wanyu/IteraTeR_v2 huggingface dataset:
Original:  The approach can directly consider any data sets that can be expressed in a matrix, including those from attribute-based representations, ontologies, associations and networks.
Revised:  The approach can directly consider any data sets that can be expressed in a matrix, including those from feature-based representations, ontologies, associations and networks.
Edit intent: clarity
Original:  We demonstrate its utility on a gene function prediction problem in a case study with eleven different data sources .
Revised:  We demonstrate its utility on a gene function prediction task with eleven different data sources .
Edit intent: clarity
Original:  The distance Ramsey number R_{{\it D}}(s,t,d) is the minimum number n such that for any graph G on n vertices, either G contains an induced s -vertex subgraph isomorphic to a distance graph in \Real^d or \bar {G} contains an induced t -vertex subgraph isomorphic to a distance graph in \Real^d .
Revised:  The distance Ramsey number R_{{\it D}}(s,t,d) is the minimum number n such that for any graph G on n vertices, either G contains an induced s -vertex subgraph isomorphic to a distance graph in \Real^d or \bar {G} contains an induced t -vertex subgraph isomorphic to the distance graph in \Real^d .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain the upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds on R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) , which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% {[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% %DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Edit intent: coherence
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% {[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% (\lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil \frac{s{[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil,\lceil {[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil \frac{s{[d/2]} }\rceil .
Edit intent: fluency
Original:  We obtain  upper and lower bounds for R_{{\it D}}(s,s,d)  which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil .
Revised:  We obtain upper and lower bounds for R_{{\it D}}(s,s,d) which are similar to the bounds for the classical Ramsey number R %DIFDELCMD < \left(\left \lceil %DIFDELCMD < %%% \frac{s{[d/2]} }%DIFDELCMD < \right \rceil%%% ,%DIFDELCMD < \left \lceil %%% \frac{s{[d/2]} }%DIFDELCMD < \right %DIFDELCMD < \rceil\right)%%% \lceil {[d/2]} }\rceil\lceil {[d/2]} }\rceil) .
Edit intent: fluency
Original:  The proof relies on a link to a certain structural rigidity question on curves.
Revised:  An important step in the proof involves understanding the structural rigidity of certain frameworks on curves.
Edit intent: clarity
Original: The idea of having the geolocation database monitor the sec- ondary use of TV white space (TVWS) spectrum and assist in coordinating the secondary usage is gaining ground.
Revised: The idea of having the geolocation database monitor the secondary use of TV white space (TVWS) spectrum and assist in coordinating the secondary usage is gaining ground.
Edit intent: fluency
Original:  Con- sidering the home networking use case, we leverage the ge- olocation database for interference-aware coordinated TVWS sharing among secondary users (home networks) using short- term auctions {\em   .
Revised:  Considering the home networking use case, we leverage the ge- olocation database for interference-aware coordinated TVWS sharing among secondary users (home networks) using short- term auctions {\em .
Edit intent: fluency
Original:  Con- sidering the home networking use case, we leverage the ge- olocation database for interference-aware coordinated TVWS sharing among secondary users (home networks) using short- term auctions {\em   .
Revised:  Con- sidering the home networking use case, we leverage the geolocation database for interference-aware coordinated TVWS sharing among secondary users (home networks) using short- term auctions {\em .
Edit intent: fluency
Original:  Con- sidering the home networking use case, we leverage the ge- olocation database for interference-aware coordinated TVWS sharing among secondary users (home networks) using short- term auctions {\em   .
Revised:  Con- sidering the home networking use case, we leverage the ge- olocation database for interference-aware coordinated TVWS sharing among secondary users (home networks) using {\em .
Edit intent: clarity
Original:  To enable this  framework, we propose an on- line{\em   multi-unit, iterative truthful auction mechanism VERUM that takes into consideration spatially heterogeneous spec- trum availability, an inherent characteristic in the TVWS context.
Revised:  To enable this framework, we propose an on- line{\em multi-unit, iterative truthful mechanism called VERUM that takes into consideration spatially heterogeneous spec- trum availability, an inherent characteristic in the TVWS context.
Edit intent: clarity
Original:  To enable this  framework, we propose an on- line{\em   multi-unit, iterative truthful auction mechanism VERUM that takes into consideration spatially heterogeneous spec- trum availability, an inherent characteristic in the TVWS context.
Revised:  To enable this framework, we propose an on- line{\em multi-unit, iterative truthful auction mechanism VERUM that takes into consideration spatially heterogeneous spectrum availability, an inherent characteristic in the TVWS context.
Edit intent: fluency
Original:  Evaluation results from scenarios with real home distribu- tions in urban and dense-urban environments and using re- alistic TVWS spectrum availability maps show that VERUM performs close to optimal allocation in terms of revenue for the coordinating spectrum manager.
Revised:  Evaluation results from scenarios with real home distributions in urban and dense-urban environments and using re- alistic TVWS spectrum availability maps show that VERUM performs close to optimal allocation in terms of revenue for the coordinating spectrum manager.
Edit intent: fluency
Original:  Evaluation results from scenarios with real home distribu- tions in urban and dense-urban environments and using re- alistic TVWS spectrum availability maps show that VERUM performs close to optimal allocation in terms of revenue for the coordinating spectrum manager.
Revised:  Evaluation results from scenarios with real home distribu- tions in urban and dense-urban environments and using realistic TVWS spectrum availability maps show that VERUM performs close to optimal allocation in terms of revenue for the coordinating spectrum manager.
Edit intent: fluency
Original:  Taken together, VERUM can be seen to offer incentives to subscribed users through greater spectrum availability (as measured by percentage of winning bidders) as well as to spectrum coordinator through revenue generation.
Edit intent: clarity
Original:  Comparison with two existing efficient and truthful multi-unit spectrum auction schemes, VERITAS and SATYA, shows that VERUM fares better in terms of rev- enue, spectrum utilization and percentage of winning bid- ders in diverse conditions  .
Revised:  Comparison with two existing efficient and truthful multi-unit spectrum auction schemes, VERITAS and SATYA, shows that VERUM fares better in terms of revenue, spectrum utilisation and percentage of winning bid- ders in diverse conditions .
Edit intent: fluency
Original:  Comparison with two existing efficient and truthful multi-unit spectrum auction schemes, VERITAS and SATYA, shows that VERUM fares better in terms of rev- enue, spectrum utilization and percentage of winning bid- ders in diverse conditions  .
Revised:  Comparison with two existing efficient and truthful multi-unit spectrum auction schemes, VERITAS and SATYA, shows that VERUM fares better in terms of rev- enue, spectrum utilization and percentage of winning bidders in diverse conditions .
Edit intent: fluency
Original:  Accordingly, a population can accept mutations without altering its phenotype, as long as they transform its genotype into another one on the same set.
Revised:  Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the same set.
Edit intent: clarity
Original:  In this letter we analyze this effect by studying the dynamics of random walks (RW) on assortative networks with arbitrary topology  .
Revised:  By studying the dynamics of random walks (RW) on assortative networks with arbitrary topology .
Edit intent: coherence
Original:  From the biological viewpoint, this "phenotypic entrapment" entails an acceleration in the fixation of neutral mutations, thus implying a non-uniform increase in the ticking rate of the molecular clock with the age of branches in phylogenetic trees .
Revised:  From the biological viewpoint, this "phenotypic entrapment" entails a systematic increase in the ticking rate of the molecular clock with the age of branches in phylogenetic trees .
Edit intent: clarity
Original:  From the biological viewpoint, this "phenotypic entrapment" entails an acceleration in the fixation of neutral mutations, thus implying a non-uniform increase in the ticking rate of the molecular clock with the age of branches in phylogenetic trees .
Revised:  From the biological viewpoint, this "phenotypic entrapment" entails an acceleration in the fixation of neutral mutations, thus implying a non-uniform increase in the overdispersion of the process with time and an acceleration in the fixation rate of neutral mutations .
Edit intent: clarity
Original:  We also show that this effect is stronger the larger the fitness of the current phenotype relative to that of neighboring phenotypes .
Revised:  We also quantify the variation of these effects with the size of the phenotype and with its fitness relative to that of neighboring phenotypes .
Edit intent: clarity
Original:  We also show that this effect is stronger the larger the fitness of the current phenotype relative to that of neighboring phenotypes .
Revised:  We also show that this effect is stronger the larger the fitness of the current phenotype relative to that of neighbouring alternatives .
Edit intent: clarity
Original:  A new statistical test is defined to assess the significance of a group of proteins when found in several genesets of a given database.
Revised:  A new statistical test is proposed to assess the significance of a group of proteins when found in several genesets of a given database.
Edit intent: clarity
Original:  A new statistical test is defined to assess the significance of a group of proteins when found in several genesets of a given database.
Revised:  A new statistical test is defined to assess the significance of a group of symbols when found in several genesets of a given database.
Edit intent: clarity
Original:  Applied to protein pairs, the thresholded p-values of the test define a graph structure on the set of proteins .
Revised:  Applied to protein pairs, the thresholded p-values of the test define a graph structure on the set of symbols .
Edit intent: clarity
Original:  The method can be applied to any database, and is illustrated on the KEGG database and on specific selections from the MSygDB C2 database.
Revised:  The method can be applied to any database, and is illustrated MSigDB C2 database.
Edit intent: clarity
Original:  Most of the protein associations detected in KEGG and cancer-related genesets of MSigDB C2 match already known interactions.
Revised:  Many of the symbol associations detected in KEGG and cancer-related genesets of MSigDB C2 match already known interactions.
Edit intent: clarity
Original:  Most of the protein associations detected in KEGG and cancer-related genesets of MSigDB C2 match already known interactions.
Revised:  Most of the protein associations detected in C2 match already known interactions.
Edit intent: clarity
Original:  They could indicate potentially interesting protein-protein interactions, if validated by biological evidence.
Revised:  These associations unveal new candidates for gene or protein interactions, needing further investigation for biological evidence.
Edit intent: clarity
Original: We study the problem of conjunctive query evaluation over sets of queries;
Revised: We study the problem of conjunctive query evaluation relative to a class of queries;
Edit intent: clarity
Original:  this problem is formulated here as the relational homomorphism problem over a set of structures A, wherein each instance must be a pair of structures such that the first structure is an element of A.
Revised:  this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of structures such that the first structure is an element of A.
Edit intent: clarity
Original:  This binary relation is defined in terms of a notion which we call graph deconstruction and which is a variant of the well-known notion of tree decomposition.
Revised:  This relation is defined in terms of a notion which we call graph deconstruction and which is a variant of the well-known notion of tree decomposition.
Edit intent: clarity
Original:  We then use this graph hierarchy to infer a complexity hierarchy of homomorphism problems which is comprehensive up to a computationally very weak notion of reduction, namely, a parameterized form of quantifier-free reductions.
Revised:  We then use this hierarchy of graph classes to infer a complexity hierarchy of homomorphism problems which is comprehensive up to a computationally very weak notion of reduction, namely, a parameterized form of quantifier-free reductions.
Edit intent: clarity
Original:  We then use this graph hierarchy to infer a complexity hierarchy of homomorphism problems which is comprehensive up to a computationally very weak notion of reduction, namely, a parameterized form of quantifier-free reductions.
Revised:  We then use this graph hierarchy to infer a complexity hierarchy of homomorphism problems which is comprehensive up to a computationally very weak notion of reduction, namely, a parameterized version of quantifier-free reductions.
Edit intent: clarity
Original:  We also present and develop the theory of  pebble games which solve the homomorphism problems where the cores of the structures in A have bounded tree depth ;
Revised:  We then present and develop the theory of pebble games which solve the homomorphism problems where the cores of the structures in A have bounded tree depth ;
Edit intent: coherence
Original:  Given k sequences q_1, ..., q_k of labeled bins and a positive integer p . The goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places.
Revised:  Given k sequences q_1, ..., q_k of labeled bins and a positive integer p , the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places.
Edit intent: fluency
Original:  Given k sequences q_1, ..., q_k of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places.
Revised:  Given k sequences q_1, ..., q_k of labeled bins and a positive integer p, the aim is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places.
Edit intent: clarity
Original:  Given k sequences q_1, ..., q_k of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto a pallet located at one of p stack-up places.
Revised:  Given k sequences q_1, ..., q_k of labeled bins and a positive integer p, the goal is to stack-up the bins by iteratively removing the first bin of one of the k sequences and put it onto an initially empty pallet located at one of p stack-up places.
Edit intent: clarity
Original:  Each of these pallets has to contain bins of only one label, bins of different labels have to be placed on different pallets  . After all bins of one label have been removed from the given sequences, the corresponding place becomes available for a pallet of bins of another label.
Revised:  Bins with different pallet labels have to be placed on different pallets . After all bins of one label have been removed from the given sequences, the corresponding place becomes available for a pallet of bins of another label.
Edit intent: clarity