wanyu/IteraTeR_v2 huggingface dataset:
Original:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Revised:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Edit intent: clarity
Original:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a selective advantage s arising at the population frontier in the limit of small selective advantage s.
Revised:  We consider an arbitrary time dependence of the range expansion radius R(t)=R_0(1+t/t^*)^{\Theta}, where t^* is a cross-over time, \Theta is a growth exponent, and R_0 is the initial radius . Guided by recent results for two-dimensional inflating range expansions, we identify the key dimensionless parameters and universal functions that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier in the limit of small selective advantage s.
Edit intent: fluency
Original:  We focus on linearly inflating expansions (\Theta=1 spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) , treadmilling expansions (\Theta=0, with cells in the interior removed by apoptosis or a similar process) , and "marginally inflating" (\Theta=1/2) expansions .
Revised:  We focus on linearly inflating expansions (\Theta=1 spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations (\Theta=0, with cells in the interior removed by apoptosis or a similar process) , and "marginally inflating" (\Theta=1/2) expansions .
Edit intent: clarity
Original:  We find that inflating fronts can enhance mutant survival probabilities by factors of 100 or more  .
Revised:  We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more .
Edit intent: clarity
Original:  Availability: PMCE is freely available at URL The code to replicate all the analyses is available at: URL Contacts: daniele.ramazzotti@unimib.it, alex.graudenzi@ibfm.cnr.it 
Revised:  Availability: PMCE is freely available at URL in addition to the code to replicate all the analyses is available at: URL Contacts: daniele.ramazzotti@unimib.it, alex.graudenzi@ibfm.cnr.it 
Edit intent: clarity
Original:  Availability: PMCE is freely available at URL The code to replicate all the analyses is available at: URL Contacts: daniele.ramazzotti@unimib.it, alex.graudenzi@ibfm.cnr.it 
Revised:  Availability: PMCE is freely available at URL The code to replicate all the analyses is available at: URL Contacts: daniele.ramazzotti@unimib.it, alex.graudenzi@ibfm.cnr.it .
Edit intent: fluency
Original:  We consider standard smoothness regularization based on H^1- or H^2 -norms of the velocity field .
Revised:  We consider standard smoothness regularization based on H^1- or H^2 -seminorms .
Edit intent: clarity
Original:   We use a preconditioned,  matrix-free, inexact Gauss-Newton-Krylov reduced space sequential quadratic programming (RSQP) method for numerical optimization.
Revised:  We use a preconditioned, matrix-free, inexact Newton-Krylov method for numerical optimization.
Edit intent: coherence
Original:  A parameter continuation , which can intuitively be informed about regularity requirements, is designed to estimate an optimal regularization parameter.
Revised:  A parameter continuation is designed to estimate an optimal regularization parameter.
Edit intent: clarity
Original:  Regularity is ensured by controlling geometric features of the deformation field.
Revised:  Regularity is ensured by controlling the geometric properties of the deformation field.
Edit intent: clarity
Original:  Overall, we arrive at a black-box solver that exploits computational tools  precisely tailored for solving the optimality system.
Revised:  Overall, we arrive at a black-box solver that exploits computational tools that are precisely tailored for solving the optimality system.
Edit intent: fluency
Original:  We formulate the non-rigid image registration problem as a problem of optimal control.
Revised:  We formulate the nonrigid image registration problem as a problem of optimal control.
Edit intent: fluency
Original:  Tikhonov regularization  ensures well-posedness.
Revised:  Tikhonov regularization on the control ensures well-posedness.
Edit intent: clarity
Original:  We use a Fourier pseudo-spectral discretization in space and a Chebyshev pseudo-spectral discretization in time.
Revised:  We use a Fourier pseudospectral discretization in space and a Chebyshev pseudo-spectral discretization in time.
Edit intent: fluency
Original:  We use a Fourier pseudo-spectral discretization in space and a Chebyshev pseudo-spectral discretization in time.
Revised:  We use a Fourier pseudo-spectral discretization in space and a Chebyshev pseudospectral discretization in time.
Edit intent: fluency
Original:  The latter allows us to reduce the number of unknowns and enables the time-adaptive inversion for non-stationary velocity fields.
Edit intent: coherence
Original:  Overall, we arrive at a black-box solver that exploits computational tools that are precisely tailored for solving the optimality system .
Revised:  Overall, we arrive at a black-box solver .
Edit intent: coherence
Original:  We compare the designed Newton-Krylov methods with a globalized Picard method ( preconditioned gradient descent ) .
Revised:  We compare the designed Newton-Krylov methods with a globalized preconditioned gradient descent ) .
Edit intent: clarity
Original:  We benchmark the performance of the most scalable methods for the Poisson problem  : the Fast Fourier Transform (FFT), the Fast Multipole Method (FMM), the geometric multigrid (GMG) and algebraic multigrid (AMG).
Revised:  We benchmark the performance of the scalable methods for the Poisson problem : the Fast Fourier Transform (FFT), the Fast Multipole Method (FMM), the geometric multigrid (GMG) and algebraic multigrid (AMG).
Edit intent: clarity
Original:   The GMG and FMM are novel parallel schemes using high-order approximation  for Poisson problems developed in our group.
Revised:  The GMG and FMM are novel parallel schemes using high-order approximation schemes for Poisson problems developed in our group.
Edit intent: clarity
Original:  Our results show that FFT is the method of choice for smooth source functions that can be resolved with a uniform mesh . However, it loses its performance in the presence of highly localized features in the source function .
Revised:  Our results indicate that FFT is the method of choice for smooth source functions that can be resolved with a uniform mesh . However, it loses its performance in the presence of highly localized features in the source function .
Edit intent: clarity
Original:  Our results show that FFT is the method of choice for smooth source functions that can be resolved with a uniform mesh . However, it loses its performance in the presence of highly localized features in the source function .
Revised:  Our results show that FFT is the method of choice for smooth source functions that require uniform resolution . However, it loses its performance in the presence of highly localized features in the source function .
Edit intent: clarity
Original:  Our results show that FFT is the method of choice for smooth source functions that can be resolved with a uniform mesh . However, it loses its performance in the presence of highly localized features in the source function .
Revised:  Our results show that FFT is the method of choice for smooth source functions that can be resolved with a uniform mesh . However, FFT loses its performance in the presence of highly localized features in the source function .
Edit intent: coherence
Original:  Our results show that FFT is the method of choice for smooth source functions that can be resolved with a uniform mesh . However, it loses its performance in the presence of highly localized features in the source function .
Revised:  Our results show that FFT is the method of choice for smooth source functions that can be resolved with a uniform mesh . However, it loses its performance advantage when the source function has highly localized features in the source function .
Edit intent: clarity
Original: From molecular dynamics and quantum chemistry, to plasma physics and computational astrophysics, Poisson solvers in the unit cube are used in many applications in computational science and engineering.
Edit intent: coherence
Original:  In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the Fast Fourier Transform (FFT), the Fast Multipole Method (FMM), the geometric multigrid (GMG)  and algebraic multigrid (AMG).
Revised:  In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the fast Fourier transform (FFT), the Fast Multipole Method (FMM), the geometric multigrid (GMG) and algebraic multigrid (AMG).
Edit intent: fluency
Original:  In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the Fast Fourier Transform (FFT), the Fast Multipole Method (FMM), the geometric multigrid (GMG)  and algebraic multigrid (AMG).
Revised:  In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the Fast Fourier Transform (FFT), the fast multipole method (FMM), the geometric multigrid (GMG) and algebraic multigrid (AMG).
Edit intent: fluency
Original:  In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the Fast Fourier Transform (FFT), the Fast Multipole Method (FMM), the geometric multigrid (GMG)  and algebraic multigrid (AMG).
Revised:  In this work, we benchmark and discuss the performance of the scalable methods for the Poisson problem which are used widely in practice: the Fast Fourier Transform (FFT), the Fast Multipole Method (FMM), the geometric multigrid (GMG) , and algebraic multigrid (AMG).
Edit intent: fluency
Original:  The GMG and FMM are novel parallel schemes using high-order approximation schemes for Poisson problems with continuous forcing functions (the source or right-hand side).
Revised:  The GMG and FMM are parallel solvers that use high-order approximation schemes for Poisson problems with continuous forcing functions (the source or right-hand side).
Edit intent: clarity
Original:  We have tested all of the methods with different source functions (the right hand side in the Poisson problem).
Revised:  We have tested all of the methods with different source functions (the right-hand side in the Poisson problem).
Edit intent: fluency
Original: We study fixation in large, but finite  populations with two types, and dynamics governed by birth-death processes.
Revised: We study fixation in large, but finite , populations with two types, and dynamics governed by birth-death processes.
Edit intent: fluency
Original:  By considering a restricted class of such processes, which includes most classical evolutionary processes, we derive a continuous approximation for the probability of fixation that is valid beyond the weak-selection (WS) limit.
Revised:  By considering a restricted class of such processes, we derive a continuous approximation for the probability of fixation that is valid beyond the weak-selection (WS) limit.
Edit intent: clarity
Original:  Indeed, in the derivation three regimes naturally appear: selection-driven, balanced, and quasi-neutral --- the latter two require WS, while the former can appear with or without WS. From the continuous approximations, we then obtain asymptotic approximations for evolutions with at most one equilibrium, in the selection-driven regime, that does not preclude a weak-selection regime.
Revised:  From the continuous approximations, we then obtain asymptotic approximations for evolutions with at most one equilibrium, in the selection-driven regime, that does not preclude a weak-selection regime.
Edit intent: coherence
Original:  Indeed, in the derivation three regimes naturally appear: selection-driven, balanced, and quasi-neutral --- the latter two require WS, while the former can appear with or without WS. From the continuous approximations, we then obtain asymptotic approximations for evolutions with at most one equilibrium, in the selection-driven regime, that does not preclude a weak-selection regime.
Revised:  Indeed, in the derivation three regimes naturally appear: selection-driven, balanced, and quasi-neutral --- the latter two require WS, while the former can appear with or without WS. From the continuous approximations, we then obtain asymptotic approximations for evolutionary dynamics with at most one equilibrium, in the selection-driven regime, that does not preclude a weak-selection regime.
Edit intent: clarity
Original:  We also show that  outside of the weak-selection regime the dynamics of large populations can have very little resemblance to the infinite population case .
Revised:  We also show that , outside of the weak-selection regime the dynamics of large populations can have very little resemblance to the infinite population case .
Edit intent: fluency
Original:  In addition, we also show results for the case of two equilibria.
Revised:  In addition, we also present results for the case of two equilibria.
Edit intent: clarity
Original:  Finally, we present a continuous restatement of the definition of an ESS_N strategy, that is valid for large populations .
Revised:  Finally, we present a continuous restatement of the definition of an ESS .
Edit intent: clarity
Original: Using a structural default model considered in Lipton and Sepp ( 2009 ) we propose a new approach to introducing correlated jumps into this framework.
Revised: The structural default model considered in Lipton and Sepp ( 2009 ) we propose a new approach to introducing correlated jumps into this framework.
Edit intent: fluency
Original: Using a structural default model considered in Lipton and Sepp ( 2009 ) we propose a new approach to introducing correlated jumps into this framework.
Revised: Using a structural default model of Lipton and Sepp ( 2009 ) we propose a new approach to introducing correlated jumps into this framework.
Edit intent: clarity
Original: Using a structural default model considered in Lipton and Sepp ( 2009 ) we propose a new approach to introducing correlated jumps into this framework.
Revised: Using a structural default model considered in Lipton and Sepp , 2009 ) we propose a new approach to introducing correlated jumps into this framework.
Edit intent: fluency
Original: Although several measurements and analyses are done to support the idea that the brain is energy-optimized, there is one disturbing, contradictory observation: In theory, computation limited by thermal noise can occur as cheaply as ~2.9\cdot 10^{-21} joules per bit (kTln2).
Revised: Although several measurements and analyses support the idea that the brain is energy-optimized, there is one disturbing, contradictory observation: In theory, computation limited by thermal noise can occur as cheaply as ~2.9\cdot 10^{-21} joules per bit (kTln2).
Edit intent: clarity
Original:  Unfortunately, for a neuron , the ostensible discrepancy from this minimum is startling -
Revised:  Unfortunately, for a neuron the ostensible discrepancy from this minimum is startling -
Edit intent: fluency
Original:  Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise , (kT)^{1/2 . Moreover, when computation is defined as the addition of activated fNa's,  a biophysically plausible mechanism produces the appropriate number of bits for the cost to hit the minimumjoules .
Revised:  Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise . Moreover, when computation is defined as the addition of activated fNa's, a biophysically plausible mechanism produces the appropriate number of bits for the cost to hit the minimumjoules .
Edit intent: coherence
Original:  Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise , (kT)^{1/2 . Moreover, when computation is defined as the addition of activated fNa's,  a biophysically plausible mechanism produces the appropriate number of bits for the cost to hit the minimumjoules .
Revised:  Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise , (kT)^{1/2 . Moreover, defining computation as the addition of activated fNa's, a biophysically plausible mechanism produces the appropriate number of bits for the cost to hit the minimumjoules .
Edit intent: coherence
Original:  Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise , (kT)^{1/2 . Moreover, when computation is defined as the addition of activated fNa's,  a biophysically plausible mechanism produces the appropriate number of bits for the cost to hit the minimumjoules .
Revised:  Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise , (kT)^{1/2 . Moreover, when computation is defined as the addition of activated fNa's, yields a biophysically plausible mechanism produces the appropriate number of bits for the cost to hit the minimumjoules .
Edit intent: fluency
Original:  Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise , (kT)^{1/2 . Moreover, when computation is defined as the addition of activated fNa's,  a biophysically plausible mechanism produces the appropriate number of bits for the cost to hit the minimumjoules .
Revised:  Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise , (kT)^{1/2 . Moreover, when computation is defined as the addition of activated fNa's, a biophysically plausible mechanism for approaching the desired minimum .
Edit intent: clarity
Original:  This mechanism, requiring something like the electrical engineer's equalizer (not much more than the action potential generating conductances), only operates just at or just below threshold.
Revised:  This mechanism, requiring something like the electrical engineer's equalizer (not much more than the action potential generating conductances), only operates at threshold.
Edit intent: clarity
Original:  This active filter modifies the last few synaptic excitations, providing barely enough energy to transport the last set of mostly sub-threshold gating charges .
Revised:  This active filter modifies the last few synaptic excitations, providing barely enough energy to allow the last sub-threshold gating charges .
Edit intent: clarity
Original:  This active filter modifies the last few synaptic excitations, providing barely enough energy to transport the last set of mostly sub-threshold gating charges .
Revised:  This active filter modifies the last few synaptic excitations, providing barely enough energy to transport the last set of mostly sub-threshold gating charge to transport .
Edit intent: clarity
Original:  That is, the last, threshold-achieving S4-subunit activation requires an energy that matches the information being provided by the last few synaptic events, a ratio that is  kTln2 joules per bit.
Revised:  That is, the last, threshold-achieving S4-subunit activation requires an energy that matches the information being provided by the last few synaptic events, a ratio that is near kTln2 joules per bit.
Edit intent: clarity
Original:  We propose an ontology of mathematical knowledge, covering  wide range of fields of mathematics.
Revised:  We propose an ontology of mathematical knowledge, covering a wide range of fields of mathematics.
Edit intent: fluency
Original:  Indeed, we consider approximation with respect to the fully one-way LOCC norm or relative entropy, compared to the parallel one-way LOCC norm of earlier work, while the error bound is kept essentially the same.
Revised:  Indeed, we consider approximation with respect to the fully one-way LOCC norm or relative entropy, compared to the parallel one-way LOCC measurements of earlier work, while the error bound is kept essentially the same.
Edit intent: clarity
Original:  Of particular interest are  a quasipolynomial-time algorithm which distinguishes multipartite density matrices with entanglement larger than a small constant amount (measured with a variant of the relative entropy of entanglement) from separable, and  a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations.
Revised:  Of particular interest are a quasipolynomial-time algorithm which distinguishes multipartite density matrices with entanglement larger than a small constant amount (measured with a variant of the relative entropy of entanglement) from separable, and (ii) a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations.
Edit intent: coherence
Original:  The approximation is measured by distinguishability under fully one-way LOCC (local operations and classical communication) measurements , compared to the parallel one-way LOCC measurements of earlier work, while the error bound is kept essentially the same .
Revised:  The approximation is measured by distinguishability under fully one-way LOCC (local operations and classical communication) measurements , compared to the parallel one-way LOCC measurements was used for measuring the approximation, with essentially the same .
Edit intent: clarity