wanyu/IteraTeR_v2 huggingface dataset:
Original:  Since LPis solvable in polynomial time and we have a model which is of polynomial size in n, the paper is thus offering (although, incidentally) a proof of the equality of the computational complexity classes "P" and "NP " . The non-applicability and numerical refutations of existing extended formulations results (such as Braun et al. (2015) or Fiorini et al. (2015) in particular) are briefly discussed in an appendix. *:
Revised:  Since LPis solvable in polynomial time and we have a model which is of polynomial size in n, the paper is thus offering (although, incidentally) a proof of the equality of the computational complexity classes "P" and "NP . The non-applicability and numerical refutations of existing extended formulations results (such as Braun et al. (2015) or Fiorini et al. (2015) in particular) are briefly discussed in an appendix. *:
Edit intent: fluency
Original:  Since LPis solvable in polynomial time and we have a model which is of polynomial size in n, the paper is thus offering (although, incidentally) a proof of the equality of the computational complexity classes "P" and "NP " . The non-applicability and numerical refutations of existing extended formulations results (such as Braun et al. (2015) or Fiorini et al. (2015) in particular) are briefly discussed in an appendix. *:
Revised:  Since LPis solvable in polynomial time and we have a model which is of polynomial size in n, the paper is thus offering (although, incidentally) a proof of the equality of the computational complexity classes "P" and "NP " . The non-applicability and numerical refutations of existing extended formulations results (such as Braun et al. (2015) or Fiorini et al. (2015) in particular) are briefly discussed *:
Edit intent: clarity
Original: We consider a network of processor-sharing queues with state-dependent service rates.
Revised: We consider a system of processor-sharing queues with state-dependent service rates.
Edit intent: clarity
Original:  Nonetheless, if binary codes are compared in terms of the cosine similarity rather than the Hamming distance, there is no fast exact sequential procedure to find the K closest items to the query other than the exhaustive search.
Revised:  Nonetheless, if binary codes are compared in terms of cosine similarity rather than the Hamming distance, there is no fast exact sequential procedure to find the K closest items to the query other than the exhaustive search.
Edit intent: fluency
Original:  To handle this issue, we first elaborate on the relation between the Hamming distance and the cosine similarity.
Revised:  To handle this issue, we first elaborate on the connection between the Hamming distance and the cosine similarity.
Edit intent: fluency
Original:  This allows finding the sequence of buckets to check in the hash table.
Revised:  Doing this allows us to systematically find the probing sequence in the hash table.
Edit intent: clarity
Original: In a real-world network, shared by several users, telehaptic applications involving delay-sensitive multimedia communication between remote locations demand distinct Quality of Service (QoS) guarantees for different media components.
Revised: Telehaptic applications involve delay-sensitive multimedia communication between remote locations demand distinct Quality of Service (QoS) guarantees for different media components.
Edit intent: clarity
Original: In a real-world network, shared by several users, telehaptic applications involving delay-sensitive multimedia communication between remote locations demand distinct Quality of Service (QoS) guarantees for different media components.
Revised: In a real-world network, shared by several users, telehaptic applications involving delay-sensitive multimedia communication between remote locations with distinct Quality of Service (QoS) guarantees for different media components.
Edit intent: clarity
Original: In a real-world network, shared by several users, telehaptic applications involving delay-sensitive multimedia communication between remote locations demand distinct Quality of Service (QoS) guarantees for different media components.
Revised: In a real-world network, shared by several users, telehaptic applications involving delay-sensitive multimedia communication between remote locations demand distinct Quality of Service (QoS) requirements for different media components.
Edit intent: clarity
Original:  These QoS constraints pose a variety of challenges, especially when the network cross-traffic is unknown and time-varying  .
Revised:  These QoS constraints pose a variety of challenges, especially when the communication occurs over a shared network, with unknown and time-varying .
Edit intent: clarity
Original:  In this work, we propose an application layer congestion control protocol for telehaptic applications operating over shared networks, termed as dynamic packetization module (DPM).
Revised:  In this work, we propose a transport layer congestion control protocol for telehaptic applications operating over shared networks, termed as dynamic packetization module (DPM).
Edit intent: clarity
Original:  To monitor the network congestion, we devise a novel network feedback module, which communicates the end-to-end delays encountered by the telehaptic packets to the respective transmitters , with negligible overhead.
Revised:  To monitor the network congestion, we devise a novel network feedback module, which communicates the end-to-end delays encountered by the telehaptic packets to the respective transmitters with negligible overhead.
Edit intent: fluency
Original:  We also report the qualitative results of a real-time telepottery experiment with several human subjects, which reveal that DPM preserves the quality of telehaptic activity even under heavily congested network scenarios.
Revised:  We also report qualitative results of a real-time telepottery experiment with several human subjects, which reveal that DPM preserves the quality of telehaptic activity even under heavily congested network scenarios.
Edit intent: fluency
Original:  Finally, we compare the performance of DPM with existing telehaptic communication protocols , and conclude that DPM outperforms other techniques .
Revised:  Finally, we compare the performance of DPM with existing telehaptic communication protocols and demonstrate that DPM outperforms other techniques .
Edit intent: clarity
Original:  Finally, we compare the performance of DPM with existing telehaptic communication protocols , and conclude that DPM outperforms other techniques .
Revised:  Finally, we compare the performance of DPM with existing telehaptic communication protocols , and conclude that DPM outperforms these protocols .
Edit intent: clarity
Original:  Next, we extend the MSCG method to stochastic simulation and optimization problems by augmenting the method with the following ingredients: (1) a reference domain formulation that allows us to treat geometric errors and manufacturing uncertaintiesin a consistent manner ;
Revised:  Next, we extend the MSCG method to stochastic simulation and optimization problems by augmenting the method with the following ingredients: (1) a reference domain formulation that allows us to treat geometric variability resulting from manufacturing uncertainties ;
Edit intent: clarity
Original:  (2) a reduced basis approximation at the subdomain level that drastically accelerates the solution of the parametrized local subproblems;
Revised:  (2) a reduced basis approximation to solve the parametrized local subproblems;
Edit intent: clarity
Original:  (3) computation of a gradient of an objective function;
Revised:  (3) a gradient computation of the objective function;
Edit intent: fluency
Original:  and (4) a model and variance reduction technique that enables the accelerated computation of statistical outputs by exploiting the statistical correlation between the MSCG method and the reduced basis approximation.
Revised:  and (4) a model and variance reduction technique that enables the accelerated computation of statistical outputs by exploiting the statistical correlation between the MSCG solution and the reduced basis approximation.
Edit intent: clarity
Original:  The proposed method is thus well suited for both deterministic and stochastic simulations, as well as robust design of heterogeneous materials .
Revised:  The proposed method is thus well suited for both deterministic and stochastic simulations, as well as robust design of photonic crystals .
Edit intent: clarity
Original:  We provide numerical results to demonstrate the convergence of the MSCG method, as well as two photonic crystal applications to illustrate its advantages for stochastic simulation and robust design problems .
Revised:  We provide numerical results to demonstrate the convergence of the MSCG method, as well as two photonic crystal applications to illustrate its advantages for stochastic simulation and robust design .
Edit intent: clarity
Original:  Autophagy selectivity must not only select the correct type of organelle, but  must discriminate between individual organelles of the same kind .
Revised:  Autophagy selectivity must not only select the correct type of organelle, but also must discriminate between individual organelles of the same kind .
Edit intent: fluency
Original:  In the context of peroxisomes, we use computational models to explore the hypothesis that physical clustering of autophagy receptor proteins on the surface of each organelle provides an appropriate all-or-none signal for degradation.
Revised:  In the context of peroxisomes, we use computational models to explore the hypothesis that physical clustering of autophagy receptor proteins on the organelle surface can provide an appropriate all-or-none signal for degradation.
Edit intent: clarity
Original:  This effect can explain the increased catalase signal that results from experimental siRNA inhibition of p62.
Revised:  This effect can explain the increased catalase signal that results from siRNA inhibition of p62.
Edit intent: clarity
Original:  We also consider receptor cluster formation on individual peroxisomes with enhanced levels of ubiquitinand find that size-selectivity, but not cluster formation , is suppressed.
Revised:  Excess ubiquitin, resulting from damaged organelles, suppresses size-selectivity but not cluster formation , is suppressed.
Edit intent: clarity
Original: Networks are used to represent relationships between entities in many complex systems, spanning from online social networks to biological cell development and brain activity .
Revised: Networks are used to represent relationships between entities in many complex systems, spanning from online social networks to biological cell development and brain connectivity .
Edit intent: clarity
Original:  However, current research lacks a rigorous validation framework which employs standard statistical validation.
Revised:  However, current research lacks a rigorous methodology which employs standard statistical validation.
Edit intent: clarity
Original: Networks are used to represent relationships between entities in many complex systems, spanning from online social networks to biological cell development and brain connectivity.
Revised: Networks represent relationships between entities in many complex systems, spanning from online social networks to biological cell development and brain connectivity.
Edit intent: clarity
Original: Networks are used to represent relationships between entities in many complex systems, spanning from online social networks to biological cell development and brain connectivity.
Revised: Networks are used to represent relationships between entities in many complex systems, spanning from online social interactions to biological cell development and brain connectivity.
Edit intent: clarity
Original:  In many cases, relationships between entities are unambiguously known: are two users friends in a social network?
Revised:  In many cases, relationships between entities are unambiguously known: are two users 'friends' in a social network?
Edit intent: clarity
Original:  These are unambiguous and directly observable in the system in question.
Revised:  These are directly observable in the system in question.
Edit intent: clarity
Original:  Who infected whom in a disease outbreak  ? Existing approaches  use specialized knowledge in different home domains to infer and measure the goodness of inferred network for a specific task  .
Revised:  Who infected whom in a disease outbreak ? Existing approaches use specialized knowledge to infer and measure the goodness of inferred network for a specific task .
Edit intent: clarity
Original:  Who infected whom in a disease outbreak  ? Existing approaches  use specialized knowledge in different home domains to infer and measure the goodness of inferred network for a specific task  .
Revised:  Who infected whom in a disease outbreak ? Existing approaches use specialized knowledge in different home domains to infer and measure the quality of inferred network for a specific task .
Edit intent: clarity
Original:  In this survey, we examine  how network representations are learned from non-network data, the variety of questions and tasks on these data over several domains, and  validation strategies for measuring the inferred network's capability of answering questions on the original system of interest.
Revised:  In this survey, we examine how network representations are learned from non-network data, the variety of questions and tasks on these representations over several domains, and validation strategies for measuring the inferred network's capability of answering questions on the original system of interest.
Edit intent: fluency
Original:  In this survey, we examine  how network representations are learned from non-network data, the variety of questions and tasks on these data over several domains, and  validation strategies for measuring the inferred network's capability of answering questions on the original system of interest.
Revised:  In this survey, we examine how network representations are learned from non-network data, the variety of questions and tasks on these data over several domains, and validation strategies for measuring the inferred network's capability of answering questions on the system of interest.
Edit intent: clarity
Original:  Existing approaches for inferring networks from data are found across many application domains , and use specialized knowledge to infer and measure the quality of inferred network for a specific task or hypothesis.
Revised:  Existing approaches for inferring networks from data are found across many application domains and use specialized knowledge to infer and measure the quality of inferred network for a specific task or hypothesis.
Edit intent: fluency
Original:  secondly , the game itself has an intrinsically interesting and novel mathematical structure --- it actually presents a new technical problem with a surprising amount of informative predictions which arise from the rich parameter space that defines all kinds of possibilities for the networked international environments.
Revised:  secondly , the game presents a new technical problem with a surprising amount of informative predictions which arise from the rich parameter space that defines all kinds of possibilities for the networked international environments.
Edit intent: coherence
Original:  The predictions both motivate major theoretical results (e.g., Nash equilibrium existence ) and shed light on real world politics .
Revised:  The predictions both motivate major theoretical results (e.g., Nash equilibrium existence .
Edit intent: coherence
Original:  In particular, a sufficient condition on the weight in the Hilbert space of forward rate volatility curves is given that ensures existence of the long bond volatility process, the long bond process and the long-term factorization of the SDF into discounting at the rate of return on the long bond and a martingale component defining the long forward measure, the long-term limit of T-forward measures.
Revised:  A sufficient condition on the weight in the Hilbert space of forward rate volatility curves is given that ensures existence of the long bond volatility process, the long bond process and the long-term factorization of the SDF into discounting at the rate of return on the long bond and a martingale component defining the long forward measure, the long-term limit of T-forward measures.
Edit intent: coherence
Original:  T. Akiyama , T. Nishizeki, and N. Saito \mbox{ akiyama have shown that the Hamiltonian cycle problem is NP-complete in planar bipartite graph with maximum degree 3. Using this reduction, we show that the Hamiltonian cycle problem is NP-complete in split graphs.
Revised:  T. Akiyama , T. Nishizeki, and N. Saito \mbox{ akiyama have shown that the Hamiltonian cycle problem is NP-complete in planar bipartite graphs with maximum degree 3. Using this reduction, we show that the Hamiltonian cycle problem is NP-complete in split graphs.
Edit intent: fluency
Original:  We believe that the structural results presented in this paper can be used to show similar dichotomy result for Hamiltonian path  and other variants of Hamiltonian cycle problem .
Revised:  We believe that the structural results presented in this paper can be used to show similar dichotomy result for Hamiltonian path and other variants of HCYCLE .
Edit intent: clarity
Original:  Then we show that the problem of colouring the visibility graph of a given point set with 5 colours is NP-hard.
Revised:  Then we show that the problem of deciding whether the visibility graph of a given point set with 5 colours is NP-hard.
Edit intent: clarity
Original: We present a modeling framework for the dynamics of a population of individuals with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait  . Competition influences individual demographics, affecting population size, which feeds back on the dynamics of transfer.
Revised: We present a model for the dynamics of a population of individuals with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait . Competition influences individual demographics, affecting population size, which feeds back on the dynamics of transfer.
Edit intent: clarity
Original: We present a modeling framework for the dynamics of a population of individuals with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait  . Competition influences individual demographics, affecting population size, which feeds back on the dynamics of transfer.
Revised: We present a modeling framework for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait . Competition influences individual demographics, affecting population size, which feeds back on the dynamics of transfer.
Edit intent: clarity
Original:  This feedback is captured with a stochastic individual-based model, from which a deterministic approximation for large populations is derived.
Revised:  We consider a stochastic individual-based model, from which a deterministic approximation for large populations is derived.
Edit intent: clarity
Original:  The limiting process is the solution of a non linear integro-differential equation.
Revised:  The limiting process is the solution of a nonlinear integro-differential equation.
Edit intent: fluency
Original:  At the same time, we show that on a set of functions constrained only by their degree of smoothness, a ReLU network architecture cannot in general achieve approximation accuracy with better than a power law dependence on the network size, regardless of its depth.
Revised:  At the same time, we show that on functions constrained only by their degree of smoothness, a ReLU network architecture cannot in general achieve approximation accuracy with better than a power law dependence on the network size, regardless of its depth.
Edit intent: clarity
Original:  At the same time, we show that on a set of functions constrained only by their degree of smoothness, a ReLU network architecture cannot in general achieve approximation accuracy with better than a power law dependence on the network size, regardless of its depth.
Revised:  At the same time, we show that on a set of functions constrained only by their degree of smoothness, ReLU networks cannot in general achieve approximation accuracy with better than a power law dependence on the network size, regardless of its depth.
Edit intent: clarity
Original:  At the same time, we show that on a set of functions constrained only by their degree of smoothness, a ReLU network architecture cannot in general achieve approximation accuracy with better than a power law dependence on the network size, regardless of its depth.
Revised:  At the same time, we show that on a set of functions constrained only by their degree of smoothness, a ReLU network architecture cannot in general achieve approximation accuracy with better than a power law dependence on the network size, regardless of their depth.
Edit intent: fluency
Original: We study how approximation errors of neural networks with ReLU activation functionsdepend on the depth of the network .
Revised: We study expressive power of shallow and deep neural networks with ReLU activation functionsdepend on the depth of the network .
Edit intent: clarity
Original: We establish foundational results on the satisfiability problem in string logic with equations, regular membership and Presburger constraints over length functions.
Revised: In this paper, we consider the satisfiability problem in string logic with equations, regular membership and Presburger constraints over length functions.
Edit intent: clarity
Original: We establish foundational results on the satisfiability problem in string logic with equations, regular membership and Presburger constraints over length functions.
Revised: We establish foundational results on the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions.
Edit intent: fluency
Original:   The essence of our decision procedure is a sound and complete algorithm to enumerate an equivalent set of solvable disjuncts for a string formula.
Revised:  The essence of our procedure is an algorithm to enumerate an equivalent set of solvable disjuncts for a string formula.
Edit intent: clarity
Original:   The essence of our decision procedure is a sound and complete algorithm to enumerate an equivalent set of solvable disjuncts for a string formula.
Revised:  The essence of our decision procedure is a sound and complete algorithm to enumerate an equivalent set of solvable disjuncts for the formula.
Edit intent: clarity
Original:  We further  provide a complexity analysis of our decision procedure to show that it runs, in the worst case, in doubly exponential time.
Revised:  We further provide a complexity analysis of our decision procedure to prove that it runs, in the worst case, in doubly exponential time.
Edit intent: fluency
Original: With current efforts to design Future Internet Architectures (FIAs), the evaluation and comparison of different proposals has emerged as an open research area . Previously, metrics such as bandwidth or latency have commonly been used to compare FIAs to IP networks.
Revised: With current efforts to design Future Internet Architectures (FIAs), the evaluation and comparison of different proposals is an interesting research challenge . Previously, metrics such as bandwidth or latency have commonly been used to compare FIAs to IP networks.
Edit intent: clarity
Original:  Specifically, we address two questions: 1) which of the proposed FIA candidates achieves the lowest energy footprint ? ;
Revised:  Specifically, we address two questions: 1) which of the proposed FIA candidates achieves the lowest energy footprint ;
Edit intent: fluency
Original:  and 2) which set of design choices yields a power efficient network architecture?
Revised:  and 2) which set of design choices yields a power-efficient network architecture?
Edit intent: fluency