wanyu/IteraTeR_v2 huggingface dataset:
Original:  The running time of both these algorithms , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi}  ] \emph{ - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Revised:  The running time of both these algorithms , however, is d^{\Omega(1/\alpha^4) and the error bounds on \|\Pi} RY] \emph{ - \Pi_*\|_F grow with r (which can be \Omega(d) ) . In this work, we improve on these results on all three fronts: dimension-independent error via a faster fixed-polynomial running time under less restrictive distributional assumptions.
Edit intent: clarity
Original:  Our result only needs D to have certifiably hypercontractive degree 2 polynomials - a condition satisfied by a much broader family of distributions in contrast to certifiable anticoncentration .
Revised:  Our result only needs D to have certifiably hypercontractive degree 2 polynomials .
Edit intent: clarity
Original:  As a result, in addition to Gaussians, our algorithm applies to  uniform distribution on the hypercube and q-ary cubes and arbitrary product distributions with subgaussian marginals.
Revised:  As a result, in addition to Gaussians, our algorithm applies to the uniform distribution on the hypercube and q-ary cubes and arbitrary product distributions with subgaussian marginals.
Edit intent: fluency
Original:  Given a network system with a proactive defense strategy, an intelligent attacker needs to repeatedly perform reconnaissance to learn about the locations of intrusion detection systems and re-plan optimally to reach the target while avoiding detection.
Revised:  Given a network system with a proactive defense strategy, an intelligent attacker needs to perform reconnaissance repeatedly to learn about the locations of intrusion detection systems and re-plan optimally to reach the target while avoiding detection.
Edit intent: fluency
Original:  To compute the attacker's strategy for security evaluation, we develop a receding-horizon planning algorithm in a risk-sensitive Markov decision process with a time-varying reward function.
Revised:  To compute the attacker's strategy for security evaluation, we develop a receding-horizon planning algorithm using a risk-sensitive Markov decision process with a time-varying reward function.
Edit intent: clarity
Original:  This study provides insights for designing proactive defense strategies against online and multi-stage attacks carried out by a resourceful attacker.
Revised:  This study provides insights for designing proactive defense strategies against online and multi-stage attacks by a resourceful attacker.
Edit intent: clarity
Original:  In this work, we utilize the PageRank function on the lower-star filtration of the graph as input to persistent homology to study the problem of graph similarity.
Revised:  In this article, we use the PageRank function on the lower-star filtration of the graph as input to persistent homology to study the problem of graph similarity.
Edit intent: clarity
Original:  In this work, we utilize the PageRank function on the lower-star filtration of the graph as input to persistent homology to study the problem of graph similarity.
Revised:  In this work, we utilize the PageRank function along with persistent homology to study the problem of graph similarity.
Edit intent: clarity
Original:  This cannibalization appears to set limits on the integration of wind and solar, and thus contradict studies that show that high shares are cost effective.
Revised:  This cannibalization appears to set limits on the integration of wind and solar, and thus contradicts studies that show that high shares are cost effective.
Edit intent: fluency
Original:  Correlated generation from variable renewable sources depresses market prices, which can cause wind and solar to cannibalize their own revenues and prevent them from covering their costs from the market.
Revised:  Correlated generation from variable renewable sources depresses market prices, which can cause wind and solar to cannibalise their own revenues and prevent them from covering their costs from the market.
Edit intent: fluency
Original:  This cannibalization appears to set limits on the integration of wind and solar, and thus contradicts studies that show that high shares are cost effective.
Revised:  This cannibalisation appears to set limits on the integration of wind and solar, and thus contradicts studies that show that high shares are cost effective.
Edit intent: fluency
Original:  This cannibalization appears to set limits on the integration of wind and solar, and thus contradicts studies that show that high shares are cost effective.
Revised:  This cannibalization appears to set limits on the integration of wind and solar, and thus to contradict studies that show that high shares are cost effective.
Edit intent: fluency
Original:  Here we show from theory and with numerical examples how market incentives interact with prices, revenue and costs for renewable electricity systems.
Revised:  Here we show from theory and with simulation examples how market incentives interact with prices, revenue and costs for renewable electricity systems.
Edit intent: clarity
Original: We discuss the problem of learning collaborative behaviour  in multi-agent systems using deep reinforcement learning (DRL) . A connectivity-driven communication (CDC) algorithm is proposed to address three key aspects: what agents to involve in the communication, what information content to share, and how often to share it.
Revised: We discuss the problem of learning collaborative behaviour through communication in multi-agent systems using deep reinforcement learning (DRL) . A connectivity-driven communication (CDC) algorithm is proposed to address three key aspects: what agents to involve in the communication, what information content to share, and how often to share it.
Edit intent: clarity
Original: We discuss the problem of learning collaborative behaviour  in multi-agent systems using deep reinforcement learning (DRL) . A connectivity-driven communication (CDC) algorithm is proposed to address three key aspects: what agents to involve in the communication, what information content to share, and how often to share it.
Revised: We discuss the problem of learning collaborative behaviour in multi-agent systems using deep reinforcement learning . A connectivity-driven communication (CDC) algorithm is proposed to address three key aspects: what agents to involve in the communication, what information content to share, and how often to share it.
Edit intent: clarity
Original:  We introduce the notion of a connectivity network, modelled as a weighted graph , where nodes represent agentsand edges represent the degree of connectivity between pairs of agents .
Revised:  The multi-agent system is modelled as a weighted graph , where nodes represent agentsand edges represent the degree of connectivity between pairs of agents .
Edit intent: clarity
Original:  We introduce the notion of a connectivity network, modelled as a weighted graph , where nodes represent agentsand edges represent the degree of connectivity between pairs of agents .
Revised:  We introduce the notion of a connectivity network, modelled as a weighted graph with nodes representing agents. The unknown edge weights reflect the degree of connectivity between pairs of agents .
Edit intent: clarity
Original:  We introduce the notion of a connectivity network, modelled as a weighted graph , where nodes represent agentsand edges represent the degree of connectivity between pairs of agents .
Revised:  We introduce the notion of a connectivity network, modelled as a weighted graph , where nodes represent agentsand edges represent the degree of communication between pairs of agents .
Edit intent: clarity
Original:  The optimal graph topology is learned end-to-end concurrently with the stochastic policy so as to maximise future expected returns.
Revised:  The optimal graph topology is learned end-to-end concurrently with the agents' policy so as to maximise future expected returns.
Edit intent: clarity
Original:  The communication patterns depend on the graph's topology through a diffusion process on the graph, the heat kernel, which is found by exponentiating the Laplacian eigensystem through time and is fully differentiable.
Edit intent: coherence
Original:  We survey several current visualizations .
Revised:  We plot several examples and study the benefits and limitations of each technique .
Edit intent: clarity
Original:  We then introduce an approach that can take advantage of colormaps in python 's matplotlib library and describe an implementation  .
Revised:  We then introduce a method of visualization that can take advantage of colormaps in python 's matplotlib library and describe an implementation .
Edit intent: clarity
Original:  We then introduce an approach that can take advantage of colormaps in python 's matplotlib library and describe an implementation  .
Revised:  We then introduce an approach that can take advantage of colormaps in Python 's matplotlib library and describe an implementation .
Edit intent: fluency
Original:  We then introduce an approach that can take advantage of colormaps in python 's matplotlib library and describe an implementation  .
Revised:  We then introduce an approach that can take advantage of colormaps in python 's matplotlib library , describe an implementation .
Edit intent: fluency
Original:  Here, we discuss insights that we can draw from these models  , especially as inputs for designing strategies to control the epidemics.
Revised:  Here, the insights that can be drawn from these models , especially as inputs for designing strategies to control the epidemics.
Edit intent: clarity
Original:  Here, we discuss insights that we can draw from these models  , especially as inputs for designing strategies to control the epidemics.
Revised:  Here, we discuss insights that we can draw from these models are discussed , especially as inputs for designing strategies to control the epidemics.
Edit intent: clarity
Original:  We also present proposed model-based strategies on how to prevent the spread of the disease in local setting, such as during large social gatherings  .
Revised:  Proposed model-based strategies on how to prevent the spread of the disease in local setting, such as during large social gatherings .
Edit intent: coherence
Original: In this paper, we propose  a novel diagonal sweeping domain decomposition method  with source transfer for solving the high-frequency Helmholtz equation in R^n with n%DIFDELCMD < }%%% =2 or 3.
Revised: In this paper, we propose a novel diagonal sweeping domain decomposition method with source transfer for solving the high-frequency Helmholtz equation in R^n n%DIFDELCMD < }%%% =2 or 3.
Edit intent: fluency
Original: In this paper, we propose  a novel diagonal sweeping domain decomposition method  with source transfer for solving the high-frequency Helmholtz equation in R^n with n%DIFDELCMD < }%%% =2 or 3.
Revised: In this paper, we propose a novel diagonal sweeping domain decomposition method with source transfer for solving the high-frequency Helmholtz equation in R^n with %DIFDELCMD < }%%% =2 or 3.
Edit intent: clarity
Original:  In this method , the computational domain is partitioned into structured subdomains along all spatial directions (i.e., checkerboard domain decomposition) and a set of diagonal sweeps over the subdomains are specially designed to solve the global system efficiently.
Revised:  In this method , the computational domain is partitioned into structured subdomains along all spatial directions (i.e., checkerboard domain decomposition) and a set of diagonal sweeps over the subdomains are specially designed to solve the system efficiently.
Edit intent: clarity
Original:  Although the sweeping usually implies sequential subdomain solves, the number of sequential steps required for each sweep in the method is only proportional to the n-th root of the number of subdomains when the domain decomposition is quasi-uniform with respect to all directions, thus the method is very suitable to parallel computing for solving problems with multiple right-hand sides through the pipeline processing.
Revised:  Although the sweeping usually implies sequential subdomain solves, the number of sequential steps required for each sweep in the method is only proportional to the n-th root of the number of subdomains when the domain decomposition is quasi-uniform with respect to all directions, thus it is very suitable to parallel computing for solving problems with multiple right-hand sides through the pipeline processing.
Edit intent: fluency
Original:  Extensive numerical experiments in two and three dimensions are presented to show the effectiveness and efficiency of the proposed method.
Revised:  Extensive numerical experiments in two and three dimensions are presented to demonstrate the effectiveness and efficiency of the proposed method.
Edit intent: fluency
Original:  As } a generalisation of usual Hermite polynomials, which are orthogonal with respect to the weight function |x|^{2\mu }%DIFDELCMD < \e%%% ^{-x^2,\mu>-\frac 12 on the whole line.
Revised:  As } a generalisation of }%DIFDELCMD < \e%%% ^{-x^2,\mu>-\frac 12 on the whole line.
Edit intent: clarity
Original:  As } a generalisation of usual Hermite polynomials, which are orthogonal with respect to the weight function |x|^{2\mu }%DIFDELCMD < \e%%% ^{-x^2,\mu>-\frac 12 on the whole line.
Revised:  As } a generalisation of usual Hermite polynomials, which are orthogonal with respect to the weight function |x|^{2\mu }%DIFDELCMD < \e%%% ,\mu>-\frac 12 on the whole line.
Edit intent: clarity
Original:  The first is to construct the generalised Hermite polynomials and generalised Hermite functions (GHFs) in arbitrary d dimensions, which }  are orthogonal with respect to |\bx|^{2\mu} \e^{-|\bx|^2} and |\bx |^{2\mu}  in \mathbb R^d , respectively.
Revised:  The first is to construct the generalised Hermite polynomials and generalised Hermite functions (GHFs) in arbitrary d dimensions, which } are orthogonal with respect to |\bx|^{2\mu} \e^{-|\bx|^2} (resp. |\bx |^{2\mu} in \mathbb R^d , respectively.
Edit intent: coherence
Original:  The first is to construct the generalised Hermite polynomials and generalised Hermite functions (GHFs) in arbitrary d dimensions, which }  are orthogonal with respect to |\bx|^{2\mu} \e^{-|\bx|^2} and |\bx |^{2\mu}  in \mathbb R^d , respectively.
Revised:  The first is to construct the generalised Hermite polynomials and generalised Hermite functions (GHFs) in arbitrary d dimensions, which } are orthogonal with respect to |\bx|^{2\mu} \e^{-|\bx|^2} and |\bx |^{2\mu} ) in \mathbb R^d , respectively.
Edit intent: coherence
Original:  and (ii) A-GHFs are orthogonal with respect to the inner product [u,v]_{H^s(\mathbb R^d)}=((-\Delta)^{ \frac s  2}u, (-\Delta)^{ \frac s  2} v )_{\mathbb R^d} associated with the integral fractional Laplacian.
Revised:  and (ii) A-GHFs are orthogonal with respect to the inner product [u,v]_{H^s(\mathbb R^d)}=((-\Delta)^{ s 2}u, (-\Delta)^{ \frac s 2} v )_{\mathbb R^d} associated with the integral fractional Laplacian.
Edit intent: fluency
Original:  and (ii) A-GHFs are orthogonal with respect to the inner product [u,v]_{H^s(\mathbb R^d)}=((-\Delta)^{ \frac s  2}u, (-\Delta)^{ \frac s  2} v )_{\mathbb R^d} associated with the integral fractional Laplacian.
Revised:  and (ii) A-GHFs are orthogonal with respect to the inner product [u,v]_{H^s(\mathbb R^d)}=((-\Delta)^{ \frac s 2}u, (-\Delta)^{ s 2} v )_{\mathbb R^d} associated with the integral fractional Laplacian.
Edit intent: fluency
Original:  As a corollary, this implies that ex_{d+1}(n, K_{H,t}) = O(n^{d+1-1/t}) when H is a d-uniform hypergraph  in which all edges are pairwise disjoint, which generalizes an upper bound proved by Mubayi and Verstra\"{e}te (JCTA, 2004).
Revised:  This also implies that ex_{d+1}(n, K_{H,t}) = O(n^{d+1-1/t}) when H is a d-uniform hypergraph in which all edges are pairwise disjoint, which generalizes an upper bound proved by Mubayi and Verstra\"{e}te (JCTA, 2004).
Edit intent: clarity
Original:   Given sample access to two Bayesian networks P_1 and P_2 over known directed acyclic graphs G_1 and G_2 having n nodes and bounded in-degree, approximate d_{tv}(P_1,P_2)
Revised:  - Given sample access to two Bayesian networks P_1 and P_2 over known directed acyclic graphs G_1 and G_2 having n nodes and bounded in-degree, approximate d_{tv}(P_1,P_2)
Edit intent: fluency
Original:  samples and time  Given sample access to two ferromagnetic Ising models P_1 and P_2 on n variables with bounded width, approximate d_{tv}(P_1, P_2)
Revised:  samples and time - Given sample access to two ferromagnetic Ising models P_1 and P_2 on n variables with bounded width, approximate d_{tv}(P_1, P_2)
Edit intent: clarity
Original:  samples and time  Given sample access to two n-dimensional Gaussians P_1 and P_2, approximate d_{tv}(P_1, P_2)
Revised:  samples and time - Given sample access to two n-dimensional Gaussians P_1 and P_2, approximate d_{tv}(P_1, P_2)
Edit intent: fluency
Original:  samples and time  Given access to observations from two causal models P and Q on n variables that are defined over known causal graphs, approximate d_{tv}(P_a, Q_a) to within additive error \epsilon using poly(n,\epsilon) samples, where P_a and Q_a are the interventional distributions obtained by the intervention do(A=a) on P and Q respectively for a particular variable A  Our results are the first efficient distance approximation algorithms for these well-studied problems.
Revised:  samples and time - Given access to observations from two causal models P and Q on n variables that are defined over known causal graphs, approximate d_{tv}(P_a, Q_a) to within additive error \epsilon using poly(n,\epsilon) samples, where P_a and Q_a are the interventional distributions obtained by the intervention do(A=a) on P and Q respectively for a particular variable A Our results are the first efficient distance approximation algorithms for these well-studied problems.
Edit intent: fluency
Original:  samples and time  Given access to observations from two causal models P and Q on n variables that are defined over known causal graphs, approximate d_{tv}(P_a, Q_a) to within additive error \epsilon using poly(n,\epsilon) samples, where P_a and Q_a are the interventional distributions obtained by the intervention do(A=a) on P and Q respectively for a particular variable A  Our results are the first efficient distance approximation algorithms for these well-studied problems.
Revised:  samples and time Given access to observations from two causal models P and Q on n variables that are defined over known causal graphs, approximate d_{tv}(P_a, Q_a) to within additive error \epsilon using poly(n,\epsilon) samples, where P_a and Q_a are the interventional distributions obtained by the intervention do(A=a) on P and Q respectively for a particular variable A . Our results are the first efficient distance approximation algorithms for these well-studied problems.
Edit intent: fluency
Original:  The two methods are efficiently implemented in the E prover and its ENIGMA learning-guided framework and evaluated on the MPTP large-theory benchmark . Both methods are shown to achieve comparable real-time performance to state-of-the-art symbol-based methods  .
Revised:  The two methods are efficiently implemented in the E prover and its ENIGMA learning-guided framework and evaluated on the MPTP large-theory benchmark and shown to achieve comparable real-time performance to state-of-the-art symbol-based methods .
Edit intent: coherence
Original: Calculating the yield limit Y_c of a viscoplastic fluid flow is a challenging problem, often needing iteration in the rheological parameters to approach the plastic limit, as well as accurate computations that account properly for the yield stress and potentially adaptive meshing.
Revised: Calculating the yield limit Y_c of a viscoplastic fluid flow is a challenging problem, often needing iteration in the rheological parameters to approach this limit, as well as accurate computations that account properly for the yield stress and potentially adaptive meshing.
Edit intent: clarity
Original:  Here we approach the problem of 3D particle settling and how to compute the yield limit directly, i.e. without iteratively changing the rheology to approach the plastic yield limit.
Revised:  Here we approach the problem of 3D particle settling and how to compute the yield limit directly, i.e. without iteratively changing the rheology to approach the yield limit.
Edit intent: clarity
Original:  The  approach develops tools from optimization theory, taking advantage of the fact that Y_c is defined via a minimization problem.
Revised:  The presented approach develops tools from optimization theory, taking advantage of the fact that Y_c is defined via a minimization problem.
Edit intent: clarity
Original:  We give a recipe for proving mixing time bounds of Langevin dynamics in order to sample from manifolds of local optima of the function f in settings where the distribution is well-concentrated around them.
Revised:  First, we give a recipe for proving mixing time bounds of Langevin dynamics in order to sample from manifolds of local optima of the function f in settings where the distribution is well-concentrated around them.
Edit intent: coherence
Original:  The formulation of biologically inspired networks capable to perform complex computations can mediate a synergetic interaction between Machine Learning and Neuroscience bringing to mutual benefits and helping to improve our understanding of biological and artificial intelligence.
Revised:  The formulation of biologically inspired RSNNs in order to improve our understanding of biological and artificial intelligence.
Edit intent: clarity
Original:  Even though several models have been proposed , it remains a challenging task to design RSNNs which use biologically plausible mechanisms .
Revised:  Even though several models have been proposed but it remains a challenging task to design RSNNs which use biologically plausible mechanisms .
Edit intent: coherence
Original:  Even though several models have been proposed , it remains a challenging task to design RSNNs which use biologically plausible mechanisms .
Revised:  Even though several models have been proposed , it remains a challenge to design RSNNs which use biologically plausible mechanisms .
Edit intent: clarity
Original:  Even though several models have been proposed , it remains a challenging task to design RSNNs which use biologically plausible mechanisms .
Revised:  Even though several models have been proposed , it remains a challenging task to design RSNNs that use biologically plausible mechanisms .
Edit intent: fluency
Original:  We propose a general probabilistic framework which relies on the principle of maximizing the likelihood for the network to solve the task .
Revised:  We propose a general probabilistic framework that relies on the principle of maximizing the likelihood for the network to solve the task .
Edit intent: fluency
Original:  We propose a general probabilistic framework which relies on the principle of maximizing the likelihood for the network to solve the task .
Revised:  We propose a general probabilistic framework which relies on the principle of maximizing the likelihood for the network to reproduce some temporal dynamics .
Edit intent: clarity
Original:  Our model is very general and it can be applied to a wide variety of network architectures and types of biological neurons.
Revised:  Our model is general and it can be applied to a wide variety of network architectures and types of biological neurons.
Edit intent: clarity
Original:  The derived plasticity learning rule is specific to each neuron model producing a theoretical prediction which can be verified experimentally .
Revised:  The derived plasticity learning rule is specific to each neuron model and can produce a theoretical prediction which can be verified experimentally .
Edit intent: clarity