wanyu/IteraTeR_v2 huggingface dataset:
Original:  \mbox{ AKKLR a natural 2^{d+1}-query test for this property  ]  and showed that it accepts every degree d polynomial with probability 1, while rejecting functions that are \Omega(1) -far with probability \Omega (1/(d 2^{d})).
Revised:  \mbox{ AKKLR a natural 2^{d+1}-query test for this property ] and showed that it accepts every degree d polynomial with probability 1, while rejecting functions that are Omega(1) -far with probability \Omega (1/(d 2^{d})).
Edit intent: fluency
Original:  We give an asymptotically optimal analysis of their testshowing that it rejects functions that are (even only) \Omega (2^{-d})-far with \Omega(1) -probability (so the rejection probability is a universal constant independent of d and n).
Revised:  We give an asymptotically optimal analysis of this test, and show that it rejects functions that are (even only) \Omega (2^{-d})-far with \Omega(1) -probability (so the rejection probability is a universal constant independent of d and n).
Edit intent: clarity
Original:  We give an asymptotically optimal analysis of their testshowing that it rejects functions that are (even only) \Omega (2^{-d})-far with \Omega(1) -probability (so the rejection probability is a universal constant independent of d and n).
Revised:  We give an asymptotically optimal analysis of their testshowing that it rejects functions that are (even only) Omega (2^{-d})-far with \Omega(1) -probability (so the rejection probability is a universal constant independent of d and n).
Edit intent: fluency
Original:  We give an asymptotically optimal analysis of their testshowing that it rejects functions that are (even only) \Omega (2^{-d})-far with \Omega(1) -probability (so the rejection probability is a universal constant independent of d and n).
Revised:  We give an asymptotically optimal analysis of their testshowing that it rejects functions that are (even only) \Omega (2^{-d})-far with Omega(1) -probability (so the rejection probability is a universal constant independent of d and n).
Edit intent: fluency
Original:   Our proof works by induction on n , and yields a new analysis of even the classical Blum-Luby-Rubinfeld \mbox{ \cite{BLR }\hspace{0pt} }  linearity test, for the setting of functions mapping %DIFDELCMD < \F%%%  _2^n to %DIFDELCMD < \F%%%  _2. The optimality follows from a tighter analysis of counterexamples to the "inverse conjecture for the Gowers norm"
Revised:  Our proof works by induction on n and yields a new analysis of even the classical Blum-Luby-Rubinfeld \mbox{ \cite{BLR }\hspace{0pt} } linearity test, for the setting of functions mapping %DIFDELCMD < \F%%% _2^n to %DIFDELCMD < \F%%% _2. The optimality follows from a tighter analysis of counterexamples to the "inverse conjecture for the Gowers norm"
Edit intent: fluency
Original:   Our proof works by induction on n , and yields a new analysis of even the classical Blum-Luby-Rubinfeld \mbox{ \cite{BLR }\hspace{0pt} }  linearity test, for the setting of functions mapping %DIFDELCMD < \F%%%  _2^n to %DIFDELCMD < \F%%%  _2. The optimality follows from a tighter analysis of counterexamples to the "inverse conjecture for the Gowers norm"
Revised:  Our proof works by induction on n , and yields a new analysis of even the classical Blum-Luby-Rubinfeld }\hspace{0pt} } linearity test, for the setting of functions mapping %DIFDELCMD < \F%%% _2^n to %DIFDELCMD < \F%%% _2. The optimality follows from a tighter analysis of counterexamples to the "inverse conjecture for the Gowers norm"
Edit intent: clarity
Original:   Our proof works by induction on n , and yields a new analysis of even the classical Blum-Luby-Rubinfeld \mbox{ \cite{BLR }\hspace{0pt} }  linearity test, for the setting of functions mapping %DIFDELCMD < \F%%%  _2^n to %DIFDELCMD < \F%%%  _2. The optimality follows from a tighter analysis of counterexamples to the "inverse conjecture for the Gowers norm"
Revised:  Our proof works by induction on n , and yields a new analysis of even the classical Blum-Luby-Rubinfeld \mbox{ \cite{BLR }\hspace{0pt} } linearity test, for the setting of functions mapping %DIFDELCMD < \F%%% _2^n to %DIFDELCMD < \F%%% F _2. The optimality follows from a tighter analysis of counterexamples to the "inverse conjecture for the Gowers norm"
Edit intent: clarity
Original:  constructed by \mbox{ \cite{GT,LMS}\hspace{0pt} }  . Our result gives a new relationship between the (d+1)^{\rm{st}-Gowers norm of a function and its maximal correlation with degree d polynomials.
Revised:  constructed by \mbox{ \cite{GT,LMS}\hspace{0pt} } . Our result }-Gowers norm of a function and its maximal correlation with degree d polynomials.
Edit intent: clarity
Original: test also }  improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also }   implies a " query-hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Revised: test also } improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson }\hspace{0pt} . Finally, the optimality of our result also } implies a " query-hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Edit intent: fluency
Original: test also }  improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also }   implies a " query-hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Revised: test also } improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also } . Third, it implies a " query-hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Edit intent: coherence
Original: test also }  improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also }   implies a " query-hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Revised: test also } improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also } implies a " query hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Edit intent: fluency
Original: test also }  improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also }   implies a " query-hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Revised: test also } improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also } implies a " query-hierarchy " result for property testing of affine-invariant properties. That is, for every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Edit intent: coherence
Original: test also }  improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also }   implies a " query-hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives a linear-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Revised: test also } improves the parameters of an XOR lemma for polynomials given by Viola and Wigderson \mbox{ \cite{VW}\hspace{0pt} . Finally, the optimality of our result also } implies a " query-hierarchy " result for property testing of linear-invariant properties: For every function q(n), it gives an affine-invariant property that is testable with O(q(n))-queries, but not with o(q(n))-queries, complementing an analogous result of \mbox{ \cite{GKNR08 }\hspace{0pt} } [ for graph properties.
Edit intent: fluency
Original:  Specifically, this framework provides 1) a specification language which supports the concise and direct description of formal systems, 2) a mechanism for animating the specification language thereby producing prototypes of encoded systems, and 3) a logic for proving properties of specifications and therefore of the systems they encode.
Revised:  Specifically, this framework provides a specification language which supports the concise and direct description of formal systems, 2) a mechanism for animating the specification language thereby producing prototypes of encoded systems, and 3) a logic for proving properties of specifications and therefore of the systems they encode.
Edit intent: fluency
Original:  Specifically, this framework provides 1) a specification language which supports the concise and direct description of formal systems, 2) a mechanism for animating the specification language thereby producing prototypes of encoded systems, and 3) a logic for proving properties of specifications and therefore of the systems they encode.
Revised:  Specifically, this framework provides 1) a specification language which supports the concise and direct description of formal systems, a mechanism for animating the specification language thereby producing prototypes of encoded systems, and 3) a logic for proving properties of specifications and therefore of the systems they encode.
Edit intent: fluency
Original:  Specifically, this framework provides 1) a specification language which supports the concise and direct description of formal systems, 2) a mechanism for animating the specification language thereby producing prototypes of encoded systems, and 3) a logic for proving properties of specifications and therefore of the systems they encode.
Revised:  Specifically, this framework provides 1) a specification language which supports the concise and direct description of formal systems, 2) a mechanism for animating the specification language thereby producing prototypes of encoded systems, and a logic for proving properties of specifications and therefore of the systems they encode.
Edit intent: coherence
Original:  The primary contributions of these thesis are 1) a meta-logic called G which allows for sophisticated reasoning  over high-level specifications of computations , 2) a system called Abella which embodies the reasoning component of the proposed framework and allows for interactive reasoning about specifications, and 3) applications carried out in Abella which demonstrate the expressiveness and naturalness of the proposed framework
Revised:  The primary contributions of these thesis are 1) a meta-logic called G with capabilities for sophisticated reasoning over high-level specifications of computations , 2) a system called Abella which embodies the reasoning component of the proposed framework and allows for interactive reasoning about specifications, and 3) applications carried out in Abella which demonstrate the expressiveness and naturalness of the proposed framework
Edit intent: clarity
Original:  The primary contributions of these thesis are 1) a meta-logic called G which allows for sophisticated reasoning  over high-level specifications of computations , 2) a system called Abella which embodies the reasoning component of the proposed framework and allows for interactive reasoning about specifications, and 3) applications carried out in Abella which demonstrate the expressiveness and naturalness of the proposed framework
Revised:  The primary contributions of these thesis are 1) a meta-logic called G which allows for sophisticated reasoning over high-level specifications of computations , 2) a system called Abella based on G; and several reasoning examples which demonstrate the expressiveness and naturalness of the proposed framework
Edit intent: clarity
Original: The presence of self-organized criticality in biology is often evidenced through the power-law scaling of event size distributions represented in logarithmic scale .
Revised: The presence of self-organized criticality in biology is often evidenced by a power-law scaling of event size distributions represented in logarithmic scale .
Edit intent: clarity
Original:  This result is however not robust to change in detection threshold, or to more severe statistical analyses such as the Kolmogorov-Smirnoff test.
Revised:  However, this result is not robust to change in detection threshold, or to more severe statistical analyses such as the Kolmogorov-Smirnoff test.
Edit intent: fluency
Original:  This result is however not robust to change in detection threshold, or to more severe statistical analyses such as the Kolmogorov-Smirnoff test.
Revised:  This result is however not robust to change in detection threshold, or when tested using more rigorous statistical analyses such as the Kolmogorov-Smirnoff test.
Edit intent: clarity
Original:  This result is however not robust to change in detection threshold, or to more severe statistical analyses such as the Kolmogorov-Smirnoff test.
Revised:  This result is however not robust to change in detection threshold, or to more severe statistical analyses such as the Kolmogorov-Smirnov test.
Edit intent: clarity
Original:  We next investigate this problem analytically  and show that indeed, spurious power-law scaling can appear from stochastic processes without the presence of underlying self-organized criticality.
Revised:  We next investigate this problem analytically , and show that indeed, spurious power-law scaling can appear from stochastic processes without the presence of underlying self-organized criticality.
Edit intent: fluency
Original:  We next investigate this problem analytically  and show that indeed, spurious power-law scaling can appear from stochastic processes without the presence of underlying self-organized criticality.
Revised:  We next investigate this problem analytically and show that , indeed, stochastic processes can produce spurious power-law scaling can appear from stochastic processes without the presence of underlying self-organized criticality.
Edit intent: clarity
Original:  We next investigate this problem analytically  and show that indeed, spurious power-law scaling can appear from stochastic processes without the presence of underlying self-organized criticality.
Revised:  We next investigate this problem analytically and show that indeed, spurious power-law scaling without the presence of underlying self-organized criticality.
Edit intent: clarity
Original:  However, this power-law is only apparent in logarithmic representations, but does not resist to more severe analysis such as the Kolmogorov-Smirnoff test.
Revised:  However, this power-law is only apparent in logarithmic representations, and does not survive more rigorous analysis such as the Kolmogorov-Smirnoff test.
Edit intent: clarity
Original:  In the present paper the notion of cell temperament is introduced  being analogous to the thermodynamic temperature  .
Revised:  In the present paper the notion of cell temperament is introduced , being analogous to the thermodynamic temperature .
Edit intent: fluency
Original:  While the latter is due to the thermal motion of the surrounding matter, the cells motion is generally associated to their vitality.
Revised:  While the latter is due to the thermal motion of surrounding matter, the cells motion is generally associated to their vitality.
Edit intent: fluency
Original:  In the present paper the notion of cell temperament is introduced, being analogous to the thermodynamic temperature, which is directly related to the entropy production in the cell.
Revised:  In the present paper the concept of cell temperament is introduced, being analogous to the thermodynamic temperature, which is directly related to the entropy production in the cell.
Edit intent: fluency
Original: The migration of living cells usually obeys the Einstein law of Brownian motion.
Revised: The migration of living cells obeys usually the Einstein law of Brownian motion.
Edit intent: fluency
Original:  While the latter is due to the thermal motion of surrounding matter, the cells motion is generally associated to their vitality.
Revised:  While the latter is due to the thermal motion of surrounding matter, the cells locomotion is generally associated to their vitality.
Edit intent: clarity
Original:  In the present paper the concept of cell temperament is introduced, being analogous to the thermodynamic temperature , which is directly related to the entropy production in the cell .
Revised:  In the present paper the concept of cell temperament is introduced, being analogous to thermodynamic temperature and related to the entropy production in the cell .
Edit intent: clarity
Original:  Because liquidity issues the trading firms split large orders across  trading destinations to optimize their execution.
Revised:  Because of liquidity issues, the trading firms split large orders across trading destinations to optimize their execution.
Edit intent: fluency
Original:  Because liquidity issues the trading firms split large orders across  trading destinations to optimize their execution.
Revised:  Because liquidity issues the trading firms split large orders across several trading destinations to optimize their execution.
Edit intent: clarity
Original:  To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on  reinforcement ideas.
Revised:  To solve this problem we devised two stochastic recursive learning procedures which adjust the proportions of the order to be sent to the different venues, one based on an optimization principle, the other on some reinforcement ideas.
Edit intent: clarity
Original:  We investigate both procedures from a theoretical point of view .
Revised:  Both procedures are investigated from a theoretical point of view .
Edit intent: clarity
Original:  In particular, we prove convergence results for the optimization algorithm when the innovations are supposed to be Markov stationary and ergodic (and speed with some mixing properties or when they are i.i.d. ) . Finally, we compare the behaviours of both algorithms on several simulations results (with simulated data and real data ).
Revised:  In particular, we prove convergence results for the optimization algorithm under some light ergodic (or "averaging") assumption on the input data process. No Markov property is needed. When the inputs are i.i.d. ) . Finally, we compare the behaviours of both algorithms on several simulations results (with simulated data and real data ).
Edit intent: coherence
Original:  In particular, we prove convergence results for the optimization algorithm when the innovations are supposed to be Markov stationary and ergodic (and speed with some mixing properties or when they are i.i.d. ) . Finally, we compare the behaviours of both algorithms on several simulations results (with simulated data and real data ).
Revised:  In particular, we prove convergence results for the optimization algorithm when the innovations are supposed to be Markov stationary and ergodic (and speed with some mixing properties or when they are i.i.d. ) . Finally, the mutual performances of both algorithms on several simulations results (with simulated data and real data ).
Edit intent: clarity
Original:  In particular, we prove convergence results for the optimization algorithm when the innovations are supposed to be Markov stationary and ergodic (and speed with some mixing properties or when they are i.i.d. ) . Finally, we compare the behaviours of both algorithms on several simulations results (with simulated data and real data ).
Revised:  In particular, we prove convergence results for the optimization algorithm when the innovations are supposed to be Markov stationary and ergodic (and speed with some mixing properties or when they are i.i.d. ) . Finally, we compare the behaviours of both algorithms are compared on simulated and real data ).
Edit intent: clarity
Original:  We evaluate their performances with respect to an "oracle" strategy of an "insider" who could knowa priori the executed quantities by every venues.
Revised:  We evaluate their performances with respect to an "oracle" strategy devised by an "insider" who could knowa priori the executed quantities by every venues.
Edit intent: clarity
Original:  We evaluate their performances with respect to an "oracle" strategy of an "insider" who could knowa priori the executed quantities by every venues.
Revised:  We evaluate their performances with respect to an "oracle" strategy of an "insider" who a priori the executed quantities by every venues.
Edit intent: clarity
Original:  We evaluate their performances with respect to an "oracle" strategy of an "insider" who could knowa priori the executed quantities by every venues.
Revised:  We evaluate their performances with respect to an "oracle" strategy of an "insider" who could knowknows a priori the executed quantities by every venues.
Edit intent: fluency
Original: In analyses of combinatorial algorithms, a substantial amount of effort has often to be spent on the discussion of special cases.
Revised: In analyses of algorithms, a substantial amount of effort has often to be spent on the discussion of special cases.
Edit intent: clarity
Original:  An algorithm is called resistant against null cases if any null case can be disregarded in the analysis of both its solution quality and resource requirements.
Revised:  An algorithm is called robust if any null case can be disregarded in the analysis of both its solution quality and resource requirements.
Edit intent: clarity
Original:  We show that resistance against null cases is only a matter of breaking ties in the right way.
Revised:  We show that achieving robustness is only a matter of breaking ties in the right way.
Edit intent: clarity
Original:  We show that resistance against null cases is only a matter of breaking ties in the right way.
Revised:  We show that resistance against null cases is only a matter of breaking ties the right way.
Edit intent: fluency
Original:  These receptors are more than 80\% identical in DNA sequences and have 107 base pair mismatches among them.
Revised:  These receptors are more than 80\% identical in DNA sequences and have 108 base pair mismatches among them.
Edit intent: fluency