wanyu/IteraTeR_v2 huggingface dataset:
Original:  Results: We present exact analytical and simulation-based results for the time to extinction of a stochastic model of population dynamics that includes growth, environmental stochasticity and localized density-dependent competition .
Revised:  Results: We present exact analytical and simulation-based results for extinction times of our stochastic model and compare the different effects of environmental stochasticity and localized density-dependent competition .
Edit intent: clarity
Original:  Results: We present exact analytical and simulation-based results for the time to extinction of a stochastic model of population dynamics that includes growth, environmental stochasticity and localized density-dependent competition .
Revised:  Results: We present exact analytical and simulation-based results for the time to extinction of a stochastic model of population dynamics that includes growth, environmental stochasticity and intrinsic demographic stochasticity .
Edit intent: clarity
Original:  Namely, even if the majority of the nodes are controlled by a malicious adversary and the topology of the network is changing at each round, then as long as there is some path of non-corrupted nodes connecting the sender and receiver at each round (though this path may change at every round) we construct a protocol with bounded memory per processor that achieves optimal transfer rate and negligible decoding error.
Revised:  Namely, even if the majority of the nodes are controlled by a malicious adversary and the topology of the network is changing at each round, then as long as there is some path of non-corrupted nodes connecting the sender and receiver through honest nodes (though this path may change at every round) we construct a protocol with bounded memory per processor that achieves optimal transfer rate and negligible decoding error.
Edit intent: clarity
Original:  Namely, even if the majority of the nodes are controlled by a malicious adversary and the topology of the network is changing at each round, then as long as there is some path of non-corrupted nodes connecting the sender and receiver at each round (though this path may change at every round) we construct a protocol with bounded memory per processor that achieves optimal transfer rate and negligible decoding error.
Revised:  Namely, even if the majority of the nodes are controlled by a malicious adversary and the topology of the network is changing at each round, then as long as there is some path of non-corrupted nodes connecting the sender and receiver at each round (though this path may change at every round) we construct a protocol with bounded memory per processor that achieves optimal transfer rate with negligible decoding error.
Edit intent: fluency
Original:  This protocol will transmit polynomially many messages of polynomial size with constant overhead per bit.
Edit intent: coherence
Original: We present Kovalenko's Full-Rank Limit as a tight probabilistic lower-bound for Error-Performances of Low-Density Parity-Check codes and Luby Transform codes over Binary Erasure Channels.
Revised: We present Kovalenko's full-rank limit as a tight probabilistic lower-bound for Error-Performances of Low-Density Parity-Check codes and Luby Transform codes over Binary Erasure Channels.
Edit intent: fluency
Original:  Associated with the limit, we derive its Full-Rank Overhead as a tight lower-bound for Stable Overheads for successful Maximum-Likelihood Decoding of the codes.
Revised:  Associated with the limit, we derive a full-rank overhead as a lower bound for stable overheads for successful maximum-likelihood decoding of the codes.
Edit intent: clarity
Original:  The question is motivated by a question in CR geometry.
Revised:  The question is motivated by a problem in CR geometry.
Edit intent: clarity
Original:  It is known that the sharp estimate d \leq 2N-3 holds .
Revised:  A sharp estimate d \leq 2N-3 holds .
Edit intent: clarity
Original:  In particular, a complete classification of polynomials minimizing N is an important first step in the complete classification of CR maps of spheres in different dimensions.
Revised:  In particular, a complete classification of polynomials minimizing N is an important first step in the complete classification of CR maps between spheres in different dimensions.
Edit intent: clarity
Original: For wireless transmission, the assumption that the transmitter always obtains the channel state information (CSI)  is unreasonable because of feedback delays, estimation error and quantization error.
Revised: For wireless transmission, the assumption that the transmitter always receives the channel state information (CSI) is unreasonable because of feedback delays, estimation error and quantization error.
Edit intent: clarity
Original: For wireless transmission, the assumption that the transmitter always receives the channel state information (CSI) perfectly is unreasonable because of feedback delays, estimation error and quantization error.
Revised: For wireless transmission, the assumption that the transmitter always obtains the channel state information (CSI) perfectly is unreasonable because of feedback delays, estimation error and quantization error.
Edit intent: clarity
Original: For wireless transmission, the assumption that the transmitter always receives the channel state information (CSI) perfectly is unreasonable because of feedback delays, estimation error and quantization error.
Revised: For wireless transmission, the assumption that the transmitter always receives the channel state information (CSI) is unreasonable because of feedback delays, estimation error and quantization error.
Edit intent: clarity
Original:  In order to avoid the system's degradation, a more concrete analysis of wireless transmission schedule under imperfect CSI is needed.
Revised:  In order to avoid the system's degradation, a more concrete analysis of wireless transmission under imperfect CSI is needed.
Edit intent: clarity
Original:  In this paper, the downlink transmission based on parital channel state information due to feedback delays in a multiuser Orthogonal Frequency Division Modulation (MU-OFDM) based CR system is investigated.
Revised:  In this paper, the downlink transmission based on partial channel state information due to feedback delays in a multiuser Orthogonal Frequency Division Modulation (MU-OFDM) based CR system is investigated.
Edit intent: fluency
Original:  The more the partial CSI is correlated to the real CSI, the higher data rate  achieved.
Revised:  The more the partial CSI is correlated to the real CSI, the higher data rate is achieved.
Edit intent: coherence
Original:  Some prescribed quality of service (QoS) requirements will not be satisfied.
Revised:  Some prescribed quality of service (QoS) requirements may not be satisfied.
Edit intent: clarity
Original:  In this paper, the downlink transmission based on partial channel state information due to feedback delays in a multiuser Orthogonal Frequency Division Modulation (MU-OFDM) based CR system is investigated.
Revised:  In this paper, the downlink transmission based on partial channel state information due to feedback delays in a multiuser Orthogonal Frequency Division Multiplexing (MU-OFDM) based CR system is investigated.
Edit intent: clarity
Original: A ``pairing function'' J associates a unique natural number z to any two natural numbers x,y such that for two ``unpairing functions'' K and L, the equalities K(J(x,y))=x, L(J(x,y))=y and J(K(z),L(z))=z hold.
Revised: A "pairing function" J associates a unique natural number z to any two natural numbers x,y such that for two ``unpairing functions'' K and L, the equalities K(J(x,y))=x, L(J(x,y))=y and J(K(z),L(z))=z hold.
Edit intent: fluency
Original: A ``pairing function'' J associates a unique natural number z to any two natural numbers x,y such that for two ``unpairing functions'' K and L, the equalities K(J(x,y))=x, L(J(x,y))=y and J(K(z),L(z))=z hold.
Revised: A ``pairing function'' J associates a unique natural number z to any two natural numbers x,y such that for two "unpairing functions" K and L, the equalities K(J(x,y))=x, L(J(x,y))=y and J(K(z),L(z))=z hold.
Edit intent: fluency
Original:  The paper is organized as a self-contained literate Prolog program, available at URL %DIFDELCMD < {\em %%% Keywords: logic programming and computational mathematics, pairing/unpairing functions, encodings of boolean functions, binary decision diagrams, natural number representations of truth tables
Revised:  The paper is organized as a self-contained literate Prolog program, available at URL %DIFDELCMD < {\em %%% Keywords: logic programming and computational mathematics, pairing/unpairing functions, encodings of boolean functions, binary decision diagrams, natural number representations of truth tables
Edit intent: fluency
Original:  Optimal allocating transmit power, bits and subcarriers among cognitive radio users  can achieve high throughput while satisfying the given quality of services (QoS) requirements .
Revised:  Optimal allocating transmit power, bits and subcarriers among cognitive radio users can achieve high throughput while satisfying the given quality of services (QoS) requirement .
Edit intent: fluency
Original:  The problem of dynamic allocation of transmit power, bits and secondary users in multiuser OFDM  systems is a combinatorial optimization problem and is computationally complex.
Revised:  The problem of dynamic resource allocation in multiuser OFDM systems is a combinatorial optimization problem and is computationally complex.
Edit intent: clarity
Original:  Accordingly, a simple while efficient algorithm is needed.
Revised:  In order to solve the resource allocation problem efficiently, efficient and simple algorithms are needed.
Edit intent: clarity
Original:  In order to achieve better performance, we need to select appropriate local search method and evolutionary operators for a memetic algorithm.
Revised:  In order to achieve better performance, we need to choose appropriate local search method and evolutionary operators for a memetic algorithm.
Edit intent: fluency
Original:  Accordingly, we derive a simple while efficient memetic algorithm with appropriate local search method and evolutionary operators for the resource allocation problem .
Revised:  Appropriate local search and evolutionary operators for the resource allocation problem .
Edit intent: coherence
Original:  Accordingly, we derive a simple while efficient memetic algorithm with appropriate local search method and evolutionary operators for the resource allocation problem .
Revised:  Accordingly, we derive a simple while efficient memetic algorithm with appropriate local search method and evolutionary operators are derived for the proposed MA .
Edit intent: clarity
Original:  Flow is weighted away from blockages , inducing an effective interaction  .
Revised:  Flow is weighted away from blocked arteries , inducing an effective interaction .
Edit intent: clarity
Original:  Our main aim is to determine if there is crossover behavior or a phase transition as the arterial tree becomes increasingly obstructed.
Edit intent: coherence
Original:  We discuss free-flowing and heavily congested limits and examine the change from free-flow to congestion using numerics.
Revised:  We discuss free flowing and heavily congested limits and examine the change from free-flow to congestion using numerics.
Edit intent: fluency
Original:  We discuss free-flowing and heavily congested limits and examine the change from free-flow to congestion using numerics.
Revised:  We discuss free-flowing and heavily congested limits and examine the transition from free flow to congestion using numerics.
Edit intent: fluency
Original:   An order parameter for the non-equilibrium critical behavior is identified as the overlap between blockagesshadows.
Revised:  An order parameter for non-equilibrium critical behavior is identified as the overlap between blockagesshadows.
Edit intent: fluency
Original:  Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide , by a fixed point method, a constructive method for effectively computing their unique solution.
Revised:  Using this new point of view allows us to prove that these equations are well-posed on any finite time interval and to provide a constructive method for effectively computing their unique solution.
Edit intent: coherence
Original:  These results shed some new light on such neural mass models as the one of Jansen and Rit \mbox{ jansen-rit:95 : their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis.
Revised:  These results shed some new light on such neural mass models as the one of Jansen and Rit \mbox{ jansen-rit:95 : their dynamics appears as a coarse approximation of the much richer dynamics that emerges from our analysis.
Edit intent: fluency
Original:  The mechanism follows a Kramers  process, whereby the complementary chains overcome a potential barrier through Brownian motion.
Revised:  The mechanism follows a Kramers ' process, whereby the complementary chains overcome a potential barrier through Brownian motion.
Edit intent: fluency
Original:  For the DNA of bacteriophages T7, T4 and PhiX174 \phiX174 as well as that of Escherichia coli , the bimolecular rate k2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single-strands : k_2 \sim N^\alpha, \prop  with an experimentally determined exponent \alpha = 0.51 \pm 0.01.
Revised:  For the DNA of bacteriophages T7, T4 and \phiX174 as well as that of Escherichia coli , the bimolecular rate k2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single-strands : k_2 \sim N^\alpha, \prop with an experimentally determined exponent \alpha = 0.51 \pm 0.01.
Edit intent: coherence
Original:  For the DNA of bacteriophages T7, T4 and PhiX174 \phiX174 as well as that of Escherichia coli , the bimolecular rate k2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single-strands : k_2 \sim N^\alpha, \prop  with an experimentally determined exponent \alpha = 0.51 \pm 0.01.
Revised:  For the DNA of bacteriophages T7, T4 and PhiX174 \phiX174 as well as for Escherichia coli DNA , the bimolecular rate k2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single-strands : k_2 \sim N^\alpha, \prop with an experimentally determined exponent \alpha = 0.51 \pm 0.01.
Edit intent: clarity
Original:  For the DNA of bacteriophages T7, T4 and PhiX174 \phiX174 as well as that of Escherichia coli , the bimolecular rate k2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single-strands : k_2 \sim N^\alpha, \prop  with an experimentally determined exponent \alpha = 0.51 \pm 0.01.
Revised:  For the DNA of bacteriophages T7, T4 and PhiX174 \phiX174 as well as that of Escherichia coli , the bimolecular rate k_2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single-strands : k_2 \sim N^\alpha, \prop with an experimentally determined exponent \alpha = 0.51 \pm 0.01.
Edit intent: fluency
Original:  For the DNA of bacteriophages T7, T4 and PhiX174 \phiX174 as well as that of Escherichia coli , the bimolecular rate k2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single-strands : k_2 \sim N^\alpha, \prop  with an experimentally determined exponent \alpha = 0.51 \pm 0.01.
Revised:  For the DNA of bacteriophages T7, T4 and PhiX174 \phiX174 as well as that of Escherichia coli , the bimolecular rate k2 of the reaction increases as a power law of the average degree of polymerization <N> of the reacting single- strands : k_2 \sim N^\alpha, \prop with an experimentally determined exponent \alpha = 0.51 \pm 0.01.
Edit intent: fluency
Original:  This length dependence results from a thermodynamic excluded-volume effect.
Revised:  The length dependence results from a thermodynamic excluded-volume effect.
Edit intent: fluency
Original:  The value theoretically predicted for the exponent is \alpha = 1-\nu \theta_2, where \nu is Flory  swelling exponent ( \nu \approx 0.588) and \theta_2  a critical exponent introduced by des Cloizeaux (\theta_2 \approx 0.82), yielding \alpha = 0.52 \pm 0.01  in agreement with the experimental results.
Revised:  The value theoretically predicted for the exponent is \alpha = 1-\nu \theta_2, where \nu is Flory swelling exponent ( nu approx 0.588) and \theta_2 a critical exponent introduced by des Cloizeaux (\theta_2 \approx 0.82), yielding \alpha = 0.52 \pm 0.01 in agreement with the experimental results.
Edit intent: fluency
Original:  The value theoretically predicted for the exponent is \alpha = 1-\nu \theta_2, where \nu is Flory  swelling exponent ( \nu \approx 0.588) and \theta_2  a critical exponent introduced by des Cloizeaux (\theta_2 \approx 0.82), yielding \alpha = 0.52 \pm 0.01  in agreement with the experimental results.
Revised:  The value theoretically predicted for the exponent is \alpha = 1-\nu \theta_2, where \nu is Flory swelling exponent ( \nu \approx 0.588) and \theta_2 is a critical exponent introduced by des Cloizeaux (\theta_2 \approx 0.82), yielding \alpha = 0.52 \pm 0.01 in agreement with the experimental results.
Edit intent: fluency
Original:  The value theoretically predicted for the exponent is \alpha = 1-\nu \theta_2, where \nu is Flory  swelling exponent ( \nu \approx 0.588) and \theta_2  a critical exponent introduced by des Cloizeaux (\theta_2 \approx 0.82), yielding \alpha = 0.52 \pm 0.01  in agreement with the experimental results.
Revised:  The value theoretically predicted for the exponent is \alpha = 1-\nu \theta_2, where \nu is Flory swelling exponent ( \nu \approx 0.588) and \theta_2 a critical exponent introduced by des Cloizeaux (\theta_2 \approx 0.82), yielding \alpha = 0.52 \pm 0.01 , in agreement with the experimental results.
Edit intent: fluency
Original:  An intriguing algorithmic consequence is that although the problem is NP-hard, we can find cutsizes that are asymptotically within a factor 1 of optimal -- and possibly even the optimum itself -- in polynomial time for typical instances near the phase transition.
Revised:  An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 of optimal -- and possibly even the optimum itself -- in polynomial time for typical instances near the phase transition.
Edit intent: clarity
Original:  We prove that it is decidable whether a given k-automatic sequence is squarefree (or overlap-free , or cubefree, etc.)
Revised:  We prove that it is decidable whether a given k-automatic sequence is overlap-free (or squareefree , or cubefree, etc.)
Edit intent: fluency
Original: In this paper we examine decision problems associated with various classes of convex languages, studied by Ang and Brzozowski (under the name "continuous languages '' ).
Revised: In this paper we examine decision problems associated with various classes of convex languages, studied by Ang and Brzozowski (under the name "continuous languages " ).
Edit intent: fluency
Original: We develop equilibrium and kinetic theories that describe the dynamic assembly of viral capsid proteins on a charged central core, such as a charge-functionalized nanoparticle .
Revised: We develop equilibrium and kinetic theories that describe the assembly of viral capsid proteins on a charged central core, such as a charge-functionalized nanoparticle .
Edit intent: clarity
Original:  We model interactions between capsid proteins and nanoparticle surfaces as the adsorption of a polyelectrolyte brush onto a surface with opposite charge, using the full nonlinear Poisson Boltzmann equation.
Revised:  We model interactions between capsid proteins and nanoparticle surfaces as the interaction of polyelectrolyte brushes with opposite charge, using the full nonlinear Poisson Boltzmann equation.
Edit intent: clarity
Original:  We model interactions between capsid proteins and nanoparticle surfaces as the adsorption of a polyelectrolyte brush onto a surface with opposite charge, using the full nonlinear Poisson Boltzmann equation.
Revised:  We model interactions between capsid proteins and nanoparticle surfaces as the adsorption of a polyelectrolyte brush onto a surface with opposite charge, using the nonlinear Poisson Boltzmann equation.
Edit intent: clarity
Original:  However, the model predicts a stronger dependence of nanoparticle incorporation efficiency on functionalized charge density then measured an experiment;
Revised:  However, the models predict a stronger dependence of nanoparticle incorporation efficiency on functionalized charge density then measured an experiment;
Edit intent: coherence
Original:  In addition to discussing future something design of applications for nanoparticle capsid systems, we discuss broader implications for understanding assembly around charged cores such as nucleic acids.
Revised:  In addition to discussing future experiments for nanoparticle-capsid systems, we discuss broader implications for understanding assembly around charged cores such as nucleic acids.
Edit intent: clarity
Original:  Enabled by a novel means of fingerprinting  trajectories, our study reveals a profound insensitivity of folding mechanisms to the omission of non-native interactions.
Revised:  Enabled by a novel means of fingerprinting folding trajectories, our study reveals a profound insensitivity of folding mechanisms to the omission of non-native interactions.
Edit intent: fluency
Original:  We find instead that the crucial factor in discriminating among folding pathways is the heterogeneity of native contact energies . Non-native attractions can shape overall kinetics by stabilizing the unfolded state, but they do not affect even detailed features of routes to the native state .
Revised:  We find instead that the crucial factor in discriminating among topological pathways is the heterogeneity of native contact energies . Non-native attractions can shape overall kinetics by stabilizing the unfolded state, but they do not affect even detailed features of routes to the native state .
Edit intent: clarity
Original:  We find instead that the crucial factor in discriminating among folding pathways is the heterogeneity of native contact energies . Non-native attractions can shape overall kinetics by stabilizing the unfolded state, but they do not affect even detailed features of routes to the native state .
Revised:  We find instead that the crucial factor in discriminating among folding pathways is the heterogeneity of native contact energies .
Edit intent: coherence
Original:  First, we prove hardness results for the nonuniversality and inequivalence problem for these NFAs.
Revised:  First, we prove hardness results for the nonuniversality and inequivalence problems for these NFAs.
Edit intent: fluency
Original:  We study the behavior of maximal blocks of \Delta letters in \mathbf\mb w, and prove the following: let (i_k,j_k) denote the starting and ending positions, respectively, of the k'th maximal \Delta-block in \mathbf \mb w.
Revised:  We study the behavior of maximal blocks of \Delta letters in \mathbf\mb w, and prove the following: let (i_k,j_k) denote the starting and ending positions, respectively, of the k'th maximal \Delta-block in \mb w.
Edit intent: fluency
Original:  Then k\to\infty (j_k/i_k) is algebraic if \mathbf \mb w is morphic, and rational if \mathbf \mb w is automatic.
Revised:  Then k\to\infty (j_k/i_k) is algebraic if \mb w is morphic, and rational if \mathbf \mb w is automatic.
Edit intent: fluency
Original:  Then k\to\infty (j_k/i_k) is algebraic if \mathbf \mb w is morphic, and rational if \mathbf \mb w is automatic.
Revised:  Then k\to\infty (j_k/i_k) is algebraic if \mathbf \mb w is morphic, and rational if \mb w is automatic.
Edit intent: fluency