wanyu/IteraTeR_full_sent huggingface dataset:
Original: We study a model of electoral accountability and selection (EAS) in which voters with heterogeneous horizontal preferences pay limited attention to the incumbent's performance using personalized news aggregators . Extreme voters' aggregators exhibit an own-party bias, which hampers their abilities to discern good and bad performances.
Revised: We study a model of electoral accountability and selection (EAS) in which voters with heterogeneous horizontal preferences pay limited attention to the incumbent's performance data into personalized signals through paying limited attention . Extreme voters' aggregators exhibit an own-party bias, which hampers their abilities to discern good and bad performances.
Edit intent: meaning-changed
Original: We study a model of electoral accountability and selection (EAS) in which voters with heterogeneous horizontal preferences pay limited attention to the incumbent's performance using personalized news aggregators . Extreme voters' aggregators exhibit an own-party bias, which hampers their abilities to discern good and bad performances.
Revised: We study a model of electoral accountability and selection (EAS) in which voters with heterogeneous horizontal preferences pay limited attention to the incumbent's performance using personalized news aggregators . Extreme voters' signals exhibit an own-party bias, which hampers their abilities to discern good and bad performances.
Edit intent: clarity
Original: The brain performs many nonlinear computations through intricate spiking neural networks (SNNs). How neural network dynamics relate to arbitrary computations under these constraints is still an open question. As a strong constraint, these networks are hypothesized to be robust to perturbations and use minimal energy. The theory of Spike Coding Networks (SCNs)derives the required connectivity and dynamics for both information representation and linear dynamical systems from first principles, and achieves robustness and efficiency.Nonlinear dynamical systems have thus far only been implemented in SCNs by filtering neural inputs through sets of nonlinear dendritic basis functions.While this approach works well, it relies on providing a rich enough basis set as well as supervised trainingof the connectivity weights. Another way to implement nonlinear computations is through multiplicatively interacting synapses. However, there is currently no principled way to implement such synapses in SCNs. Here ,  we extend the core SCN derivations to implement polynomial dynamical systems, from which also the need for such multiplicatively interacting synapses arises .
Revised: The brain performs many nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While recurrent spiking networks implementing linear computations can be directly derived and easily understood (e.g., in the spike coding network framework), the connectivity required for nonlinear computations can be harder to interpret, as they require additional non-linearities (e.g. , we extend the core SCN derivations to implement polynomial dynamical systems, from which also the need for such multiplicatively interacting synapses arises .
Edit intent: coherence
Original:  However, there is currently no principled way to implement such synapses in SCNs. Here ,  we extend the core SCN derivations to implement polynomial dynamical systems, from which also the need for such multiplicatively interacting synapses arises .
Revised:  However, there is currently no principled way to implement such synapses in SCNs. Here , dendritic or synaptic) weighted through supervised training. Here we extend the core SCN derivations to implement polynomial dynamical systems, from which also the need for such multiplicatively interacting synapses arises .
Edit intent: meaning-changed
Original:  However, there is currently no principled way to implement such synapses in SCNs. Here ,  we extend the core SCN derivations to implement polynomial dynamical systems, from which also the need for such multiplicatively interacting synapses arises .
Revised:  However, there is currently no principled way to implement such synapses in SCNs. Here , we extend the spike coding framework to implement any polynomial dynamical system. This results in networks requiring multiplicative synapses, which we term the multiplicative spike coding network (mSCN) .
Edit intent: meaning-changed
Original:  We demonstrate our approach with a highly accurate Lorenz attractor implementation, as well as a second-order approximation of a double pendulum. We additionally demonstrate how to implement higher-order polynomials using sequential networks with only pair-wise synapses.
Revised:  We demonstrate how the required connectivity for several nonlinear dynamical systems can be directly implemented in mSCNs, without training. We also show how to carry out higher-order polynomials using sequential networks with only pair-wise synapses.
Edit intent: meaning-changed
Original:  We additionally demonstrate how to implement higher-order polynomials using sequential networks with only pair-wise synapses. Finally, we derive upper bounds and expected numbers of connections based on the sparsity of the underlying representation .
Revised:  We additionally demonstrate how to implement higher-order polynomials using sequential networks with only pair-wise multiplicative synapses, and provide expected numbers of connections based on the sparsity of the underlying representation .
Edit intent: clarity
Original:  Overall, our work provides an alternative way to directly implement nonlinear computations in spike coding networks, and expands our understanding about the potential functions of multiplicative synapses. Furthermore, due to the high accuracy and low energy usage of our approach , this work may be of interest for neuromorphic computing.
Revised:  Overall, our work provides an alternative way to directly implement nonlinear computations in spiking neural networks, while keeping all the attractive features of standard SCNs (such as robustness, irregular and sparse firing, and interpretable connectivity). Finally, we discuss the biological plausibility of our approach, and how the high accuracy and low energy usage of our approach , this work may be of interest for neuromorphic computing.
Edit intent: meaning-changed
Original:  While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the infinite symmetric group  on the natural numbers .
Revised:  While developing rearrangement operations on the natural numbers, we discovered that the bi-immune rearrangements generate an uncountable subgroup of the infinite symmetric group (Sym(\mathbb{N on the natural numbers .
Edit intent: meaning-changed
Original:  Using GPA, we obtained speedups on a Volta V100 GPU ranging from 1.03\times to 3.86 \times, with a geometric mean of 1.22\times.
Revised:  Using GPA, we obtained speedups on a Volta V100 GPU ranging from 1.01\times to 3.53 \times, with a geometric mean of 1.22\times.
Edit intent: meaning-changed
Original:  \%introduced the Ranking algorithm with the optimal 1-\frac{1 Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called AdWords driven by online advertising and obtained the optimal 1-1{e} competitive ratio in the special case of small bids .
Revised:  Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called AdWords driven by online advertising and obtained the optimal 1-1{e} competitive ratio in the special case of small bids .
Edit intent: clarity
Original:  \%introduced the Ranking algorithm with the optimal 1-\frac{1 Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called AdWords driven by online advertising and obtained the optimal 1-1{e} competitive ratio in the special case of small bids .
Revised:  \%introduced the Ranking algorithm with the optimal 1-\frac{1 Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called AdWords driven by online advertising and obtained the optimal 1-1{e} competitive ratio in the special case of small bids .
Edit intent: fluency
Original:  Inserting a segment amounts to delete all the triangles it intersects , define two polygons that fill the so generated hole and have the segment as shared basis, and then re-triangulate each polygon separately.
Revised:  Inserting a segment amounts to : (1) deleting all the triangles it intersects , define two polygons that fill the so generated hole and have the segment as shared basis, and then re-triangulate each polygon separately.
Edit intent: meaning-changed
Original:  Inserting a segment amounts to delete all the triangles it intersects , define two polygons that fill the so generated hole and have the segment as shared basis, and then re-triangulate each polygon separately.
Revised:  Inserting a segment amounts to delete all the triangles it intersects ; (2) filling the so generated hole and have the segment as shared basis, and then re-triangulate each polygon separately.
Edit intent: meaning-changed
Original:  Inserting a segment amounts to delete all the triangles it intersects , define two polygons that fill the so generated hole and have the segment as shared basis, and then re-triangulate each polygon separately.
Revised:  Inserting a segment amounts to delete all the triangles it intersects , define two polygons that fill the so generated hole with two polygons that have the wanted segment as shared basis, and then re-triangulate each polygon separately.
Edit intent: clarity
Original:  Inserting a segment amounts to delete all the triangles it intersects , define two polygons that fill the so generated hole and have the segment as shared basis, and then re-triangulate each polygon separately.
Revised:  Inserting a segment amounts to delete all the triangles it intersects , define two polygons that fill the so generated hole and have the segment as shared edge; (3) triangulate each polygon separately.
Edit intent: meaning-changed
Original:  In this paper we prove that the polygons generated evacuating the triangles that intersect a constrained segment are such that all their convex vertices but two can be used to form triangles in an earcut fashion, without the need to check whether other polygon points are located within each ear.
Revised:  In this paper we prove that these polygons are such that all their convex vertices but two can be used to form triangles in an earcut fashion, without the need to check whether other polygon points are located within each ear.
Edit intent: coherence
Original:  Drawing inspiration from models in biology, physics, and social psychology, we apply a sigmoidal saturating function to inter-agent and intra-agent exchanges of opinions. The saturating function is the only nonlinearity in the model, yet we prove how it yields rapid and reliable formation of consensus, dissensus , and opinion cascades as a function of just a few parameters.
Revised:  Drawing inspiration from models in biology, physics, and social psychology, we apply a sigmoidal saturating function to inter-agent and intra-agent opinion exchanges. This yields simply parameterized dynamics that exhibit the range of opinion formation behaviors predicted by model-independent bifurcation theory but not exhibited by linear models or existing nonlinear models. Behaviors include rapid and reliable formation of consensus, dissensus , and opinion cascades as a function of just a few parameters.
Edit intent: meaning-changed
Original:  The saturating function is the only nonlinearity in the model, yet we prove how it yields rapid and reliable formation of consensus, dissensus , and opinion cascades as a function of just a few parameters.
Revised:  The saturating function is the only nonlinearity in the model, yet we prove how it yields rapid and reliable formation of multistable consensus and dissensus states, even in homogeneous networks, as well as ultra-sensitivity to inputs , and opinion cascades as a function of just a few parameters.
Edit intent: meaning-changed
Original:  The saturating function is the only nonlinearity in the model, yet we prove how it yields rapid and reliable formation of consensus, dissensus , and opinion cascades as a function of just a few parameters. We further show how the network opinion dynamics exhibit both robustness to disturbance and ultrasensitivity to inputs. We design feedback dynamics for system parameters that enable active tuning of implicit thresholds in opinion formation for sensitivity to inputs, robustness to changes in input, opinion cascades, and flexible transitions between consensus and dissensus .
Revised:  The saturating function is the only nonlinearity in the model, yet we prove how it yields rapid and reliable formation of consensus, dissensus , robustness to changes in input, opinion cascades, and flexible transitions between consensus and dissensus .
Edit intent: coherence
Original:  We design feedback dynamics for system parameters that enable active tuning of implicit thresholds in opinion formation for sensitivity to inputs, robustness to changes in input, opinion cascades, and flexible transitions between consensus and dissensus . The general model can be used for systematic control design in a range of engineering problems including network systems, multi-robot coordination, task allocation, and decision making for spatial navigation. It can also be used for systematic examination of questions in biology and social science ranging from cognitive control and networksin the brain, to resilience in collective animal behavior to changing environmental conditions, to information spreading and political polarization in social networks .
Revised:  We design feedback dynamics for system parameters that enable active tuning of implicit thresholds in opinion formation for sensitivity to inputs, robustness to changes in input, opinion cascades, and flexible transitions between consensus and dissensus , and opinion cascades. Augmenting the opinion dynamics with feedback dynamics for the attention parameter results in tunable thresholds that govern sensitivity and robustness. The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization in social networks .
Edit intent: clarity
Original:  It can also be used for systematic examination of questions in biology and social science ranging from cognitive control and networksin the brain, to resilience in collective animal behavior to changing environmental conditions, to information spreading and political polarization in social networks .
Revised:  It can also be used for systematic examination of questions in biology and social science ranging from cognitive control and networksin the brain, to resilience in collective animal behavior to changing environmental conditions, to information spreading and political polarization to collective decision making and dynamic task allocation .
Edit intent: clarity
Original:  We extend the famous EXTRA and DIGing methods with accelerated variance reduction (VR), and propose two methods , which require the time of O(( \sqrt{n\kappa_s +n)\log1{\epsilon})
Revised:  We extend the widely used EXTRA and DIGing methods with accelerated variance reduction (VR), and propose two methods , which require the time of O(( \sqrt{n\kappa_s +n)\log1{\epsilon})
Edit intent: clarity
Original:  We extend the famous EXTRA and DIGing methods with accelerated variance reduction (VR), and propose two methods , which require the time of O(( \sqrt{n\kappa_s +n)\log1{\epsilon})
Revised:  We extend the famous EXTRA and DIGing methods with variance reduction (VR), and propose two methods , which require the time of O(( \sqrt{n\kappa_s +n)\log1{\epsilon})
Edit intent: clarity
Original:  We extend the famous EXTRA and DIGing methods with accelerated variance reduction (VR), and propose two methods , which require the time of O(( \sqrt{n\kappa_s +n)\log1{\epsilon})
Revised:  We extend the famous EXTRA and DIGing methods with accelerated variance reduction (VR), and propose two methods : VR-EXTRA and VR-DIGing. The proposed VR-EXTRA requires the time of O(( \sqrt{n\kappa_s +n)\log1{\epsilon})
Edit intent: meaning-changed
Original:  We extend the famous EXTRA and DIGing methods with accelerated variance reduction (VR), and propose two methods , which require the time of O(( \sqrt{n\kappa_s +n)\log1{\epsilon})
Revised:  We extend the famous EXTRA and DIGing methods with accelerated variance reduction (VR), and propose two methods , which require the time of O(( \kappa_s +n)\log1{\epsilon})
Edit intent: meaning-changed
Original:  stochastic gradient evaluations and O( \sqrt{\kappa_b\kappa_c \log1{\epsilon}) communication rounds to reach precision \epsilon, where \kappa_s and \kappa_b are the stochastic condition number and batch condition number for strongly convex and smooth problems,  \kappa_c is the condition number of the communication network, and n is the sample size on each distributed node.
Revised:  stochastic gradient evaluations and O( (\kappa_b+\kappa_c) \log1{\epsilon}) communication rounds to reach precision \epsilon, where \kappa_s and \kappa_b are the stochastic condition number and batch condition number for strongly convex and smooth problems, \kappa_c is the condition number of the communication network, and n is the sample size on each distributed node.
Edit intent: meaning-changed
Original:  stochastic gradient evaluations and O( \sqrt{\kappa_b\kappa_c \log1{\epsilon}) communication rounds to reach precision \epsilon, where \kappa_s and \kappa_b are the stochastic condition number and batch condition number for strongly convex and smooth problems,  \kappa_c is the condition number of the communication network, and n is the sample size on each distributed node.
Revised:  stochastic gradient evaluations and O( \sqrt{\kappa_b\kappa_c \log1{\epsilon}) communication rounds to reach precision \epsilon, where \kappa_s and \kappa_b are the stochastic condition number and batch condition number for strongly convex and smooth problems, respectively, \kappa_c is the condition number of the communication network, and n is the sample size on each distributed node.
Edit intent: clarity
Original:  } Our stochastic gradient computation complexity is the same as the  single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
Revised:  } Our stochastic gradient computation complexities are the same as the single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
Edit intent: clarity
Original:  } Our stochastic gradient computation complexity is the same as the  single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
Revised:  } Our stochastic gradient computation complexity is the same as the ones of single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
Edit intent: clarity
Original:  } Our stochastic gradient computation complexity is the same as the  single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
Revised:  } Our stochastic gradient computation complexity is the same as the single-machine VR methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
Edit intent: meaning-changed
Original:  } Our stochastic gradient computation complexity is the same as the  single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
Revised:  } Our stochastic gradient computation complexity is the same as the single-machine accelerated variance reduction methods, such as SAG, SAGA, and SVRG, and our communication complexities keep the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal.
Edit intent: meaning-changed
Original:  } Our stochastic gradient computation complexity is the same as the  single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as the accelerated full batch decentralized methods, such as MSDA, and they are both optimal. We also propose the non-accelerated VR based EXTRA and DIGing, and provide explicit complexities, for example, the O(( \kappa_s +n)\log\frac{1}{\epsilon}) stochastic gradient computation complexity and the O((\kappa_b+\kappa_c) \log\frac{1}{\epsilon}) communication complexity for the VR based EXTRA.
Revised:  } Our stochastic gradient computation complexity is the same as the single-machine accelerated variance reduction methods, such as Katyusha, and our communication complexity is the same as those of EXTRA and DIGing, respectively. To further speed up the convergence, we also propose the non-accelerated VR based EXTRA and DIGing, and provide explicit complexities, for example, the O(( \kappa_s +n)\log\frac{1}{\epsilon}) stochastic gradient computation complexity and the O((\kappa_b+\kappa_c) \log\frac{1}{\epsilon}) communication complexity for the VR based EXTRA.
Edit intent: clarity
Original:  We also propose the non-accelerated VR based EXTRA and DIGing, and provide explicit complexities, for example, the O(( \kappa_s +n)\log\frac{1}{\epsilon}) stochastic gradient computation complexity and the O((\kappa_b+\kappa_c) \log\frac{1}{\epsilon}) communication complexity for the VR based EXTRA.
Revised:  We also propose the accelerated VR-EXTRA and VR-DIGing with both the optimal O(( \kappa_s +n)\log\frac{1}{\epsilon}) stochastic gradient computation complexity and the O((\kappa_b+\kappa_c) \log\frac{1}{\epsilon}) communication complexity for the VR based EXTRA.
Edit intent: clarity
Original:  We also propose the non-accelerated VR based EXTRA and DIGing, and provide explicit complexities, for example, the O(( \kappa_s +n)\log\frac{1}{\epsilon}) stochastic gradient computation complexity and the O((\kappa_b+\kappa_c) \log\frac{1}{\epsilon}) communication complexity for the VR based EXTRA.
Revised:  We also propose the non-accelerated VR based EXTRA and DIGing, and provide explicit complexities, for example, the O(( \sqrt{n\kappa_s +n)\log\frac{1}{\epsilon}) stochastic gradient computation complexity and the O((\kappa_b+\kappa_c) \log\frac{1}{\epsilon}) communication complexity for the VR based EXTRA.
Edit intent: meaning-changed
Original:  We also propose the non-accelerated VR based EXTRA and DIGing, and provide explicit complexities, for example, the O(( \kappa_s +n)\log\frac{1}{\epsilon}) stochastic gradient computation complexity and the O((\kappa_b+\kappa_c) \log\frac{1}{\epsilon}) communication complexity for the VR based EXTRA.
Revised:  We also propose the non-accelerated VR based EXTRA and DIGing, and provide explicit complexities, for example, the O(( \kappa_s +n)\log\frac{1}{\epsilon}) stochastic gradient computation complexity and O(\sqrt{\kappa_b\kappa_c \log\frac{1}{\epsilon}) communication complexity for the VR based EXTRA.
Edit intent: meaning-changed