wanyu/IteraTeR_v2 huggingface dataset:
Original:  Second system contains equations describing the changes of general populations age structure, completed with subsystems of equations describing the selection of the strategies within each age class  .
Revised:  Second system contains equations describing the changes of the general population's age structure, completed with subsystems of equations describing the selection of the strategies within each age class .
Edit intent: fluency
Original:  In particular, we examine a notion of nondeterministic many-one CFL reducibility and conduct a ground work to formulate a coherent framework for further expositions.
Revised:  In particular, we examine a notion of many-one CFL reducibility and conduct a ground work to formulate a coherent framework for further expositions.
Edit intent: clarity
Original:  Two more powerful reducibilities-bounded truth-table and Turing CFL-reducibilities--are also discussed in comparison.
Revised:  Two more powerful reducibilities--bounded truth-table and Turing CFL-reducibilities--are also discussed in comparison.
Edit intent: fluency
Original:  Basic structural properties are proven for each level of this CFL hierarchy.
Revised:  For each level of this CFL hierarchy.
Edit intent: clarity
Original:  The first and second levels of the hierarchy are proven to be different.
Revised:  The first and second levels of the hierarchy are different.
Edit intent: clarity
Original:  The rest of the hierarchy (more strongly, the Boolean hierarchy built over each level of the CFL hierarchy) is also infinite unless the polynomial hierarchy over NP collapses.
Revised:  The rest of the hierarchy (more strongly, the Boolean hierarchy built over each level of the hierarchy) is also infinite unless the polynomial hierarchy over NP collapses.
Edit intent: clarity
Original:  This follows from a characterization of the Boolean hierarchy over the k-th level of the polynomial hierarchy in terms of the Boolean hierarchy over the k+ 1-st level of the CFL hierarchy  . Similarly, the complexity class Theta( p, k) is related to the  k-th level of the CFL hierarchy .
Revised:  This follows from a characterization of the Boolean hierarchy over the k-th level of the polynomial hierarchy in terms of the Boolean hierarchy over the k+ 1st level of the CFL hierarchy . Similarly, the complexity class Theta( p, k) is related to the k-th level of the CFL hierarchy .
Edit intent: fluency
Original:  We show that BPCFL-a bounded-error probabilistic version of CFL-is not included in CFL even in the presence of advice.
Revised:  We show that BPCFL--a bounded-error probabilistic version of CFL-is not included in CFL even in the presence of advice.
Edit intent: fluency
Original:  We show that BPCFL-a bounded-error probabilistic version of CFL-is not included in CFL even in the presence of advice.
Revised:  We show that BPCFL-a bounded-error probabilistic version of CFL--is not included in CFL even in the presence of advice.
Edit intent: fluency
Original:  Using a cellular growth phenotype, we show that integrating mRNA and microRNA data with genotypic data substantially increases performance .
Revised:  Using a cellular growth phenotype, we show that integrating mRNA and microRNA expression data substantially increases performance .
Edit intent: clarity
Original:  We provide guidelines on how to choose the similarity matrices and an R package to implement OmicKriging URL
Revised:  We provide guidelines on how to choose the similarity matrices and an R package to implement OmicKriging .
Edit intent: fluency
Original:  We complement our empirical results with a suite of worst-case theoretical bounds for both random sampling and random projections methods.
Revised:  We complement our empirical results with a suite of worst-case theoretical bounds for both random sampling and random projection methods.
Edit intent: fluency
Original:  These bounds are qualitatively superior to existing bounds---e.g. , improved additive-error bounds for the spectral and Frobenius norm errors and relative-error bounds for the trace norm error .
Revised:  These bounds are qualitatively superior to existing bounds---e.g. improved additive-error bounds for the spectral and Frobenius norm errors and relative-error bounds for the trace norm error .
Edit intent: fluency
Original:  These bounds are qualitatively superior to existing bounds---e.g. , improved additive-error bounds for the spectral and Frobenius norm errors and relative-error bounds for the trace norm error .
Revised:  These bounds are qualitatively superior to existing bounds---e.g. , improved additive-error bounds for spectral and Frobenius norm errors and relative-error bounds for the trace norm error .
Edit intent: fluency
Original:  These bounds are qualitatively superior to existing bounds---e.g. , improved additive-error bounds for the spectral and Frobenius norm errors and relative-error bounds for the trace norm error .
Revised:  These bounds are qualitatively superior to existing bounds---e.g. , improved additive-error bounds for the spectral and Frobenius norm error and relative-error bounds for the trace norm error .
Edit intent: fluency
Original:  We break this trend by presenting a polynomial-time algorithm for optimizing quantum circuits while taking the actual implementation of fault-tolerant logical gates into consideration.
Revised:  Here we present a polynomial-time algorithm for optimizing quantum circuits while taking the actual implementation of fault-tolerant logical gates into consideration.
Edit intent: coherence
Original:  We break this trend by presenting a polynomial-time algorithm for optimizing quantum circuits while taking the actual implementation of fault-tolerant logical gates into consideration.
Revised:  We break this trend by presenting a polynomial-time algorithm for optimizing quantum circuits that takes the actual implementation of fault-tolerant logical gates into consideration.
Edit intent: clarity
Original:  Our algorithm resynthesizes quantum circuits composed of CNOT and T gates, the latter being typically the most costly gate in fault-tolerant models, e.g., those based on the Steane or surface codes, with the purpose of minimizing both T-depth and T-count .
Revised:  Our algorithm re-synthesizes quantum circuits composed of CNOT and T gates, the latter being typically the most costly gate in fault-tolerant models, e.g., those based on the Steane or surface codes, with the purpose of minimizing both T-depth and T-count .
Edit intent: fluency
Original:  Our algorithm resynthesizes quantum circuits composed of CNOT and T gates, the latter being typically the most costly gate in fault-tolerant models, e.g., those based on the Steane or surface codes, with the purpose of minimizing both T-depth and T-count .
Revised:  Our algorithm resynthesizes quantum circuits composed of CNOT and T gates, the latter being typically the most costly gate in fault-tolerant models, e.g., those based on the Steane or surface codes, with the purpose of minimizing both T-count .
Edit intent: clarity
Original:  The tested benchmarks show up to 99 \% reduction in T-depth and up to 42 \% reduction in T-count .
Revised:  The tested benchmarks show up to 99 \% reduction in T-count and up to 42 \% reduction in T-count .
Edit intent: fluency
Original: This paper revisits the problem of characterizing the highest spatial throughput -- or spatial capacity -- of wireless networks in bits/s/Hz/ square meter in light of some recent results.
Revised: This paper revisits the problem of characterizing the highest spatial throughput -- or spatial capacity -- of wireless networks in bits/s/Hz/ in light of some recent results.
Edit intent: clarity
Original:  We analyze the expected maximum achievable sum rates over a given area based on the capacity regions of Gaussian point-to-point codes in Poisson distributed wireless networks under two decoding rules , namely (i) IAN : treating interference as noise, and (ii) OPT: jointly detecting the strongest interfering signals , treating the others as noise.
Revised:  We analyze the expected maximum achievable sum rates over a given area based on the capacity regions of Gaussian point-to-point codes in Poisson distributed wireless networks under two decoding rules : treating interference as noise, and (ii) OPT: jointly detecting the strongest interfering signals , treating the others as noise.
Edit intent: coherence
Original:  We analyze the expected maximum achievable sum rates over a given area based on the capacity regions of Gaussian point-to-point codes in Poisson distributed wireless networks under two decoding rules , namely (i) IAN : treating interference as noise, and (ii) OPT: jointly detecting the strongest interfering signals , treating the others as noise.
Revised:  We analyze the expected maximum achievable sum rates over a given area based on the capacity regions of Gaussian point-to-point codes in Poisson distributed wireless networks under two decoding rules , namely (i) IAN : treating interference as noise, and jointly detecting the strongest interfering signals , treating the others as noise.
Edit intent: clarity
Original:  We analyze the expected maximum achievable sum rates over a given area based on the capacity regions of Gaussian point-to-point codes in Poisson distributed wireless networks under two decoding rules , namely (i) IAN : treating interference as noise, and (ii) OPT: jointly detecting the strongest interfering signals , treating the others as noise.
Revised:  We analyze the expected maximum achievable sum rates over a given area based on the capacity regions of Gaussian point-to-point codes in Poisson distributed wireless networks under two decoding rules , namely (i) IAN : treating interference as noise, and (ii) OPT: jointly detecting the strongest interfering signals treating the others as noise.
Edit intent: fluency
Original:  We also compare these results to the ones obtained for a scenario where transmitters code their messages at predetermined fixed rates that are tuned to optimize the average spatial throughput , regardless of particular realizations of the network.
Revised:  We also compare these results to the ones obtained for a scenario where transmitters code their messages at predetermined rates that are tuned to optimize the average spatial throughput , regardless of particular realizations of the network.
Edit intent: clarity
Original:  We also compare these results to the ones obtained for a scenario where transmitters code their messages at predetermined fixed rates that are tuned to optimize the average spatial throughput , regardless of particular realizations of the network.
Revised:  We also compare these results to the ones obtained for a scenario where transmitters code their messages at predetermined fixed rates that are chosen to optimize the average spatial throughput , regardless of particular realizations of the network.
Edit intent: clarity
Original:  We also compare these results to the ones obtained for a scenario where transmitters code their messages at predetermined fixed rates that are tuned to optimize the average spatial throughput , regardless of particular realizations of the network.
Revised:  We also compare these results to the ones obtained for a scenario where transmitters code their messages at predetermined fixed rates that are tuned to optimize the expected spatial throughput -- regardless of particular realizations of the network.
Edit intent: clarity
Original:  We analytically show that, when the same decoding rule and network density are considered, the spatial-capacity-achieving scheme always outperforms the spatial throughput obtained with the best predetermined fixed rate strategy.
Revised:  We analytically show that, when the same decoding rule and network density are considered, the cognitive spatial throughput always outperforms the spatial throughput obtained with the best predetermined fixed rate strategy.
Edit intent: clarity
Original:  This extends the idea of a migraine generator region in the brainstem to a larger network and is still simple and explicit enough to be amenable for future mathematical analysis .
Revised:  This extends the idea of a migraine generator region in the brainstem to a larger network and is still simple and explicit enough to open up possibilities for mathematical modeling in the future .
Edit intent: clarity
Original: In this paper we consider the time complexity of adding two n-bit numbers together within the tile self-assembly model.
Revised: In this paper we consider the time complexity of adding two n-bit numbers within the tile self-assembly model.
Edit intent: clarity
Original:  Within this frame work, we examine the time complexity of computing the sum  of 2 n-bit numbers, where the input numbers are encoded in an initial seed assembly, and the output sum is encoded in the final, terminal assembly of the system.
Revised:  Within this frame work, we examine the time complexity of computing the sum of 2 n-bit numbers, where the input numbers are encoded in an initial seed assembly, and the output is encoded in the final, terminal assembly of the system.
Edit intent: clarity
Original:  We show that this problem, along with multiplication , has a worst case lower bound of \Omega(n) in 2D assembly, and \Omega(\sqrt[3]{n}) in 3D assembly.
Revised:  We show that the problems of addition and multiplication have worst case lower bound of \Omega(n) in 2D assembly, and \Omega(\sqrt[3]{n}) in 3D assembly.
Edit intent: clarity
Original:  We show that this problem, along with multiplication , has a worst case lower bound of \Omega(n) in 2D assembly, and \Omega(\sqrt[3]{n}) in 3D assembly.
Revised:  We show that this problem, along with multiplication , has a worst case lower bounds of \Omega(n) in 2D assembly, and \Omega(\sqrt[3]{n}) in 3D assembly.
Edit intent: fluency
Original:  Finally , we consider average case complexity of addition over uniformly distributed n-bit strings and show how to achieve O(\log n) average case time with a simultaneous O(n) worst case run time in 2D.
Revised:  Further , we consider average case complexity of addition over uniformly distributed n-bit strings and show how to achieve O(\log n) average case time with a simultaneous O(n) worst case run time in 2D.
Edit intent: coherence
Original:  These results directly yields forbidden induced subgraphs characterizations of those graphs for which the PoC of every induced subgraph is bounded by t, for t \in \{1,4/ 3 ,3 / 2\ , namely, graphs whose PoC is strictly greater than the PoC of any proper induced subgraph , the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle.
Revised:  These results directly yields forbidden induced subgraphs characterizations of those graphs for which the PoC of every induced subgraph is bounded by some real number t. We obtain forbidden induced subgraph characterizations for every real value t \leq 3 ,3 / 2\ , namely, graphs whose PoC is strictly greater than the PoC of any proper induced subgraph , the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle.
Edit intent: clarity
Original:  These results directly yields forbidden induced subgraphs characterizations of those graphs for which the PoC of every induced subgraph is bounded by t, for t \in \{1,4/ 3 ,3 / 2\ , namely, graphs whose PoC is strictly greater than the PoC of any proper induced subgraph , the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle.
Revised:  These results directly yields forbidden induced subgraphs characterizations of those graphs for which the PoC of every induced subgraph is bounded by t, for t \in \{1,4/ 3 / 2\ , namely, graphs whose PoC is strictly greater than the PoC of any proper induced subgraph , the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle.
Edit intent: coherence
Original:  These results directly yields forbidden induced subgraphs characterizations of those graphs for which the PoC of every induced subgraph is bounded by t, for t \in \{1,4/ 3 ,3 / 2\ , namely, graphs whose PoC is strictly greater than the PoC of any proper induced subgraph , the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle.
Revised:  These results directly yields forbidden induced subgraphs characterizations of those graphs for which the PoC of every induced subgraph is bounded by t, for t \in \{1,4/ 3 ,3 / 2\ , namely, graphs whose price of connectivity is strictly greater than the PoC of any proper induced subgraph , the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle.
Edit intent: clarity
Original:  These results directly yields forbidden induced subgraphs characterizations of those graphs for which the PoC of every induced subgraph is bounded by t, for t \in \{1,4/ 3 ,3 / 2\ , namely, graphs whose PoC is strictly greater than the PoC of any proper induced subgraph , the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle.
Revised:  These results directly yields forbidden induced subgraphs characterizations of those graphs for which the PoC of every induced subgraph is bounded by t, for t \in \{1,4/ 3 ,3 / 2\ , namely, graphs whose PoC is strictly greater than that of any proper induced subgraph , the class of decision problems that can be solved in polynomial time, provided we can make O(\log n) queries to an NP-oracle.
Edit intent: clarity
Original: We prove the existence of a function c :%DIFDELCMD < \N %%%  \to %DIFDELCMD < \N %%%  such that the vertices of every planar graph with maximum degree \Delta can be 3-colored in such a way that each monochromatic component has at most c (\Delta) vertices.
Revised: We prove the existence of a function %DIFDELCMD < \N %%% \to %DIFDELCMD < \N %%% such that the vertices of every planar graph with maximum degree \Delta can be 3-colored in such a way that each monochromatic component has at most c (\Delta) vertices.
Edit intent: clarity
Original: Our work focuses on the extended orbit problem: determining whether a target vector space V may be reached from a  point x under repeated application of a linear transformation A.
Revised: Our work focuses on the extended orbit problem: determining whether a target vector space V may be reached from a starting point x under repeated application of a linear transformation A.
Edit intent: clarity
Original: Our work focuses on the extended orbit problem: determining whether a target vector space V may be reached from a  point x under repeated application of a linear transformation A.
Revised: Our work focuses on the extended orbit problem: determining whether a target vector space V may be reached from a point x under repeated applications of a linear transformation A.
Edit intent: fluency
Original: A pathway-based mean-field theory (PBMFT) that was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys.
Revised: A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys.
Edit intent: coherence
Original:  The new system is hyperbolic with linear convection terms , which is more numerically solvable than the nonlinear convection-diffusion system in the original PBMFT model . Under certain assumptions, the new system can recover the original model.
Revised:  The new system is hyperbolic with linear convection terms . Under certain assumptions, the new system can recover the original model.
Edit intent: coherence
Original:  For this purpose, we propose a systematic framework and start with formulating and optimizing these performance metrics for a single-user case.
Revised:  For this purpose, we propose a systematic framework and start with formulating and optimizing these performance metrics for the single-user case.
Edit intent: fluency
Original:  This framework enables us to analytically compare the performance metrics of users under different system parameters and settings.
Revised:  This framework enables us to analytically compare the performance metrics under different system parameters and settings.
Edit intent: clarity
Original:  Then, we extend the study of feedback-less RLNC schemes to a multi-user broadcast case.
Revised:  Then, we extend the study of feedback-less RLNC schemes to the multi-user broadcast case.
Edit intent: fluency
Original:  Our approach consists in adapting and further developing an established reinforcement learning algorithm called the fitted Q iteration.
Revised:  Our approach consists in adapting an established reinforcement learning algorithm called the fitted Q iteration.
Edit intent: clarity
Original:  Our framework thus put in competition two well-known dynamical properties of scale-free networks: the fast propagation of diseases and the promotion of cooperative behaviours .
Revised:  Our framework thus put in competition two well-known dynamical properties of scale-free networks: the fast propagation of diseases and the promotion of cooperative behaviors .
Edit intent: fluency
Original:  Our results show that when vaccine is perfect scale-free networks enhance the vaccination behaviour with respect to random graphs with homogeneous connectivity patterns.
Revised:  Our results show that when vaccine is perfect scale-free networks enhance the vaccination behavior with respect to random graphs with homogeneous connectivity patterns.
Edit intent: fluency
Original:  Using within-patient longitudinal sequence data, we find that the evolution of drug resistance in HIV occurs by one mutation at a time and involves both hard and soft selective sweeps.
Revised:  By analyzing within-patient longitudinal sequence data, we find that the evolution of drug resistance in HIV occurs by one mutation at a time and involves both hard and soft selective sweeps.
Edit intent: clarity
Original:  Using within-patient longitudinal sequence data, we find that the evolution of drug resistance in HIV occurs by one mutation at a time and involves both hard and soft selective sweeps.
Revised:  Using within-patient longitudinal sequence data, we find that the evolution of drug resistance usually occurs by the fixation of one drug-resistance mutation at a time and involves both hard and soft selective sweeps.
Edit intent: clarity
Original:  Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be 1.5 x 10^5 (95\% confidence interval 0.8 x 10^5, 4.8 x 10^5 ).
Revised:  Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be 1.5 * 10^5 (95\% confidence interval 0.8 x 10^5, 4.8 x 10^5 ).
Edit intent: clarity
Original:  Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be 1.5 x 10^5 (95\% confidence interval 0.8 x 10^5, 4.8 x 10^5 ).
Revised:  Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be 1.5 x 10^5 (95\% confidence interval 0.8 * 10^5, 4.8 x 10^5 ).
Edit intent: clarity
Original:  Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be 1.5 x 10^5 (95\% confidence interval 0.8 x 10^5, 4.8 x 10^5 ).
Revised:  Using the frequency of occurrence of hard and soft sweeps we estimate the effective population size of HIV to be 1.5 x 10^5 (95\% confidence interval 0.8 x 10^5, 4.8 * 10^5 ).
Edit intent: clarity
Original:  We also observe that genetic diversity at non-synonymous sites recovers after a selective sweep to its pre-sweep value within 18 months, whereas that at synonymous sites still remains depressed after this time period .
Revised:  Finally, our fourth observation is that genetic diversity at non-synonymous sites recovers after a selective sweep to its pre-sweep value within 18 months, whereas that at synonymous sites still remains depressed after this time period .
Edit intent: coherence