . Using the known transcripts from these two well-annotated genomes as a benchmark, we assessed how SOAPdenovo-Trans and other competing software handle the practical issues of alterna-tive splicing and variable expression levels.
Revised:  Its performance was evaluated on 2Gb and 5Gb of transcriptome data from mouse and rice . Using the known transcripts from these two well-annotated genomes as a benchmark, we assessed how SOAPdenovo-Trans and other competing software handle the practical issues of alternative splicing and variable expression levels.
Edit intent: fluency
Original:  Compared with other de novo transcriptome assemblers, SOAPdenovo-Trans provides high-er contiguity, lower redundancy, and faster execution.
Revised:  Our conclusion is that SOAPdenovo-Trans provides high-er contiguity, lower redundancy, and faster execution.
Edit intent: clarity
Original:  Compared with other de novo transcriptome assemblers, SOAPdenovo-Trans provides high-er contiguity, lower redundancy, and faster execution.
Revised:  Compared with other de novo transcriptome assemblers, SOAPdenovo-Trans provides higher contiguity, lower redundancy, and faster execution.
Edit intent: fluency
Original:  Our model turns out to be analytically solvable, which enables us a direct comparison of its predictions with empirical counterparts, for instance, with so significant and commonly used quantity as  velocity autocorrelation function.
Revised:  Our model turns out to be analytically solvable, which enables a direct comparison of its predictions with empirical counterparts, for instance, with so significant and commonly used quantity as velocity autocorrelation function.
Edit intent: coherence
Original:  Our model turns out to be analytically solvable, which enables us a direct comparison of its predictions with empirical counterparts, for instance, with so significant and commonly used quantity as  velocity autocorrelation function.
Revised:  Our model turns out to be analytically solvable, which enables us a direct comparison of its predictions with empirical counterparts, for instance, with so significant and commonly used quantity as a velocity autocorrelation function.
Edit intent: fluency
Original:  The memory present in the model is understood as dependence between successive share price jumps , while waiting times between price changes are considered as i.i.d. random variables.
Revised:  The memory present in the model is understood as dependence between successive share price jumps , while waiting times between jumps are considered as i.i.d. random variables.
Edit intent: clarity
Original:  Our model turns out to be  analytically solvable, which enables a direct comparison of its predictions with  empirical counterparts, for instance, with so significant and commonly used quantity as a velocity autocorrelation function.
Revised:  Our model turns out to be analytically solvable, which enables a direct comparison of its predictions with empirical counterparts, for instance, with empirical velocity autocorrelation function.
Edit intent: clarity
Original:  This work strongly extends the capabilities of the CTRW formalism.
Revised:  Thus this paper significantly extends the capabilities of the CTRW formalism.
Edit intent: clarity
Original: Accurate simulation of image formation remains under-exploited for  biological phase microscopy methods that employ partially coherent illumination , despite being important for the design of imaging systems and the reconstruction algorithms.
Revised: Image simulation remains under-exploited for biological phase microscopy methods that employ partially coherent illumination , despite being important for the design of imaging systems and the reconstruction algorithms.
Edit intent: clarity
Original: Accurate simulation of image formation remains under-exploited for  biological phase microscopy methods that employ partially coherent illumination , despite being important for the design of imaging systems and the reconstruction algorithms.
Revised: Accurate simulation of image formation remains under-exploited for biological phase microscopy methods , because of difficulties in simulating partially coherent illumination , despite being important for the design of imaging systems and the reconstruction algorithms.
Edit intent: clarity
Original:  We present an open-source MATLAB toolbox, microlith URL that provides accurate simulation of the 3D image of a thin specimen under any partially coherent imaging system, including coherent or incoherentsystems.
Revised:  We present an open-source toolbox, microlith URL that provides accurate simulation of the 3D image of a thin specimen under any partially coherent imaging system, including coherent or incoherentsystems.
Edit intent: clarity
Original:  We present an open-source MATLAB toolbox, microlith URL that provides accurate simulation of the 3D image of a thin specimen under any partially coherent imaging system, including coherent or incoherentsystems.
Revised:  We present an open-source MATLAB toolbox, microlith URL which accurately predicts three-dimensional images of a thin specimen under any partially coherent imaging system, including coherent or incoherentsystems.
Edit intent: clarity
Original:  We present an open-source MATLAB toolbox, microlith URL that provides accurate simulation of the 3D image of a thin specimen under any partially coherent imaging system, including coherent or incoherentsystems.
Revised:  We present an open-source MATLAB toolbox, microlith URL that provides accurate simulation of the 3D image of a thin specimen observed with any partially coherent imaging system, including coherent or incoherentsystems.
Edit intent: clarity
Original:  The comparison leads to intriguing insights about the sensitivity of the dark-field microscope to sub-resolution features and effects of specimen birefringence on differential interference contrast .
Revised:  The comparison provides new insights about the sensitivity of the dark-field microscope to sub-resolution features and effects of specimen birefringence on differential interference contrast .
Edit intent: clarity
Original: This paper is a performance study of a parallel programming model called S-Net.
Revised: This is a comparative evaluation of the performance of the coordination language S-Net.
Edit intent: clarity
Original:  The purpose of S-Net is to support writing coordination code that instantiates components as "boxes" and connects them with anonymous data streams.
Edit intent: coherence
Original:  An application is represented as a network between the standard input and output , which are two external streams connecting the whole application with its environment.
Revised:  An application is represented as a network between the standard input and output streams linking the application and the environment.
Edit intent: clarity
Original:  We evaluate S-Net using a numerical algorithm for a linear algebra problem - Cholesky decomposition.
Revised:  We evaluate S-Net on a numerical algorithm for a linear algebra problem - Cholesky decomposition.
Edit intent: clarity
Original:  We evaluate S-Net using a numerical algorithm for a linear algebra problem - Cholesky decomposition.
Revised:  We evaluate S-Net using a numerical algorithm for a linear algebra problem : Cholesky decomposition.
Edit intent: fluency
Original:  Cholesky decomposition has many important applications.
Revised:  It has many important applications.
Edit intent: clarity
Original:   Our measurements demonstrate that S-Net has a similar performance to CnC on this problem  .
Revised:  Our measurements demonstrate that S-Net has a performance similar to CnC on this problem .
Edit intent: fluency
Original:  For both implementations an effective utilisation of resources is achieved without platform-specific tuning .
Revised:  For both implementations efficient utilization of resources is achieved without platform-specific tuning .
Edit intent: clarity
Original:  Our measurements demonstrate that S-Net has a performance similar to CnC on this problem (and can even outperform the latter).
Revised:  Our measurements demonstrate that S-Net manages to outperform CnC on this problem (and can even outperform the latter).
Edit intent: clarity
Original: Location service is essential for many sensor network applications.
Revised: Accurate location information is essential for many sensor network applications.
Edit intent: clarity
Original:  We then prove a novel lower bound of expectation of AGDOP (LB-E-AGDOP) and derives a closed-form expression that relates LB-E-AGDOP to only three parameters that describe network connectivity and scale .
Revised:  We then prove a novel lower bound of expectation of AGDOP (LB-E-AGDOP) and derives a closed-form formula that relates LB-E-AGDOP to only three parameters that describe network connectivity and scale .
Edit intent: clarity
Original:  Furthermore, the paper conjectures a simple relationship between the expectation of AGDOP (E-AGDOP) and its lower bound, LB-E-AGDOP .
Revised:  Furthermore, the paper demonstrates a strong connection between LB-E-AGDOP .
Edit intent: clarity
Original:  The closed-form expressions of LB-E-AGDOP and E-AGDOP are used to analyze how accuracy evolves when the network scales up . Finally, we validate the theoretical results via numerical simulations  .
Revised:  The closed-form expressions of LB-E-AGDOP and E-AGDOP are used to analyze how accuracy evolves when the network scales up . Finally, we validate the theory via numerical simulations .
Edit intent: clarity
Original:  The following extension of the Erdo s--P\'osa theorem holds: for every h-vertex planar graph H, there exists a function f_{H} such that every graph G, either contains k disjoint copies of graphs in {\cal M}(H), or contains a set of f_{H}(k) vertices meeting every subgraph of G that belongs in {\cal M}(H).
Revised:  The following extension of the Erdo s-P\'osa Theorem holds: for every h-vertex planar graph H, there exists a function f_{H} such that every graph G, either contains k disjoint copies of graphs in {\cal M}(H), or contains a set of f_{H}(k) vertices meeting every subgraph of G that belongs in {\cal M}(H).
Edit intent: fluency
Original: This is survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT).
Revised: This article is a survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT).
Edit intent: fluency
Original:  The article is written to be accessible to graduate students.
Revised:  It is written to be accessible to graduate students.
Edit intent: fluency
Original:  In those studies, only local migration to immediate neighbor sites was considered, while long-range migration has not been considered yet, partly because the long-range migration has been generally regarded as harmful for cooperation as it would bring the population to a well-mixed state that favors defection.
Revised:  In those studies, only local migration to immediate neighbors was considered, while long-range migration has not been considered yet, partly because the long-range migration has been generally regarded as harmful for cooperation as it would bring the population to a well-mixed state that favors defection.
Edit intent: clarity
Original:  In this paper , we studied the effects of adaptive long-range migration on the evolution of cooperation through agent-based simulations of a spatial Prisoner's Dilemma game in which individuals can jump to a farther site if they are surrounded by more defectors.
Revised:  Here , we studied the effects of adaptive long-range migration on the evolution of cooperation through agent-based simulations of a spatial Prisoner's Dilemma game in which individuals can jump to a farther site if they are surrounded by more defectors.
Edit intent: coherence
Original:  In this paper , we studied the effects of adaptive long-range migration on the evolution of cooperation through agent-based simulations of a spatial Prisoner's Dilemma game in which individuals can jump to a farther site if they are surrounded by more defectors.
Revised:  In this paper , we studied the effects of adaptive long-range migration on the evolution of cooperation through agent-based simulations of a spatial Prisoner's Dilemma game where individuals can jump to a farther site if they are surrounded by more defectors.
Edit intent: clarity
Original:  Moreover, we found that cooperation emerges and remains robustly through mutation and migration even from a condition in which only defectors exist.
Edit intent: coherence
Original:  These findings demonstrate the significance of adaptive long-range migration , a naturally observed migration style in human and animal behaviors, for the evolution of cooperation.
Revised:  These findings demonstrate the significance of adaptive long-range migration for the evolution of cooperation.
Edit intent: clarity
Original: The Crow--Kimura quasispecies model with permutation invariant fitness landscape  is investigated.
Revised: The Crow--Kimura quasispecies model with permutation invariant fitness landscape - is investigated.
Edit intent: fluency
Original:  Using the fact that the mutation matrix in the case of  permutation invariant fitness landscape has a special  form, a change of the basis is found such that in  new coordinates a number of analytical results can be obtained.
Revised:  Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special form, a change of the basis is found such that in new coordinates a number of analytical results can be obtained.
Edit intent: fluency
Original:  Using the fact that the mutation matrix in the case of  permutation invariant fitness landscape has a special  form, a change of the basis is found such that in  new coordinates a number of analytical results can be obtained.
Revised:  Using the fact that the mutation matrix in the case of permutation invariant fitness landscape has a special form, a change of the basis is suggested such that in new coordinates a number of analytical results can be obtained.
Edit intent: clarity
Original:  Using the fact that the mutation matrix in the case of  permutation invariant fitness landscape has a special  form, a change of the basis is found such that in  new coordinates a number of analytical results can be obtained.
Revised:  Using the fact that the mutation matrix in the case of permutation invariant fitness landscape has a special form, a change of the basis is found such that in the new coordinates a number of analytical results can be obtained.
Edit intent: fluency
Original:  A parametric solution to the system of equation determining the quasispecies is found;
Revised:  A parametric solution to the system of equations determining the quasispecies is found;
Edit intent: fluency
Original:  A parametric solution to the system of equation determining the quasispecies is found;
Revised:  A parametric solution to the system of equation determining the quasispecies . Using
Edit intent: coherence
Original:  Using this definition, we suggest two approximate formulas , which are based on the preceding analytical results, to estimate the critical mutation rate after which the quasispecies delocalization occurs.
Revised:  Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs.
Edit intent: coherence
Original: Correct assessment of scientist's past research impact and potential for future impact is fundamental to all personnel recruitment decisions in science.
Revised: Correctly assessing a scientist's past research impact and potential for future impact is fundamental to all personnel recruitment decisions in science.
Edit intent: clarity
Original:  Here we present a cross-sectional analysis of 762 longitudinal careers drawn from three disciplines: physics, biology, and mathematics .
Revised:  Here we present a cross-sectional analysis of 762 careers drawn from three disciplines: physics, biology, and mathematics .
Edit intent: clarity
Original:  Specifically, cumulative non-decreasing measures like the h-index contain intrinsic spurious autocorrelation, resulting in a significant overestimation of their "predictive power".
Revised:  Specifically, cumulative non-decreasing measures like the h-index contain intrinsic autocorrelation, resulting in a significant overestimation of their "predictive power".
Edit intent: clarity