wanyu/IteraTeR_v2 huggingface dataset:
Original: We show that the Survey Propagation guided decimation algorithm fails to find satisfying assignments on random instances of the "Not-All-Equal-K-SAT" problem , well below the satisfiability threshold }\over   .
Revised: We show that the Survey Propagation guided decimation algorithm fails to find satisfying assignments on random instances of the "Not-All-Equal-K-SAT" problem , well below the satisfiability threshold }\over K .
Edit intent: clarity
Original:  Our analysis  applies to a broad class of algorithms that may be described as "sequential local algorithms" --such algorithms iteratively set variables based on some local information and /or local randomness, and then recurse on the reduced instance.
Revised:  Our analysis in fact applies to a broad class of algorithms that may be described as "sequential local algorithms" --such algorithms iteratively set variables based on some local information and /or local randomness, and then recurse on the reduced instance.
Edit intent: clarity
Original:  Our analysis  applies to a broad class of algorithms that may be described as "sequential local algorithms" --such algorithms iteratively set variables based on some local information and /or local randomness, and then recurse on the reduced instance.
Revised:  Our analysis applies to a broad class of algorithms described as "sequential local algorithms" --such algorithms iteratively set variables based on some local information and /or local randomness, and then recurse on the reduced instance.
Edit intent: clarity
Original:  Our analysis  applies to a broad class of algorithms that may be described as "sequential local algorithms" --such algorithms iteratively set variables based on some local information and /or local randomness, and then recurse on the reduced instance.
Revised:  Our analysis applies to a broad class of algorithms that may be described as "sequential local algorithms" . Such algorithms iteratively set variables based on some local information and /or local randomness, and then recurse on the reduced instance.
Edit intent: fluency
Original:  Our analysis  applies to a broad class of algorithms that may be described as "sequential local algorithms" --such algorithms iteratively set variables based on some local information and /or local randomness, and then recurse on the reduced instance.
Revised:  Our analysis applies to a broad class of algorithms that may be described as "sequential local algorithms" --such algorithms iteratively set variables based on some local information and then recurse on the reduced instance.
Edit intent: clarity
Original:  Survey Propagation guided as well as Belief Propagation guided decimation algorithms , studied widely in the past , fall under this category of algorithms .
Revised:  Survey Propagation-guided as well as Belief Propagation guided decimation algorithms , studied widely in the past , fall under this category of algorithms .
Edit intent: clarity
Original:  This approach of showing that local algorithms work only when the solution space is connected has been applied before in the literature: the novelty of our work is our ability to extend the approach also to sequential local algorithms }\over   .
Revised:  This approach of showing that local algorithms work only when the solution space is connected has been applied before in the literature: the novelty of our work is our ability to extend the approach also to sequential local algorithms }\over K .
Edit intent: fluency
Original: Let G be a graph of order n . A good function is a function f:V(G)\rightarrow \{-1,1\}, satisfying f(N(v))\geq 1, for each v\in V(G), where N(v)=\{u\in V(G)\, |\, uv\in E(G) \} and f(S) = u\in S f(u) .
Revised: Let G be a graph . A good function is a function f:V(G)\rightarrow \{-1,1\}, satisfying f(N(v))\geq 1, for each v\in V(G), where N(v)=\{u\in V(G)\, |\, uv\in E(G) \} and f(S) = u\in S f(u) .
Edit intent: clarity
Original:  The minimum value of f( V(G) ), taken over all good functions is denoted by \gamma(G)  . A function f:V(G)\rightarrow \{-1,1\} is called an excellent function, if f(N[v]) %DIFDELCMD < \geq1%%% \le1 , for each v\in V(G), where N[v]=\{v\} \cup N(v) . Define %DIFDELCMD < \gamma%%% \beta (G)= min \{f(V(G))\}, where f is an excellent function for G. In this paper, we present several lower and upper bounds for trees and cubic graphs.
Revised:  The minimum value of f( V(G) . For every cubic graph G of order n, we prove that \gamma(G) . A function f:V(G)\rightarrow \{-1,1\} is called an excellent function, if f(N[v]) %DIFDELCMD < \geq1%%% \le1 , for each v\in V(G), where N[v]=\{v\} \cup N(v) . Define %DIFDELCMD < \gamma%%% \beta (G)= min \{f(V(G))\}, where f is an excellent function for G. In this paper, we present several lower and upper bounds for trees and cubic graphs.
Edit intent: clarity
Original:  The minimum value of f( V(G) ), taken over all good functions is denoted by \gamma(G)  . A function f:V(G)\rightarrow \{-1,1\} is called an excellent function, if f(N[v]) %DIFDELCMD < \geq1%%% \le1 , for each v\in V(G), where N[v]=\{v\} \cup N(v) . Define %DIFDELCMD < \gamma%%% \beta (G)= min \{f(V(G))\}, where f is an excellent function for G. In this paper, we present several lower and upper bounds for trees and cubic graphs.
Revised:  The minimum value of f( V(G) ), taken over all good functions is denoted by \gamma(G) . A function f:V(G)\rightarrow \{-1,1\} is called a nice function, if f(N[v]) %DIFDELCMD < \geq1%%% \le1 , for each v\in V(G), where N[v]=\{v\} \cup N(v) . Define %DIFDELCMD < \gamma%%% \beta (G)= min \{f(V(G))\}, where f is an excellent function for G. In this paper, we present several lower and upper bounds for trees and cubic graphs.
Edit intent: clarity
Original:  The minimum value of f( V(G) ), taken over all good functions is denoted by \gamma(G)  . A function f:V(G)\rightarrow \{-1,1\} is called an excellent function, if f(N[v]) %DIFDELCMD < \geq1%%% \le1 , for each v\in V(G), where N[v]=\{v\} \cup N(v) . Define %DIFDELCMD < \gamma%%% \beta (G)= min \{f(V(G))\}, where f is an excellent function for G. In this paper, we present several lower and upper bounds for trees and cubic graphs.
Revised:  The minimum value of f( V(G) ), taken over all good functions is denoted by \gamma(G) . A function f:V(G)\rightarrow \{-1,1\} is called an excellent function, if f(N[v]) %DIFDELCMD < \geq1%%% \le1 , for each v\in V(G), where N[v]=\{v\} \cup N(v) . Define %DIFDELCMD < \gamma%%% \beta (G)= max \{f(V(G))\}, where f is an excellent function for G. In this paper, we present several lower and upper bounds for trees and cubic graphs.
Edit intent: fluency
Original:  The minimum value of f( V(G) ), taken over all good functions is denoted by \gamma(G)  . A function f:V(G)\rightarrow \{-1,1\} is called an excellent function, if f(N[v]) %DIFDELCMD < \geq1%%% \le1 , for each v\in V(G), where N[v]=\{v\} \cup N(v) . Define %DIFDELCMD < \gamma%%% \beta (G)= min \{f(V(G))\}, where f is an excellent function for G. In this paper, we present several lower and upper bounds for trees and cubic graphs.
Revised:  The minimum value of f( V(G) ), taken over all good functions is denoted by \gamma(G) . A function f:V(G)\rightarrow \{-1,1\} is called an excellent function, if f(N[v]) %DIFDELCMD < \geq1%%% \le1 , for each v\in V(G), where N[v]=\{v\} \cup N(v) . Define %DIFDELCMD < \gamma%%% \beta (G)= min \{f(V(G))\}, where f is a nice function for G. In this paper, we present several lower and upper bounds for trees and cubic graphs.
Edit intent: clarity
Original:  For every cubic graph of order n, we prove that \gamma(G) \leq 5n{7 \overline \gamma (G) \leq \frac{5n \ge  for every cubic graph G of order n, except Petersen graph,%DIFDELCMD < \gamma%%% (G)%DIFDELCMD < \le %%% \frac{3 .
Revised:  For every cubic graph of order n, we prove that \gamma(G) \leq 5n{7 \overline \gamma (G) \ge for every cubic graph G of order n, except Petersen graph,%DIFDELCMD < \gamma%%% (G)%DIFDELCMD < \le %%% \frac{3 .
Edit intent: fluency
Original:  For every cubic graph of order n, we prove that \gamma(G) \leq 5n{7 \overline \gamma (G) \leq \frac{5n \ge  for every cubic graph G of order n, except Petersen graph,%DIFDELCMD < \gamma%%% (G)%DIFDELCMD < \le %%% \frac{3 .
Revised:  For every cubic graph of order n, we prove that \gamma(G) \leq 5n{7 \overline \gamma (G) \leq \frac{5n \ge for every cubic graph G of order n, except Petersen graph,%DIFDELCMD < \gamma%%% %DIFDELCMD < \le %%% \frac{3 .
Edit intent: fluency
Original:  Our method, namely IsoDOT, provides accurate p-values for differential isoform usage testing with respect to continuous covariate or categorical covariate of any sample size . Simulation studies show that IsoDOT delivers significant improvement in sensitivity and specificity to detect differential isoform usage .
Revised:  Our method, namely IsoDOT, provides accurate p-values for differential isoform usage testing with respect to continuous covariate or categorical covariate of any sample size . Simulation studies demonstrate the high sensitivity and specificity to detect differential isoform usage .
Edit intent: clarity
Original:  Our method, namely IsoDOT, provides accurate p-values for differential isoform usage testing with respect to continuous covariate or categorical covariate of any sample size . Simulation studies show that IsoDOT delivers significant improvement in sensitivity and specificity to detect differential isoform usage .
Revised:  Our method, namely IsoDOT, provides accurate p-values for differential isoform usage testing with respect to continuous covariate or categorical covariate of any sample size . Simulation studies show that IsoDOT delivers significant improvement in sensitivity and specificity of IsoDOT .
Edit intent: clarity
Original:  By comparing the mice treated with placebo or haloperidol, we identify a group of genes (e.g., Utrn, Dmd, Grin2b, and Snap25) whose isoform usage respond to haloperidol treatment .
Revised:  By comparing the mice treated with placebo or haloperidol, we identify a group of genes whose isoform usages respond to haloperidol treatment .
Edit intent: coherence
Original: The paper discusses a connection between asymmetric reproduction -- that is reproduction in a parent-child relationship where the parent does not mutate during reproduction --, the fact that all non-parasitic lifeforms bear genes of their reproduction machinery and aging.
Revised: The paper discusses a connection between asymmetric reproduction -- that is reproduction in a parent-child relationship where the parent does not mutate during reproduction . The fact that all non-parasitic lifeforms bear genes of their reproduction machinery and aging.
Edit intent: fluency
Original: The paper discusses a connection between asymmetric reproduction -- that is reproduction in a parent-child relationship where the parent does not mutate during reproduction --, the fact that all non-parasitic lifeforms bear genes of their reproduction machinery and aging.
Revised: The paper discusses a connection between asymmetric reproduction -- that is reproduction in a parent-child relationship where the parent does not mutate during reproduction --, the fact that all non-viral lifeforms bear genes of their reproduction machinery and aging.
Edit intent: clarity
Original:  This pool market model takes into account the fact that a load modulation in one direction must usually be compensated later by a modulation of the same magnitude in the opposite one .
Revised:  This pool market model takes into account the fact that a load modulation in one direction must usually be compensated later by a modulation of the same magnitude in the opposite direction .
Edit intent: clarity
Original:  Our analysis takes into account the gaming possibilities of producers and retailers, controlling load flexibility, in the day-ahead energy and reserve markets, and in the imbalance settlement.
Revised:  Our analysis takes into account the gaming possibilities of producers and retailers, controlling load flexibility, in the day-ahead energy and reserve markets, and in imbalance settlement.
Edit intent: fluency
Original:  The procurement of  reserve is assumed to be determined, for each period, as a fixed percentage of the total consumption cleared in the energy market for the same period.
Revised:  The procurement of a reserve is assumed to be determined, for each period, as a fixed percentage of the total consumption cleared in the energy market for the same period.
Edit intent: fluency
Original:  Results show that the provision of reserve by flexible loads has negligible impact in the energy market prices but strongly decreases the cost for reserve procurement.
Revised:  The results show that the provision of reserve by flexible loads has negligible impact in the energy market prices but strongly decreases the cost for reserve procurement.
Edit intent: clarity
Original:  Results show that the provision of reserve by flexible loads has negligible impact in the energy market prices but strongly decreases the cost for reserve procurement.
Revised:  Results show that the provision of reserves by flexible loads has negligible impact in the energy market prices but strongly decreases the cost for reserve procurement.
Edit intent: fluency
Original:  Results show that the provision of reserve by flexible loads has negligible impact in the energy market prices but strongly decreases the cost for reserve procurement.
Revised:  Results show that the provision of reserve by flexible loads has a negligible impact on the energy market prices but strongly decreases the cost for reserve procurement.
Edit intent: fluency
Original:  Results show that the provision of reserve by flexible loads has negligible impact in the energy market prices but strongly decreases the cost for reserve procurement.
Revised:  Results show that the provision of reserve by flexible loads has negligible impact in the energy market prices but markedly decreases the cost for reserve procurement.
Edit intent: clarity
Original:  Results show that the provision of reserve by flexible loads has negligible impact in the energy market prices but strongly decreases the cost for reserve procurement.
Revised:  Results show that the provision of reserve by flexible loads has negligible impact in the energy market prices but strongly decreases the cost of reserve procurement.
Edit intent: fluency
Original:  However, as the rate of flexible loads increases, the system operator has to rely more and more on non-contracted reserve , which may cancel out the benefits made in the reserve procurement .
Revised:  However, as the rate of flexible loads increases, the system operator has to rely more and more on non-contracted reserves , which may cancel out the benefits made in the reserve procurement .
Edit intent: fluency
Original:  However, as the rate of flexible loads increases, the system operator has to rely more and more on non-contracted reserve , which may cancel out the benefits made in the reserve procurement .
Revised:  However, as the rate of flexible loads increases, the system operator has to rely more and more on non-contracted reserve , which may cancel out the benefits made in the procurement of reserves .
Edit intent: clarity
Original: In this article, we present Defmod, a fully unstructured, two or three dimensional, parallel finite element code for modeling crustal deformation over time scales ranging from milliseconds to thousands of years.
Revised: In this article, we present Defmod, an open source, fully unstructured, two or three dimensional, parallel finite element code for modeling crustal deformation over time scales ranging from milliseconds to thousands of years.
Edit intent: clarity
Original:  Unlike existing public domain numerical code(s) , Defmod can simulate deformation due to all major processes that make up the earthquake/rifting cycle, in non-homogeneous media.
Revised:  Unlike existing public domain numerical codes , Defmod can simulate deformation due to all major processes that make up the earthquake/rifting cycle, in non-homogeneous media.
Edit intent: clarity
Original:  It can also be used to model deformation due to processes such as post-glacial rebound, hydrological (un)loading, injection and/or withdrawal of compressible or incompressible fluids from subsurface reservoirs etc.
Revised:  It can also be used to model deformation due to processes such as post-glacial rebound, hydrological (un)loading, injection and/or withdrawal of fluids from subsurface reservoirs etc.
Edit intent: clarity
Original:  In the current version of the code, only prescribed loading is supported.
Revised:  In the current version of the code, prescribed loading is supported.
Edit intent: clarity
Original:  first, the shared nature of the wireless medium which inevitably cross couples the nodes' forwarding decisions, thus binding them together as strategic players;
Revised:  first, the shared nature of the wireless medium which inevitably cross-couples the nodes' forwarding decisions, thus binding them together as strategic players;
Edit intent: fluency
Original:  Given the nonstationarity induced by the fading process, an online solution for the formulated game would then require an adaptive procedure capable of both convergence to and tracking strategic equilibria as the environment changes.
Revised:  Given the non stationarity induced by the fading process, an online solution for the formulated game would then require an adaptive procedure capable of both convergence to and tracking strategic equilibria as the environment changes.
Edit intent: fluency
Original:  To this end, we deploy the strategic and nonstationary learning algorithm of regret tracking, the temporally adaptive variant of the celebrated regret matching algorithm, to guarantee the emergence and active tracking of the correlated equilibria in the dynamic robust forwarding game.
Revised:  To this end, we deploy the strategic and non stationary learning algorithm of regret tracking, the temporally adaptive variant of the celebrated regret matching algorithm, to guarantee the emergence and active tracking of the correlated equilibria in the dynamic robust forwarding game.
Edit intent: fluency
Original:  Simulation results reveal that our proposed solution excels in terms of both the number of transmissions and load distribution while also maintaining near perfect throughput , especially in dense crowded environments.
Revised:  Simulation results reveal that our proposed solution excels in terms of both the number of transmissions and load distribution while also maintaining near perfect delivery ratio , especially in dense crowded environments.
Edit intent: clarity
Original:  they use either structured linear algebra or basis reduction for polynomial lattices.
Revised:  they use either structured linear algebra or basis reduction of polynomial lattices.
Edit intent: clarity
Original:  Here , we reduce this  interpolation problem to a problem of simultaneous polynomial approximations, which we solve using fast algorithms for structured linear algebra.
Revised:  Here , we reduce this interpolation problem to a problem of simultaneous polynomial approximations, which we solve using fast structured linear algebra.
Edit intent: clarity
Original:  This improves the best known complexity bounds for the interpolation step of the list-decoding of Reed-Solomon codes, Parvaresh-Vardy codes or folded Reed-Solomon codes.
Revised:  This improves the best known complexity bounds for the interpolation step of the list-decoding of Reed-Solomon codes, Parvaresh-Vardy codes , and folded Reed-Solomon codes.
Edit intent: fluency
Original:  In the special case of Reed-Solomon codes , our approach has complexity O~(\ell^{\omega-1}m^2 n) , where \ell,m,n  are the list size, the multiplicity and the number of sample points  , and \omega is the exponent of linear algebra;
Revised:  In particular, for Reed-Solomon codes , our approach has complexity O~(\ell^{\omega-1}m^2 n) , where \ell,m,n are the list size, the multiplicity and the number of sample points , and \omega is the exponent of linear algebra;
Edit intent: clarity
Original:  In the special case of Reed-Solomon codes , our approach has complexity O~(\ell^{\omega-1}m^2 n) , where \ell,m,n  are the list size, the multiplicity and the number of sample points  , and \omega is the exponent of linear algebra;
Revised:  In the special case of Reed-Solomon codes , our approach has complexity O~(\ell^{\omega-1}m^2 n) , where \ell,m,n are the list size, the multiplicity , the number of sample points , and \omega is the exponent of linear algebra;
Edit intent: fluency
Original:  the speedup factor with comparison to the state of the art (Cohn and Heninger's algorithm) is \ell / m , with m%DIFDELCMD < \leqslant %%% \ell in this context .
Revised:  this accelerates the previously fastest known algorithm by a factor of \ell / m , with m%DIFDELCMD < \leqslant %%% \ell in this context .
Edit intent: clarity
Original:  the speedup factor with comparison to the state of the art (Cohn and Heninger's algorithm) is \ell / m , with m%DIFDELCMD < \leqslant %%% \ell in this context .
Revised:  the speedup factor with comparison to the state of the art (Cohn and Heninger's algorithm) is \ell / m %DIFDELCMD < \leqslant %%% \ell in this context .
Edit intent: coherence
Original:  the speedup factor with comparison to the state of the art (Cohn and Heninger's algorithm) is \ell / m , with m%DIFDELCMD < \leqslant %%% \ell in this context .
Revised:  the speedup factor with comparison to the state of the art (Cohn and Heninger's algorithm) is \ell / m , with m%DIFDELCMD < \leqslant %%% .
Edit intent: coherence
Original:   We have investigated how the specificity of this behaviour affects evolutionary dynamics using a set of coupled logistic equations, where the  carrying capacity of each genotype consists of two components: an intrinsic  part and a contribution from all genotypes present in the population.
Revised:  We have investigated the carrying capacity of each genotype consists of two components: an intrinsic part and a contribution from all genotypes present in the population.
Edit intent: clarity
Original:   We have investigated how the specificity of this behaviour affects evolutionary dynamics using a set of coupled logistic equations, where the  carrying capacity of each genotype consists of two components: an intrinsic  part and a contribution from all genotypes present in the population.
Revised:  We have investigated how the specificity of this behaviour affects evolutionary dynamics using a set of coupled logistic equations, where the carrying capacity of each cell consists of two components: an intrinsic part and a contribution from all genotypes present in the population.
Edit intent: clarity
Original: Numerous applications in scheduling, such as resource allocation or steel manufacturing, reduce to the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent vertices).
Revised: Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent vertices).
Edit intent: clarity
Original:  Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two interval graphs) and strip graphs (edge-wise unions of an interval graph and a cluster graph), on which Independent Set remains NP-hard but admits constant-factor approximations in polynomial time.
Revised:  Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two interval graphs) and strip graphs (edge-wise unions of an interval graph and a cluster graph), on which Independent Set remains NP-hard but admits constant-ratio approximations in polynomial time.
Edit intent: clarity
Original:  We show a complexity dichotomy:  Independent Set is polynomial-time solvable if both input interval graphs are cluster graphs, and  NP-hard otherwise.
Revised:  We show a complexity dichotomy: Independent Set is polynomial-time solvable if both input interval graphs are cluster graphs, and is NP-hard otherwise.
Edit intent: clarity