wanyu/IteraTeR_v2 huggingface dataset:
Original:  } This is in contrast to the best complexity of the known algorithms for the same problem in the non-symmetric situation, which is singly exponential.
Revised:  } This is in contrast to the best complexity of the known algorithms for the same problem in the non-symmetric situation, which are singly exponential.
Edit intent: fluency
Original:  We give algorithms for computing the generalized EulerPoincar\'e characteristic of such sets, whose complexities measured by the number the number of arithmetic operations in D, are polynomially bounded in terms of k and the number of polynomials in the input, assuming that the degrees of the input polynomials are bounded by a constant.
Revised:  We give algorithms for computing the generalized Euler-Poincar\'e characteristic of such sets, whose complexities measured by the number the number of arithmetic operations in D, are polynomially bounded in terms of k and the number of polynomials in the input, assuming that the degrees of the input polynomials are bounded by a constant.
Edit intent: fluency
Original: The problem of influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes.
Revised: Influence maximization in social networks has typically been studied in the context of contagion models and irreversible processes.
Edit intent: clarity
Original:  In this paper, we consider an alternate model that treats individual opinions as spins in an Ising network at dynamic equilibrium.
Revised:  In this paper, we consider an alternate model that treats individual opinions as spins in an Ising system at dynamic equilibrium.
Edit intent: clarity
Original:  We formalize the Ising influence maximization (IIM) \textit{ problem, which has a  physical interpretation as the maximization of the magnetization given a budget of external magnetic field.
Revised:  We formalize the \textit{ problem, which has a physical interpretation as the maximization of the magnetization given a budget of external magnetic field.
Edit intent: clarity
Original:  We formalize the Ising influence maximization (IIM) \textit{ problem, which has a  physical interpretation as the maximization of the magnetization given a budget of external magnetic field.
Revised:  We formalize the Ising influence maximization (IIM) \textit{ problem, which has a physical interpretation as maximizing the magnetization given a budget of external magnetic field.
Edit intent: clarity
Original:  We show that optimal strategies exhibit a phase transition from focusing influence on high-degree individuals at high interaction strengths to spreading influence among low-degree individuals at low interaction strengths .
Revised:  We show that optimal strategies exhibit a phase transition from focusing influence on high-degree individuals at high temperatures to focusing on low-degree individuals at low interaction strengths .
Edit intent: clarity
Original:  We show that optimal strategies exhibit a phase transition from focusing influence on high-degree individuals at high interaction strengths to spreading influence among low-degree individuals at low interaction strengths .
Revised:  We show that optimal strategies exhibit a phase transition from focusing influence on high-degree individuals at high interaction strengths to spreading influence among low-degree individuals at low temperatures .
Edit intent: clarity
Original:  We also establish a number of novel results about the structure of steady-states in the ferromagnetic MF Ising model on general graphs , which are of independent interest.
Revised:  We also establish a number of novel results about the structure of steady-states in the ferromagnetic MF Ising model on general graph topologies , which are of independent interest.
Edit intent: clarity
Original: We study the computational power of shallow quantum circuits with n input qubits, one output qubit, and two types of ancillary qubits: O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized qubits.
Revised: We study the computational power of shallow quantum circuits with n input qubits, one output qubit, and two types of ancillary qubits: O(\log n) initialized and %DIFDELCMD < {\rm %%% poly (n)) uninitialized qubits.
Edit intent: coherence
Original: We study the computational power of shallow quantum circuits with n input qubits, one output qubit, and two types of ancillary qubits: O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized qubits.
Revised: We study the computational power of shallow quantum circuits with n input qubits, one output qubit, and two types of ancillary qubits: O(\log n) initialized and O(%DIFDELCMD < {\rm %%% (n)) uninitialized qubits.
Edit intent: fluency
Original:  The initial state of the uninitialized ancillary qubits is arbitrary, and we have to return their state into the initial one at the end of the computation.
Revised:  The initial state of the uninitialized ancillary qubits is arbitrary, but we have to return their state into the initial one at the end of the computation.
Edit intent: coherence
Original:  First, to show the strengths of such circuits , we consider a class of symmetric functions on n bits, including those ( such as threshold functions ) for which it is not known whether there exist shallow quantum circuits with only O(\log n) initialized ancillary qubits .
Revised:  First, we show that such circuits can compute various symmetric functions on n bits, including those ( such as threshold functions ) for which it is not known whether there exist shallow quantum circuits with only O(\log n) initialized ancillary qubits .
Edit intent: clarity
Original:  First, to show the strengths of such circuits , we consider a class of symmetric functions on n bits, including those ( such as threshold functions ) for which it is not known whether there exist shallow quantum circuits with only O(\log n) initialized ancillary qubits .
Revised:  First, to show the strengths of such circuits , we consider a class of symmetric functions on n bits, such as threshold functions ) for which it is not known whether there exist shallow quantum circuits with only O(\log n) initialized ancillary qubits .
Edit intent: clarity
Original:  First, to show the strengths of such circuits , we consider a class of symmetric functions on n bits, including those ( such as threshold functions ) for which it is not known whether there exist shallow quantum circuits with only O(\log n) initialized ancillary qubits .
Revised:  First, to show the strengths of such circuits , we consider a class of symmetric functions on n bits, including those ( such as threshold functions ) for which it is not known whether these tasks can be done with only O(\log n) initialized ancillary qubits .
Edit intent: clarity
Original:  We show that , when the number of qubits on which unbounded fan-out gates act is O(%DIFDELCMD < {\rm %%% poly (\log n)), for any constant 0 \leq \delta <1, there does not exist an O(\log^{\delta parity function on n bits with O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized ancillary qubits.
Revised:  We show that %DIFDELCMD < {\rm %%% poly (\log n)), for any constant 0 \leq \delta <1, there does not exist an O(\log^{\delta parity function on n bits with O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized ancillary qubits.
Edit intent: clarity
Original:  We show that , when the number of qubits on which unbounded fan-out gates act is O(%DIFDELCMD < {\rm %%% poly (\log n)), for any constant 0 \leq \delta <1, there does not exist an O(\log^{\delta parity function on n bits with O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized ancillary qubits.
Revised:  We show that , when the number of qubits on which unbounded fan-out gates act is O(%DIFDELCMD < {\rm %%% (\log n)), for any constant 0 \leq \delta <1, there does not exist an O(\log^{\delta parity function on n bits with O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized ancillary qubits.
Edit intent: fluency
Original:  We show that , when the number of qubits on which unbounded fan-out gates act is O(%DIFDELCMD < {\rm %%% poly (\log n)), for any constant 0 \leq \delta <1, there does not exist an O(\log^{\delta parity function on n bits with O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized ancillary qubits.
Revised:  We show that , when the number of qubits on which unbounded fan-out gates act is O(%DIFDELCMD < {\rm %%% poly they cannot compute the parity function on n bits with O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized ancillary qubits.
Edit intent: clarity
Original:  We show that , when the number of qubits on which unbounded fan-out gates act is O(%DIFDELCMD < {\rm %%% poly (\log n)), for any constant 0 \leq \delta <1, there does not exist an O(\log^{\delta parity function on n bits with O(\log n) initialized and O(%DIFDELCMD < {\rm %%% poly (n)) uninitialized ancillary qubits.
Revised:  We show that , when the number of qubits on which unbounded fan-out gates act is O(%DIFDELCMD < {\rm %%% poly (\log n)), for any constant 0 \leq \delta <1, there does not exist an O(\log^{\delta parity function on n bits with O(\log n) initialized and O(%DIFDELCMD < {\rm %%% (n)) uninitialized ancillary qubits.
Edit intent: fluency
Original: We study the computational power of shallow quantum circuits with n input qubits, one output qubit, and two types of ancillary qubits: O(\log n) initialized and n^{O(1)} uninitialized qubits.
Revised: We study the computational power of shallow quantum circuits with O(\log n) initialized and n^{O(1)} uninitialized qubits.
Edit intent: clarity
Original:  The initial state of the uninitialized ancillary qubits is arbitrary , but we have to return their state into the initial one at the end of the computation .
Revised:  The initial state of the uninitialized ancillary qubits is arbitrary .
Edit intent: clarity
Original:  First, we show that such circuits can compute various symmetric functions on n bits , such as threshold functions .
Revised:  First, we show that such a circuit can compute any symmetric function on n bits , such as threshold functions .
Edit intent: clarity
Original:  Then, we consider a polynomial-time probabilistic classical algorithm with an oracle that can perform such a circuit.
Revised:  Then, we consider a polynomial-time classical algorithm with an oracle that can perform such a circuit.
Edit intent: clarity
Original:  We show that it can estimate the elements of any unitary matrix that can be implemented by a constant-depth quantum circuit on n qubits.
Revised:  We show that it can estimate the elements of any unitary matrix corresponding to a constant-depth quantum circuit on n qubits.
Edit intent: clarity
Original:  Since it is not known whether these tasks can be done with only O(\log n) initialized ancillary qubits, our results show the possibility that augmenting uninitialized ancillary qubits increases the computational power of shallow quantum circuits with only O(\log n) initialized ancillary qubits.
Revised:  Since it seems unlikely that these tasks can be done with only O(\log n) initialized ancillary qubits, our results show the possibility that augmenting uninitialized ancillary qubits increases the computational power of shallow quantum circuits with only O(\log n) initialized ancillary qubits.
Edit intent: clarity
Original:  Since it is not known whether these tasks can be done with only O(\log n) initialized ancillary qubits, our results show the possibility that augmenting uninitialized ancillary qubits increases the computational power of shallow quantum circuits with only O(\log n) initialized ancillary qubits.
Revised:  Since it is not known whether these tasks can be done with only O(\log n) initialized ancillary qubits, our results give evidences that adding uninitialized ancillary qubits increases the computational power of shallow quantum circuits with only O(\log n) initialized ancillary qubits.
Edit intent: clarity
Original:  On the other hand, we give the cases where augmenting uninitialized ancillary qubits does not.
Revised:  Lastly, to understand the limitations of uninitialized ancillary qubits does not.
Edit intent: clarity
Original: When studying the dynamics of complex systems, one can rarely sample the state of all components.
Revised: When assessing spatially-extended complex systems, one can rarely sample the state of all components.
Edit intent: clarity
Original: When studying the dynamics of complex systems, one can rarely sample the state of all components.
Revised: When studying the dynamics of complex systems, one can rarely sample the states of all components.
Edit intent: fluency
Original:  We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagation of events.
Revised:  We show that this spatial subsampling typically leads to severe underestimation of the risk of instability in systems with propagating events.
Edit intent: clarity
Original:  We analytically derived a subsampling-invariant estimator and applied it to non-linear network simulations and case reports of various diseases , recovering a close relation between vaccination rate and spreading behavior.
Revised:  We derive a subsampling-invariant estimator and applied it to non-linear network simulations and case reports of various diseases , recovering a close relation between vaccination rate and spreading behavior.
Edit intent: clarity
Original:  The estimator can be particularly useful in countries with unreliable case reports , and promises early warning if e. g. antibiotic resistant bacteria increase their infectiousness.
Revised:  The estimator can be particularly useful in countries with unreliable case reports .
Edit intent: coherence
Original:  In neuroscience, subsampling has led to contradictory hypotheses about the  collective spiking dynamics: asynchronous-irregular or critical.
Revised:  In neuroscience, subsampling has led to contradictory hypotheses about the brain's collective spiking dynamics: asynchronous-irregular or critical.
Edit intent: clarity
Original:  With the novel estimator, we demonstrated for rat, cat and monkey that collective dynamics lives in a narrow subspace between the two.
Revised:  We identify consistently for rat, cat and monkey that collective dynamics lives in a narrow subspace between the two.
Edit intent: clarity
Original: In this paper, we ask for the typical minimum rank of a fooling set matrix.
Revised: In this paper, we ask for the "typical" minimum rank of a fooling set matrix.
Edit intent: fluency
Original:  In other words, for a zero-nonzero pattern chosen at random, is the minimum rank of a fooling set closer to its lower bound n or to its trivial upper bound n . We answer to this question in the case that the density parameter, p , is constant or tends to \to 0 slowly  .
Revised:  In other words, for a zero-nonzero pattern chosen at random, is the minimum rank of a fooling set closer to its lower bound n or to its upper bound n . We answer to this question in the case that the density parameter, p , is constant or tends to \to 0 slowly .
Edit intent: clarity
Original:  Since these services exploit the online activity of users (and therefore their connectivity in social networks), we provide a method allowing a precise evaluation of the extent to which given topological metrics regarding the social network are involved in the assessment of the final user ranking.
Revised:  Since these services exploit the online activity of users (and therefore their connectivity in social networks), we provide a precise evaluation of the extent to which given topological metrics regarding the social network are involved in the assessment of the final user ranking.
Edit intent: clarity
Original:  Since these services exploit the online activity of users (and therefore their connectivity in social networks), we provide a method allowing a precise evaluation of the extent to which given topological metrics regarding the social network are involved in the assessment of the final user ranking.
Revised:  Since these services exploit the online activity of users (and therefore their connectivity in social networks), we provide a method allowing a precise evaluation of how topological metrics of the social network are involved in the assessment of the final user ranking.
Edit intent: clarity
Original:  Since these services exploit the online activity of users (and therefore their connectivity in social networks), we provide a method allowing a precise evaluation of the extent to which given topological metrics regarding the social network are involved in the assessment of the final user ranking.
Revised:  Since these services exploit the online activity of users (and therefore their connectivity in social networks), we provide a method allowing a precise evaluation of the extent to which given topological metrics regarding the social network impact the final user ranking.
Edit intent: clarity
Original:  By monitoring the impact of these modifications on the rankings of created users , we infer the weight of each topological metric in the black-box, thus reversing the service influence cookbook.
Revised:  By monitoring the impact of these modifications on the rankings of those profiles , we infer the weight of each topological metric in the black-box, thus reversing the service influence cookbook.
Edit intent: clarity
Original:  We also apply our framework to the open source RISC-V ISA, focusing on the goal of accurate, efficient, and legal compilations from C/C++ . We uncover under-specifications and potential inefficiencies in the current RISC-V ISA documentation and identify possible solutions for each.
Revised:  We also apply our framework to the open source RISC-V ISA, seeking to verify accurate, efficient, and legal compilations from C/C++ . We uncover under-specifications and potential inefficiencies in the current RISC-V ISA documentation and identify possible solutions for each.
Edit intent: clarity
Original:  As an example, we find that a RISC-V-compliant microachitecture allows 144 outcomes forbidden by C/C++ to be observed out of 1,701 litmus tests examined.
Revised:  As an example, we find that a RISC-V-compliant microarchitecture allows 144 outcomes forbidden by C/C++ to be observed out of 1,701 litmus tests examined.
Edit intent: fluency
Original:  Overall, this paper demonstrates the effectiveness of our methodology for pinpointing MCM-related issues early in the ISA design process .
Revised:  Overall, this paper demonstrates the necessity of full-stack verification for detecting MCM-related issues early in the ISA design process .
Edit intent: clarity
Original:  This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs  .
Revised:  Using this result, we design a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs .
Edit intent: clarity
Original:  This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs  .
Revised:  This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs .
Edit intent: fluency
Original:  This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs  .
Revised:  This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously best approximation factor of 1.3 for 2-connected cubic graphs .
Edit intent: clarity
Original:  On the negative side, we show that there exist simple 2-connected cubic n-vertex graphs with no spanning closed walk of length less than 5n / 4-1 .
Revised:  On the negative side, we show that there exist simple 2-connected cubic n-vertex graph contains a spanning closed walk of length less than 5n / 4-1 .
Edit intent: clarity
Original:  We model the dynamics of such molecular level measurements as Markov processes in steady state, with a unidirectional coupling between the receptor and the signal.
Revised:  We model the dynamics of such molecular level measurements as Markov processes in steady state, with a coupling between the receptor and the signal.
Edit intent: clarity
Original:  We prove exactly that, when the receptor system does not perturb the signal dynamics , the free energy consumed by the measurement process is lower bounded by the product of the mutual informationand the time-scale of signal dynamics.
Revised:  We prove exactly that, when the the signal dynamics , the free energy consumed by the measurement process is lower bounded by the product of the mutual informationand the time-scale of signal dynamics.
Edit intent: clarity
Original:  Our results apply to arbitrary network topologies and transition rates , and therefore should hold as a general principle for biomolecular information processing .
Revised:  Our results apply to arbitrary network topologies and transition rates , and therefore holds as a general principle for biomolecular information processing .
Edit intent: clarity
Original: The living cell uses a variety of molecular receptors and signaling networks to read and process chemical signals that may vary in space and time.
Revised: The living cell uses a variety of molecular receptors to read and process chemical signals that may vary in space and time.
Edit intent: clarity
Original: The living cell uses a variety of molecular receptors and signaling networks to read and process chemical signals that may vary in space and time.
Revised: The living cell uses a variety of molecular receptors and signaling networks to read and process chemical signals that vary in space and time.
Edit intent: clarity
Original:  Finally, a second order expansion for the corresponding implied volatilities is also derived and illustrated numerically.
Revised:  Finally, a second order expansion for the corresponding implied volatility is also derived and illustrated numerically.
Edit intent: fluency
Original:  Recent studies have shown that non-Poisson ( " bursty " ) behaviors in human interactions can impede the diffusion of information or infectious diseases in social networks .
Revised:  Recent studies have shown that non-Poisson ( " bursts " ) behaviors in human interactions can impede the diffusion of information or infectious diseases in social networks .
Edit intent: clarity
Original:  Those studies generally consider models in which nodes are independently active according to the same random timing process , and vary that timing .
Revised:  Those studies generally consider models in which nodes are active according to the same random timing process , and vary that timing .
Edit intent: clarity
Original:  Those studies generally consider models in which nodes are independently active according to the same random timing process , and vary that timing .
Revised:  Those studies generally consider models in which nodes are independently active according to the same random timing process and then ask which timing is optimal .
Edit intent: clarity
Original:  In this paper, we develop a simple model of diffusion on networks in which agents can differ in the autocorrelation of their activity patterns.
Revised:  In this paper, we develop a simple model of diffusion on networks in which agents differ in their activity patterns.
Edit intent: clarity