wanyu/IteraTeR_v2 huggingface dataset:
Original:  We illustrate these theoretical results by numerical experiments which suggest their generalizability to q \in \{2,3 ,4 ,\dots\}.
Revised:  We illustrate these theoretical results by numerical experiments which might indicate their generalizability to q \in \{2,3 ,4 ,\dots\}.
Edit intent: clarity
Original:  In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE ) and advanced machine learning techniques.
Revised:  In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of RVE and advanced machine learning techniques.
Edit intent: clarity
Original:  Inspired by the basic concept in artificial neural networks, we use a collection of connected simple building blocks with analytical homogenization solutions to describe complex overall material responses.
Revised:  We propose to use a collection of connected simple building blocks with analytical homogenization solutions to describe complex overall material responses.
Edit intent: clarity
Original:  Inspired by the basic concept in artificial neural networks, we use a collection of connected simple building blocks with analytical homogenization solutions to describe complex overall material responses.
Revised:  Inspired by the basic concept in artificial neural networks, we use a collection of connected mechanistic building blocks with analytical homogenization solutions to describe complex overall material responses.
Edit intent: clarity
Original:  With linear elastic RVE data from offline direct numerical simulations (DNS) , the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm, enhanced by various model compression methods.
Revised:  With linear elastic RVE data from offline DNS , the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm, enhanced by various model compression methods.
Edit intent: clarity
Original:  With linear elastic RVE data from offline direct numerical simulations (DNS) , the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm, enhanced by various model compression methods.
Revised:  With linear elastic RVE data from offline direct numerical simulations (DNS) , the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm, enhanced by model compression methods.
Edit intent: clarity
Original:  Furthermore, extrapolations of the trained network to a wide range of problems are also validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finite-strain hyperelasticity under large deformations.
Revised:  Importantly, the trained network to a wide range of problems are also validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finite-strain hyperelasticity under large deformations.
Edit intent: coherence
Original:  Furthermore, extrapolations of the trained network to a wide range of problems are also validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finite-strain hyperelasticity under large deformations.
Revised:  Furthermore, extrapolations of the trained network to a wide range of problems are validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finite-strain hyperelasticity under large deformations.
Edit intent: clarity
Original:  By discovering a proper topological representation of RVE with fewer degrees of freedom (DOF) , this intelligent material model is believed to open new possibilities of high-fidelity efficient concurrent simulations for a large-scale heterogeneous structure.
Revised:  By discovering a proper topological representation of RVE with fewer degrees of freedom , this intelligent material model is believed to open new possibilities of high-fidelity efficient concurrent simulations for a large-scale heterogeneous structure.
Edit intent: clarity
Original:  It also provides a mechanistic understanding of structure-property relations across material length scales and enables the development of parametrized microstructural database for material design and manufacturing.
Revised:  It also provides a mechanistic understanding of structure-property relations across material length scales and enables the development of parameterized microstructural database for material design and manufacturing.
Edit intent: fluency
Original: Since Bachelier 's thesis in 1900, when mathematical finance began, attempts at understanding the nature of stock market prices and at predicting them have not succeeded.
Revised: Since Bachelier in 1900, when mathematical finance began, attempts at understanding the nature of stock market prices and at predicting them have not succeeded.
Edit intent: clarity
Original:  To this day,  physicists and mathematicians working in economy consider that the evolution of security prices is largely random, and, thus, not predictable.
Revised:  To this day, the physicists and mathematicians working in economy consider that the evolution of security prices is largely random, and, thus, not predictable.
Edit intent: fluency
Original:  To this day,  physicists and mathematicians working in economy consider that the evolution of security prices is largely random, and, thus, not predictable.
Revised:  To this day, physicists and mathematicians working in economy consider that the evolution of security prices is basically random, and, thus, not predictable.
Edit intent: clarity
Original:  We show that not only is the evolution of security prices not random but it is semi-deterministic and, more remarkably, governed by a physical law.
Revised:  We show that the evolution of security prices not random but it is semi-deterministic and, more remarkably, governed by a physical law.
Edit intent: coherence
Original:  The function , which can be described as an "isodense" network of "moving" regression curves of an order greater than or equal to 1, can be conveniently represented graphically .
Revised:  The function can be described as an "isodense" network of "moving" regression curves of an order greater than or equal to 1, can be conveniently represented graphically .
Edit intent: clarity
Original:  The direct consequence is that prices are driven by these cords in a semi-deterministic manner (leaning towards deterministic).
Revised:  The direct consequence is that prices are driven by the cords in a semi-deterministic manner (leaning towards deterministic).
Edit intent: fluency
Original:  We can say that we now understand the reason behind price movements and can predict stock prices both qualitatively and quantitatively.
Revised:  We can say that we now understand the reason behind each price movement and can predict stock prices both qualitatively and quantitatively.
Edit intent: clarity
Original:  Note that time series data (not limited to financial) is input directly into the function without any fitting.
Edit intent: coherence
Original: Since Bachelier  in 1900 , when mathematical finance began, attempts at understanding the nature of stock market prices and at predicting them have not succeeded.
Revised: Since Bachelier in 1900 , when mathematical finance began, attempts at understanding the nature of prices and at predicting them have not succeeded.
Edit intent: clarity
Original:  To this day, the physicists and mathematicians working in economy consider that the evolution of security prices is basically random, and, thus,  not predictable.
Revised:  To this day, the physicists and mathematicians working in economy consider that the evolution of security prices is basically random, and, thus, inherently not predictable.
Edit intent: clarity
Original:  We show that the evolution of security prices not at all random but is largely deterministic and , more remarkably, governed by a physical law.
Revised:  We show that the evolution of security prices is not a stochastic process but largely deterministic and , more remarkably, governed by a physical law.
Edit intent: clarity
Original:  We show that the evolution of security prices not at all random but is largely deterministic and , more remarkably, governed by a physical law.
Revised:  We show that the evolution of security prices not at all random but is largely deterministic and governed by a physical law.
Edit intent: clarity
Original:  The function can be described as an "isodense" network of "moving " regression curves of an order greater than or equal to 1.
Revised:  The function can be described as an "isodense" network of moving regression curves of an order greater than or equal to 1.
Edit intent: fluency
Original:  When inputting a time series of any security into the function, new mathematical objects emerge spontaneously  .
Revised:  The salient aspect of the function is that, when inputting a time series of any security into the function, new mathematical objects emerge spontaneously .
Edit intent: clarity
Original:  Having a function that describes the evolution of the price, we now understand the reason behind each price movement and can predict stock prices both qualitatively and quantitatively.
Revised:  With a function that describes the evolution of the price, we now understand the reason behind each price movement and can predict stock prices both qualitatively and quantitatively.
Edit intent: fluency
Original:  Having a function that describes the evolution of the price, we now understand the reason behind each price movement and can predict stock prices both qualitatively and quantitatively.
Revised:  Having a function that describes the evolution of the price, we now understand the reason behind each price movement and can also predict prices both qualitatively and quantitatively.
Edit intent: clarity
Original:  The function is universal, does not rely on any fitting, and, thanks to its extreme sensitivity, reveals the hidden order present in time series data that other methods have never uncovered.
Revised:  The function is universal, does not rely on any fitting, and, due to its extreme sensitivity, reveals the hidden order present in time series data that other methods have never uncovered.
Edit intent: coherence
Original:  The function is universal, does not rely on any fitting, and, thanks to its extreme sensitivity, reveals the hidden order present in time series data that other methods have never uncovered.
Revised:  The function is universal, does not rely on any fitting, and, thanks to its extreme sensitivity, reveals the hidden order present in time series data that existing research never uncovered.
Edit intent: clarity
Original: The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two of the most famous variational models in image segmentation and image restoration, respectively.
Revised: The piecewise constant Mumford-Shah (PCMS) model and the Rudin-Osher-Fatemi (ROF) model are two important variational models in image segmentation and image restoration, respectively.
Edit intent: clarity
Original:  In this paper, we explore the linkage between these two important models.
Revised:  In this paper, we explore a linkage between these two important models.
Edit intent: fluency
Original:  In this paper, we explore the linkage between these two important models.
Revised:  In this paper, we explore the linkage between these models.
Edit intent: clarity
Original:  We prove that for  two-phase segmentation problem the optimal solution of the PCMS model can be obtained by thresholding the minimizer of the ROF model.
Revised:  We prove that for the two-phase segmentation problem the optimal solution of the PCMS model can be obtained by thresholding the minimizer of the ROF model.
Edit intent: fluency
Original:  We prove that for  two-phase segmentation problem the optimal solution of the PCMS model can be obtained by thresholding the minimizer of the ROF model.
Revised:  We prove that for two-phase segmentation problem a partial minimizer of the PCMS model can be obtained by thresholding the minimizer of the ROF model.
Edit intent: clarity
Original:  This linkage is still valid for multiphase segmentation under mild assumptions.
Revised:  A similar linkage is still valid for multiphase segmentation under mild assumptions.
Edit intent: clarity
Original:  As a by-product of the new paradigm, we derive a novel segmentation method, coined thresholded-ROF (T-ROF) method, to illustrate the virtue of manipulating image segmentation through image restoration techniques.
Revised:  As a by-product of the new paradigm, we derive a novel segmentation method, called thresholded-ROF (T-ROF) method, to illustrate the virtue of manipulating image segmentation through image restoration techniques.
Edit intent: fluency
Original:  As a by-product of the new paradigm, we derive a novel segmentation method, coined thresholded-ROF (T-ROF) method, to illustrate the virtue of manipulating image segmentation through image restoration techniques.
Revised:  As a by-product of the new paradigm, we derive a novel segmentation method, coined thresholded-ROF (T-ROF) method, to illustrate the virtue of managing image segmentation through image restoration techniques.
Edit intent: clarity
Original:  The convergence of the T-ROF method under certain conditions is proved, and elaborate experimental results and comparisons are presented.
Revised:  The convergence of the T-ROF method is proved, and elaborate experimental results and comparisons are presented.
Edit intent: clarity
Original:  This systemic point  puts the focus on distributional and network effects, rather than time-dependence.
Revised:  This systemic point of view puts the focus on distributional and network effects, rather than time-dependence.
Edit intent: clarity
Original: The maximization of submodular functions  an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of that of the optimal.
Revised: The maximization of submodular functions is an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of that of the optimal.
Edit intent: fluency
Original: The maximization of submodular functions  an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of that of the optimal.
Revised: The maximization of submodular functions an NP-Hard problem for certain subclasses of functions, for which a simple greedy algorithm has been shown to guarantee a solution whose quality is within 1/2 of the optimal.
Edit intent: clarity
Original:  Our results show that the best designs are to partition the agents into equally-sized sets , and allow agents to access the decisions of all previous agents within the same set.
Revised:  Our results show that the best designs partition the agents into equally-sized sets , and allow agents to access the decisions of all previous agents within the same set.
Edit intent: clarity
Original:  Our results show that the best designs are to partition the agents into equally-sized sets , and allow agents to access the decisions of all previous agents within the same set.
Revised:  Our results show that the best designs are to partition the agents into equally-sized sets and allow agents to access the decisions of all previous agents within the same set.
Edit intent: fluency
Original:  This model reduces to a memristor, a resistor whose resistance depends on the history of charges crossing it, coupled to a voltage source and a capacitor.
Revised:  This model reduces to a memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor.
Edit intent: clarity
Original:  Here, we use the recent quantization of the memristor to glance at the Hodgkin-Huxley model in the quantum regime.
Revised:  Here, we take advantage of the recent quantization of the memristor to glance at the Hodgkin-Huxley model in the quantum regime.
Edit intent: clarity
Original:  Here, we use the recent quantization of the memristor to glance at the Hodgkin-Huxley model in the quantum regime.
Revised:  Here, we use the recent quantization of the memristor to look into the Hodgkin-Huxley model in the quantum regime.
Edit intent: clarity
Original:  In the latter, we firstly introduce classical sources to study the quantum-classical transition, and afterwards we switch to coherent quantum sourcesin order to study the effects of entanglement . Numerical simulations show an  increment and adaptation depending on the history of signals .
Revised:  In the latter, we firstly introduce classical sources to study the quantum-classical transition, and afterwards we switch to coherent quantum sourcesin order to study the effects of entanglement . Numerical simulations show an expected increment and adaptation depending on the history of signals .
Edit intent: clarity
Original:  These results pave the way for the construction of quantum neuron networks inspired in the brain  but capable of dealing with quantum information , a step forward towards the design of neuromorphic quantum architectures with implications in quantum machine learning.
Revised:  These results pave the way for the construction of quantum neuron networks inspired in the brain but capable of dealing with quantum information . This could be considered a step forward towards the design of neuromorphic quantum architectures with implications in quantum machine learning.
Edit intent: coherence
Original:  These results pave the way for the construction of quantum neuron networks inspired in the brain  but capable of dealing with quantum information , a step forward towards the design of neuromorphic quantum architectures with implications in quantum machine learning.
Revised:  These results pave the way for the construction of quantum neuron networks inspired in the brain but capable of dealing with quantum information , a step forward towards the design of neuromorphic quantum architectures with direct applications in quantum machine learning.
Edit intent: clarity
Original: The Hodgkin-Huxley model describes the behavior of the membrane voltage in neurons, treating each element of the cell membrane as an electric circuit element, namely capacitors, memristors  and voltage sources.
Revised: The Hodgkin-Huxley model describes the behavior of the cell membrane in neurons, treating each element of the cell membrane as an electric circuit element, namely capacitors, memristors and voltage sources.
Edit intent: clarity
Original: The Hodgkin-Huxley model describes the behavior of the membrane voltage in neurons, treating each element of the cell membrane as an electric circuit element, namely capacitors, memristors  and voltage sources.
Revised: The Hodgkin-Huxley model describes the behavior of the membrane voltage in neurons, treating each part of it as an electric circuit element, namely capacitors, memristors and voltage sources.
Edit intent: clarity
Original: The Hodgkin-Huxley model describes the behavior of the membrane voltage in neurons, treating each element of the cell membrane as an electric circuit element, namely capacitors, memristors  and voltage sources.
Revised: The Hodgkin-Huxley model describes the behavior of the membrane voltage in neurons, treating each element of the cell membrane as an electric circuit element, namely capacitors, memristors , and voltage sources.
Edit intent: fluency
Original:  We focus on the activation channel of potassium ions, since it is simpler , while keeping the majority of the features identified with the original Hodgkin-Huxley model.
Revised:  We focus on the activation channel of potassium ions, due to its simplicity , while keeping the majority of the features identified with the original Hodgkin-Huxley model.
Edit intent: coherence
Original:  We focus on the activation channel of potassium ions, since it is simpler , while keeping the majority of the features identified with the original Hodgkin-Huxley model.
Revised:  We focus on the activation channel of potassium ions, since it is simpler , while keeping most of the features identified with the original Hodgkin-Huxley model.
Edit intent: fluency
Original:  We focus on the activation channel of potassium ions, since it is simpler , while keeping the majority of the features identified with the original Hodgkin-Huxley model.
Revised:  We focus on the activation channel of potassium ions, since it is simpler , while keeping the majority of the features displayed by the original model.
Edit intent: clarity
Original:  This reduces to a memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor.
Revised:  This reduced version is essentially a classical memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor.
Edit intent: clarity
Original:  Here, we take advantage of the recent quantization of the memristor to look into the Hodgkin-Huxley model in the quantum regime .
Revised:  Here, we will consider a quantized Hodgkin-Huxley model in the quantum regime .
Edit intent: clarity
Original:  Here, we take advantage of the recent quantization of the memristor to look into the Hodgkin-Huxley model in the quantum regime .
Revised:  Here, we take advantage of the recent quantization of the memristor to look into the Hodgkin-Huxley model based on a quantum memristor formalism .
Edit intent: clarity
Original:  We compare the behavior of the membrane voltage and the potassium channel conductance in both the classical and quantum realms , subjected to AC sources . Numerical simulations show an expected increment and adaptation depending on the history of signals in all regimes.
Revised:  We compare the behavior of the membrane voltage and the potassium channel conductance , when the circuit is subjected to AC sources, in both classical and quantum realms , subjected to AC sources . Numerical simulations show an expected increment and adaptation depending on the history of signals in all regimes.
Edit intent: clarity
Original:  We compare the behavior of the membrane voltage and the potassium channel conductance in both the classical and quantum realms , subjected to AC sources . Numerical simulations show an expected increment and adaptation depending on the history of signals in all regimes.
Revised:  We compare the behavior of the membrane voltage and the potassium channel conductance in both the classical and quantum realms . Numerical simulations show an expected increment and adaptation depending on the history of signals in all regimes.
Edit intent: clarity
Original:  We compare the behavior of the membrane voltage and the potassium channel conductance in both the classical and quantum realms , subjected to AC sources . Numerical simulations show an expected increment and adaptation depending on the history of signals in all regimes.
Revised:  We compare the behavior of the membrane voltage and the potassium channel conductance in both the classical and quantum realms , subjected to AC sources . Numerical simulations show an expected adaptation of the considered channel conductance depending on the history of signals in all regimes.
Edit intent: clarity