wanyu/IteraTeR_v2 huggingface dataset:
Original:  This model is  also able to explain very satisfactory all available statistical experimental data, such as PDFs and average values of turning angles and times, of both run and tumble motions.
Revised:  This model is also able to explain very satisfactory all available statistical experimental data, such as PDFs and average values of turning angles times, of both run and tumble motions.
Edit intent: clarity
Original: A Kneser graph KG_{n,k} is a graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect .
Revised: The Kneser graph KG_{n,k} is a graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect .
Edit intent: fluency
Original: A Kneser graph KG_{n,k} is a graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect .
Revised: A Kneser graph KG_{n,k} is the graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect .
Edit intent: clarity
Original: A Kneser graph KG_{n,k} is a graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect .
Revised: A Kneser graph KG_{n,k} is a graph whose vertices are the k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect .
Edit intent: clarity
Original: A Kneser graph KG_{n,k} is a graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect .
Revised: A Kneser graph KG_{n,k} is a graph whose vertices are all k-element subsets of [n], with two vertices adjacent if and only if the corresponding sets do not intersect .
Edit intent: clarity
Original: A Kneser graph KG_{n,k} is a graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets do not intersect .
Revised: A Kneser graph KG_{n,k} is a graph whose vertices are all k-element subsets of [n], with two vertices connected if and only if the corresponding sets are disjoint .
Edit intent: clarity
Original:  A famous result due to Lov\'asz states that the chromatic number of a Kneser graph KG_{n,k} is equal to n-2k+2.
Revised:  A famous result due to Lov\'asz states that the chromatic number of KG_{n,k} is equal to n-2k+2.
Edit intent: clarity
Original:  It was studied in two recent papers, one due to Kupavskii, who proposed the problem and studied it in the graph case, and the more recent one due to Alishahi and Hajiabolhassan.
Revised:  It was studied in two recent papers, one due to Kupavskii, who proposed the problem and studied the graph case, and the more recent one due to Alishahi and Hajiabolhassan.
Edit intent: clarity
Original: In this paper, we address the problem of scheduling scalable video to video streaming users in a wireless network.
Revised: In this paper, we consider the problem of scheduling scalable video to video streaming users in a wireless network.
Edit intent: clarity
Original: We propose a general numerical approach that can be used to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies when the competitive exclusion principle holds.
Revised: We propose a numerical approach to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies when the competitive exclusion principle holds.
Edit intent: clarity
Original: We propose a general numerical approach that can be used to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies when the competitive exclusion principle holds.
Revised: We propose a general numerical approach that can be used to study the invasion fitness of a mutant and to determine evolutionary singular strategies when the competitive exclusion principle holds.
Edit intent: clarity
Original: We propose a general numerical approach that can be used to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies when the competitive exclusion principle holds.
Revised: We propose a general numerical approach that can be used to study the invasion fitness of a mutant in evolutionary models and to determine evolutionary singular strategies in evolutionary structured models in which the competitive exclusion principle holds.
Edit intent: clarity
Original:  We exploit a previously derived mathematical relationship between these models to derive a general  method for analyzing the invasion fitness of stochastic models.
Revised:  We exploit a previously derived mathematical relationship between these models to derive a general method for analyzing the invasion fitness in the stochastic models.
Edit intent: clarity
Original:  Our method is based on a deterministic reduced model for which it is straightforward to determine the feasibility of invasion and the convergence-stable evolutionary singular strategy .
Revised:  Our method can be applied to the broad class of evolutionary models for which a link between the stochastic and deterministic invasion fitnesses can be established .
Edit intent: clarity
Original:  To train the neural network , we compute a measure of consistency of extracted data with existing databases , and use it as a form of noisy supervision.
Revised:  The network is trained using a measure of consistency of extracted data with existing databases , and use it as a form of noisy supervision.
Edit intent: clarity
Original:  To train the neural network , we compute a measure of consistency of extracted data with existing databases , and use it as a form of noisy supervision.
Revised:  To train the neural network , we compute a measure of consistency of extracted data with existing databases as a form of noisy supervision.
Edit intent: coherence
Original:  Our architecture combines the ability of constraint-based information extraction system to easily incorporate domain knowledge and constraints with the ability of deep neural networks to leverage large amounts of data to learn complex features.
Revised:  Our architecture combines the ability of constraint-based information extraction systems to easily incorporate domain knowledge and constraints with the ability of deep neural networks to leverage large amounts of data to learn complex features.
Edit intent: fluency
Original:  This is done by jointly considering Channel  (CSI) and Queue  (QSI) State Information when establishing vehicle-to-vehicle (V2V) links.
Revised:  This is done by jointly considering Channel State Information (CSI) and Queue (QSI) State Information when establishing vehicle-to-vehicle (V2V) links.
Edit intent: fluency
Original:  This is done by jointly considering Channel  (CSI) and Queue  (QSI) State Information when establishing vehicle-to-vehicle (V2V) links.
Revised:  This is done by jointly considering Channel (CSI) and Queue (QSI) when establishing vehicle-to-vehicle (V2V) links.
Edit intent: clarity
Original:  To validate the proposed framework  simulation results are presented and discussed where the throughput performance as well as the latency/reliability trade-offs of the proposed approach are assessed and compared to several baseline approaches recently proposed in the literature.
Revised:  To validate the proposed framework , simulation results are presented and discussed where the throughput performance as well as the latency/reliability trade-offs of the proposed approach are assessed and compared to several baseline approaches recently proposed in the literature.
Edit intent: fluency
Original:  The results obtained in our study -with performance gains in terms of reliability and delay of up to 25\% for ultra-dense vehicular scenarios and on average 50\% more paired vehicles that some of the baselines- shed light on the operational limits and practical feasibility of mmWave bands  as a viable radio access solution for future high-rate V2V communications.
Revised:  The results obtained in our study show performance gains in terms of reliability and delay of up to 25\% for ultra-dense vehicular scenarios and on average 50\% more paired vehicles that some of the baselines- shed light on the operational limits and practical feasibility of mmWave bands as a viable radio access solution for future high-rate V2V communications.
Edit intent: clarity
Original:  The results obtained in our study -with performance gains in terms of reliability and delay of up to 25\% for ultra-dense vehicular scenarios and on average 50\% more paired vehicles that some of the baselines- shed light on the operational limits and practical feasibility of mmWave bands  as a viable radio access solution for future high-rate V2V communications.
Revised:  The results obtained in our study -with performance gains in terms of reliability and delay up to 25\% for ultra-dense vehicular scenarios and on average 50\% more paired vehicles that some of the baselines- shed light on the operational limits and practical feasibility of mmWave bands as a viable radio access solution for future high-rate V2V communications.
Edit intent: clarity
Original:  The results obtained in our study -with performance gains in terms of reliability and delay of up to 25\% for ultra-dense vehicular scenarios and on average 50\% more paired vehicles that some of the baselines- shed light on the operational limits and practical feasibility of mmWave bands  as a viable radio access solution for future high-rate V2V communications.
Revised:  The results obtained in our study -with performance gains in terms of reliability and delay of up to 25\% for ultra-dense vehicular scenarios and on average 50\% more paired vehicles that some of the baselines. These results shed light on the operational limits and practical feasibility of mmWave bands as a viable radio access solution for future high-rate V2V communications.
Edit intent: coherence
Original:  The results obtained in our study -with performance gains in terms of reliability and delay of up to 25\% for ultra-dense vehicular scenarios and on average 50\% more paired vehicles that some of the baselines- shed light on the operational limits and practical feasibility of mmWave bands  as a viable radio access solution for future high-rate V2V communications.
Revised:  The results obtained in our study -with performance gains in terms of reliability and delay of up to 25\% for ultra-dense vehicular scenarios and on average 50\% more paired vehicles that some of the baselines- shed light on the operational limits and practical feasibility of mmWave bands , as a viable radio access solution for future high-rate V2V communications.
Edit intent: fluency
Original: Characterizing patient somatic mutations through next-generation sequencing tech-nologies opens up possibilities for refining cancer subtypes.
Revised: Characterizing patient somatic mutations through next-generation sequencing technologies opens up possibilities for refining cancer subtypes.
Edit intent: fluency
Original:  However, cataloguesof mutations reveal that only a small fraction of the genes are altered frequentlyin patients.
Revised:  However, catalogues of mutations reveal that only a small fraction of the genes are altered frequentlyin patients.
Edit intent: fluency
Original:  However, cataloguesof mutations reveal that only a small fraction of the genes are altered frequentlyin patients.
Revised:  However, cataloguesof mutations reveal that only a small fraction of the genes are altered frequently in patients.
Edit intent: fluency
Original:  On the other hand different genomic alterations may perturb the samepathways .
Revised:  On the other hand different genomic alterations may perturb the same pathways .
Edit intent: fluency
Original:  We propose a novel clustering procedure that quantifies the similaritiesof patients from their mutational profile on pathways via a novel graph kernel.
Revised:  We propose a novel clustering procedure that quantifies the similarities of patients from their mutational profile on pathways via a novel graph kernel.
Edit intent: fluency
Original:  For each patient thevertex labels are assigned based on her altered genes.
Revised:  For each patient the vertex labels are assigned based on her altered genes.
Edit intent: fluency
Original:  Smoothed shortest pathgraph kernel (smSPK) evaluates each pair of patients by comparing their vertexlabeled pathway graphs.
Revised:  Smoothed shortest path graph kernel (smSPK) evaluates each pair of patients by comparing their vertexlabeled pathway graphs.
Edit intent: fluency
Original:  Smoothed shortest pathgraph kernel (smSPK) evaluates each pair of patients by comparing their vertexlabeled pathway graphs.
Revised:  Smoothed shortest pathgraph kernel (smSPK) evaluates each pair of patients by comparing their vertex labeled pathway graphs.
Edit intent: fluency
Original:  Our clustering procedure involves two steps: the smSPKkernel matrix derived for each pathway are input to kernel k-means algorithmand each pathway is evaluated individually.
Revised:  Our clustering procedure involves two steps: the smSPK kernel matrix derived for each pathway are input to kernel k-means algorithmand each pathway is evaluated individually.
Edit intent: fluency
Original:  Our clustering procedure involves two steps: the smSPKkernel matrix derived for each pathway are input to kernel k-means algorithmand each pathway is evaluated individually.
Revised:  Our clustering procedure involves two steps: the smSPKkernel matrix derived for each pathway are input to kernel k-means algorithm and each pathway is evaluated individually.
Edit intent: fluency
Original:  In the next step, only those pathwaysthat are successful are combined in to a single kernel input to kernel k-means tostratify patients.
Revised:  In the next step, only those pathways that are successful are combined in to a single kernel input to kernel k-means tostratify patients.
Edit intent: fluency
Original:  In the next step, only those pathwaysthat are successful are combined in to a single kernel input to kernel k-means tostratify patients.
Revised:  In the next step, only those pathwaysthat are successful are combined in to a single kernel input to kernel k-means to stratify patients.
Edit intent: fluency
Original:  Evaluating the procedure on simulated data showed that smSPKclusters patients up to 88 \% accuracy.
Revised:  Evaluating the procedure on simulated data showed that smSPK clusters patients up to 88 \% accuracy.
Edit intent: fluency
Original:  Finally to identify ovarian cancer patient subgroups, we apply our methodology to the cancer genome atlas ovarian datathat involves 481 patients.
Revised:  Finally to identify ovarian cancer patient subgroups, we apply our methodology to the cancer genome atlas ovarian data that involves 481 patients.
Edit intent: fluency
Original:  The identified subgroups are evaluated through survivalanalysis . Grouping patients into four clusters results with patients groups that aresignificantly different in their survival times (p-value \leq \le 0.005).
Revised:  The identified subgroups are evaluated through survival analysis . Grouping patients into four clusters results with patients groups that aresignificantly different in their survival times (p-value \leq \le 0.005).
Edit intent: fluency
Original:  The identified subgroups are evaluated through survivalanalysis . Grouping patients into four clusters results with patients groups that aresignificantly different in their survival times (p-value \leq \le 0.005).
Revised:  The identified subgroups are evaluated through survivalanalysis . Grouping patients into four clusters results with patients groups that are significantly different in their survival times (p-value \leq \le 0.005).
Edit intent: fluency
Original:  The identified subgroups are evaluated through survivalanalysis . Grouping patients into four clusters results with patients groups that aresignificantly different in their survival times (p-value \leq \le 0.005).
Revised:  The identified subgroups are evaluated through survivalanalysis . Grouping patients into four clusters results with patients groups that aresignificantly different in their survival times (p-value \le 0.005).
Edit intent: clarity
Original:   complete systems that are generally redundant but provide stable infinite representations.
Revised:  that is, complete systems that are generally redundant but provide stable infinite representations.
Edit intent: coherence
Original:  While frames are well-known in image and signal processing, coding theory and other areas of  mathematics, their use in numerical analysis is far less widespread.
Revised:  While frames are well-known in image and signal processing, coding theory and other areas of applied mathematics, their use in numerical analysis is far less widespread.
Edit intent: clarity
Original:  Yet, as we show via example , frames are more flexible than bases, and can be constructed easily in a range of problems where finding orthonormal bases with desirable properties is difficult or impossible.
Revised:  Yet, as we show via a series of examples , frames are more flexible than bases, and can be constructed easily in a range of problems where finding orthonormal bases with desirable properties is difficult or impossible.
Edit intent: clarity
Original:  However , we show that frame approximations can in fact be computed numerically up to an error of order \epsilon with a simple algorithm, where \epsilon is a threshold parameter that can be chosen close to machine precision.
Revised:  However , we show that an accurate frame approximation of a function f can be computed numerically up to an error of order \epsilon with a simple algorithm, where \epsilon is a threshold parameter that can be chosen close to machine precision.
Edit intent: clarity
Original:   Crucially, the order of convergence down to this limit is determined by the existence of representations of the function being approximated that are accurate and have small-norm coefficients.
Revised:  Crucially, the order of convergence down to this limit is determined by the existence of accurate, approximate representations of f in the frame that have small-norm coefficients.
Edit intent: clarity
Original:  We demonstrate the existence of such representations in all our examples.
Revised:  We demonstrate the existence of such representations in our examples.
Edit intent: clarity
Original:  In particular, even in the presence of severe ill-conditioning, the frame condition imposes sufficient mathematical structure on the redundant set in order to give rise to good approximations in finite precision calculations.
Revised:  In particular, even in the presence of severe ill-conditioning, frames impose sufficient mathematical structure on the redundant set in order to give rise to good approximations in finite precision calculations.
Edit intent: clarity
Original:  In particular, even in the presence of severe ill-conditioning, the frame condition imposes sufficient mathematical structure on the redundant set in order to give rise to good approximations in finite precision calculations.
Revised:  In particular, even in the presence of severe ill-conditioning, the frame condition imposes sufficient mathematical structure so as to give rise to good approximations in finite precision calculations.
Edit intent: clarity
Original:  In particular, even in the presence of severe ill-conditioning, the frame condition imposes sufficient mathematical structure on the redundant set in order to give rise to good approximations in finite precision calculations.
Revised:  In particular, even in the presence of severe ill-conditioning, the frame condition imposes sufficient mathematical structure on the redundant set in order to give rise to good accuracy in finite precision calculations.
Edit intent: clarity
Original: Functions of one or more variables are usually approximated with a basis ;
Revised: Functions of one or more variables are usually approximated with a basis :
Edit intent: fluency
Original:  a complete, linearly independent set of functions that spans an appropriate function space.
Revised:  a complete, linearly-independent system of functions that spans an appropriate function space.
Edit intent: clarity
Original:  The topic of this paper is the numerical approximation of functions using the more general notion of frames ;
Revised:  The topic of this paper is the numerical approximation of functions using the more general notion of frames :
Edit intent: fluency
Original:  that is, complete systems that are generally redundant but provide stable infinite representations .
Revised:  that is, complete systems that are generally redundant but provide infinite representations with bounded coefficients .
Edit intent: clarity
Original:  By means of example , we exhibit a frame which yields simple, high-order approximations of smooth , multivariate functions in complicated geometries.
Revised:  For instance , we exhibit a frame which yields simple, high-order approximations of smooth , multivariate functions in complicated geometries.
Edit intent: clarity
Original:  A major concern when using frames is that computing a best approximation typically requires solving an ill-conditioned linear system.
Revised:  A key concern when using frames is that computing a best approximation typically requires solving an ill-conditioned linear system.
Edit intent: clarity
Original:  A major concern when using frames is that computing a best approximation typically requires solving an ill-conditioned linear system.
Revised:  A major concern when using frames is that computing a best approximation requires solving an ill-conditioned linear system.
Edit intent: clarity
Original:  Nonetheless, we show that an accurate frame approximation of a function f can be computed numerically up to an error of order \epsilon with a simple algorithm , or even of order \epsilon with modifications to the algorithm.
Revised:  Nonetheless, we show that an accurate frame approximation of a function f can be computed numerically up to an error of order \epsilon , or even of order \epsilon with modifications to the algorithm.
Edit intent: clarity
Original:  Here , \epsilon is a user-controlled parameter . Crucially, the order of convergence down to this limit is determined by the existence of accurate, approximate representations of f in the frame that have small-norm coefficients.
Revised:  Here , \epsilon is a threshold value that can be chosen by the user . Crucially, the order of convergence down to this limit is determined by the existence of accurate, approximate representations of f in the frame that have small-norm coefficients.
Edit intent: clarity
Original:  Here , \epsilon is a user-controlled parameter . Crucially, the order of convergence down to this limit is determined by the existence of accurate, approximate representations of f in the frame that have small-norm coefficients.
Revised:  Here , \epsilon is a user-controlled parameter . Crucially, the order of convergence down to this limit is determined by the existence of approximate representations of f in the frame that have small-norm coefficients.
Edit intent: clarity
Original:  Here , \epsilon is a user-controlled parameter . Crucially, the order of convergence down to this limit is determined by the existence of accurate, approximate representations of f in the frame that have small-norm coefficients.
Revised:  Here , \epsilon is a user-controlled parameter . Crucially, the order of convergence down to this limit is determined by the existence of accurate, approximate representations of f in the frame possessing small-norm coefficients.
Edit intent: clarity
Original:  In particular, even in the presence of severe ill-conditioning, frames impose sufficient mathematical structure so as to give rise to good accuracy in finite precision calculations .
Revised:  In particular, even in the presence of severely ill-conditioned linear systems, the frame condition imposes sufficient mathematical structure so as to give rise to good accuracy in finite precision calculations .
Edit intent: clarity