wanyu/IteraTeR_full_sent huggingface dataset:
Original: In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs)  .
Revised: In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs) , which are related to the FBSDEs by the Pardoux-Peng theory .
Edit intent: meaning-changed
Original:  The algorithms relies on a learning process by minimizing the path-wise difference of two discrete stochastic processes, which are defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively.
Revised:  The algorithms rely on a learning process by minimizing the path-wise difference of two discrete stochastic processes, which are defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively.
Edit intent: fluency
Original:  The algorithms relies on a learning process by minimizing the path-wise difference of two discrete stochastic processes, which are defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively.
Revised:  The algorithms relies on a learning process by minimizing the pathwise difference between two discrete stochastic processes, which are defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively.
Edit intent: fluency
Original:  The algorithms relies on a learning process by minimizing the path-wise difference of two discrete stochastic processes, which are defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively.
Revised:  The algorithms relies on a learning process by minimizing the path-wise difference of two discrete stochastic processes, defined by the time discretization of the FBSDEs and the DNN representation of the PDE solutions, respectively.
Edit intent: coherence
Original:  The proposed algorithms demonstrate a convergence for a 100-dimensional Black--Scholes--Barenblatt equation at a rate similar to that of the Euler--Maruyama discretization of the FBSDEs .
Revised:  The proposed algorithms are shown to generate DNN solutions for a 100-dimensional Black--Scholes--Barenblatt equation at a rate similar to that of the Euler--Maruyama discretization of the FBSDEs .
Edit intent: meaning-changed
Original:  The proposed algorithms demonstrate a convergence for a 100-dimensional Black--Scholes--Barenblatt equation at a rate similar to that of the Euler--Maruyama discretization of the FBSDEs .
Revised:  The proposed algorithms demonstrate a convergence for a 100-dimensional Black--Scholes--Barenblatt equation , accurate in a finite region in the solution space, and has a convergence rate similar to that of the Euler--Maruyama discretization of the FBSDEs .
Edit intent: meaning-changed
Original:  The proposed algorithms demonstrate a convergence for a 100-dimensional Black--Scholes--Barenblatt equation at a rate similar to that of the Euler--Maruyama discretization of the FBSDEs .
Revised:  The proposed algorithms demonstrate a convergence for a 100-dimensional Black--Scholes--Barenblatt equation at a rate similar to that of the Euler--Maruyama discretization used for the FBSDEs. As a result, a Richardson extrapolation technique over time discretizations can be used to enhance the accuracy of the DNN solutions. For time oscillatory solutions, a multiscale DNN is shown to improve the performance of the FBSDE DNN for high frequencies .
Edit intent: meaning-changed
Original: This paper proposes Friedrichs learning as a novel deep learning methodology that can learn the weak solutions of PDEs via Friedrichs' seminal minimax formulation, which transforms the PDE problem into a minimax optimization problem to identify weak solutions.
Revised: This paper proposes Friedrichs learning as a novel deep learning methodology that can learn the weak solutions of PDEs via a minmax formulation, which transforms the PDE problem into a minimax optimization problem to identify weak solutions.
Edit intent: clarity
Original: The outer hair cell (OHC) harbors the voltage dependent protein prestin (SLC26a5)  in high density in its lateral membrane, where voltages sensed by its voltage-sensor are evidenced as a nonlinear capacitance (NLC).
Revised: The outer hair cell (OHC) membrane harbors a voltage-dependent protein, prestin (SLC26a5) in high density in its lateral membrane, where voltages sensed by its voltage-sensor are evidenced as a nonlinear capacitance (NLC).
Edit intent: clarity
Original: The outer hair cell (OHC) harbors the voltage dependent protein prestin (SLC26a5)  in high density in its lateral membrane, where voltages sensed by its voltage-sensor are evidenced as a nonlinear capacitance (NLC).
Revised: The outer hair cell (OHC) harbors the voltage dependent protein prestin (SLC26a5) , in high density in its lateral membrane, where voltages sensed by its voltage-sensor are evidenced as a nonlinear capacitance (NLC).
Edit intent: fluency
Original: The outer hair cell (OHC) harbors the voltage dependent protein prestin (SLC26a5)  in high density in its lateral membrane, where voltages sensed by its voltage-sensor are evidenced as a nonlinear capacitance (NLC).
Revised: The outer hair cell (OHC) harbors the voltage dependent protein prestin (SLC26a5) in high density , whose charge movement is evidenced as a nonlinear capacitance (NLC).
Edit intent: clarity
Original:  Despite complex component trade-offs, the low-pass roll-off in absolute magnitude of NLC,  indicative of diminishing total charge movement, poses a challenge for the role of prestin in cochlear amplification at very high frequencies.
Revised:  Despite complex component trade-offs, the low-pass roll-off in absolute magnitude of NLC, which varies little with our perturbations and is indicative of diminishing total charge movement, poses a challenge for the role of prestin in cochlear amplification at very high frequencies.
Edit intent: meaning-changed
Original:  Despite complex component trade-offs, the low-pass roll-off in absolute magnitude of NLC,  indicative of diminishing total charge movement, poses a challenge for the role of prestin in cochlear amplification at very high frequencies.
Revised:  Despite complex component trade-offs, the low-pass roll-off in absolute magnitude of NLC, indicative of diminishing total charge movement, poses a challenge for a role of voltage-driven prestin in cochlear amplification at very high frequencies.
Edit intent: clarity
Original:  In this paper  we consider the impact of these austerity measures on two different but complementary elements of crime - the crime rate and the less-studied concentration of crime - over the period 2011-2015 in England and Wales, and document four new facts.
Revised:  In this paper , we consider the impact of these austerity measures on two different but complementary elements of crime - the crime rate and the less-studied concentration of crime - over the period 2011-2015 in England and Wales, and document four new facts.
Edit intent: fluency
Original:  In this paper  we consider the impact of these austerity measures on two different but complementary elements of crime - the crime rate and the less-studied concentration of crime - over the period 2011-2015 in England and Wales, and document four new facts.
Revised:  In this paper we consider the impact of these austerity measures on two different but complementary elements of crime -- the crime rate and the less-studied concentration of crime - over the period 2011-2015 in England and Wales, and document four new facts.
Edit intent: fluency
Original:  In this paper  we consider the impact of these austerity measures on two different but complementary elements of crime - the crime rate and the less-studied concentration of crime - over the period 2011-2015 in England and Wales, and document four new facts.
Revised:  In this paper we consider the impact of these austerity measures on two different but complementary elements of crime - the crime rate and the less-studied concentration of crime -- over the period 2011-2015 in England and Wales, and document four new facts.
Edit intent: fluency
Original:  Combining these results, we document unambiguous evidence of a negative spillover of the welfare reforms at the heart of the UK government's austerity program on social welfare, which reinforced the direct inequality-enhancing effect of this program.
Revised:  Combining these results, we document unambiguous evidence of a negative spillover of the welfare reforms at the heart of the UK government's austerity program on social welfare, which reinforced the direct inequality-worsening effect of this program.
Edit intent: clarity
Original:  Towards this direction, a novel cognitive architecture for multi-agent LfD robotic learning is introduced in this paper , targeting to enable the reliable deployment of open, scalable and expandable robotic systems in large-scale and complex environments.
Revised:  Towards this direction, a novel cognitive architecture for multi-agent LfD robotic learning is introduced , targeting to enable the reliable deployment of open, scalable and expandable robotic systems in large-scale and complex environments.
Edit intent: coherence
Original:  In particular, the designed architecture capitalizes on the recent advances in the Artificial Intelligence (AI) (and especially the Deep Learning (DL)) field, by establishing a Federated Learning (FL)-based framework for incarnating a multi-human multi-robot collaborative learning environment.
Revised:  In particular, the designed architecture capitalizes on the recent advances in the Artificial Intelligence (AI) field, by establishing a Federated Learning (FL)-based framework for incarnating a multi-human multi-robot collaborative learning environment.
Edit intent: coherence
Original:  Pivotal noveltiesof the designed cognitive architecture include: a) it introduces a new FL-based formalism that extends the conventional LfD learning paradigm to support large-scale multi-agent operational settings, b) it elaborates previous FL-based self-learning robotic schemes so as to incorporate the human in the learning loop , and c) it consolidates the fundamental principles of FL with additional sophisticated AI-enabled learning methodologies for modelling the multi-level inter-dependencies among the robotic tasks.
Revised:  Pivotal noveltiesof the designed cognitive architecture a) introduces a new FL-based formalism that extends the conventional LfD learning paradigm to support large-scale multi-agent operational settings, b) it elaborates previous FL-based self-learning robotic schemes so as to incorporate the human in the learning loop , and c) it consolidates the fundamental principles of FL with additional sophisticated AI-enabled learning methodologies for modelling the multi-level inter-dependencies among the robotic tasks.
Edit intent: clarity
Original:  a) it introduces a new FL-based formalism that extends the conventional LfD learning paradigm to support large-scale multi-agent operational settings, b) it elaborates previous FL-based self-learning robotic schemes so as to incorporate the human in the learning loop , and c) it consolidates the fundamental principles of FL with additional sophisticated AI-enabled learning methodologies for modelling the multi-level inter-dependencies among the robotic tasks.
Revised:  a) it introduces a new FL-based formalism that extends the conventional LfD learning paradigm to support large-scale multi-agent operational settings, b) elaborates previous FL-based self-learning robotic schemes so as to incorporate the human in the learning loop , and c) it consolidates the fundamental principles of FL with additional sophisticated AI-enabled learning methodologies for modelling the multi-level inter-dependencies among the robotic tasks.
Edit intent: fluency
Original:  a) it introduces a new FL-based formalism that extends the conventional LfD learning paradigm to support large-scale multi-agent operational settings, b) it elaborates previous FL-based self-learning robotic schemes so as to incorporate the human in the learning loop , and c) it consolidates the fundamental principles of FL with additional sophisticated AI-enabled learning methodologies for modelling the multi-level inter-dependencies among the robotic tasks.
Revised:  a) it introduces a new FL-based formalism that extends the conventional LfD learning paradigm to support large-scale multi-agent operational settings, b) it elaborates previous FL-based self-learning robotic schemes so as to incorporate the human in the learning loop and c) it consolidates the fundamental principles of FL with additional sophisticated AI-enabled learning methodologies for modelling the multi-level inter-dependencies among the robotic tasks.
Edit intent: fluency
Original:  a) it introduces a new FL-based formalism that extends the conventional LfD learning paradigm to support large-scale multi-agent operational settings, b) it elaborates previous FL-based self-learning robotic schemes so as to incorporate the human in the learning loop , and c) it consolidates the fundamental principles of FL with additional sophisticated AI-enabled learning methodologies for modelling the multi-level inter-dependencies among the robotic tasks.
Revised:  a) it introduces a new FL-based formalism that extends the conventional LfD learning paradigm to support large-scale multi-agent operational settings, b) it elaborates previous FL-based self-learning robotic schemes so as to incorporate the human in the learning loop , and c) consolidates the fundamental principles of FL with additional sophisticated AI-enabled learning methodologies for modelling the multi-level inter-dependencies among the robotic tasks.
Edit intent: fluency
Original:  The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error . But its explicit numerical value for a certain step size , which depends on certain parameters of this class of solvers, is not automatically a good estimate of the explicit error.
Revised:  The contraction rate of this error estimate as a function of the solver's step size identifies it as a well-calibrated worst-case error , but its explicit numerical value for a certain step size , which depends on certain parameters of this class of solvers, is not automatically a good estimate of the explicit error.
Edit intent: fluency
Original: For a binary integer program (IP) \max c^{\mathsf T {\rm   x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Revised: For a binary integer program (IP) {\rm x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Edit intent: clarity
Original: For a binary integer program (IP) \max c^{\mathsf T {\rm   x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Revised: For a binary integer program (IP) \max c^{\mathsf T {\rm max x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Edit intent: meaning-changed
Original: For a binary integer program (IP) \max c^{\mathsf T {\rm   x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Revised: For a binary integer program (IP) \max c^{\mathsf T {\rm ~ c^\mathsf{T x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Edit intent: meaning-changed
Original: For a binary integer program (IP) \max c^{\mathsf T {\rm   x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Revised: For a binary integer program (IP) \max c^{\mathsf T {\rm x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-2 /n^7 -1/2 ^{ \Omega (m)}.
Edit intent: fluency
Original: For a binary integer program (IP) \max c^{\mathsf T {\rm   x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Revised: For a binary integer program (IP) \max c^{\mathsf T {\rm x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -2 ^{ \Omega (m)}.
Edit intent: fluency
Original: For a binary integer program (IP) \max c^{\mathsf T {\rm   x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ \Omega (m)}.
Revised: For a binary integer program (IP) \max c^{\mathsf T {\rm x, Ax \leq b, x \in \{0,1\}^n, where A \in R^{m \times n} and c \in R^n have independent Gaussian entries and the right-hand side b \in R^m satisfies that its negative coordinates have \ell_2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly(m)(\log n)^2 / n with probability at least 1-1 /n^7 -1/2 ^{ - (m)}.
Edit intent: meaning-changed
Original:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed  .
Revised:  Building upon recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed .
Edit intent: clarity
Original:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed  .
Revised:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), we show that the integrality gap implies that branch-and-bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed .
Edit intent: clarity
Original:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed  .
Revised:  By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires n^{\operatorname{poly}(m)} time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed . We derive this result via a novel meta-theorem, which relates the size of branch-and-bound trees and the integrality gap for random logconcave IPs .
Edit intent: meaning-changed
Original:  Inspired by recent developments in commodity smile modeling , we present a multi-factor stochastic local-volatility model able to jointly calibrate plain vanilla options both on VIX futures and VXX notes  .
Revised:  Inspired by recent developments in commodity smile modelling , we present a multi-factor stochastic local-volatility model able to jointly calibrate plain vanilla options both on VIX futures and VXX notes .
Edit intent: fluency
Original:  Inspired by recent developments in commodity smile modeling , we present a multi-factor stochastic local-volatility model able to jointly calibrate plain vanilla options both on VIX futures and VXX notes  .
Revised:  Inspired by recent developments in commodity smile modeling , we present a multi-factor stochastic-local volatility model that is able to jointly calibrate plain vanilla options both on VIX futures and VXX notes .
Edit intent: clarity
Original:  Inspired by recent developments in commodity smile modeling , we present a multi-factor stochastic local-volatility model able to jointly calibrate plain vanilla options both on VIX futures and VXX notes  .
Revised:  Inspired by recent developments in commodity smile modeling , we present a multi-factor stochastic local-volatility model able to jointly calibrate plain vanilla options both on VIX futures and VXX notes , thus going beyond the failure of purely stochastic or simply local volatility models .
Edit intent: meaning-changed