wanyu/IteraTeR_v2 huggingface dataset:
Original: We present a dynamical model that describes the evolution of offer and demand in a financial market .
Revised: We present a dynamical model for the price evolution of financial assets .
Edit intent: clarity
Original:  One of the most appealing characteristics of such a system is the presence of large oscillations in the number of agents sharing the same perspective .
Revised:  One of the most appealing properties of such a system is the presence of large oscillations in the number of agents sharing the same perspective .
Edit intent: fluency
Original:  The dynamics is inspired in a model for describing predator-prey population evolution: agents change their mind through self- or mutual influence , and the decision is adopted on a random basis, with no direct influence of the price itself.
Revised:  The dynamics is inspired by a model for describing predator-prey population evolution: agents change their mind through self- or mutual influence , and the decision is adopted on a random basis, with no direct influence of the price itself.
Edit intent: fluency
Original:  The dynamics is inspired in a model for describing predator-prey population evolution: agents change their mind through self- or mutual influence , and the decision is adopted on a random basis, with no direct influence of the price itself.
Revised:  The dynamics is inspired in a model for describing predator-prey population evolution: agents change their mind through self- or mutual interaction , and the decision is adopted on a random basis, with no direct influence of the price itself.
Edit intent: clarity
Original: A subgraph T of a digraph D is an {\em outbranching } if T is an oriented spanning tree with only one vertex of in-degree zero (called the {\em root}).
Revised: A subgraph T of a digraph D is an {\em out-branching } if T is an oriented spanning tree with only one vertex of in-degree zero (called the {\em root}).
Edit intent: fluency
Original:  In the {\sc Directed k-Leaf} Problem, we  given a digraph D and an integral parameter k, and we are to decide whether D has an out-branching with at least k leaves.
Revised:  In the {\sc Directed k-Leaf} Problem, we are given a digraph D and an integral parameter k, and we are to decide whether D has an out-branching with at least k leaves.
Edit intent: fluency
Original:  We describe a new algorimth for the problem of running time 3.72^{k}\cdot n^{O(1)}.
Revised:  We describe a new algorithm for the problem of running time 3.72^{k}\cdot n^{O(1)}.
Edit intent: fluency
Original: It turns out that a slightly generalised Margrabe formula exhibits symmetry properties leading to semi-static hedges of rather general options in the bivariate Black-Scholes economy .
Revised: It turns out that in the bivariate Black-Scholes economy Margrabe type options exhibit symmetry properties leading to semi-static hedges of rather general options in the bivariate Black-Scholes economy .
Edit intent: clarity
Original:  Since the semi-static hedges in the Black-Scholes economy are exact, a closed form valuation formula of a certain weighted barrier swap-option can be easily derived.
Revised:  Since the semi-static hedges in the Black-Scholes economy are exact, closed form valuation formula of a certain weighted barrier swap-option can be easily derived.
Edit intent: fluency
Original:  Since the semi-static hedges in the Black-Scholes economy are exact, a closed form valuation formula of a certain weighted barrier swap-option can be easily derived.
Revised:  Since the semi-static hedges in the Black-Scholes economy are exact, a closed form valuation formulas for certain barrier options can be easily derived.
Edit intent: clarity
Original:  We evaluate our algorithms on the America Online query log dataset.
Revised:  We demonstrate applicability of our algorithms to the America Online query log dataset.
Edit intent: clarity
Original:  Given an MDP, M, and given multiple linear-time (\omega -regular or LTL) properties \varphi _i , and probabilities r _i \in [0,1], i=1,...,k, we ask whether there exists a strategy \sigma for the controller such that, for all i, the probability that a trajectory of M controlled by \sigma satisfies \varphi _i is at least r _i .
Revised:  Given an MDP, M, and given multiple linear-time (\omega -regular or LTL) properties \varphi \_i , and probabilities r _i \in [0,1], i=1,...,k, we ask whether there exists a strategy \sigma for the controller such that, for all i, the probability that a trajectory of M controlled by \sigma satisfies \varphi _i is at least r _i .
Edit intent: clarity
Original:  Given an MDP, M, and given multiple linear-time (\omega -regular or LTL) properties \varphi _i , and probabilities r _i \in [0,1], i=1,...,k, we ask whether there exists a strategy \sigma for the controller such that, for all i, the probability that a trajectory of M controlled by \sigma satisfies \varphi _i is at least r _i .
Revised:  Given an MDP, M, and given multiple linear-time (\omega -regular or LTL) properties \varphi _i , and probabilities r _i \in [0,1], i=1,...,k, we ask whether there exists a strategy \sigma for the controller such that, for all i, the probability that a trajectory of M controlled by \sigma satisfies \varphi _i is at least r \_i .
Edit intent: clarity
Original:  Note that there can be trade-offs between different properties: satisfying property \varphi _1 with high probability may necessitate satisfying \varphi _2 with low probability.
Revised:  Note that there can be trade-offs between different properties: satisfying property \varphi \_1 with high probability may necessitate satisfying \varphi _2 with low probability.
Edit intent: fluency
Original:  Note that there can be trade-offs between different properties: satisfying property \varphi _1 with high probability may necessitate satisfying \varphi _2 with low probability.
Revised:  Note that there can be trade-offs between different properties: satisfying property \varphi _1 with high probability may necessitate satisfying \varphi \_2 with low probability.
Edit intent: fluency
Original:  Viewing this as a multi-objective optimization problem, we want information about the "trade-off curve" or %DIFDELCMD < {\em %DIFDELCMD < %%% Pareto curve for maximizing the probabilities of different properties.
Revised:  Viewing this as a multi-objective optimization problem, we want information about the "trade-off curve" or %DIFDELCMD < {\em %DIFDELCMD < %%% Pareto curve for maximizing the probabilities of different properties.
Edit intent: fluency
Original:  Our dichotomy theorem extends to the case in which the relation H is weighted, and the goal is to compute the partition function , which is the sum of weights of the homomorphisms.
Revised:  Our dichotomy theorem extends to the case in which the relation H is weighted, and the goal is to compute the partition function , which is the sum of weights of the homomorphisms.
Edit intent: fluency
Original:  I will review the few existing applications of Bayesian update rules to both discrete and continuous opinion problems and I show that several traditional models can be obtained as special cases or approximations from these Bayesian models.
Revised:  I will review the few existing applications of Bayesian update rules to both discrete and continuous opinion problems and show that several traditional models can be obtained as special cases or approximations from these Bayesian models.
Edit intent: fluency
Original:  For instance, a Turing machine is designed as a machine that always produces results with absolute certainty when reaching one of its halting states.
Edit intent: coherence
Original:  In particular, I postulate uncertainty about whether a bit is part of the program code , and is thus a known fact, or belongs to the machine input .
Revised:  In particular, I postulate uncertainty about whether a bit belongs to the program code , and is thus a known fact, or belongs to the machine input .
Edit intent: clarity
Original:  According to this intrinsic uncertaintyassumption, every result will be flawed with uncertainty and computations become meaningful only in combination with a given confidence level.
Revised:  According to this intrinsic uncertaintyassumption, every result will be flawed with uncertainty and computations become meaningful only in combination with a confidence level.
Edit intent: clarity
Original:  For the use-case of interactively entering and manipulating mathematical expressions  there is a need of a scripting front-end for our libraries.
Revised:  For the use-case of interactively entering and manipulating mathematical expressions , there is a need of a scripting front-end for our libraries.
Edit intent: fluency
Original:  We conclude , that with minor problems  any of these languages is suitable for our purpose.
Revised:  We conclude that, with minor problems any of these languages is suitable for our purpose.
Edit intent: fluency
Original:  We conclude , that with minor problems  any of these languages is suitable for our purpose.
Revised:  We conclude , that with minor problems , any of these languages is suitable for our purpose.
Edit intent: fluency
Original: We propose techniques for learning a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications.
Revised: We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications.
Edit intent: clarity
Original:  Our rank learning method uses the graph Helmholtzian, the graph theoretic analogue of the Helmholtz operator or vector Laplacian, in much the same way the graph Laplacian is an analogue of the Laplace operator or scalar Laplacian.
Revised:  Our statistical ranking method uses the graph Helmholtzian, the graph theoretic analogue of the Helmholtz operator or vector Laplacian, in much the same way the graph Laplacian is an analogue of the Laplace operator or scalar Laplacian.
Edit intent: clarity
Original:  Also, sensor's transceivers such as CC2420 provide multiple channels and  ] ]   channel switch latency of CC2420 transceiver is very short just about 200 micro seconds \mus .
Revised:  Also, sensor's transceivers such as CC2420 provide multiple channels and ], ] channel switch latency of CC2420 transceiver is very short just about 200 micro seconds \mus .
Edit intent: fluency
Original:  Also, sensor's transceivers such as CC2420 provide multiple channels and  ] ]   channel switch latency of CC2420 transceiver is very short just about 200 micro seconds \mus .
Revised:  Also, sensor's transceivers such as CC2420 provide multiple channels and ] ] and channel switch latency of CC2420 transceiver is very short just about 200 micro seconds \mus .
Edit intent: coherence
Original:  Also, sensor's transceivers such as CC2420 provide multiple channels and  ] ]   channel switch latency of CC2420 transceiver is very short just about 200 micro seconds \mus .
Revised:  Also, sensor's transceivers such as CC2420 provide multiple channels and ] ] channel switch latency of CC2420 transceiver is just about 200 micro seconds \mus .
Edit intent: coherence
Original:  Also, sensor's transceivers such as CC2420 provide multiple channels and  ] ]   channel switch latency of CC2420 transceiver is very short just about 200 micro seconds \mus .
Revised:  Also, sensor's transceivers such as CC2420 provide multiple channels and ] ] channel switch latency of CC2420 transceiver is very short just about 200 \mus .
Edit intent: clarity
Original: We are considering the \NP-hard problem of finding a spanning tree with many internal vertices.
Revised: We consider the \NP-hard problem of finding a spanning tree with many internal vertices.
Edit intent: coherence
Original:  This problem is a generalization of the famous and well-studied {\sc Hamiltonian Path} problem.
Revised:  This problem is a generalization of the famous {\sc Hamiltonian Path} problem.
Edit intent: clarity
Original:  We present an dynamic-programming approach for general and degree-bounded graphs obtaining a run times of the form \Oh^*(c^n) (c \le 3).
Revised:  Our dynamic-programming approach for general and degree-bounded graphs obtaining a run times of the form \Oh^*(c^n) (c \le 3).
Edit intent: clarity
Original:  We present an dynamic-programming approach for general and degree-bounded graphs obtaining a run times of the form \Oh^*(c^n) (c \le 3).
Revised:  We present an dynamic-programming algorithms for general and degree-bounded graphs obtaining a run times of the form \Oh^*(c^n) (c \le 3).
Edit intent: clarity
Original:  We present an dynamic-programming approach for general and degree-bounded graphs obtaining a run times of the form \Oh^*(c^n) (c \le 3).
Revised:  We present an dynamic-programming approach for general and degree-bounded graphs have running times of the form \Oh^*(c^n) (c \le 3).
Edit intent: clarity
Original:  It only consumes polynomial space and achieves a run time of \Oh^*( 1.8916^n) \rt\rtkii  .
Revised:  It only needs polynomial space and achieves a run time of \Oh^*( 1.8916^n) \rt\rtkii .
Edit intent: clarity
Original:  It only consumes polynomial space and achieves a run time of \Oh^*( 1.8916^n) \rt\rtkii  .
Revised:  It only consumes polynomial space and has a running time of \Oh^*( 1.8916^n) \rt\rtkii .
Edit intent: clarity
Original:  This problem is a generalization of the famous %DIFDELCMD < {\sc %%% Hamiltonian Path problem.
Revised:  This problem is a generalization of the famous %DIFDELCMD < {\sc %%% Hamiltonian Path problem.
Edit intent: fluency
Original:  Our dynamic-programming algorithms for general and degree-bounded graphs have running times of the form %DIFDELCMD < \Oh%%% ^* (c^n) (c %DIFDELCMD < \le %%%  3).
Revised:  Our dynamic-programming algorithms for general and degree-bounded graphs have running times of the form %DIFDELCMD < \Oh%%% O* (c^n) (c %DIFDELCMD < \le %%% 3).
Edit intent: fluency
Original:  It only needs polynomial space and has a running time of %DIFDELCMD < \Oh%%% ^*(%DIFDELCMD < \rt%%%  ^n) when analyzed with respect to the number of vertices.
Revised:  It only needs polynomial space and has a running time of %DIFDELCMD < \Oh%%% %DIFDELCMD < \rt%%% ^n) when analyzed with respect to the number of vertices.
Edit intent: coherence
Original:  We find surprisingly simple conditions that specify whether a strategy is more abundant than the average , 1/n,  in the mutation-selection equilibrium.
Revised:  We find surprisingly simple conditions that specify whether a strategy is more abundant on average than 1/n, in the mutation-selection equilibrium.
Edit intent: clarity
Original:  Our results allow a complete characterization of n by n games in the limit of weak selection.
Revised:  Our results allow a complete characterization of n*n games in the limit of weak selection.
Edit intent: clarity
Original:  Several aspects of this process have been already investigated in the literature.
Revised:  Several aspects of this process have already been investigated in the literature.
Edit intent: fluency
Original:  In the present paper, we mainly get quantitative estimates for the exponential convergence to equilibrium, in terms of the W_1 Wasserstein coupling distance, for the process and also for its embedded chain.
Revised:  In the present paper, we mainly get quantitative estimates for the convergence to equilibrium, in terms of the W_1 Wasserstein coupling distance, for the process and also for its embedded chain.
Edit intent: clarity
Original:  We give a comprehensive characterization of weighted voting games which can be solved in polynomial time.
Revised:  We give a comprehensive classification of weighted voting games which can be solved in polynomial time.
Edit intent: clarity
Original:  On the positive side, we take this barrier to our advantage and show that approximate reconstruction (within a satisfactory degree of approximation) allows us to break the information theoretic lower bound of%DIFDELCMD < \Omega%%% (d^2 \log n) that is known for exact reconstruction of d-sparse vectors of length n via non-adaptive measurements, by a multiplicative factor%DIFDELCMD < \Omega%%% (d).
Revised:  On the positive side, we %DIFDELCMD < \Omega%%% (d^2 \log n) that is known for exact reconstruction of d-sparse vectors of length n via non-adaptive measurements, by a multiplicative factor%DIFDELCMD < \Omega%%% (d).
Edit intent: clarity
Original:  On the positive side, we take this barrier to our advantage and show that approximate reconstruction (within a satisfactory degree of approximation) allows us to break the information theoretic lower bound of%DIFDELCMD < \Omega%%% (d^2 \log n) that is known for exact reconstruction of d-sparse vectors of length n via non-adaptive measurements, by a multiplicative factor%DIFDELCMD < \Omega%%% (d).
Revised:  On the positive side, we take this barrier to our advantage and show that approximate reconstruction (within a satisfactory degree of approximation) allows us to break the information theoretic lower bound of%DIFDELCMD < \Omega%%% (d^2 \log n) that is known for exact reconstruction of d-sparse vectors of length n via non-adaptive %DIFDELCMD < \Omega%%% (d).
Edit intent: clarity
Original:  Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with m=O(d \log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives (for any constant \delta < 1) and O (m/d) false negatives within the measurement outcomes .
Revised:  Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with m=O(d log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives (for any constant \delta < 1) and O (m/d) false negatives within the measurement outcomes .
Edit intent: fluency
Original:  Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with m=O(d \log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives (for any constant \delta < 1) and O (m/d) false negatives within the measurement outcomes .
Revised:  Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with m=O(d \log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives and \Omega (m/d) false negatives within the measurement outcomes .
Edit intent: clarity
Original:  Furthermore, we obtain several explicit  constructions, in particular one matching the randomized trade-off but using m = O(d^{1+o(1)} \log n) measurements.
Revised:  Furthermore, we obtain several explicit constructions, in particular one matching the randomized trade-off but using m = O(d^{1+o(1)} log n) measurements.
Edit intent: coherence
Original: We study combinatorial group testing schemes for learning d-sparse boolean vectors using highly unreliable disjunctive measurements.
Revised: We study combinatorial group testing schemes for learning d-sparse Boolean vectors using highly unreliable disjunctive measurements.
Edit intent: fluency
Original:  Simple randomized instantiations of this construction give\Omega non-adaptive \Omega measurement schemes, with m=O(d log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives and \Omega (m/d) false negatives within the measurement outcomes, for any constant \delta < 1. None of these parameters can be substantially improved without dramatically affecting the others.
Revised:  Simple randomized instantiations of this construction give\Omega non-adaptive \Omega(d). Specifically, we give simple randomized constructions of non-adaptive measurement schemes, with m=O(d log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives and \Omega (m/d) false negatives within the measurement outcomes, for any constant \delta < 1. None of these parameters can be substantially improved without dramatically affecting the others.
Edit intent: clarity
Original:  Simple randomized instantiations of this construction give\Omega non-adaptive \Omega measurement schemes, with m=O(d log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives and \Omega (m/d) false negatives within the measurement outcomes, for any constant \delta < 1. None of these parameters can be substantially improved without dramatically affecting the others.
Revised:  Simple randomized instantiations of this construction give\Omega non-adaptive \Omega measurement schemes, with m=O(d \log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives and \Omega (m/d) false negatives within the measurement outcomes, for any constant \delta < 1. None of these parameters can be substantially improved without dramatically affecting the others.
Edit intent: fluency
Original:  Simple randomized instantiations of this construction give\Omega non-adaptive \Omega measurement schemes, with m=O(d log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives and \Omega (m/d) false negatives within the measurement outcomes, for any constant \delta < 1. None of these parameters can be substantially improved without dramatically affecting the others.
Revised:  Simple randomized instantiations of this construction give\Omega non-adaptive \Omega measurement schemes, with m=O(d log n) measurements, that allow efficient reconstruction of d-sparse vectors up to O(d) false positives even in the presence of \delta m false positives and O (m/d) false negatives within the measurement outcomes, for any constant \delta < 1. None of these parameters can be substantially improved without dramatically affecting the others.
Edit intent: fluency
Original:  Furthermore, we obtain several explicit (and incomparable) constructions, in particular one matching the randomized trade-off but using m = O(d^{1+o(1)} log n) measurements.
Revised:  Furthermore, we obtain several explicit constructions, in particular one matching the randomized trade-off but using m = O(d^{1+o(1)} log n) measurements.
Edit intent: clarity
Original:  We also obtain explicit constructions that allow fast reconstruction in time poly \poly (m), which would be sublinear in n for sufficiently sparse vectors  .
Revised:  We also obtain explicit constructions that allow fast reconstruction in time \poly (m), which would be sublinear in n for sufficiently sparse vectors .
Edit intent: fluency
Original: In this article, we present a novel technique for boosting the order of accuracy of formally low-order finite difference schemes for time dependent partial differential equations by optimally selecting the time step used to advance the numerical solution .
Revised: In this article, we present a novel technique for boosting the order of accuracy of finite difference schemes for time dependent partial differential equations by optimally selecting the time step used to advance the numerical solution .
Edit intent: clarity
Original:  The asset value is inevitably determined by subjective beliefs and fantasies loosely bound by market constraints.
Revised:  The asset value is determined by subjective beliefs and fantasies loosely bound by market constraints.
Edit intent: clarity