wanyu/IteraTeR_v2 huggingface dataset:
Original: Despite the central role of mobility in wireless networks, there are surprisingly few fundamental results on its properties .
Revised: Despite the central role of mobility in wireless networks, analytical study on its impact on network performance is notoriously difficult .
Edit intent: clarity
Original:  This paper aims to address this gap by proposing a new random waypoint (RWP) mobility model defined on the entire plane and applying it to analyze two key cellular network parameters: handover rate and sojourn time.
Revised:  This paper aims to address this gap by proposing a random waypoint (RWP) mobility model defined on the entire plane and applying it to analyze two key cellular network parameters: handover rate and sojourn time.
Edit intent: clarity
Original:  Stochastic properties of the proposed model are carefully investigated.
Revised:  We first analyze the stochastic properties of the proposed model are carefully investigated.
Edit intent: clarity
Original:  We present novel closed-form expressions for both handover rate and sojourn time .
Revised:  We present analytic expressions for both handover rate and sojourn time .
Edit intent: clarity
Original:  Also , we find that the Poisson-Voronoi model is about as accurate in terms of mobility evaluation as hexagonal model, though being a bit more pessimistic in that it predicts a higher handover rate and lower sojourn time.
Revised:  Also , we find that the Poisson-Voronoi model is about as accurate in terms of mobility evaluation as hexagonal model, though being more pessimistic in that it predicts a higher handover rate and lower sojourn time.
Edit intent: clarity
Original: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)}  even when the inputs are restricted to  3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Revised: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial (depending in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)} even when the inputs are restricted to 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Edit intent: clarity
Original: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)}  even when the inputs are restricted to  3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Revised: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) time the minimum number of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)} even when the inputs are restricted to 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Edit intent: clarity
Original: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)}  even when the inputs are restricted to  3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Revised: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and the minimum number of literals of pure Horn CNF representations to within factors of 2^{O(\log^{1-o(1)} n)} even when the inputs are restricted to 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Edit intent: clarity
Original: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)}  even when the inputs are restricted to  3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Revised: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)} . This is the case even when the inputs are restricted to 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Edit intent: coherence
Original: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)}  even when the inputs are restricted to  3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Revised: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)} even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Edit intent: fluency
Original: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)}  even when the inputs are restricted to  3-CNFs with O(n^{1+\varepsilon}) clauses, for some small \varepsilon>0.
Revised: For a pure Horn Boolean function on n variables, we show that unless P=NP, it is not possible to approximate in polynomial time ( in n) the minimum numbers of clauses and literals to within factors of 2^{O(\log^{1-o(1)} n)} even when the inputs are restricted to 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Edit intent: clarity
Original:  We show that unless P=NP, it is not possible to approximate in polynomial (depending in n) time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within factors of 2^{ O( \log^{1-o(1)} n ) }. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Revised:  We show that unless P=NP, it is not possible to approximate in polynomial time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within factors of 2^{ O( \log^{1-o(1)} n ) }. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Edit intent: clarity
Original:  We show that unless P=NP, it is not possible to approximate in polynomial (depending in n) time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within factors of 2^{ O( \log^{1-o(1)} n ) }. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Revised:  We show that unless P=NP, it is not possible to approximate in polynomial (depending in n) time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within a factor of 2^{ O( \log^{1-o(1)} n ) }. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Edit intent: fluency
Original:  We show that unless P=NP, it is not possible to approximate in polynomial (depending in n) time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within factors of 2^{ O( \log^{1-o(1)} n ) }. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Revised:  We show that unless P=NP, it is not possible to approximate in polynomial (depending in n) time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within factors of 2^{ \log^{1-o(1)} n ) }. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Edit intent: fluency
Original:  We show that unless P=NP, it is not possible to approximate in polynomial (depending in n) time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within factors of 2^{ O( \log^{1-o(1)} n ) }. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Revised:  We show that unless P=NP, it is not possible to approximate in polynomial (depending in n) time the minimum number of clauses and the minimum number of literals of pure Horn CNF representations to within factors of 2^{ O( \log^{1-o(1)} n }. This is the case even when the inputs are restricted to pure Horn 3-CNFs with O(n^{1+\varepsilon}) clauses, for some small positive constant \varepsilon.
Edit intent: fluency
Original:  Furthermore, we show that even in the presence of sub-exponential (also depending in n) time , it is  not possible to obtain constant factor approximations for such problems unless the Exponential Time Hypothesis turns out to be false.
Revised:  Furthermore, we show that even allowing sub-exponential (also depending in n) time , it is not possible to obtain constant factor approximations for such problems unless the Exponential Time Hypothesis turns out to be false.
Edit intent: clarity
Original:  Furthermore, we show that even in the presence of sub-exponential (also depending in n) time , it is  not possible to obtain constant factor approximations for such problems unless the Exponential Time Hypothesis turns out to be false.
Revised:  Furthermore, we show that even in the presence of sub-exponential time computation , it is not possible to obtain constant factor approximations for such problems unless the Exponential Time Hypothesis turns out to be false.
Edit intent: clarity
Original:  Furthermore, we show that even in the presence of sub-exponential (also depending in n) time , it is  not possible to obtain constant factor approximations for such problems unless the Exponential Time Hypothesis turns out to be false.
Revised:  Furthermore, we show that even in the presence of sub-exponential (also depending in n) time , it is still not possible to obtain constant factor approximations for such problems unless the Exponential Time Hypothesis turns out to be false.
Edit intent: clarity
Original: We present scalable programmable quantum circuit schemes to simulate any given real unitary by setting the angle values in the circuit.
Revised: We present scalable programmable quantum circuit schemes to simulate any given operator by setting the angle values in the circuit.
Edit intent: clarity
Original:  We present a new quantum circuit design technique resulting  two general programmable circuit schemes.
Revised:  We present a new quantum circuit design technique resulting in two general programmable circuit schemes.
Edit intent: fluency
Original:  This provides a fixed circuit design whose angles are determined from the elements of the given matrix, which can be non-unitary, in an efficient way.
Revised:  This provides a fixed circuit design whose angles are determined from the elements of the given matrix-which can be non-unitary-in an efficient way.
Edit intent: fluency
Original:  We also give both  classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations , and the quantum complexities of them are almost the same  as non-general circuits  .
Revised:  We also give both the classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations , and the quantum complexities of them are almost the same as non-general circuits .
Edit intent: fluency
Original:  We also give both  classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations , and the quantum complexities of them are almost the same  as non-general circuits  .
Revised:  We also give both classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations . They have almost the same as non-general circuits .
Edit intent: clarity
Original:  This allows us to identify the transient states which contribute most to the slowdown effect, and enables us to provide an understanding of slowdown in the takeover of a small group of cooperators by defectors: Defection spreads quickly initially, but the final steps to takeover can be delayed significantly .
Revised:  This allows us to identify the transient states which contribute most to the slowdown effect, and enables us to provide an understanding of slowdown in the takeover of a small group of cooperators by defectors: Defection spreads quickly initially, but the final steps to takeover can be delayed substantially .
Edit intent: clarity
Original:  Our general result is that C(n)= O( n /( A ( 1-lambda_2)) ) , where lambda_2 is the absolute value of the second largest eigenvalue of the transition matrix of the random walk, A= (sum d^2(v))/(d^2 n),  and d is the average node degree.
Revised:  Our main result is that C(n)= O( n /( A ( 1-lambda_2)) ) , where lambda_2 is the absolute value of the second largest eigenvalue of the transition matrix of the random walk, A= (sum d^2(v))/(d^2 n), and d is the average node degree.
Edit intent: clarity
Original:  Our general result is that C(n)= O( n /( A ( 1-lambda_2)) ) , where lambda_2 is the absolute value of the second largest eigenvalue of the transition matrix of the random walk, A= (sum d^2(v))/(d^2 n),  and d is the average node degree.
Revised:  Our general result is that C(n)= O( n /( 1-lambda_2)) ) , where lambda_2 is the absolute value of the second largest eigenvalue of the transition matrix of the random walk, A= (sum d^2(v))/(d^2 n), and d is the average node degree.
Edit intent: fluency
Original:  We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X_1 ,..., X_k , the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y_1 ,..., Y_l .
Revised:  We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X1 ,..., X_k , the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y_1 ,..., Y_l .
Edit intent: clarity
Original:  We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X_1 ,..., X_k , the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y_1 ,..., Y_l .
Revised:  We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X_1 ,..., Xk , the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y_1 ,..., Y_l .
Edit intent: clarity
Original:  We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X_1 ,..., X_k , the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y_1 ,..., Y_l .
Revised:  We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X_1 ,..., X_k , the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y1 ,..., Y_l .
Edit intent: clarity
Original:  We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X_1 ,..., X_k , the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y_1 ,..., Y_l .
Revised:  We introduce the notion of function, rather than predicate, computation by representing the output of a function f:N^k --> N^l by a count of some molecular species, i.e., if the CRN starts with n_1,...,n_k molecules of some "input" species X_1 ,..., X_k , the CRN is guaranteed to converge to having f(n_1,...,n_k) molecules of the "output" species Y_1 ,..., Yl .
Edit intent: fluency
Original:  We show that a function f:N^k --> N^l is deterministically computed by a CRN if and only if its graph {(x,y) \in N^k x N^l | f(x) = y} is a semilinear set.
Revised:  We show that a function f:N^k --> N^l is deterministically computed by a CRN if and only if its graph {(x,y) | f(x) = y} is a semilinear set.
Edit intent: clarity
Original:  Finally, we show that each semilinear function f can be computed on input x in expected time O(polylog  |x|  ).
Revised:  Furthermore, each semilinear function f can be computed on input x in expected time O(polylog |x| ).
Edit intent: coherence
Original:  Finally, we show that each semilinear function f can be computed on input x in expected time O(polylog  |x|  ).
Revised:  Finally, we show that each semilinear function f can be computed on input x in expected time O(polylog ( |x| ).
Edit intent: fluency
Original:  Finally, we show that each semilinear function f can be computed on input x in expected time O(polylog  |x|  ).
Revised:  Finally, we show that each semilinear function f can be computed on input x in expected time O(polylog |x| ) ).
Edit intent: fluency
Original:  In the F-Deletion problem, we are given an n-vertex , m-edge graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F as a minor.
Revised:  In the F-Deletion problem, we are given an n-vertex graph G and an integer k as input, and asked whether at most k vertices can be deleted from G such that the resulting graph does not contain a graph from F as a minor.
Edit intent: clarity
Original:  The highlights of our work are - A randomized O(nm) time constant factor approximation algorithm for the optimization version of Planar F-Deletion. - A randomized  O(2^{O(k)} n) time parameterized algorithm for Planar F-Deletion when F is connected.
Revised:  The highlights of our work are - A constant factor approximation algorithm for the optimization version of Planar F-Deletion. - A randomized O(2^{O(k)} n) time parameterized algorithm for Planar F-Deletion when F is connected.
Edit intent: clarity
Original:   These algorithms unify, generalize, and improve over a multitude of results in the literature.
Revised:  These algorithms unify, generalize, and improve a multitude of results in the literature.
Edit intent: clarity
Original: We use information theoretic achievable rate formu- las for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a destination node.
Revised: We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a destination node.
Edit intent: fluency
Original: We use information theoretic achievable rate formu- las for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a destination node.
Revised: We use information theoretic achievable rate formu- las for the multi-relay channel to study the problem of optimal placement of relay nodes along the straight line joining a source node and a sink node.
Edit intent: clarity
Original:  The achievable rate formulas that we utilize are for full-duplex radios at the relays and decode- and-forward relaying.
Revised:  The achievable rate formulas that we use are for full-duplex radios at the relays and decode- and-forward relaying.
Edit intent: fluency
Original:  Our main results are the following, where logs are to base 2: *  Q_1^*(f)>=(  log fool^1(f) -1) / 2. This result is tight via superdense coding, and gives optimal bounds for basic functions like equality and disjointness (for the former, no super-constant lower bound  seems to follow from other known techniques). * NQ(f)>=log \fool^1(f)/2 + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f)~0.613 log fool^1(f).
Revised:  Our main results are the following, where logs are to base 2: * Q_1^*(f)>=( log fool^1(f) - 1 / 2. This result is tight via superdense coding, and gives optimal bounds for basic functions like equality and disjointness (for the former, no super-constant lower bound seems to follow from other known techniques). * NQ(f)>=log \fool^1(f)/2 + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f)~0.613 log fool^1(f).
Edit intent: fluency
Original:  Our main results are the following, where logs are to base 2: *  Q_1^*(f)>=(  log fool^1(f) -1) / 2. This result is tight via superdense coding, and gives optimal bounds for basic functions like equality and disjointness (for the former, no super-constant lower bound  seems to follow from other known techniques). * NQ(f)>=log \fool^1(f)/2 + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f)~0.613 log fool^1(f).
Revised:  Our main results are the following, where logs are to base 2: * Q_1^*(f)>=( log fool^1(f) -1) / 2, which is essentially optimal by superdense coding. No super-constant lower bound seems to follow from other known techniques). * NQ(f)>=log \fool^1(f)/2 + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f)~0.613 log fool^1(f).
Edit intent: coherence
Original:  Our main results are the following, where logs are to base 2: *  Q_1^*(f)>=(  log fool^1(f) -1) / 2. This result is tight via superdense coding, and gives optimal bounds for basic functions like equality and disjointness (for the former, no super-constant lower bound  seems to follow from other known techniques). * NQ(f)>=log \fool^1(f)/2 + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f)~0.613 log fool^1(f).
Revised:  Our main results are the following, where logs are to base 2: * Q_1^*(f)>=( log fool^1(f) -1) / 2. This result is tight via superdense coding, and gives optimal bounds for basic functions like equality and disjointness (for the former, no super-constant lower bound for equality seems to follow from other known techniques). * NQ(f)>=log \fool^1(f)/2 + 1. We do not know if the factor 1/2 is needed in this result, but it cannot be replaced by 1: we give an example where NQ(f)~0.613 log fool^1(f).
Edit intent: fluency
Original: Representatives of several Internet access providers have expressed their wish to see a substantial change in the pricing policies of the Internet.
Revised: Representatives of several Internet service providers (ISPs) have expressed their wish to see a substantial change in the pricing policies of the Internet.
Edit intent: clarity