wanyu/IteraTeR_v2 huggingface dataset:
Original: We propose and analyze zeroth-order algorithms for optimization over Riemannian manifolds, where we observe only potentially noisy evaluations of the objective function.
Revised: Stochastic zeroth-order algorithms for optimization over Riemannian manifolds, where we observe only potentially noisy evaluations of the objective function.
Edit intent: clarity
Original:  As a proof of concept, we demonstrate the applicability of our method to the problem of black-box attacks to deep neural networks, by providing simulation and real-world image data based experimental results.
Revised:  As a proof of concept, we demonstrate the applicability of our algorithms by simulation results.
Edit intent: clarity
Original:  For these settings, we characterize the oracle complexity of our algorithms to obtain appropriately defined notions of \epsilon-stationary point or \epsilon-approximate local minimizer.
Revised:  For these settings, we analyze the oracle complexity of our algorithms to obtain appropriately defined notions of \epsilon-stationary point or \epsilon-approximate local minimizer.
Edit intent: clarity
Original:  In an intersection crossing task with broad continuous behavioral variations, we find that our approach outperforms the state-of-the-art algorithms achieving the same performance as a planning algorithm with knowledge of the true behaviors of other agents.
Revised:  Our approach outperforms the state-of-the-art algorithms achieving the same performance as a planning algorithm with knowledge of the true behaviors of other agents.
Edit intent: coherence
Original:  In an intersection crossing task with broad continuous behavioral variations, we find that our approach outperforms the state-of-the-art algorithms achieving the same performance as a planning algorithm with knowledge of the true behaviors of other agents.
Revised:  In an intersection crossing task with broad continuous behavioral variations, we find that our approach outperforms the state-of-the-art algorithms achieving the same performance as a planner with knowledge of the true behaviors of other agents.
Edit intent: fluency
Original:  GLPs are Markov processes constructed by splitting L\'evy random bridges (LRBs) into non-overlapping subprocesses via time changes.
Revised:  GLPs are Markov processes constructed by splitting L\'evy random bridges into non-overlapping subprocesses via time changes.
Edit intent: clarity
Original: In this work we add a graph theoretical perspective to a classical problemof fairly allocating indivisible items to several agents.
Revised: We consider the fair allocation of indivisible items to several agents and add a graph theoretical perspective to a classical problemof fairly allocating indivisible items to several agents.
Edit intent: clarity
Original:  We finish with a discussion of promising future directions of research and the tools and resources needed to facilitate AI research  .
Revised:  We also review datasets, tools, and resources needed to facilitate AI research .
Edit intent: clarity
Original:  Finally, we discuss strategic considerations related to the operational implementation of projects, multidisciplinary partnerships , and open science.
Revised:  Finally, we discuss strategic considerations related to the operational implementation of multidisciplinary partnerships and open science.
Edit intent: clarity
Original: As a prime feature of 5G networks, Network Slicing has opened up several new avenues of research.
Edit intent: coherence
Original:  Mobility management in a network-sliced environment, in particular, introduces new and complex research challenges.
Revised:  Mobility management in a sliced 5G network introduces new and complex research challenges.
Edit intent: clarity
Original:  Mobility management in a network-sliced environment, in particular, introduces new and complex research challenges.
Revised:  Mobility management in a network-sliced environment, in particular, introduces new and complex challenges.
Edit intent: clarity
Original:  This motivates the need for new mobility management solutions, which, by convention , are required to be standards-compliant.
Revised:  This motivates the need for new mobility management solutions, which, by convention are required to be standards-compliant.
Edit intent: fluency
Original:  The existing 3GPP standard procedures only enable users to change (or switch) slices.
Revised:  A detailed overview of the relevant 3GPP standard procedures only enable users to change (or switch) slices.
Edit intent: clarity
Original: Since the inception of cryptocurrencies, an increasing number of financial institutions are gettinginvolved in cryptocurrency trading.
Revised: Since the inception of cryptocurrencies, an increasing number of financial institutions are getting involved in cryptocurrency trading.
Edit intent: fluency
Original:  It is therefore important to summarise existing research papersand results on cryptocurrency trading.
Revised:  It is therefore important to summarise existing research papers and results on cryptocurrency trading.
Edit intent: fluency
Original:  This paper provides a comprehensive survey of cryptocurrencytrading research, by covering 118 research papers on various aspects of cryptocurrency trading (e.g.,cryptocurrency trading systems, bubble and extreme condition, prediction of volatility and return,crypto-assets portfolio construction and crypto-assets, technical trading and others).
Revised:  This paper provides a comprehensive survey of cryptocurrency trading research, by covering 118 research papers on various aspects of cryptocurrency trading (e.g.,cryptocurrency trading systems, bubble and extreme condition, prediction of volatility and return,crypto-assets portfolio construction and crypto-assets, technical trading and others).
Edit intent: fluency
Original:  This paper alsoanalyses datasets, research trends and distribution among research objects (contents/properties) andtechnologies , concluding with promising opportunities in cryptocurrency trading 
Revised:  This paper also analyses datasets, research trends and distribution among research objects (contents/properties) andtechnologies , concluding with promising opportunities in cryptocurrency trading 
Edit intent: fluency
Original:  This paper alsoanalyses datasets, research trends and distribution among research objects (contents/properties) andtechnologies , concluding with promising opportunities in cryptocurrency trading 
Revised:  This paper alsoanalyses datasets, research trends and distribution among research objects (contents/properties) and technologies , concluding with promising opportunities in cryptocurrency trading 
Edit intent: fluency
Original:  This paper alsoanalyses datasets, research trends and distribution among research objects (contents/properties) andtechnologies , concluding with promising opportunities in cryptocurrency trading 
Revised:  This paper alsoanalyses datasets, research trends and distribution among research objects (contents/properties) andtechnologies , concluding with promising opportunities in cryptocurrency trading .
Edit intent: fluency
Original: Since the inception of cryptocurrencies, an increasing number of financial institutions are getting involved in cryptocurrency trading.
Revised: In recent years, the tendency of the number of financial institutions are getting involved in cryptocurrency trading.
Edit intent: coherence
Original:  Even though they share some commonalities with more traditional assets, they have a separate nature of its own and their behaviour as an asset is still under the process of being understood.
Revised:  Although they have some commonalities with more traditional assets, they have a separate nature of its own and their behaviour as an asset is still under the process of being understood.
Edit intent: fluency
Original:  Even though they share some commonalities with more traditional assets, they have a separate nature of its own and their behaviour as an asset is still under the process of being understood.
Revised:  Even though they share some commonalities with more traditional assets, they have their own separate nature and their behaviour as an asset is still under the process of being understood.
Edit intent: clarity
Original:  Even though they share some commonalities with more traditional assets, they have a separate nature of its own and their behaviour as an asset is still under the process of being understood.
Revised:  Even though they share some commonalities with more traditional assets, they have a separate nature of its own and their behaviour as an asset is still in the process of being understood.
Edit intent: clarity
Original:  This paper provides a comprehensive survey of cryptocurrency trading research, by covering 126 research papers on various aspects of cryptocurrency trading ( eg. , cryptocurrency trading systems, bubble and extreme condition , prediction of volatility and return, crypto-assets portfolio construction and crypto-assets, technical trading and others).
Revised:  This paper provides a comprehensive survey of cryptocurrency trading research, by covering 126 research papers on various aspects of cryptocurrency trading ( e.g. , cryptocurrency trading systems, bubble and extreme condition , prediction of volatility and return, crypto-assets portfolio construction and crypto-assets, technical trading and others).
Edit intent: fluency
Original:  This paper provides a comprehensive survey of cryptocurrency trading research, by covering 126 research papers on various aspects of cryptocurrency trading ( eg. , cryptocurrency trading systems, bubble and extreme condition , prediction of volatility and return, crypto-assets portfolio construction and crypto-assets, technical trading and others).
Revised:  This paper provides a comprehensive survey of cryptocurrency trading research, by covering 126 research papers on various aspects of cryptocurrency trading ( eg. , cryptocurrency trading systems, bubble and extreme conditions , prediction of volatility and return, crypto-assets portfolio construction and crypto-assets, technical trading and others).
Edit intent: fluency
Original:  A polynomial correlation between the parameters is formulated, giving an upper bound for the time of the peak of new infected.
Revised:  A polynomial correlation between the parameters gives an upper bound for the time of the peak of new infected.
Edit intent: clarity
Original:  A plenty of well-performed approximation algorithms have been designed for the maximization of monotone/non-monotone submodular functions over a variety of constraints.
Revised:  Plenty of well-performing approximation algorithms have been designed for the maximization of monotone/non-monotone submodular functions over a variety of constraints.
Edit intent: fluency
Original:  When the ratio between the maximum capacity and the minimum capacity of the bins is bounded by a constant , we provide a (1/2-\epsilon)-approximation algorithm which is also combinatorial and deterministic.
Revised:  In the general case , we provide a (1/2-\epsilon)-approximation algorithm which is also combinatorial and deterministic.
Edit intent: clarity
Original:  We can further boost the approximation ratio to (1 - 1 / e - \epsilon ) with the help of continuous greedy technique, which gives a tight randomized approximation algorithm for this case .
Revised:  We finally show a 1-1 / e - \epsilon ) with the help of continuous greedy technique, which gives a tight randomized approximation algorithm for this case .
Edit intent: clarity
Original:  When the capacity of bins are identical, we design a combinatorial and deterministic algorithm which can achieve the tight approximation ratio (1 - 1 / e-\epsilon).
Revised:  When the capacity of bins are identical, we design a combinatorial and deterministic algorithm which achieves an almost tight approximation ratio (1 - 1 / e-\epsilon).
Edit intent: clarity
Original:  We finally show a 1-1/e-\epsilon  randomized algorithm for the general case, thus achieving the same result as Fairstein et al. (ESA20) .
Revised:  We finally show a 1-1/e-\epsilon ) randomized algorithm for the general case, thus achieving the same result as Fairstein et al. (ESA20) .
Edit intent: fluency
Original:  We finally show a 1-1/e-\epsilon  randomized algorithm for the general case, thus achieving the same result as Fairstein et al. (ESA20) .
Revised:  We finally show a 1-1/e-\epsilon randomized algorithm for the general case, thus matching the result of Fairstein et al. (ESA20) .
Edit intent: clarity
Original:  Plenty of well-performing approximation algorithms have been designed for the maximization of monotone/ non-monotone  submodular functions over a variety of constraints.
Revised:  Plenty of well-performing approximation algorithms have been designed for the maximization of (monotone or non-monotone submodular functions over a variety of constraints.
Edit intent: fluency
Original:  Plenty of well-performing approximation algorithms have been designed for the maximization of monotone/ non-monotone  submodular functions over a variety of constraints.
Revised:  Plenty of well-performing approximation algorithms have been designed for the maximization of monotone/ non-monotone ) submodular functions over a variety of constraints.
Edit intent: fluency
Original:  It includes as special cases an axiomatic characterisation for choice functions based on (sets of) total orders, (sets of) weak orders, (sets of) coherent lower previsions and (sets of) probability measures.
Revised:  It includes as special cases axiomatic characterisations for choice functions based on (sets of) total orders, (sets of) weak orders, (sets of) coherent lower previsions and (sets of) probability measures.
Edit intent: fluency
Original: All propositions from the set of events for an agent in a multi-agent system might not be simultaneously verifiable .
Revised: In multi-agent systems, agents observe data, and use them to make inferences and take actions. As a result sensing and control naturally interfere, more so from a real-time perspective. A natural consequence is that in multi-agent systems there are propositions based on the set of events for an agent in a multi-agent system might not be simultaneously verifiable .
Edit intent: coherence
Original: All propositions from the set of events for an agent in a multi-agent system might not be simultaneously verifiable .
Revised: All propositions from the set of observed events that might not be simultaneously verifiable .
Edit intent: clarity
Original:  In this paper , we revisit the concepts of \textit{event-state-operation structure} and  relationship of incompatibility from  literature and use them as a tool to study the  algebraic structure of the set of events.
Revised:  In this paper , we revisit the concepts of \textit{event-state-operation structure} and relationship of incompatibility from the literature and use them as a tool to study the algebraic structure of the set of events.
Edit intent: fluency
Original:  We present an example from multi-agent hypothesis testing where the set of events does not form a Boolean algebra  but forms an ortholattice.
Revised:  We present an example from multi-agent hypothesis testing where the set of events does not form a Boolean algebra , but forms an ortholattice.
Edit intent: fluency
Original:  A possible construction of a ' noncommutative probability space', accounting for incompatible events (events which cannot be simultaneously verified) is discussed.
Revised:  A possible construction of a ` noncommutative probability space', accounting for incompatible events (events which cannot be simultaneously verified) is discussed.
Edit intent: fluency
Original:  A possible construction of a ' noncommutative probability space', accounting for incompatible events (events which cannot be simultaneously verified) is discussed.
Revised:  A possible construction of a ' noncommutative probability space', accounting for incompatible events is discussed.
Edit intent: clarity
Original:  As a possible decision-making problem in such a probability space, we consider the binary hypothesis testing problem .
Revised:  We formulate and solve the binary hypothesis testing problem .
Edit intent: clarity
Original:  We  hope this dataset can help researchers around the world better understand the spread dynamics of COVID-19 at a regional level, to inform intervention and mitigation strategies for policymakers.
Revised:  We hope this dataset can help researchers around the world better understand the spreading dynamics of COVID-19 at a regional level, to inform intervention and mitigation strategies for policymakers.
Edit intent: fluency
Original: We extend a fictitious domain-type finite element method, called \phi-FEM and introduced in arXiv:1903.03703 math.
Revised: We extend a fictitious domain-type finite element method, called \phi-FEM math.
Edit intent: coherence
Original:  The numerical experiments confirm the theoretical results.
Revised:  The numerical experiments confirm these results.
Edit intent: clarity
Original:  Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints.
Revised: The Surjective Constraint Satisfaction Problem (SCSP) is the problem of deciding whether there exists a surjective assignment to a set of variables subject to some specified constraints.
Edit intent: fluency
Original:  Additionally, we disprove the conjecture saying that  SCSP over a constraint language \Gamma is equivalent to  CSP over the same language with constants.
Revised:  Additionally, we disprove the conjecture saying that the SCSP over a constraint language \Gamma is equivalent to CSP over the same language with constants.
Edit intent: fluency
Original:  Additionally, we disprove the conjecture saying that  SCSP over a constraint language \Gamma is equivalent to  CSP over the same language with constants.
Revised:  Additionally, we disprove the conjecture saying that SCSP over a constraint language \Gamma is equivalent to the CSP over the same language with constants.
Edit intent: clarity
Original:  Our counter example also shows that the complexity of  SCSP cannot be described in terms of polymorphisms of the constraint language.
Revised:  Our counter example also shows that the complexity of the SCSP cannot be described in terms of polymorphisms of the constraint language.
Edit intent: fluency
Original:  In this paper we show that one of the most popular variants of the SCSP, called No-Rainbow Problem, is NP-Hard.
Revised:  In this paper we show that the most famous SCSP, called No-Rainbow Problem, is NP-Hard.
Edit intent: clarity
Original:  Additionally, we disprove the conjecture saying that the SCSP over a constraint language \Gamma is equivalent to the CSP over the same language with constants .
Revised:  Additionally, we disprove the conjecture saying that the SCSP over a constraint language \Gamma and the CSP over the same language with constants .
Edit intent: clarity
Original:  To succeed, agents must coordinate both their high-level plans (e.g. , what sub-task they should work on) and their low-level actions (e.g. , avoiding collisions).
Revised:  To succeed, agents must coordinate both their high-level plans (e.g. what sub-task they should work on) and their low-level actions (e.g. , avoiding collisions).
Edit intent: fluency
Original: This article presents a new primal-dual weak Galerkin finite element method for the tangential boundary value problem of div-curl systems with low-regularity solutions .
Revised: This article presents a new primal-dual weak Galerkin finite element method for the div-curl systems with low-regularity solutions .
Edit intent: coherence
Original:  The numerical scheme is based on a weak formulation, called the primal equation, involving no partial derivatives for the exact solution supplemented by the its dual form in the context of weak Galerkin .
Revised:  The numerical scheme is based on a weak variational form involving no partial derivatives for the exact solution supplemented by the its dual form in the context of weak Galerkin .
Edit intent: clarity
Original:  The numerical scheme is based on a weak formulation, called the primal equation, involving no partial derivatives for the exact solution supplemented by the its dual form in the context of weak Galerkin .
Revised:  The numerical scheme is based on a weak formulation, called the primal equation, involving no partial derivatives of the exact solution supplemented by the its dual form in the context of weak Galerkin .
Edit intent: fluency
Original:  Optimal order error estimates in L^2 are established for vector fields with H^\alpha (\Omega) -regularity,\alpha > 0.
Revised:  Optimal order error estimates in L^2 are established for vector fields with H^\alpha (\Omega) ,\ \theta > 0.
Edit intent: clarity
Original:  The mathematical theory was derived for connected domains with general topological properties (namely, arbitrary  Betti numbers).
Revised:  The mathematical theory was derived on connected domains with general topological properties (namely, arbitrary Betti numbers).
Edit intent: fluency
Original:  Numerical results are reported to not only verify the theoretical convergence but also demonstrate the performance of the new method .
Revised:  Numerical results are reported to confirm the theoretical convergence but also demonstrate the performance of the new method .
Edit intent: fluency
Original:  Numerical results are reported to not only verify the theoretical convergence but also demonstrate the performance of the new method .
Revised:  Numerical results are reported to not only verify the theoretical convergence .
Edit intent: clarity
Original:  Brain-inspired Spiking Neural Networks (SNNs) use spatiotemporal spike patterns to encode and transmit information, which is biologically realistic, and suitable for ultra-low-power event-driven neuromorphic implementation.
Revised:  Brain-inspired Spiking Neural Networks (SNNs) use spatio-temporal spike patterns to encode and transmit information, which is biologically realistic, and suitable for ultra-low-power event-driven neuromorphic implementation.
Edit intent: fluency
Original:  Brain-inspired Spiking Neural Networks (SNNs) use spatiotemporal spike patterns to encode and transmit information, which is biologically realistic, and suitable for ultra-low-power event-driven neuromorphic implementation.
Revised:  Brain-inspired Spiking Neural Networks (SNNs) use spatiotemporal spike patterns to represent and transmit information, which is biologically realistic, and suitable for ultra-low-power event-driven neuromorphic implementation.
Edit intent: clarity
Original:  Brain-inspired Spiking Neural Networks (SNNs) use spatiotemporal spike patterns to encode and transmit information, which is biologically realistic, and suitable for ultra-low-power event-driven neuromorphic implementation.
Revised:  Brain-inspired Spiking Neural Networks (SNNs) use spatiotemporal spike patterns to encode and transmit information, which is not only biologically realistic but also suitable for ultra-low-power event-driven neuromorphic implementation.
Edit intent: clarity
Original:  Therefore, Deep Spiking Neural Networks ( DSNNs) represent a promising direction in artificial intelligence , with the potential to benefit from the best of both worlds .
Revised:  Therefore, Deep Spiking Neural Networks ( DeepSNNs) provides promising directions for artificial intelligence applications .
Edit intent: clarity
Original:  However, the training of DSNNs is challenging because standard error back-propagation (BP) algorithms are not directly applicable.
Revised:  However, training of DeepSNNs is not straightforward because the well-studied error back-propagation (BP) algorithms are not directly applicable.
Edit intent: clarity
Original:  However, the training of DSNNs is challenging because standard error back-propagation (BP) algorithms are not directly applicable.
Revised:  However, the training of DSNNs is challenging because standard error back-propagation (BP) algorithm is not directly applicable.
Edit intent: coherence