wanyu/IteraTeR_full_sent huggingface dataset:
Original:  We prove here that this method is applicable to any linear PDE (of arbitrary order) the source of which is a linear combination of one-dimensional delta distributions and derivatives thereof supported at an arbitrary number of particles. We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience models (describing neural populations ), parabolic equations with applications to financial models (describing price formation), second-order hyperbolic equations with applications to wave acoustics, and finally elliptic(Poisson) equations .
Revised:  We prove here that this method is applicable to any linear PDE (of arbitrary order) the source of which is a linear combination of one-dimensional delta distributions and derivatives thereof supported on a one-dimensional subspace of the problem domain. We then implement it to numerically solve a variety of relevant PDEs: hyperbolic ( with applications to neuroscience models (describing neural populations ), parabolic equations with applications to financial models (describing price formation), second-order hyperbolic equations with applications to wave acoustics, and finally elliptic(Poisson) equations .
Edit intent: clarity
Original:  We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience models (describing neural populations ), parabolic equations with applications to financial models (describing price formation), second-order hyperbolic equations with applications to wave acoustics, and finally elliptic(Poisson) equations .
Revised:  We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience and acoustics ), parabolic equations with applications to financial models (describing price formation), second-order hyperbolic equations with applications to wave acoustics, and finally elliptic(Poisson) equations .
Edit intent: clarity
Original:  We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience models (describing neural populations ), parabolic equations with applications to financial models (describing price formation), second-order hyperbolic equations with applications to wave acoustics, and finally elliptic(Poisson) equations .
Revised:  We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience models (describing neural populations ), parabolic ( with applications to financial models (describing price formation), second-order hyperbolic equations with applications to wave acoustics, and finally elliptic(Poisson) equations .
Edit intent: fluency
Original:  We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience models (describing neural populations ), parabolic equations with applications to financial models (describing price formation), second-order hyperbolic equations with applications to wave acoustics, and finally elliptic(Poisson) equations .
Revised:  We furthermore apply this method to obtain numerical solutions for various types of distributionally-sourced PDEs: we consider first-order hyperbolic equations with applications to neuroscience models (describing neural populations ), parabolic equations with applications to finance), and elliptic. We generically obtain improved convergence rates relative to typical past implementations relying on delta function approximations .
Edit intent: meaning-changed
Original:  Issues to consider when developing such methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many change points as contained in potentially high-dimensional data sets .
Revised:  Issues to consider when developing change point analysis methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many change points as contained in potentially high-dimensional data sets .
Edit intent: clarity
Original:  Issues to consider when developing such methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many change points as contained in potentially high-dimensional data sets .
Revised:  Issues to consider when developing such methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many changes as contained in potentially high-dimensional data sets .
Edit intent: clarity
Original:  Issues to consider when developing such methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many change points as contained in potentially high-dimensional data sets .
Revised:  Issues to consider when developing such methods include computational demands, difficulties arising from either limited amount of data or a large number of covariates, and arriving at statistical tests with sufficient power to detect as many change points as contained in potentially high-dimensional time series .
Edit intent: clarity
Original:  The method's flexibility to incorporate useful features from other change point detection techniques is highlighted . The advantages of PARCS over existing approaches are demonstrated through a series of simulation experiments,  followed by a real data application to neural recordings from rat medial prefrontal cortex during learning.
Revised:  The method's flexibility to incorporate useful features from other change point detection techniques is highlighted , and its advantages over alternative approaches are demonstrated through a series of simulation experiments, followed by a real data application to neural recordings from rat medial prefrontal cortex during learning.
Edit intent: clarity
Original:  The advantages of PARCS over existing approaches are demonstrated through a series of simulation experiments,  followed by a real data application to neural recordings from rat medial prefrontal cortex during learning.
Revised:  The advantages of PARCS over existing approaches are demonstrated through a series of simulation experiments, along with potential drawbacks and suggestions to remedy them. This is followed by a real data application to neural recordings from rat medial prefrontal cortex during learning.
Edit intent: meaning-changed
Original:  The Moth Olfactory Network is among the simplest biological neural systems that can learn, and its architecture includes key structural elements  widespread in biological neural nets, such as cascaded networks, competitive inhibition, high intrinsic noise, sparsity, reward mechanisms, and Hebbian plasticity.
Revised:  The Moth Olfactory Network is among the simplest biological neural systems that can learn, and its architecture includes key structural elements and mechanisms widespread in biological neural nets, such as cascaded networks, competitive inhibition, high intrinsic noise, sparsity, reward mechanisms, and Hebbian plasticity.
Edit intent: clarity
Original:  We assign a computational model of the Moth Olfactory Network the task of learning to read the MNIST digits. This model, MothNet, is closely aligned with the moth's known biophysics and with in vivo electrode data , including data collected from moths learning new odors.
Revised:  We assign a computational model of the Moth Olfactory Network , closely aligned with the moth's known biophysics and with in vivo electrode data , including data collected from moths learning new odors.
Edit intent: coherence
Original:  In this few-samples regime, it substantially outperforms standard machine learning methods such as nearest-neighbors, support-vector machines, and convolutional neural networks ( CNNs) .
Revised:  In this few-samples regime, it substantially outperforms standard machine learning methods such as nearest-neighbors, support-vector machines, and convolutional neural networks ( NNs), and matches specialized one-shot transfer-learning methods but without the need for pre-training .
Edit intent: meaning-changed
Original:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains , can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of DNNs current learning rate limitations .
Revised:  The MothNet architecture illustrates how algorithmic structures derived from biological brains , can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of DNNs current learning rate limitations .
Edit intent: clarity
Original:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains , can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of DNNs current learning rate limitations .
Revised:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of DNNs current learning rate limitations .
Edit intent: fluency
Original:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains , can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of DNNs current learning rate limitations .
Revised:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains , can be used to build alternative NNs that may avoid some of DNNs current learning rate limitations .
Edit intent: clarity
Original:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains , can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of DNNs current learning rate limitations .
Revised:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains , can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of the learning rate limitations .
Edit intent: clarity
Original:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains , can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of DNNs current learning rate limitations . This novel, bio-inspired neural network architecture offers a valuable complementary approach to DNN design .
Revised:  The MothNet architecture illustrates how our proposed algorithmic structures , derived from biological brains , can be used to build alternative deep neural nets (DNNs) that may potentially avoid some of DNNs current learning rate limitations of current engineered NNs .
Edit intent: clarity
Original: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O   if there is an O -staircase contained in P that connects them .
Revised: Let \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O if there is an O -staircase contained in P that connects them .
Edit intent: clarity
Original: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O   if there is an O -staircase contained in P that connects them .
Revised: Given a set \mathcal{O of k orientations in the plane, and let P be a simple polygon P \mathcal{O if there is an O -staircase contained in P that connects them .
Edit intent: meaning-changed
Original: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O   if there is an O -staircase contained in P that connects them .
Revised: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon in the plane. Given two points p,q inside P, we say that p \mathcal{O if there is an O -staircase contained in P that connects them .
Edit intent: meaning-changed
Original: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O   if there is an O -staircase contained in P that connects them .
Revised: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O sees if there is an O -staircase contained in P that connects them .
Edit intent: fluency
Original: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O   if there is an O -staircase contained in P that connects them .
Revised: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O q if there is an O -staircase contained in P that connects them .
Edit intent: meaning-changed
Original: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O   if there is an O -staircase contained in P that connects them .
Revised: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O if there is an O - contained in P that connects them .
Edit intent: meaning-changed
Original: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O   if there is an O -staircase contained in P that connects them .
Revised: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O if there is an O -staircasestaircase contained in P that connects them .
Edit intent: fluency
Original: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O   if there is an O -staircase contained in P that connects them .
Revised: Given a set \mathcal{O of k orientations in the plane, two points inside a simple polygon P \mathcal{O if there is an O -staircase contained in P that connects p and q .
Edit intent: meaning-changed
Original:  This work initiates the study of the computation and maintenance of the \mathcal{O}-{\rm Kernel } of a polygon P as we rotate the set \mathcal{O} by an angle \theta, denoted \mathcal{O}-{\rm Kernel }_{\theta}(P).
Revised:  This work initiates the study of the computation and maintenance of \mathcal{O}-{\rm Kernel } of a polygon P as we rotate the set \mathcal{O} by an angle \theta, denoted \mathcal{O}-{\rm Kernel }_{\theta}(P).
Edit intent: fluency
Original:  This work initiates the study of the computation and maintenance of the \mathcal{O}-{\rm Kernel } of a polygon P as we rotate the set \mathcal{O} by an angle \theta, denoted \mathcal{O}-{\rm Kernel }_{\theta}(P).
Revised:  This work initiates the study of the computation and maintenance of the \mathcal{O}-{\rm Kernel } (P) as we rotate the set \mathcal{O} by an angle \theta, denoted \mathcal{O}-{\rm Kernel }_{\theta}(P).
Edit intent: clarity
Original:  In particular, we  is formed by either one or two orthogonal orientations, \mathcal{O}=\{0^\circ\} or \mathcal{O}=\{0^\circ,90^\circ\}.
Revised:  In particular, we consider the case when the set \mathcal{O is formed by either one or two orthogonal orientations, \mathcal{O}=\{0^\circ\} or \mathcal{O}=\{0^\circ,90^\circ\}.
Edit intent: clarity
Original: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}}  -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}}  -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Revised: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where \}} -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}} -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Edit intent: fluency
Original: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}}  -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}}  -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Revised: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}} : (i) \mathcal{O -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}} -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Edit intent: meaning-changed
Original: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}}  -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}}  -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Revised: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}} -{\rm Kernel }_{\theta}(P) is not empty , (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}} -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Edit intent: fluency
Original: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}}  -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}}  -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Revised: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}} -{\rm Kernel }_{\theta}(P) is not empty and (ii) 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}} -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Edit intent: meaning-changed
Original: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}}  -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}}  -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Revised: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}} -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in {2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}} -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Edit intent: coherence
Original: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}}  -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}}  -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Revised: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}} -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}} \mathcal{O -{\rm Kernel }_{\theta}(P) are maximum or minimum.
Edit intent: meaning-changed
Original: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}}  -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}}  -{\rm Kernel }_{\theta}(P) are maximum or minimum. These results extend previous works by Gewali, Palios, Rawlins, Schuierer, and Wood .
Revised: {\rm Kernel }_{\theta}(P) while \theta varies in [-\frac{\pi}{2},\frac{\pi}{2}), obtaining the angular intervals where the \{0^{o\}} -{\rm Kernel }_{\theta}(P) is not empty and (ii) for orthogonal polygons P, computing the orientation \theta\in 0, \frac{\pi{2}) such that the area and/or the perimeter of the \{0^{o},90^{o}\}} -{\rm Kernel }_{\theta}(P) optimizes area or perimeter. Further, we show how the algorithms can be improved when P is a simple orthogonal polygon .
Edit intent: meaning-changed
Original:  By considering a "maximum likelihood" criterion function, our estimator becomes the K-ML estimator in Aguirregabiria and Mira (  2007) . By considering a "minimum distance" criterion function, it defines a new K-MD estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) .
Revised:  By considering a "maximum likelihood" criterion function, our estimator becomes the K-ML estimator in Aguirregabiria and Mira ( 2007) , Pesendorfer and Schmidt-Dengler (2008) .
Edit intent: coherence
Original:  By considering a "minimum distance" criterion function, it defines a new K-MD estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) .
Revised:  By considering a "minimum distance" criterion function, it defines a new K-MD estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) , and Pakes et al. (2007).
Edit intent: meaning-changed
Original:  First, the optimal 1-MD estimator is optimal in the class of K-MD estimators for all K . In other words, additional policy iterations do not provide asymptotic efficiency gains relative to the optimal 1-MD estimator.
Revised:  First, the optimal 1-MD estimator is optimal in the class of K-MD estimators . In other words, additional policy iterations do not provide asymptotic efficiency gains relative to the optimal 1-MD estimator.
Edit intent: clarity
Original:  Second, the optimal 1-MD estimator is more or equally asymptotically efficient than any K-ML estimator for all K  .
Revised:  Second, the optimal 1-MD estimator is more or equally asymptotically efficient than any K-ML estimator for all K . Finally, the appendix provides appropriate conditions under which the optimal 1-MD estimator is asymptotically efficient .
Edit intent: meaning-changed