wanyu/IteraTeR_v2 huggingface dataset:
Original:  We further prove that the above superior limits are  finite if and only if the development in continued fraction of \alpha has bounded partial quotients, equivalently if and only if s_{\alpha} is \beta-power free for some real number \beta.
Revised:  We further prove that act finite if and only if the development in continued fraction of \alpha has bounded partial quotients, equivalently if and only if s_{\alpha} is \beta-power free for some real number \beta.
Edit intent: clarity
Original:  We further prove that the above superior limits are  finite if and only if the development in continued fraction of \alpha has bounded partial quotients, equivalently if and only if s_{\alpha} is \beta-power free for some real number \beta.
Revised:  We further prove that the above superior limits are is finite if and only if the development in continued fraction of \alpha has bounded partial quotients, equivalently if and only if s_{\alpha} is \beta-power free for some real number \beta.
Edit intent: fluency
Original:  We further prove that the above superior limits are  finite if and only if the development in continued fraction of \alpha has bounded partial quotients, equivalently if and only if s_{\alpha} is \beta-power free for some real number \beta.
Revised:  We further prove that the above superior limits are finite if and only if the development in continued fraction of \alpha has bounded partial quotients, that is, if and only if s_{\alpha} is \beta-power free for some real number \beta.
Edit intent: coherence
Original:  Concerning the infinite Fibonacci word, we prove that: i \textit{ ) The longest prefix that is an abelian repetition of period F_j, j>1, has length F_j( F_{j+1}+F_{j-1} +1)-2 if j is even or F_j( F_{j+1}+F_{j-1} )-2 if j is odd, where F_{n} is the nth Fibonacci number;
Revised:  Concerning the infinite Fibonacci word, we prove that: \textit{ ) The longest prefix that is an abelian repetition of period F_j, j>1, has length F_j( F_{j+1}+F_{j-1} +1)-2 if j is even or F_j( F_{j+1}+F_{j-1} )-2 if j is odd, where F_{n} is the nth Fibonacci number;
Edit intent: coherence
Original:  \emph{ii \textit{ ) The smallest abelian period of any factor of the Fibonacci word is a Fibonacci number.
Revised:  \emph{ \textit{ ) The smallest abelian period of any factor of the Fibonacci word is a Fibonacci number.
Edit intent: fluency
Original:  \emph{ii \textit{ ) The smallest abelian period of any factor of the Fibonacci word is a Fibonacci number.
Revised:  \emph{ii \textit{ii ) The smallest abelian period of any factor of the Fibonacci word is a Fibonacci number.
Edit intent: fluency
Original:  From the previous results, we derive the exact formula for the smallest abelian periods of the Fibonacci finite words . More precisely, we prove that for j\geq 3, the Fibonacci word f_j, of length F_{j, has smallest abelian period equal to F_{\lfloor{j/2}\rfloor} if j = 0, 1, 2}%DIFDELCMD < \mod{4}%%% , or to F_{1+\lfloor{j/2\rfloor} if j = 3}%DIFDELCMD < \mod{4}%%% .
Revised:  From the previous results, we derive the exact formula for the smallest abelian periods of the Fibonacci finite words , has smallest abelian period equal to F_{\lfloor{j/2}\rfloor} if j = 0, 1, 2}%DIFDELCMD < \mod{4}%%% , or to F_{1+\lfloor{j/2\rfloor} if j = 3}%DIFDELCMD < \mod{4}%%% .
Edit intent: coherence
Original: Richomme, Saari and Zamboni  proved that at every position of an infinite Sturmian word starts an abelian power of exponent k , for every positive integer k . Here, we improve on this result , studying the maximal exponent of abelian powers and abelian repetitions occurring in infinite Sturmian words.
Revised: Richomme, Saari and Zamboni proved that at every position of a Sturmian word starts an abelian power of exponent k , for every positive integer k . Here, we improve on this result , studying the maximal exponent of abelian powers and abelian repetitions occurring in infinite Sturmian words.
Edit intent: fluency
Original: Richomme, Saari and Zamboni  proved that at every position of an infinite Sturmian word starts an abelian power of exponent k , for every positive integer k . Here, we improve on this result , studying the maximal exponent of abelian powers and abelian repetitions occurring in infinite Sturmian words.
Revised: Richomme, Saari and Zamboni proved that at every position of an infinite Sturmian word starts an abelian power of exponent k , for every positive integer k . Here, we improve on this result by studying the maximum exponents of abelian powers and abelian repetitions occurring in infinite Sturmian words.
Edit intent: fluency
Original:  More precisely, we give a formula for computing the maximal exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of }  period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Revised:  We give a formula for computing the maximal exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of } period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Edit intent: coherence
Original:  More precisely, we give a formula for computing the maximal exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of }  period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Revised:  More precisely, we give a formula for computing the maximum exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of } period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Edit intent: fluency
Original:  More precisely, we give a formula for computing the maximal exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of }  period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Revised:  More precisely, we give a formula for computing the maximal exponent of an abelian power of of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of } period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Edit intent: clarity
Original:  More precisely, we give a formula for computing the maximal exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of }  period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Revised:  More precisely, we give a formula for computing the maximal exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of } abelian period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Edit intent: clarity
Original:  More precisely, we give a formula for computing the maximal exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of }  period m starting at a given position n in the Sturmian word s_{\alpha,\rho of rotation angle \alpha and initial point \rho.
Revised:  More precisely, we give a formula for computing the maximal exponent of an abelian power of period m occurring in any Sturmian word s_{\alpha of rotation angle \alpha, and a formula for computing the maximal exponent of an abelian power of } period m starting at a given position in any Sturmian word of rotation angle \alpha and initial point \rho.
Edit intent: clarity
Original:  Starting from these results , we introduce the abelian critical exponent act as the quantity act = \limsup k_{m}/m= \limsup k'_{m}/m, where k_{m} (resp. k'_{m}) denotes the maximal exponent of an abelian power (resp.~of an abelian repetition) of abelian period m . We prove that \textit{act \geq \sqrt{5 the equality holds for the Fibonacci word.
Revised:  Starting from these results , we introduce the abelian critical exponent act as the quantity act = limsup\ k_{m}/m= \limsup k'_{m}/m, where k_{m} (resp. k'_{m}) denotes the maximal exponent of an abelian power (resp.~of an abelian repetition) of abelian period m . We prove that \textit{act \geq \sqrt{5 the equality holds for the Fibonacci word.
Edit intent: clarity
Original:  Starting from these results , we introduce the abelian critical exponent act as the quantity act = \limsup k_{m}/m= \limsup k'_{m}/m, where k_{m} (resp. k'_{m}) denotes the maximal exponent of an abelian power (resp.~of an abelian repetition) of abelian period m . We prove that \textit{act \geq \sqrt{5 the equality holds for the Fibonacci word.
Revised:  Starting from these results , we introduce the abelian critical exponent act as the quantity act = \limsup k_{m}/m= limsup\ k'_{m}/m, where k_{m} (resp. k'_{m}) denotes the maximal exponent of an abelian power (resp.~of an abelian repetition) of abelian period m . We prove that \textit{act \geq \sqrt{5 the equality holds for the Fibonacci word.
Edit intent: clarity
Original:  Starting from these results , we introduce the abelian critical exponent act as the quantity act = \limsup k_{m}/m= \limsup k'_{m}/m, where k_{m} (resp. k'_{m}) denotes the maximal exponent of an abelian power (resp.~of an abelian repetition) of abelian period m . We prove that \textit{act \geq \sqrt{5 the equality holds for the Fibonacci word.
Revised:  Starting from these results , we introduce the abelian critical exponent act as the quantity act = \limsup k_{m}/m= \limsup k'_{m}/m, where k_{m} (resp. k'_{m}) denotes the maximum exponent of an abelian power (resp.~of an abelian repetition) of abelian period m . We prove that \textit{act \geq \sqrt{5 the equality holds for the Fibonacci word.
Edit intent: fluency
Original:  Starting from these results , we introduce the abelian critical exponent act as the quantity act = \limsup k_{m}/m= \limsup k'_{m}/m, where k_{m} (resp. k'_{m}) denotes the maximal exponent of an abelian power (resp.~of an abelian repetition) of abelian period m . We prove that \textit{act \geq \sqrt{5 the equality holds for the Fibonacci word.
Revised:  Starting from these results , we introduce the abelian critical exponent act as the quantity act = \limsup k_{m}/m= \limsup k'_{m}/m, where k_{m} (resp. k'_{m}) denotes the maximal exponent of an abelian power (resp.~of an abelian repetition) of abelian period m . We prove that \textit{ \geq \sqrt{5 the equality holds for the Fibonacci word.
Edit intent: clarity
Original:  We further prove that \textit{act is finite if and only if the development in continued fraction of \alpha has bounded partial quotients, that is, if and only if s_{\alpha} is \beta -power free for some real number \beta.
Revised:  We further prove that \textit{act is finite if and only if \alpha has bounded partial quotients, that is, if and only if s_{\alpha} is \beta -power free for some real number \beta.
Edit intent: clarity
Original:  We further prove that \textit{act is finite if and only if the development in continued fraction of \alpha has bounded partial quotients, that is, if and only if s_{\alpha} is \beta -power free for some real number \beta.
Revised:  We further prove that \textit{act is finite if and only if the development in continued fraction of \alpha has bounded partial quotients, that is, if and only if s_{\alpha} is \beta -power-free for some real number \beta.
Edit intent: fluency
Original:  Concerning the infinite Fibonacci word, we prove that: \textit{i ) The longest prefix that is an abelian repetition of period F_j, j>1, has length F_j( F_{j+1}+F_{j-1} +1)-2 if j is even or F_j( F_{j+1}+F_{j-1} )-2 if j is odd, where F_{ n } is the nth Fibonacci number;
Revised:  Concerning the infinite Fibonacci word, we prove that: \textit{i ) The longest prefix that is an abelian repetition of period F_j, j>1, has length F_j( F_{j+1}+F_{j-1} +1)-2 if j is even or F_j( F_{j+1}+F_{j-1} )-2 if j is odd, where F_{ n } is the nth Fibonacci number;
Edit intent: fluency
Original:  Concerning the infinite Fibonacci word, we prove that: \textit{i ) The longest prefix that is an abelian repetition of period F_j, j>1, has length F_j( F_{j+1}+F_{j-1} +1)-2 if j is even or F_j( F_{j+1}+F_{j-1} )-2 if j is odd, where F_{ n } is the nth Fibonacci number;
Revised:  Concerning the infinite Fibonacci word, we prove that: \textit{i ) The longest prefix that is an abelian repetition of period F_j, j>1, has length F_j( F_{j+1}+F_{j-1} +1)-2 if j is even or F_j( F_{j+1}+F_{j-1} )-2 if j is odd, where F_{ j } is the nth Fibonacci number;
Edit intent: clarity
Original:  Concerning the infinite Fibonacci word, we prove that: \textit{i ) The longest prefix that is an abelian repetition of period F_j, j>1, has length F_j( F_{j+1}+F_{j-1} +1)-2 if j is even or F_j( F_{j+1}+F_{j-1} )-2 if j is odd, where F_{ n } is the nth Fibonacci number;
Revised:  Concerning the infinite Fibonacci word, we prove that: \textit{i ) The longest prefix that is an abelian repetition of period F_j, j>1, has length F_j( F_{j+1}+F_{j-1} +1)-2 if j is even or F_j( F_{j+1}+F_{j-1} )-2 if j is odd, where F_{ n } is the jth Fibonacci number;
Edit intent: clarity
Original:  \textit{ii ) The smallest abelian period of any factor of the Fibonacci word is a Fibonacci number.
Revised:  \textit{ ) The smallest abelian period of any factor of the Fibonacci word is a Fibonacci number.
Edit intent: clarity
Original:  \textit{ii ) The smallest abelian period of any factor of the Fibonacci word is a Fibonacci number.
Revised:  \textit{ii ii) The minimum abelian period of any factor of the Fibonacci word is a Fibonacci number.
Edit intent: clarity
Original:  \textit{ii ) The smallest abelian period of any factor of the Fibonacci word is a Fibonacci number.
Revised:  \textit{ii ) The smallest abelian period of any factor is a Fibonacci number.
Edit intent: clarity
Original:  From the previous results , we derive the exact formula for the smallest abelian periods of the Fibonacci finite words.
Revised:  Further , we derive the exact formula for the smallest abelian periods of the Fibonacci finite words.
Edit intent: coherence
Original:  From the previous results , we derive the exact formula for the smallest abelian periods of the Fibonacci finite words.
Revised:  From the previous results , we derive a formula for the smallest abelian periods of the Fibonacci finite words.
Edit intent: clarity
Original:  From the previous results , we derive the exact formula for the smallest abelian periods of the Fibonacci finite words.
Revised:  From the previous results , we derive the exact formula for the smallest abelian periods of the finite Fibonacci words.
Edit intent: fluency
Original:  ~Math. ~Soc. ~ 83: ~79--95, ~ 2011) proved that at every position of a Sturmian word starts an abelian power of exponent k for every k > 0. We improve on this result by studying the maximum exponents of abelian powers and abelian repetitions (an abelian repetition is an analogue of a fractional power) in Sturmian words.
Revised:  ~Math. ~Soc. ~ 83: 79-95, 2011) proved that at every position of a Sturmian word starts an abelian power of exponent k for every k > 0. We improve on this result by studying the maximum exponents of abelian powers and abelian repetitions (an abelian repetition is an analogue of a fractional power) in Sturmian words.
Edit intent: fluency
Original:  Further, we derive a formula for the minimum abelian periods of the finite Fibonacci words .
Revised:  Further, we derive a formula for the minimum abelian periods of the finite Fibonacci words 
Edit intent: fluency
Original: This paper proposes a novel congestion control algorithm for low-delay communication over best effort packet switched networks.
Revised: This paper proposes a novel congestion control algorithm for delay-constrained communication over best effort packet switched networks.
Edit intent: clarity
Original:  Due to the presence of buffers in the internal network nodes, each congestion  leads to buffer queueing and thus to an increasing delivery delay.
Revised:  Due to the presence of buffers in the internal network nodes, each congestion episode leads to buffer queueing and thus to an increasing delivery delay.
Edit intent: clarity
Original:  Our target is to propose a congestion control algorithm able to both maintain a low queueing delay when the network conditions allows for it and to avoid starvation when competing against flows controlled by other types of policies.
Revised:  Our target is to propose a congestion control algorithm able to both maintain a bounded queueing delay when the network conditions allows for it and to avoid starvation when competing against flows controlled by other types of policies.
Edit intent: clarity
Original:  Our Low-Delay Congestion Control algorithm exactly achieves this double objective by using a non-linear mapping between the experienced delay and the penalty value used in rate update equation in the controller, and by combining delay and loss feedback information in a single term based on packet interarrival measurements.
Revised:  Our Delay-Constrained Congestion Control algorithm exactly achieves this double objective by using a non-linear mapping between the experienced delay and the penalty value used in rate update equation in the controller, and by combining delay and loss feedback information in a single term based on packet interarrival measurements.
Edit intent: clarity
Original: This paper proposes a novel congestion control algorithm for delay-constrained communication over best effort packet switched networks.
Edit intent: clarity
Original:  Due to the presence of buffers in the internal network nodes, each congestion episode leads to buffer queueing and thus to an increasing delivery delay.
Revised:  Due to the presence of buffers in the inner network nodes, each congestion episode leads to buffer queueing and thus to an increasing delivery delay.
Edit intent: fluency
Original:  Due to the presence of buffers in the internal network nodes, each congestion episode leads to buffer queueing and thus to an increasing delivery delay.
Revised:  Due to the presence of buffers in the internal network nodes, each congestion event leads to buffer queueing and thus to an increasing delivery delay.
Edit intent: clarity
Original:  It is therefore essential to properly control congestions in delay-sensitive applications . Delay-based congestion algorithms could offer a viable solution since they tend to minimize the queueing delay.
Revised:  It is therefore essential to properly control congestions in delay-sensitive applications . Delay-based congestion algorithms are a viable solution since they tend to minimize the queueing delay.
Edit intent: clarity
Original:  It is therefore essential to properly control congestions in delay-sensitive applications . Delay-based congestion algorithms could offer a viable solution since they tend to minimize the queueing delay.
Revised:  It is therefore essential to properly control congestions in delay-sensitive applications . Delay-based congestion algorithms could offer a viable solution as they target to limit the experienced end-to-end delay.
Edit intent: clarity
Original:  Unfortunately  they do not cohabit well with other types of congestion algorithms, such as loss-based algorithms, that are not regulated by delay constraints .
Revised:  Unfortunately , they do not cohabit well with other types of congestion algorithms, such as loss-based algorithms, that are not regulated by delay constraints .
Edit intent: fluency
Original:  Unfortunately  they do not cohabit well with other types of congestion algorithms, such as loss-based algorithms, that are not regulated by delay constraints .
Revised:  Unfortunately they do not perform well when sharing the bandwidth with congestion control algorithms not regulated by delay constraints .
Edit intent: clarity
Original:  Our target is to propose a congestion control algorithm able to both maintain a bounded queueing delay when the network conditions allows for it and to avoid starvation when competing against flowscontrolled by other types of policies.
Revised:  Our target is to propose a congestion control algorithm able to both maintain a bounded queueing delay when competing with other delay-based flows, and avoid starvation when competing against flowscontrolled by other types of policies.
Edit intent: clarity
Original:  Our Delay-Constrained Congestion Control algorithm exactly achieves this double objective by using a non-linear mapping between the experienced delay and the penalty value used in rate update equation in the controller, and by combining delay and loss feedback information in a single term based on packet interarrival measurements.
Revised:  Our Delay-Constrained Congestion Control algorithm exactly achieves this double objective by using a non-linear mapping between the experienced delay and the price function and 2) we combine both delay and loss feedback information in a single term based on packet interarrival measurements.
Edit intent: clarity
Original:  Our Delay-Constrained Congestion Control algorithm exactly achieves this double objective by using a non-linear mapping between the experienced delay and the penalty value used in rate update equation in the controller, and by combining delay and loss feedback information in a single term based on packet interarrival measurements.
Revised:  Our Delay-Constrained Congestion Control algorithm exactly achieves this double objective by using a non-linear mapping between the experienced delay and the penalty value used in rate update equation in the controller, and by combining delay and loss information into a single price term based on packet interarrival measurements.
Edit intent: clarity
Original:  We  provide a stability analysis of our new algorithm and show its performance in simulation results that are carried out in the NS3 framework.
Revised:  We then provide a stability analysis of our new algorithm and show its performance in simulation results that are carried out in the NS3 framework.
Edit intent: coherence
Original:  We  provide a stability analysis of our new algorithm and show its performance in simulation results that are carried out in the NS3 framework.
Revised:  We provide a stability analysis for our novel algorithm and we show its performance in simulation results that are carried out in the NS3 framework.
Edit intent: clarity
Original:  We  provide a stability analysis of our new algorithm and show its performance in simulation results that are carried out in the NS3 framework.
Revised:  We provide a stability analysis of our new algorithm and show its performance in the simulation results carried out in the NS3 framework.
Edit intent: clarity
Original:  Holding the Sharpe ratio constant, higher  volatility leads to superior returns through lower costs .
Revised:  Holding the Sharpe ratio constant, higher asset volatility leads to superior returns through lower costs .
Edit intent: clarity
Original:  In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long term return given average volatility.
Revised:  In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long term returns given average volatility.
Edit intent: fluency