wanyu/IteraTeR_v2 huggingface dataset:
Original:  and %DIFDELCMD < \g%%%  =(g_1,\ldots,g_m) be two sets of m %DIFDELCMD < \geqslant %%%  1 non-linear polynomials over K[x_1,\ldots,x_n] \) being a field)} . We consider the computational problem of finding if any an invertible transformation on the variables mapping %DIFDELCMD < \f %%% to%DIFDELCMD < \g%%%  . The corresponding equivalence problem is known as {\it Isomorphism of Polynomials with one Secret} ({\tt IP1S}) and is a fundamental problem in multivariate cryptography ;
Revised:  and %DIFDELCMD < \g%%% =(g_1,\ldots,g_m) be two sets of m %DIFDELCMD < \geqslant %%% 1 non-linear polynomials over K[x_1,\ldots,x_n] \) being a field)} . We consider the computational problem of finding if any an invertible transformation on the variables mapping %DIFDELCMD < \f %%% %DIFDELCMD < \g%%% . The corresponding equivalence problem is known as {\it Isomorphism of Polynomials with one Secret} ({\tt IP1S}) and is a fundamental problem in multivariate cryptography ;
Edit intent: clarity
Original:  Agrawal and Saxena show that Graph Isomorphism (%DIFDELCMD < {\tt %%% GI ) reduces to equivalence of cubic polynomials with respect to an invertible linear change of variables.
Revised:  Agrawal and Saxena show that Graph Isomorphism (%DIFDELCMD < {\tt %%% ) reduces to equivalence of cubic polynomials with respect to an invertible linear change of variables.
Edit intent: clarity
Original:  This strongly suggests that solving equivalence problems efficiently,%DIFDELCMD < {\it %DIFDELCMD < %%% i.e. in polynomial-time, is a very challenging algorithmic task.
Revised:  This strongly suggests that solving equivalence problems efficiently,%DIFDELCMD < {\it %DIFDELCMD < %%% in polynomial-time, is a very challenging algorithmic task.
Edit intent: coherence
Original:  a particular case of importance in cryptography and somewhat justifying {\it a posteriori} the fact that { %DIFDELCMD < \tt %%% GI \it  } reduces to only cubic instances of {\tt IP1S}  . To this end, we show that {\tt IP1S} for quadratic polynomials can be reduced to a variant of the classical module isomorphism problem in representation theory, which involves to test the orthogonal simultaneous conjugacy of symmetric matrices.
Revised:  a particular case of importance in cryptography and somewhat justifying {\it a posteriori} the fact that { %DIFDELCMD < \tt %%% \it } reduces to only cubic instances of {\tt IP1S} . To this end, we show that {\tt IP1S} for quadratic polynomials can be reduced to a variant of the classical module isomorphism problem in representation theory, which involves to test the orthogonal simultaneous conjugacy of symmetric matrices.
Edit intent: clarity
Original:  this latter problem was shown by Chistov, Ivanyos and Karpinski to be equivalent of finding an invertible matrix in the linear space \mathbb{K}^{n \times n} of n \times n matrices over \K and to compute the square root in a matrix algebra.
Revised:  this latter problem was shown by Chistov, Ivanyos and Karpinski to be equivalent to finding an invertible matrix in the linear space \mathbb{K}^{n \times n} of n \times n matrices over \K and to compute the square root in a matrix algebra.
Edit intent: fluency
Original:  While computing square roots of matrices can be be done efficiently using numerical methods, it seems difficult to control the bit complexity of such methods.
Revised:  While computing square roots of matrices can be done efficiently using numerical methods, it seems difficult to control the bit complexity of such methods.
Edit intent: fluency
Original: Let f=(f _1,\ldots,f_m ) and g=(g _1,\ldots,g_m ) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x_1,\ldots,x_n] (\(K\) } [x\_1,...,x\_n] (K } being a field).
Revised: Let f=(f \_1,...,f\_m ) and g=(g _1,\ldots,g_m ) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x_1,\ldots,x_n] (\(K\) } [x\_1,...,x\_n] (K } being a field).
Edit intent: fluency
Original: Let f=(f _1,\ldots,f_m ) and g=(g _1,\ldots,g_m ) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x_1,\ldots,x_n] (\(K\) } [x\_1,...,x\_n] (K } being a field).
Revised: Let f=(f _1,\ldots,f_m ) and g=(g _1,\ldots,g_m ) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x_1,\ldots,x_n] (\(K\) } \mathbb{K[x\_1,...,x\_n] (K } being a field).
Edit intent: fluency
Original:  A randomized polynomial-time algorithm for solving {\tt IP} when \(\mathbf{f=(x_1^d,\ldots,x_n^d)\) } =(x\_1^d,...,x\_n^d)\) } is presented.
Revised:  A randomized polynomial-time algorithm for solving {\tt IP} when \(\mathbf{f=(x_1^d,\ldots,x_n^d)\) } \(\mathbf{f=(x\_1^d,...,x\_n^d)\) } is presented.
Edit intent: coherence
Original: Let f=(f\_1, ... ,f\_m) and g=(g\_1, ... ,g\_m) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x\_1,...,x\_n] } [x\_1,\ldots,x\_n] } (K being a field).
Revised: Let f=(f\_1, \ldots ,f\_m) and g=(g\_1, ... ,g\_m) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x\_1,...,x\_n] } [x\_1,\ldots,x\_n] } (K being a field).
Edit intent: fluency
Original: Let f=(f\_1, ... ,f\_m) and g=(g\_1, ... ,g\_m) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x\_1,...,x\_n] } [x\_1,\ldots,x\_n] } (K being a field).
Revised: Let f=(f\_1, ... ,f\_m) and g=(g\_1, \ldots ,g\_m) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x\_1,...,x\_n] } [x\_1,\ldots,x\_n] } (K being a field).
Edit intent: fluency
Original: Let f=(f\_1, ... ,f\_m) and g=(g\_1, ... ,g\_m) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x\_1,...,x\_n] } [x\_1,\ldots,x\_n] } (K being a field).
Revised: Let f=(f\_1, ... ,f\_m) and g=(g\_1, ... ,g\_m) be two sets of m\geq 1 nonlinear polynomials over \mathbb{K[x\_1,...,x\_n] } \mathbb{K[x\_1,\ldots,x\_n] } (K being a field).
Edit intent: fluency
Original:  A randomized polynomial-time algorithm for solving {\tt IP} when \(\mathbf{f=(x\_1^d,...,x\_n^d)\) } =(x\_1^d,\ldots,x\_n^d)\) } is presented.
Revised:  A randomized polynomial-time algorithm for solving {\tt IP} when \(\mathbf{f=(x\_1^d,...,x\_n^d)\) } \(\mathbf{f=(x\_1^d,\ldots,x\_n^d)\) } is presented.
Edit intent: coherence
Original: In this note we present tight lower bounds on the information-based complexity of large-scale smooth convex minimization problems .
Revised: We derive lower bounds on the information-based complexity of large-scale smooth convex minimization problems .
Edit intent: clarity
Original:  On the other hand, we prove lower bounds for the complexity of convex optimization over \ell^p -balls , for 1 \leq p < 2, by combining a random subspace method with the p  = \infty lower bounds .
Revised:  On the other hand, we prove lower bounds for the complexity of convex optimization over \ell^p -balls , 1 \leq p < 2, by combining a random subspace method with the p = \infty lower bounds .
Edit intent: coherence
Original:  On the other hand, we prove lower bounds for the complexity of convex optimization over \ell^p -balls , for 1 \leq p < 2, by combining a random subspace method with the p  = \infty lower bounds .
Revised:  On the other hand, we prove lower bounds for the complexity of convex optimization over \ell^p -balls , for 1 < 2, by combining a random subspace method with the p = \infty lower bounds .
Edit intent: clarity
Original:  On the other hand, we prove lower bounds for the complexity of convex optimization over \ell^p -balls , for 1 \leq p < 2, by combining a random subspace method with the p  = \infty lower bounds .
Revised:  On the other hand, we prove lower bounds for the complexity of convex optimization over \ell^p -balls , for 1 \leq p < 2, by combining a random subspace method with the p < = \infty lower bounds .
Edit intent: fluency
Original: In this paper we prove that Y_5, the Yao graph with five cones, is a spanner with stretch factor \rho = \frac{1{1-2\frac{3\pi{20}}} \approx 10.87}  \approx 3.74} . Since Y_5 is the only Yao graph whose status of being a spanner or not was open, this completes the picture of the Yao graphs that are spanners: a Yao graph Y_k is a spanner if and only if k \geq 4.
Revised: In this paper we prove that Y_5, the Yao graph with five cones, is a spanner with stretch factor \rho = {1-2\frac{3\pi{20}}} \approx 10.87} \approx 3.74} . Since Y_5 is the only Yao graph whose status of being a spanner or not was open, this completes the picture of the Yao graphs that are spanners: a Yao graph Y_k is a spanner if and only if k \geq 4.
Edit intent: fluency
Original:  In contrast to the above result , we also show that YY_5, the Yao-Yao graph with five cones, is not a spanner.
Revised:  We complement the above result , we also show that YY_5, the Yao-Yao graph with five cones, is not a spanner.
Edit intent: clarity
Original:  We then show that for the one-dimensional case, where each sensor can monitor a contiguous region of possibly different lengths,  the MLCP solution is equal to the DSCP solution, and can be found in polynomial time.
Revised:  We then show that for the one-dimensional case, where each sensor can monitor a contiguous region of possibly different lengths, we show that the MLCP solution is equal to the DSCP solution, and can be found in polynomial time.
Edit intent: coherence
Original:  For the special case of the geometric MLCP , where each sensor can monitor a circular area with a given radius around itself, we combine existing results to show that a 1+\epsilon approximation algorithm exists for any \epsilon >0.
Revised:  For the special case of the geometric MLCP , where each sensor can monitor a circular area with a given radius around itself, we combine existing results to derive a 1+\epsilon approximation algorithm exists for any \epsilon >0.
Edit intent: clarity
Original:  For the special case of the geometric MLCP , where each sensor can monitor a circular area with a given radius around itself, we combine existing results to show that a 1+\epsilon approximation algorithm exists for any \epsilon >0.
Revised:  For the special case of the geometric MLCP , where each sensor can monitor a circular area with a given radius around itself, we combine existing results to show that a 1+\epsilon approximation algorithm for solving MLCP for any \epsilon >0.
Edit intent: clarity
Original: In this study, a method for detecting a trend change in a multiregional epidemic is developed for a standard epidemiological SIR compartment model and a meta-population network model.
Revised: A method for detecting a trend change in a multiregional epidemic is developed for a standard epidemiological SIR compartment model and a meta-population network model.
Edit intent: clarity
Original:  The method is applicable for the study to investigate how the isolation, quarantine, or public awareness work after the onset of an outbreak from a time series of the number of new cases  in multiple geographical regions  .
Revised:  The method is applicable to the investigation of the efficacy of the implemented public health intervention from a time series of the number of new cases in multiple geographical regions .
Edit intent: clarity
Original:  The method is applicable for the study to investigate how the isolation, quarantine, or public awareness work after the onset of an outbreak from a time series of the number of new cases  in multiple geographical regions  .
Revised:  The method is applicable for the study to investigate how the isolation, quarantine, or public awareness work after the onset of an outbreak from a time series of the number of new cases reported in multiple geographical regions .
Edit intent: clarity
Original: A method for detecting a trend change in a multiregional epidemic is developed for a standard epidemiological SIR compartment model and a meta-population network model.
Revised: A method for detecting a trend change in cross-border epidemic transmission is developed for a standard epidemiological SIR compartment model and a meta-population network model.
Edit intent: clarity
Original:  The method is applicable to the investigation of the efficacy of the implemented public health intervention  from a time series of the number of new cases reported in multiple geographical regions.
Revised:  The method is applicable to investigating the efficacy of the implemented public health intervention from a time series of the number of new cases reported in multiple geographical regions.
Edit intent: fluency
Original:  The change point of the probability of  movements was one week after the WHO worldwide alert on the SARS outbreak .
Revised:  It is found that the change point of the probability of movements was one week after the WHO worldwide alert on the SARS outbreak .
Edit intent: coherence
Original:  The change point of the probability of  movements was one week after the WHO worldwide alert on the SARS outbreak .
Revised:  The change point of the probability of travel movements was one week after the WHO worldwide alert on the SARS outbreak .
Edit intent: clarity
Original:  The pandemic did not affect travels despite the WHO alert .
Revised:  The pandemic did not affect potential travelers despite the WHO alert .
Edit intent: clarity
Original:  We show that this transition is robust against many modifications of the model, and is induced by an asymmetry between the rate of hiring and the rate of firing of the firms.
Revised:  We show that this transition is induced by an asymmetry between the rate of hiring and the rate of firing of the firms.
Edit intent: clarity
Original:  This asymmetry is induced , in Mark I, by the interest rate.
Revised:  This asymmetry is , in Mark I, by the interest rate.
Edit intent: clarity
Original:  As the interest rate increases, the firms become more and more reluctant to take further loans  .
Revised:  As the interest rate increases, firms become more and more reluctant to take further loans .
Edit intent: fluency
Original:  The unemployment level remains small until a tipping point  beyond which the economy suddenly collapses.
Revised:  The unemployment level remains small until a tipping point , beyond which the economy suddenly collapses.
Edit intent: fluency
Original:  We have also explored several natural extensions  .
Revised:  We have explored several natural extensions .
Edit intent: clarity
Original:  We have also explored several natural extensions  .
Revised:  We have also explored several natural extensions of the model .
Edit intent: clarity
Original:  Our motivation is to understand the large macro-economic fluctuations observed in the "Mark I" ABM.
Revised:  Our motivation is to understand the large macro-economic fluctuations observed in the 'Mark I' ABM.
Edit intent: fluency
Original:  Our central finding is the generic existence of a phase transition between a "good economy" where unemployment is low, and a "bad economy" where unemployment is high.
Revised:  Our major finding is the generic existence of a phase transition between a "good economy" where unemployment is low, and a "bad economy" where unemployment is high.
Edit intent: clarity
Original:  Our central finding is the generic existence of a phase transition between a "good economy" where unemployment is low, and a "bad economy" where unemployment is high.
Revised:  Our central finding is the generic existence of a phase transition between a 'good economy' where unemployment is low, and a "bad economy" where unemployment is high.
Edit intent: fluency
Original:  Our central finding is the generic existence of a phase transition between a "good economy" where unemployment is low, and a "bad economy" where unemployment is high.
Revised:  Our central finding is the generic existence of a phase transition between a "good economy" where unemployment is low, and a 'bad economy' where unemployment is high.
Edit intent: fluency
Original:  This asymmetry is, in Mark I, due to the fact that as the interest rate increases, firms become more and more reluctant to take further loans and have to reduce their workforce.
Edit intent: coherence
Original:  We allow the hiring/firing propensity to depend on the financial fragility of firms, and introduce simple wage update policies.
Revised:  We also introduce simple wage update policies.
Edit intent: clarity
Original:  We allow the hiring/firing propensity to depend on the financial fragility of firms, and introduce simple wage update policies.
Revised:  We allow the hiring/firing propensity to depend on the financial fragility of firms, and introduce simple wage policies.
Edit intent: clarity
Original:  This leads to inflation (in the "good" phase) or deflation (in the "bad" phase), but leaves the overall phase diagram of the model essentially unchanged.
Revised:  This leads to inflation (in the 'good' phase) or deflation (in the "bad" phase), but leaves the overall phase diagram of the model essentially unchanged.
Edit intent: fluency
Original:  This leads to inflation (in the "good" phase) or deflation (in the "bad" phase), but leaves the overall phase diagram of the model essentially unchanged.
Revised:  This leads to inflation (in the "good" phase) or deflation (in the 'bad' phase), but leaves the overall phase diagram of the model essentially unchanged.
Edit intent: fluency
Original:  This result allows to characterize the complexity of the reachability problem for one of the most studied class of counter machines cav10,comon-jurski98, and has a direct impact for other problems in program verification , such as the complexity of satisfiability problems for logics interpreted over integer arrays \mbox{ lia,cav09 .
Revised:  This result allows to characterize the complexity of the reachability problem for one of the most studied class of counter machines cav10,comon-jurski98, and has a potential impact for other problems in program verification , such as the complexity of satisfiability problems for logics interpreted over integer arrays \mbox{ lia,cav09 .
Edit intent: clarity
Original:  This result allows to characterize the complexity of the reachability problem for one of the most studied class of counter machines cav10,comon-jurski98, and has a direct impact for other problems in program verification , such as the complexity of satisfiability problems for logics interpreted over integer arrays \mbox{ lia,cav09 .
Revised:  This result allows to characterize the complexity of the reachability problem for one of the most studied class of counter machines cav10,comon-jurski98, and has a direct impact for other problems in program verification .
Edit intent: clarity
Original:  We are investigating the difference between the multiplicities of the factors of the Gr\"obner basis and the resultant.
Revised:  We are investigating the difference between the multiplicity of the factors of the Gr\"obner basis and the resultant.
Edit intent: fluency
Original: Data centers consume an enormous amount of energy and incur high electricity cost.
Revised: Data centers consume a large amount of energy and incur high electricity cost.
Edit intent: fluency
Original:  In this paper, we focus on the familiar problem of reducing data center energy cost with two new perspectives.
Revised:  In this paper, we study the familiar problem of reducing data center energy cost with two new perspectives.
Edit intent: clarity
Original:  First, we find, through an empirical study of contracts of electric utilities that power Google data centers, that demand charge per kW for the maximum power used is a substantial component of the total cost , in addition to the energy charge for the total kWh energy used .
Revised:  First, we find, through an empirical study of contracts from electric utilities powering Google data centers, that demand charge per kW for the maximum power used is a substantial component of the total cost , in addition to the energy charge for the total kWh energy used .
Edit intent: clarity
Original:  First, we find, through an empirical study of contracts of electric utilities that power Google data centers, that demand charge per kW for the maximum power used is a substantial component of the total cost , in addition to the energy charge for the total kWh energy used .
Revised:  First, we find, through an empirical study of contracts of electric utilities that power Google data centers, that demand charge per kW for the maximum power used is a major component of the total cost , in addition to the energy charge for the total kWh energy used .
Edit intent: clarity
Original:  First, we find, through an empirical study of contracts of electric utilities that power Google data centers, that demand charge per kW for the maximum power used is a substantial component of the total cost , in addition to the energy charge for the total kWh energy used .
Revised:  First, we find, through an empirical study of contracts of electric utilities that power Google data centers, that demand charge per kW for the maximum power used is a substantial component of the total cost .
Edit intent: coherence
Original:  Second, many services such as Web search do tolerate partial execution of the requests because the response quality is a concave function of processing time.
Revised:  Second, many services such as Web search tolerate partial execution of the requests because the response quality is a concave function of processing time.
Edit intent: clarity
Original:  The model makes use of the concept of market information about future supply and demand as a basis for valuation.
Revised:  The model uses the concept of market information about future supply and demand as a basis for valuation.
Edit intent: clarity
Original:  Physical ownership of a commodity is regarded as providing a stream of "convenience dividends " equivalent to a continuous cash flow.
Revised:  Physical ownership of a commodity is taken to provide a stream of "convenience dividends " equivalent to a continuous cash flow.
Edit intent: clarity
Original:  Physical ownership of a commodity is regarded as providing a stream of "convenience dividends " equivalent to a continuous cash flow.
Revised:  Physical ownership of a commodity is regarded as providing a stream of convenience dividends equivalent to a continuous cash flow.
Edit intent: fluency
Original:  The price of a commodity is given by the expectation of the totality of the discounted risk-adjusted future convenience dividend, conditional on the information provided by the market filtration.
Revised:  The price of a commodity is the expectation under a suitable pricing measure of the totality of the discounted risk-adjusted future convenience dividend, conditional on the information provided by the market filtration.
Edit intent: clarity
Original:  In the situation where the dividend rate is modelled by an Ornstein-Uhlenbeck process, the prices of options on commodities can be derived in closed form , both in the case when underlying is the spot price, and in the case when underlying is a futures price .
Revised:  In the situation where the dividend rate is modelled by an Ornstein-Uhlenbeck process, the prices of options on commodities can be derived in closed form .
Edit intent: coherence
Original:  The approach presented can be applied to other assets that can yield potentially negative effective cash flows, such as real estate, factories, refineries, mines, and power generating plants.
Revised:  The approach that we present can be applied to other assets that can yield potentially negative effective cash flows, such as real estate, factories, refineries, mines, and power generating plants.
Edit intent: clarity
Original:  The approach presented can be applied to other assets that can yield potentially negative effective cash flows, such as real estate, factories, refineries, mines, and power generating plants.
Revised:  The approach presented can be applied to other assets that yield potentially negative effective cash flows, such as real estate, factories, refineries, mines, and power generating plants.
Edit intent: fluency
Original: We consider the continuous time presentation of the strand symmetric phylogenetic substitution model (in which rate matrices are unchanged under  Watson-Crick base conjugation).
Revised: We consider the continuous-time presentation of the strand symmetric phylogenetic substitution model (in which rate matrices are unchanged under Watson-Crick base conjugation).
Edit intent: fluency