wanyu/IteraTeR_v2 huggingface dataset:
Original:  We then turn to an apparently weaker system, namely, polynomial calculus (PC) where polynomials are written as ordered formulas ( " PC over ordered formulas " , for short) .
Revised:  We then turn to an apparently weaker system, namely, polynomial calculus (PC) where polynomials are written as ordered formulas ( PC over ordered formulas " , for short) .
Edit intent: fluency
Original:  We then turn to an apparently weaker system, namely, polynomial calculus (PC) where polynomials are written as ordered formulas ( " PC over ordered formulas " , for short) .
Revised:  We then turn to an apparently weaker system, namely, polynomial calculus (PC) where polynomials are written as ordered formulas ( " PC over ordered formulas , for short) .
Edit intent: fluency
Original:  This is an algebraic propositional proof system that operates with noncommutative polynomials in which the order of products in all monomials respects a fixed linear order on the variables, and where proof-lines are written as noncommutative formulas .
Revised:  This is an algebraic propositional proof system that operates with noncommutative polynomials in which the order of products in every monomial respects a fixed linear order on the variables, and where proof-lines are written as noncommutative formulas .
Edit intent: clarity
Original:  The reason for this biological property  be available to the observers of nature seems to be a question never asked.
Revised:  The reason for this biological property to be available to the observers of nature seems to be a question never asked.
Edit intent: fluency
Original:  In this special case, circuitry for artificial dendritespermits a simulation of dynamic dendritic processing .
Revised:  This is demonstrated below using dynamic circuit analysis. Medical knowledge aside, this observation points to the possibility of specially coated conductors to accomplish artificial dendrites .
Edit intent: clarity
Original:  We begin with a convex optimization method based on the paper " Minimizing Effective Resistance of a Graph " [Ghosh, Boyd  Saberi].
Revised:  We begin with a convex optimization method based on the paper `` Minimizing Effective Resistance of a Graph " [Ghosh, Boyd Saberi].
Edit intent: fluency
Original:  We begin with a convex optimization method based on the paper " Minimizing Effective Resistance of a Graph " [Ghosh, Boyd  Saberi].
Revised:  We begin with a convex optimization method based on the paper " Minimizing Effective Resistance of a Graph '' [Ghosh, Boyd Saberi].
Edit intent: fluency
Original:  We begin with a convex optimization method based on the paper " Minimizing Effective Resistance of a Graph " [Ghosh, Boyd  Saberi].
Revised:  We begin with a convex optimization method based on the paper " Minimizing Effective Resistance of a Graph " [Ghosh, Boyd \& Saberi].
Edit intent: fluency
Original:  We want to route flow from a set of demand nodes to a root node, where the cost of routing x total flow along an edge is proportional to f(x) for some concave, non-decreasing function f satisfying f(0)=0.
Revised:  We wish to route flow from a set of demand nodes to a root node, where the cost of routing x total flow along an edge is proportional to f(x) for some concave, non-decreasing function f satisfying f(0)=0.
Edit intent: fluency
Original:  We present a simple, fast, deterministic, combinatorial algorithm that takes a set of demands and constructs a single tree T such that for all f the cost f(T) is a 49.48 -approximation of the optimal cost for that f.
Revised:  We present a simple, fast, combinatorial algorithm that takes a set of demands and constructs a single tree T such that for all f the cost f(T) is a 49.48 -approximation of the optimal cost for that f.
Edit intent: clarity
Original: We show two universal, Boolean, deterministic logic schemes based on binary noise timefunctions that can be realized without time averaging units.
Revised: We show two universal, Boolean, deterministic logic schemes based on binary noise timefunctions that can be realized without time-averaging units.
Edit intent: clarity
Original:  (c) The Garay-Jakobsson-MacKenzie (GJM) protocol, while fair and abuse-free, is not attack-free by our definition and is hence not a solution of AGS;
Revised:  (c) the Garay-Jakobsson-MacKenzie (GJM) protocol, while fair and abuse-free, is not attack-free by our definition and is hence not a solution of AGS;
Edit intent: fluency
Original:  The solution to assume-guarantee synthesis can be computed efficiently as the secure equilibrium solution of 3-player graph games.
Revised:  The solution to assume-guarantee synthesis can be computed efficiently as the secure equilibrium solution of three-player graph games.
Edit intent: fluency
Original:  First, we show how to specify the objectives of the participating agents and the trusted third party (TTP) as path formulas in LTL and prove that the satisfaction of these objectives imply fairness and abuse-freeness;
Revised:  First, we show how to specify the objectives of the participating agents and the trusted third party (TTP) as path formulas in Linear Temporal Logic (LTL) and prove that the satisfaction of these objectives imply fairness and abuse-freeness;
Edit intent: clarity
Original:  (c) the Garay-Jakobsson-MacKenzie (GJM) protocol, while fair and abuse-free, is not attack-free by our definition and is hence not a solution of AGS;
Revised:  (c) the Garay-Jakobsson-MacKenzie (GJM) protocol, while fair and abuse-free, is not attack-free and is hence not a solution of AGS;
Edit intent: clarity
Original:  First, we show how to specify the objectives of the participating agents and the trusted third party (TTP) as path formulas in Linear Temporal Logic (LTL ) and prove that the satisfaction of these objectives imply fairness and abuse-freeness;
Revised:  First, we show how to specify the objectives of the participating agents and the trusted third party (TTP) as path formulas in LTL and prove that the satisfaction of these objectives imply fairness and abuse-freeness;
Edit intent: clarity
Original:  A geometric graph contains a (k,l)-crossing family if there are a pair of edge subsets E_1,E_2 such that |E_1| = k and |E_2| = l, the edges in E_1 are pairwise crossing, the edges in E_2 are pairwise crossing, and every edges in E_1 is disjoint to every edge in E_2.
Revised:  A geometric graph contains a (k,l)-crossing family if there is a pair of edge subsets E_1,E_2 such that |E_1| = k and |E_2| = l, the edges in E_1 are pairwise crossing, the edges in E_2 are pairwise crossing, and every edges in E_1 is disjoint to every edge in E_2.
Edit intent: fluency
Original:  We also show that N(k)=O(k^2) and give an O(\log k) time algorithm for computing N( \lceil\rceil  k) \lfloor\rfloor .
Revised:  We also show that \lceil\rceil k) \lfloor\rfloor .
Edit intent: coherence
Original:  A k-chain of a regular n-gon is the segment of the boundary of the regular n-gon formed by a set of k ~ (\leq n) consecutive vertices of the regular n-gon.
Revised:  A k-chain of a regular n-gon is the segment of the boundary of the regular n-gon formed by a set of k (\leq n) consecutive vertices of the regular n-gon.
Edit intent: clarity
Original:  We also show that \lceil\pi m(m+1)-\pi^2/4\rceil \leq N(k) \leq \lfloor\pi m(m+1)+1\rfloor, where k ~ (=2m+1) is any odd positive integer.
Revised:  We also show that \lceil\pi m(m+1)-\pi^2/4\rceil \leq N(k) \leq \lfloor\pi m(m+1)+1\rfloor, where k (=2m+1) is any odd positive integer.
Edit intent: clarity
Original:  Furthermore, we present a connection between the SUBSET FEEDBACK VERTEX SET problem and terminal separation problems such as MULTIWAY CUT and MULTICUT . We show that SUBSET FEEDBACK VERTEX SET is a generalisation of MULTIWAY CUT and with an additional constraint SUBSET FEEDBACK VERTEX SET becomes as hard as MULTICUT.
Revised:  The SUBSET FEEDBACK VERTEX SET problem and terminal separation problems such as MULTIWAY CUT and MULTICUT . We show that SUBSET FEEDBACK VERTEX SET is a generalisation of MULTIWAY CUT and with an additional constraint SUBSET FEEDBACK VERTEX SET becomes as hard as MULTICUT.
Edit intent: coherence
Original:  Furthermore, we present a connection between the SUBSET FEEDBACK VERTEX SET problem and terminal separation problems such as MULTIWAY CUT and MULTICUT . We show that SUBSET FEEDBACK VERTEX SET is a generalisation of MULTIWAY CUT and with an additional constraint SUBSET FEEDBACK VERTEX SET becomes as hard as MULTICUT.
Revised:  Furthermore, we present a connection between the SUBSET FEEDBACK VERTEX SET problem and terminal separation problems such as MULTIWAY CUT and MULTICUT : SUBSET FEEDBACK VERTEX SET is a generalisation of MULTIWAY CUT and with an additional constraint SUBSET FEEDBACK VERTEX SET becomes as hard as MULTICUT.
Edit intent: coherence
Original:  Our results imply that in some sense SUBSET FVS falls between MULTIWAY CUT and MULTICUT.
Revised:  In some sense SUBSET-FVS falls between MULTIWAY CUT and MULTICUT.
Edit intent: clarity
Original: The FEEDBACK VERTEX SET problem , given an undirected graph G and an integer k, asks whether there exists a set of at most k vertices that hits all  cycles in the graph G. FEEDBACK VERTEX SET was intensively studied from the parameterized perspective .
Revised: The FEEDBACK VERTEX SET problem , given an undirected graph G and an integer k, to find a set of at most k vertices that hits all cycles in the graph G. FEEDBACK VERTEX SET was intensively studied from the parameterized perspective .
Edit intent: clarity
Original: The FEEDBACK VERTEX SET problem , given an undirected graph G and an integer k, asks whether there exists a set of at most k vertices that hits all  cycles in the graph G. FEEDBACK VERTEX SET was intensively studied from the parameterized perspective .
Revised: The FEEDBACK VERTEX SET problem , given an undirected graph G and an integer k, asks whether there exists a set of at most k vertices that hits all the cycles in the graph G. FEEDBACK VERTEX SET was intensively studied from the parameterized perspective .
Edit intent: fluency
Original:  We  begin by showing that this problem is FPT when parameterized by |S|.
Revised:  We begin by showing that this problem is fixed-parameter tractable when parametrized by |S|.
Edit intent: clarity
Original:  Moreover, we present an algorithm which reduces the size of |S | to O(k^3) in 2^O(k log k)n^O(1) time using kernelization techniques such as the 2-Expansion Lemma, Menger's theorem and Gallai's theorem.
Revised:  Next we present an algorithm which reduces the size of |S | to O(k^3) in 2^O(k log k)n^O(1) time using kernelization techniques such as the 2-Expansion Lemma, Menger's theorem and Gallai's theorem.
Edit intent: coherence
Original:  Moreover, we present an algorithm which reduces the size of |S | to O(k^3) in 2^O(k log k)n^O(1) time using kernelization techniques such as the 2-Expansion Lemma, Menger's theorem and Gallai's theorem.
Revised:  Moreover, we present an algorithm which reduces the size of |S | to O(k^3) , using kernelization techniques such as the 2-Expansion Lemma, Menger's theorem and Gallai's theorem.
Edit intent: coherence
Original:  These two results prove that the SUBSET FEEDBACK VERTEX SET problem is FPT when parameterized by k and the time complexity of our algorithm is 2^O(k log k) n^O(1) . The SUBSET FEEDBACK VERTEX SET problem is closely related to terminal separation problems such as MULTIWAY CUT and MULTICUT: SUBSET FEEDBACK VERTEX SET is a generalisation of MULTIWAY CUT and with an additional constraint SUBSET FEEDBACK VERTEX SET becomes as hard as MULTICUT.
Revised:  These two facts allow us to give a 2^O(k log k) n^O(1) . The SUBSET FEEDBACK VERTEX SET problem is closely related to terminal separation problems such as MULTIWAY CUT and MULTICUT: SUBSET FEEDBACK VERTEX SET is a generalisation of MULTIWAY CUT and with an additional constraint SUBSET FEEDBACK VERTEX SET becomes as hard as MULTICUT.
Edit intent: clarity
Original:  This proves a conjecture due to Magniez, Mathieu, and Nayak (2009) and rigorously establishes the peculiar power of bi-directional streams over unidirectional onesobserved in the algorithms they present.
Revised:  This proves a conjecture due to Magniez, Mathieu, and Nayak (2009) and rigorously establishes that bi-directional streams over unidirectional onesobserved in the algorithms they present.
Edit intent: clarity
Original: We show an Omega(sqrt (n) /T) lower bound for the space required by any unidirectional constant-error randomized T-pass streaming algorithm that recognizes whether an expression over two types of parenthesis is well-parenthesized.
Revised: We show an Omega(sqrt n /T) lower bound for the space required by any unidirectional constant-error randomized T-pass streaming algorithm that recognizes whether an expression over two types of parenthesis is well-parenthesized.
Edit intent: clarity
Original:  This proves a conjecture due to Magniez, Mathieu, and Nayak (2009) and rigorously establishes that bi-directional streams are exponentially more efficient in space usage as compared with unidirectional ones.
Revised:  This proves a conjecture due to Magniez, Mathieu, and Nayak (2009) and rigorously establishes that bidirectional streams are exponentially more efficient in space usage as compared with unidirectional ones.
Edit intent: fluency
Original:  We obtain the lower bound by analyzing the information that is necessarily revealed by the players about their respective inputs in a two-party communication protocol for a variant of the Index function, namely Augmented Index.
Revised:  We obtain the lower bound by establishing the minimum amount of information that is necessarily revealed by the players about their respective inputs in a two-party communication protocol for a variant of the Index function, namely Augmented Index.
Edit intent: clarity
Original:  The standard Feynman-Kac theorem cannot be directly applied because the diffusion coefficients may  degenerate on the boundaries of the state space and grow faster than linearly .
Revised:  The standard Feynman-Kac theorem cannot be directly applied because the diffusion coefficients may degenerate on the boundaries of the state space .
Edit intent: clarity
Original:  for example, the volatility process in our model can potentially reach zero and either stay there or instantaneously reflect, and asset-price processes may be strict local martingales under a given risk-neutral measure .
Revised:  for example, the volatility process in our model can potentially reach zero and either stay there or instantaneously reflect, and asset-price processes may be strict local martingale .
Edit intent: clarity
Original:  Our main result is the existence and uniqueness of classical solutions to the valuation equation .
Revised:  Our main result is a necessary and sufficient condition on the uniqueness of classical solutions to the valuation equation .
Edit intent: clarity
Original:  It is shown that the value function is the smallest nonnegative classical solution to the valuation equation .
Revised:  It is shown that the value function is the unique nonnegative classical solution to the valuation equation .
Edit intent: clarity
Original:  when the payoff is of linear growth , the uniqueness holds if and only if the asset-price process is a martingale.
Revised:  when the payoff is of linear growth , the uniqueness holds if and only if the asset-price is a martingale.
Edit intent: clarity
Original:  The LEACH 4%DIFDELCMD < ] %%% and PEGASIS 5%DIFDELCMD < ] %%% protocols provide elegant solutions to this problem, but may not always result in optimal performance.
Revised:  The LEACH 4%DIFDELCMD < ] %%% 5%DIFDELCMD < ] %%% protocols provide elegant solutions to this problem, but may not always result in optimal performance.
Edit intent: coherence
Original:  In other words, a power-efficient Medium Access Control (MAC) protocol is required to satisfy the stringent WBAN requirements , including low-power consumption.
Revised:  In other words, a power-efficient Medium Access Control (MAC) protocol is required to satisfy the stringent WBAN requirements including low-power consumption.
Edit intent: fluency
Original:  Then we study low-power MAC protocols proposed/investigated for a WBAN with emphasis on their strengths and weaknesses.
Revised:  Then we study low-power MAC protocols proposed/investigated for WBAN with emphasis on their strengths and weaknesses.
Edit intent: fluency
Original:  We also review different power-efficient mechanisms for a WBAN.
Revised:  We also review different power-efficient mechanisms for WBAN.
Edit intent: fluency
Original:  A brief plan of the second part 2%DIFDELCMD < ] %%% is given.
Revised:  2%DIFDELCMD < ] %%% is given.
Edit intent: clarity
Original:  A brief plan of the second part 2%DIFDELCMD < ] %%% is given.
Revised:  A brief plan of the second part %DIFDELCMD < ] %%% is given.
Edit intent: fluency
Original:  A brief plan of the second part 2%DIFDELCMD < ] %%% is given.
Revised:  A brief plan of the second part 2%DIFDELCMD < ] %%% 
Edit intent: clarity
Original:  The population dynamics of each population is calculated from individual level processes, and each species is characterised by the trait : size at maturation (m*).
Revised:  The population dynamics of each population is calculated from individual level processes, and each species is characterised by the trait ' size at maturation (m*).
Edit intent: fluency
Original:  We have used TOSSIM 1%DIFDELCMD < ]%%% , a well known simulator for wireless sensor networks, for our simulation.
Revised:  We have used TOSSIM %DIFDELCMD < ]%%% , a well known simulator for wireless sensor networks, for our simulation.
Edit intent: clarity
Original:  It can simulate with nesC 8%DIFDELCMD < ] %DIFDELCMD < %%% source code in TinyOS 2%DIFDELCMD < ] %%% environment, subsequently which may be used for real test bed situation without any significant modifications.
Revised:  It can simulate with nesC %DIFDELCMD < ] %DIFDELCMD < %%% source code in TinyOS 2%DIFDELCMD < ] %%% environment, subsequently which may be used for real test bed situation without any significant modifications.
Edit intent: clarity
Original:  It can simulate with nesC 8%DIFDELCMD < ] %DIFDELCMD < %%% source code in TinyOS 2%DIFDELCMD < ] %%% environment, subsequently which may be used for real test bed situation without any significant modifications.
Revised:  It can simulate with nesC 8%DIFDELCMD < ] %DIFDELCMD < %%% 2%DIFDELCMD < ] %%% environment, subsequently which may be used for real test bed situation without any significant modifications.
Edit intent: clarity
Original:  It can simulate with nesC 8%DIFDELCMD < ] %DIFDELCMD < %%% source code in TinyOS 2%DIFDELCMD < ] %%% environment, subsequently which may be used for real test bed situation without any significant modifications.
Revised:  It can simulate with nesC 8%DIFDELCMD < ] %DIFDELCMD < %%% source code in TinyOS 2%DIFDELCMD < ] %%% 
Edit intent: coherence
Original: This paper investigates the optimal harvesting strategy for a single species living in random environments , whose growth is given by a regime-switching diffusion.
Revised: This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion.
Edit intent: fluency
Original:  Harvesting is introduced as a stochastic control .
Revised:  Harvesting acts as a (stochastic) control on the size of the population .
Edit intent: clarity
Original:  Consequently one no longer obtains continuity of the value function for free using the standard arguments as those in regular or singular stochastic control problems  .
Revised:  Consequently one no longer obtains continuity of the value function using the standard arguments as those in regular or singular stochastic control problems .
Edit intent: clarity
Original:  Consequently one no longer obtains continuity of the value function for free using the standard arguments as those in regular or singular stochastic control problems  .
Revised:  Consequently one no longer obtains continuity of the value function for free using the standard arguments as in regular or singular stochastic control problems .
Edit intent: clarity
Original:  Further, we show that the value function is a viscosity solution of a coupled system of quasi-variational inequalities .
Revised:  Further, it is shown that the value function is a viscosity solution of a coupled system of quasi-variational inequalities .
Edit intent: clarity
Original:  Based upon the verification theorem, we explicitly construct an \varepsilon-optimal harvesting strategy and demonstrate two examples in detail.
Revised:  Based upon the verification theorem, an \varepsilon-optimal harvesting strategy and demonstrate two examples in detail.
Edit intent: clarity
Original:  Based upon the verification theorem, we explicitly construct an \varepsilon-optimal harvesting strategy and demonstrate two examples in detail.
Revised:  Based upon the verification theorem, we explicitly construct an \varepsilon-optimal harvesting strategy is constructed and two examples are analyzed in detail.
Edit intent: clarity
Original:  The novelties of this paper include the considerations of abrupt changes in the random environments and the state and regime dependent marginal yield function , which significantly affect the dynamics of the population size of the species and the optimal harvesting strategy.
Revised:  The novelties of this paper include the modeling of abrupt changes in the random environments and the state and regime dependent marginal yield function , which significantly affect the dynamics of the population size of the species and the optimal harvesting strategy.
Edit intent: clarity
Original:  The novelties of this paper include the considerations of abrupt changes in the random environments and the state and regime dependent marginal yield function , which significantly affect the dynamics of the population size of the species and the optimal harvesting strategy.
Revised:  The novelties of this paper include the considerations of abrupt changes in the random environments and the state- and regime-dependent marginal yield function , which significantly affect the dynamics of the population size of the species and the optimal harvesting strategy.
Edit intent: fluency
Original:  The novelties of this paper include the considerations of abrupt changes in the random environments and the state and regime dependent marginal yield function , which significantly affect the dynamics of the population size of the species and the optimal harvesting strategy.
Revised:  The novelties of this paper include the considerations of abrupt changes in the random environments and the state and regime dependent marginal yield function ; these aspects of the model significantly affect the dynamics of the population size of the species and the optimal harvesting strategy.
Edit intent: clarity
Original:  While these considerations allows us to better approximate the real world dynamics, they bring much difficulty in the analysis.
Revised:  While these dependencies enable a better approximation of the real world dynamics, they bring much difficulty in the analysis.
Edit intent: clarity
Original:  While these considerations allows us to better approximate the real world dynamics, they bring much difficulty in the analysis.
Revised:  While these considerations allows us to better approximate the real world dynamics, they add considerable difficulty to the analysis.
Edit intent: clarity
Original:  This is a singular stochastic control problem , with both the extinction time and  harvesting policy depending on the initial condition.
Revised:  This is a singular stochastic control problem with both the extinction time and harvesting policy depending on the initial condition.
Edit intent: fluency
Original:  This is a singular stochastic control problem , with both the extinction time and  harvesting policy depending on the initial condition.
Revised:  This is a singular stochastic control problem , with both the extinction time and the optimal harvesting policy depending on the initial condition.
Edit intent: clarity