wanyu/IteraTeR_v2 huggingface dataset:
Original:  The tuning of \lambda(\cdot) is achieved via a closed-loop control law based on thealgebraic equation \lambda(t)  ^p\|\nabla\Phi(x(t))\|^{p-1} = \theta for a given \theta > 0. We prove the existence and uniqueness of a local solution to this closed-loop ODE by the Banach fixed-point theorem.
Revised:  The tuning of \lambda(\cdot) is achieved via a closed-loop control law based on thealgebraic equation \lambda(t) ) ^p\|\nabla\Phi(x(t))\|^{p-1} = \theta for a given \theta > 0. We prove the existence and uniqueness of a local solution to this closed-loop ODE by the Banach fixed-point theorem.
Edit intent: fluency
Original:  The tuning of \lambda(\cdot) is achieved via a closed-loop control law based on thealgebraic equation \lambda(t)  ^p\|\nabla\Phi(x(t))\|^{p-1} = \theta for a given \theta > 0. We prove the existence and uniqueness of a local solution to this closed-loop ODE by the Banach fixed-point theorem.
Revised:  The tuning of \lambda(\cdot) is achieved via a closed-loop control law based on thealgebraic equation \lambda(t) ^p\|\nabla\Phi(x(t))\|^{p-1} = \theta for a given \theta > 0. We prove the existence and uniqueness of a local solution to this system via the Banach fixed-point theorem.
Edit intent: clarity
Original:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{large-step A-HPE framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , }  and the other of which leads to a new  p-th order tensor algorithm.
Revised:  Our second contribution is to provide two algorithmic frameworks obtained from discretization of our continuous-time system , one of which generalizes the \textsf{large-step A-HPE framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , } and the other of which leads to a new p-th order tensor algorithm.
Edit intent: clarity
Original:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{large-step A-HPE framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , }  and the other of which leads to a new  p-th order tensor algorithm.
Revised:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{ framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , } and the other of which leads to a new p-th order tensor algorithm.
Edit intent: clarity
Original:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{large-step A-HPE framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , }  and the other of which leads to a new  p-th order tensor algorithm.
Revised:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{large-step A-HPE }\hspace{0pt} , } and the other of which leads to a new p-th order tensor algorithm.
Edit intent: clarity
Original:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{large-step A-HPE framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , }  and the other of which leads to a new  p-th order tensor algorithm.
Revised:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{large-step A-HPE framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , } large-step A-HPE framework and the other of which leads to a new p-th order tensor algorithm.
Edit intent: fluency
Original:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{large-step A-HPE framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , }  and the other of which leads to a new  p-th order tensor algorithm.
Revised:  We present two frameworks for implicit time discretization of the ODE , one of which generalizes the \textsf{large-step A-HPE framework of~\mbox{ \cite{Monteiro-2013-Accelerated}\hspace{0pt} , } and the other of which leads to a new optimal p-th order tensor algorithm.
Edit intent: clarity
Original:   A highlight of our analysis is that we show that all of the p-th order optimal tensor algorithms in this paper minimize the squared gradient norm at a rate of \mathcal{O (k^{-3p})  .
Revised:  A highlight of our analysis is that we show that all of the p-th order optimal tensor algorithms that we discuss minimize the squared gradient norm at a rate of \mathcal{O (k^{-3p}) .
Edit intent: clarity
Original: Jacobi-type algorithms for simultaneous approximate diagonalization of symmetric real tensors (or partially symmetric complextensors) have been widely used in independent component analysis (ICA) because of its high performance.
Revised: Jacobi-type algorithms for simultaneous approximate diagonalization of real (or complex) symmetric tensors have been widely used in independent component analysis (ICA) because of its high performance.
Edit intent: clarity
Original: Jacobi-type algorithms for simultaneous approximate diagonalization of symmetric real tensors (or partially symmetric complextensors) have been widely used in independent component analysis (ICA) because of its high performance.
Revised: Jacobi-type algorithms for simultaneous approximate diagonalization of symmetric real tensors (or partially symmetric complextensors) have been widely used in independent component analysis (ICA) because of their good performance.
Edit intent: clarity
Original:  In this paper, we mainly review  our recent results in a series of papers about the weak convergence and global convergence of these Jacobi-type algorithms , under both of two pair selection rules .
Revised:  In this paper, we mainly review our recent results in a series of papers about weak and global convergence of these Jacobi-type algorithms , under both of two pair selection rules .
Edit intent: fluency
Original:  In this paper, we mainly review  our recent results in a series of papers about the weak convergence and global convergence of these Jacobi-type algorithms , under both of two pair selection rules .
Revised:  In this paper, we mainly review our recent results in a series of papers about the weak convergence and global convergence of these Jacobi-type algorithms .
Edit intent: coherence
Original:  First, it presents a novel approach called DeepBiRD which is inspired from human visual perception and exploits layout features to identify individual references in a scientific publication.
Revised:  First, it presents a novel approach called DeepBiRD which is inspired by human visual perception and exploits layout features to identify individual references in a scientific publication.
Edit intent: fluency
Original:  Second, we present a new dataset for image-based reference detection with 2401 scans containing 12244 references, all manually annotated for individual reference.
Revised:  Second, we release a large dataset for image-based reference detection with 2401 scans containing 12244 references, all manually annotated for individual reference.
Edit intent: clarity
Original:  Secondly it performs layout driven reference detection using Mask R-CNN in a given scientific publication.
Revised:  Secondly it performs layout driven reference detection using Mask R-CNN on a given scientific publication.
Edit intent: fluency
Original:  DeepBiRD detected 2.5 times more references than current state-of-the-art approach on their own dataset.
Revised:  DeepBiRD significantly outperformed the current state-of-the-art approach on their own dataset.
Edit intent: clarity
Original:  DeepBiRD detected 2.5 times more references than current state-of-the-art approach on their own dataset.
Revised:  DeepBiRD detected 2.5 times more references than current state-of-the-art approach on their dataset.
Edit intent: clarity
Original:  Therefore, suggesting that DeepBiRD is significantly superior in performance, generalizable and independent of any domain or referencing style.
Revised:  Therefore, suggesting that DeepBiRD is significantly superior in performance, generalized, and independent of any domain or referencing style.
Edit intent: clarity
Original: Detectability of discrete event systems has been introduced as a generalization of other state-estimation properties  studied in the literature , including stability or observability.
Revised: Detectability has been introduced as a generalization of other state-estimation properties studied in the literature , including stability or observability.
Edit intent: clarity
Original: Detectability of discrete event systems has been introduced as a generalization of other state-estimation properties  studied in the literature , including stability or observability.
Revised: Detectability of discrete event systems has been introduced as a generalization of state-estimation properties studied in the literature , including stability or observability.
Edit intent: clarity
Original: Detectability of discrete event systems has been introduced as a generalization of other state-estimation properties  studied in the literature , including stability or observability.
Revised: Detectability of discrete event systems has been introduced as a generalization of other state-estimation properties of discrete event systems studied in the literature , including stability or observability.
Edit intent: fluency
Original:  It is a property whether the current and subsequent states of a systems can be determined based on observations.
Revised:  It is a property whether the current and subsequent states of a system can be determined based on observations.
Edit intent: fluency
Original:  Since the requirement to exactly determine the current and subsequent states may be too strict in some applications , a relaxed notion of D-detectability has been introduced, distinguishing only certain pairs of states rather than all states.
Revised:  Since , in some applications, to exactly determine the current and subsequent states may be too strict in some applications , a relaxed notion of D-detectability has been introduced, distinguishing only certain pairs of states rather than all states.
Edit intent: clarity
Original:  Since the requirement to exactly determine the current and subsequent states may be too strict in some applications , a relaxed notion of D-detectability has been introduced, distinguishing only certain pairs of states rather than all states.
Revised:  Since the requirement to exactly determine the current and subsequent states may be too strict , a relaxed notion of D-detectability has been introduced, distinguishing only certain pairs of states rather than all states.
Edit intent: clarity
Original:  The complexity of verifying weak (periodic) D-detectability follows from the results for verifying detectability, and hence is PSpace-complete .
Revised:  Deciding weak (periodic) D-detectability follows from the results for verifying detectability, and hence is PSpace-complete .
Edit intent: clarity
Original:  The complexity of verifying weak (periodic) D-detectability follows from the results for verifying detectability, and hence is PSpace-complete .
Revised:  The complexity of verifying weak (periodic) D-detectability is PSpace-complete .
Edit intent: clarity
Original:  Similarly, Shu and Lin constructed a detector that can check, in polynomial time, both strong (periodic) detectability and strong D-detectability  .
Revised:  Similarly, Shu and Lin constructed a detector that can check, in polynomial time, both strong (periodic) detectability or strong D-detectability .
Edit intent: fluency
Original:  However, the case of strong periodic D-detectability is more involved, and, to the best of our knowledge, the question whether it can be verified in polynomial time is open.
Revised:  However, to the best of our knowledge, the question whether it can be verified in polynomial time is open.
Edit intent: coherence
Original:  We answer this question by showing that there is no algorithm verifying the strong periodic D-detectability property in polynomial time, unless every problemsolvable in polynomial space can be solved in polynomial time.
Revised:  We answer this question by showing that deciding strong periodic D-detectability property in polynomial time, unless every problemsolvable in polynomial space can be solved in polynomial time.
Edit intent: clarity
Original:  We further show that the strong periodic D-detectability property cannot be verified in polynomial time even for systems having only a single observable event, unless P = NP  .
Revised:  We further show that the strong periodic D-detectability even for systems having only a single observable event, unless P = NP .
Edit intent: clarity
Original:  We further show that the strong periodic D-detectability property cannot be verified in polynomial time even for systems having only a single observable event, unless P = NP  .
Revised:  We further show that the strong periodic D-detectability property cannot be verified in polynomial time even for systems with a single observable event, unless P = NP .
Edit intent: clarity
Original:  If the kernel is Gaussian we show that the approximate Fekete points in one dimension are the solution to a convex optimisation problem and that the interpolants convergence with a super-exponential rate.
Revised:  If the kernel is Gaussian we show that the approximate Fekete points in one dimension are the solution to a convex optimisation problem and that the interpolants converge with a super-exponential rate.
Edit intent: fluency
Original:  A numerical experiment is provided for the Gaussian kernel.
Revised:  Numerical examples are provided for the Gaussian kernel.
Edit intent: clarity
Original: We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator.
Revised: We study the convergence of a family of numerical integration methods where the numerical integration is formulated as a finite matrix approximation to a multiplication operator.
Edit intent: fluency
Original:  A natural choice of method for this study is the theory of strong resolvent convergence which has previously been mostly applied to study the convergence of approximations of differential operators.
Revised:  The method chosen in this study is the theory of strong resolvent convergence which has previously been mostly applied to study the convergence of approximations of differential operators.
Edit intent: clarity
Original:  A natural choice of method for this study is the theory of strong resolvent convergence which has previously been mostly applied to study the convergence of approximations of differential operators.
Revised:  A natural choice of method for this study is the theory of strong resolvent convergence which has previously been applied to study the convergence of approximations of differential operators.
Edit intent: clarity
Original: We study the convergence of a family of numerical integration methods where the numerical integration is formulated as a finite matrix approximation to a multiplication operator.
Revised: We study the convergence of a family of numerical integration methods where the numerical integral is formulated as a finite matrix approximation to a multiplication operator.
Edit intent: fluency
Original:  The method chosen in this study is the theory of strong resolvent convergence which has previously been  applied to study the convergence of approximations of differential operators.
Revised:  A natural choice of method for this study is the theory of strong resolvent convergence which has previously been applied to study the convergence of approximations of differential operators.
Edit intent: clarity
Original: We propose and study numerically the implicit approximation in time of the Navier--Stokes equations by a Galerkin--collocation method in time combined with inf-sup stable finite element methods in space.
Revised: We propose and study numerically the implicit approximation in time of the Navier-Stokes equations by a Galerkin--collocation method in time combined with inf-sup stable finite element methods in space.
Edit intent: fluency
Original: We propose and study numerically the implicit approximation in time of the Navier--Stokes equations by a Galerkin--collocation method in time combined with inf-sup stable finite element methods in space.
Revised: We propose and study numerically the implicit approximation in time of the Navier--Stokes equations by a Galerkin-collocation method in time combined with inf-sup stable finite element methods in space.
Edit intent: fluency
Original:  The conceptual basis of the Galerkin--collocation approach is the establishment of a direct connection between the Galerkin method and the classical collocation methods, with the perspective of achieving the accuracy of the former with reduced computational costs in terms of less complex algebraic systems of the latter.
Revised:  The conceptual basis of the Galerkin-collocation approach is the establishment of a direct connection between the Galerkin method and the classical collocation methods, with the perspective of achieving the accuracy of the former with reduced computational costs in terms of less complex algebraic systems of the latter.
Edit intent: fluency
Original:  As a further ingredient, we employ the Nitsche method to impose all boundary conditions in weak form .
Revised:  As a further ingredient, we employ Nitsche's method to impose all boundary conditions in weak form .
Edit intent: fluency
Original:  Then, we propose a multi-robot exploration algorithm for hunters and a multi-robot task allocation algorithm for gatherers, both in a distributed manner and based on innovative notions of " certainty and uncertainty profit margins "  . Statistical analysis of  simulation results confirms the efficacy of the proposed algorithms . Besides, it is statistically proven that the proposed solutions function fairly, i.e. for each type of agent , the overall workload is distributed equally .
Revised:  Then, we propose a multi-robot exploration algorithm for hunters and a multi-robot exploration algorithm for hunters based on innovative notions of " certainty and uncertainty profit margins " . Statistical analysis of simulation results confirms the efficacy of the proposed algorithms . Besides, it is statistically proven that the proposed solutions function fairly, i.e. for each type of agent , the overall workload is distributed equally .
Edit intent: clarity
Original:  Then, we propose a multi-robot exploration algorithm for hunters and a multi-robot task allocation algorithm for gatherers, both in a distributed manner and based on innovative notions of " certainty and uncertainty profit margins "  . Statistical analysis of  simulation results confirms the efficacy of the proposed algorithms . Besides, it is statistically proven that the proposed solutions function fairly, i.e. for each type of agent , the overall workload is distributed equally .
Revised:  Then, we propose a multi-robot exploration algorithm for hunters and a multi-robot task allocation algorithm for gatherers, both in a distributed manner and based on innovative notions of " certainty and uncertainty profit margins " . Statistical analysis of extensive simulation results confirms the efficacy of the proposed algorithms . Besides, it is statistically proven that the proposed solutions function fairly, i.e. for each type of agent , the overall workload is distributed equally .
Edit intent: clarity
Original:  Then, we propose a multi-robot exploration algorithm for hunters and a multi-robot task allocation algorithm for gatherers, both in a distributed manner and based on innovative notions of " certainty and uncertainty profit margins "  . Statistical analysis of  simulation results confirms the efficacy of the proposed algorithms . Besides, it is statistically proven that the proposed solutions function fairly, i.e. for each type of agent , the overall workload is distributed equally .
Revised:  Then, we propose a multi-robot exploration algorithm for hunters and a multi-robot task allocation algorithm for gatherers, both in a distributed manner and based on innovative notions of " certainty and uncertainty profit margins " . Statistical analysis of simulation results confirms the efficacy of the proposed algorithms . Besides, it is statistically proven that the overall workload is distributed equally for each type of agent , the overall workload is distributed equally .
Edit intent: clarity
Original: We restate theorems of Hutchinson on list-colouring extendability for outerplanar graphs in terms of non-vanishing monomials in a graph polynomial, this way obtaining Alon-Tarsi equivalent for her work.
Revised: We restate theorems of Hutchinson on list-colouring extendability for outerplanar graphs in terms of non-vanishing monomials in a graph polynomial, which yields an Alon-Tarsi equivalent for her work.
Edit intent: coherence
Original:  This allows to simplify the proofs as well as obtain more general results.
Revised:  This allows to simplify her proofs as well as obtain more general results.
Edit intent: clarity
Original: Autonomous vehicles (AVs ) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions.
Revised: Automated vehicles (AV ) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions.
Edit intent: clarity
Original: Autonomous vehicles (AVs ) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions.
Revised: Autonomous vehicles (AVs ) have the potential to provide cost-effective mobility options along with system-level benefits in terms of congestion and vehicular emissions.
Edit intent: clarity
Original:  In this study, we propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on a freeway network which accounts for commuters' demand split among AVs and LVs via a logit model.
Revised:  We propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on a freeway network which accounts for commuters' demand split among AVs and LVs via a logit model.
Edit intent: coherence
Original:  Our numerical results reveal that the optimal lane design of freeway network is non-trivial and can inform on the value of accounting for endogenous demand in the proposed freeway network design problem .
Revised:  Our numerical results reveal that the optimal lane design of freeway network is non-trivial and can inform on the value of accounting for endogenous demand in the proposed freeway network design .
Edit intent: clarity
Original: Automated vehicles (AV) have the potential to provide cost-effective mobility options along with  system-level benefits in terms of congestion and vehicular emissions.
Revised: Automated vehicles (AV) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions.
Edit intent: clarity
Original:  We propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on a freeway network which accounts for commuters' demand split among AVs and LVs via a logit model  .
Revised:  However, it is necessary to find the crucial locations in the network where providing these dedicated lanes would reap the maximum benefits. In this study, we propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on a freeway network which accounts for commuters' demand split among AVs and LVs via a logit model .
Edit intent: coherence
Original:  We propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on a freeway network which accounts for commuters' demand split among AVs and LVs via a logit model  .
Revised:  We propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on freeway networks which accounts for commuters' demand split among AVs and LVs via a logit model .
Edit intent: fluency