wanyu/IteraTeR_v2 huggingface dataset:
Original:  We use this framework on several real networks, compare its predictions to those of classical  control theory, and identify the topological characteristics that underlie the commonalities and differencesbetween these frameworks .
Revised:  We use this framework on several real networks, compare its predictions to those of classical control theory, and identify the topological characteristics that underlie the observed differences .
Edit intent: clarity
Original:  This feedback-based framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors, regardless of the dynamic details and system parameters.
Revised:  This feedback-based framework provides realizable node overrides that steer a system towards any of its natural long term dynamic behaviors, regardless of the specific functional forms and system parameters.
Edit intent: clarity
Original:  We use this framework on several real networks,  compare its predictions to those of classical structural control theory, and identify the topological characteristics that underlie the observed differences .
Revised:  We use this framework on several real networks, compare its predictions to those of structural controllability in control theory .
Edit intent: clarity
Original:  A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting.
Revised: Background: A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting.
Edit intent: coherence
Original:  The model is illustrated with numerical simulations that reveal epidemic outcomes correlated to the spatially dependent parameters  of the model and the spatially dependent epidemic basic reproduction number.
Revised:  The epidemic outcomes of the model are correlated to the spatially dependent parameters of the model and the spatially dependent epidemic basic reproduction number.
Edit intent: clarity
Original:  The model is applied to the 2015 Zika outbreak in the Rio de Janeiro Municipality  .
Revised:  The model is applied to the 2015 Zika outbreak in the Rio de Janeiro Municipality in Brazil .
Edit intent: clarity
Original: We present a new technique in parameterized algorithms whose purpose is to solve "resiliency versions " of decision problems.
Revised: We introduce a framework in parameterized algorithms whose purpose is to solve "resiliency versions " of decision problems.
Edit intent: clarity
Original: We present a new technique in parameterized algorithms whose purpose is to solve "resiliency versions " of decision problems.
Revised: We present a new technique in parameterized algorithms whose purpose is to solve resiliency versions of decision problems.
Edit intent: fluency
Original:  In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation  applied to it.
Revised:  In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation has been applied to it.
Edit intent: clarity
Original:  To tackle this kind of problems,  which might be of important practical interest, we introduce a notion of resiliency for Integer Linear Programs (ILP).
Revised:  To tackle these kinds of problems, which might be of important practical interest, we introduce a notion of resiliency for Integer Linear Programs (ILP).
Edit intent: fluency
Original:  To tackle this kind of problems,  which might be of important practical interest, we introduce a notion of resiliency for Integer Linear Programs (ILP).
Revised:  To tackle this kind of problems, some of which might be of important practical interest, we introduce a notion of resiliency for Integer Linear Programs (ILP).
Edit intent: clarity
Original:  To tackle this kind of problems,  which might be of important practical interest, we introduce a notion of resiliency for Integer Linear Programs (ILP).
Revised:  To tackle this kind of problems, which might be of practical interest, we introduce a notion of resiliency for Integer Linear Programs (ILP).
Edit intent: clarity
Original:  While a celebrated result from Lenstra (Mathematics of Operations Research, 1983) implies that testing ILP feasibility is Fixed-Parameter Tractable (FPT) parameterized by the number of variables (i. e. runs in time O*(f(n)), where n is the number of variables, f is some computable function, and O*(. ) suppresses polynomial terms), this tool seems too weak to solve our resiliency version in an efficient way.
Revised:  We prove that ILP Resiliency is fixed-parameter tractable (FPT) parameterized by the number of variables (i. e. runs in time O*(f(n)), where n is the number of variables, f is some computable function, and O*(. ) suppresses polynomial terms), this tool seems too weak to solve our resiliency version in an efficient way.
Edit intent: coherence
Original: We introduce a framework in parameterized algorithms whose purpose is to solve resiliency versions of decision problems  .
Revised: We introduce an extension of decision problems .
Edit intent: clarity
Original:  To demonstrate the utility of our result, we prove that resiliency versions of several concrete problems  are FPT under natural parameterizations.
Revised:  To demonstrate the utility of our result, we consider natural resiliency versions of several concrete problems are FPT under natural parameterizations.
Edit intent: clarity
Original:  To demonstrate the utility of our result, we prove that resiliency versions of several concrete problems  are FPT under natural parameterizations.
Revised:  To demonstrate the utility of our result, we prove that resiliency versions of several concrete problems , and prove that they are FPT under natural parameterizations.
Edit intent: clarity
Original:  The second concerns the Closest String problem, for which we identify and solve two different resiliency problems, extending an FPT result of Gramm et al. (  2003).
Revised:  The second concerns the Closest String problem, for which we extend an FPT result of Gramm et al. ( 2003).
Edit intent: coherence
Original:  In an earlier paper (%DIFDELCMD < {\it %%% Sharma et al.
Revised:  In %DIFDELCMD < {\it %%% Sharma et al.
Edit intent: clarity
Original:  In the past the physical origin of this apparently counter-intuitive phenomenon was traced to the nature of the force-dependence of the (de-)polymerization kinetics of the microtubules .
Revised:  In the past the physical origin of this apparently counter-intuitive phenomenon was traced to the nature of the force-dependence of the (de-)polymerization kinetics of the MTs .
Edit intent: clarity
Original:  Here first the same model kt-MT attachment is subjected to external tension that is ramped up till the attachment gets ruptured;
Revised:  Here first the same model MT-kt attachment is subjected to external tension that is ramped up till the attachment gets ruptured;
Edit intent: fluency
Original:  the trend of variation of the rupture force distribution with increasing loading rate is consistent with that displayed by the catch bonds formed in some other ligand-receptor systems{\it  {\it   .
Revised:  the trend of variation of the rupture force distribution with increasing loading rate is consistent with that displayed by the catch bonds formed in some other ligand-receptor systems{\it experiments{\it .
Edit intent: fluency
Original: If a graph G has n\ge4k vertices and more than n^2/4 edges, then it contains a copy of C_{2k+1}.
Revised: If a graph has n\ge4k vertices and more than n^2/4 edges, then it contains a copy of C_{2k+1}.
Edit intent: clarity
Original:  In 1992, Erdos, Faudree and Rousseau showed even more, that the number of edges that occur in a triangle of such a G is at least 2\lfloor n/2\rfloor+1, and this bound is tight.
Revised:  In 1992, Erdos, Faudree and Rousseau showed even more, that the number of edges that occur in a triangle is at least 2\lfloor n/2\rfloor+1, and this bound is tight.
Edit intent: clarity
Original:  Very recently, F\"uredi and Maleki constructed n-vertex graphs with more than n^2/4 edges such that only (2+2+o(1))n^2/16%DIFDELCMD < \approx0%%% .213n^2 of them occur in C_5, which disproves the conjecture for k= 2.
Revised:  Very recently, F\"uredi and Maleki constructed %DIFDELCMD < \approx0%%% .213n^2 of them occur in C_5, which disproves the conjecture for k= 2.
Edit intent: coherence
Original:  They also proved that this construction is asymptotically best possible by showing that for any \varepsilon>0 , graphs with (1 /4 +\varepsilon)n^2  edges contain at least (2+2 -\varepsilon )n^2/16  edges that occur in C_5.
Revised:  They also proved that this construction is asymptotically best possible by showing that for any \varepsilon>0 graphs with (1 /4 +\varepsilon)n^2 edges contain at least (2+2 -\varepsilon )n^2/16 edges that occur in C_5.
Edit intent: fluency
Original:  For k%DIFDELCMD < \ge3%%% , we adapt the approach to show that\ge  n-vertex graphs with more than n^2/4 edges contain at least\lfloor4}\rfloor\lfloor6}\rfloor\lfloor6}\rfloor 2n^2/ 9-o(n^2)edges that occur in C_{2k+1 . For both of these results, we also prove stability of the corresponding extremal constructions .
Revised:  For k%DIFDELCMD < \ge3%%% . Next, for all k\ge n-vertex graphs with more than n^2/4 edges contain at least\lfloor4}\rfloor\lfloor6}\rfloor\lfloor6}\rfloor 2n^2/ 9-o(n^2)edges that occur in C_{2k+1 . For both of these results, we also prove stability of the corresponding extremal constructions .
Edit intent: clarity
Original:  For k%DIFDELCMD < \ge3%%% , we adapt the approach to show that\ge  n-vertex graphs with more than n^2/4 edges contain at least\lfloor4}\rfloor\lfloor6}\rfloor\lfloor6}\rfloor 2n^2/ 9-o(n^2)edges that occur in C_{2k+1 . For both of these results, we also prove stability of the corresponding extremal constructions .
Revised:  For k%DIFDELCMD < \ge3%%% , we adapt the approach to show that\ge n-vertex graphs with more than n^2/4 edges , and show it is indeed equal to\lfloor4}\rfloor\lfloor6}\rfloor\lfloor6}\rfloor 2n^2/ 9-o(n^2)edges that occur in C_{2k+1 . For both of these results, we also prove stability of the corresponding extremal constructions .
Edit intent: coherence
Original:  For k%DIFDELCMD < \ge3%%% , we adapt the approach to show that\ge  n-vertex graphs with more than n^2/4 edges contain at least\lfloor4}\rfloor\lfloor6}\rfloor\lfloor6}\rfloor 2n^2/ 9-o(n^2)edges that occur in C_{2k+1 . For both of these results, we also prove stability of the corresponding extremal constructions .
Revised:  For k%DIFDELCMD < \ge3%%% , we adapt the approach to show that\ge n-vertex graphs with more than n^2/4 edges contain at least\lfloor4}\rfloor\lfloor6}\rfloor\lfloor6}\rfloor= 2n^2/ 9-o(n^2)edges that occur in C_{2k+1 . For both of these results, we also prove stability of the corresponding extremal constructions .
Edit intent: clarity
Original:  For k%DIFDELCMD < \ge3%%% , we adapt the approach to show that\ge  n-vertex graphs with more than n^2/4 edges contain at least\lfloor4}\rfloor\lfloor6}\rfloor\lfloor6}\rfloor 2n^2/ 9-o(n^2)edges that occur in C_{2k+1 . For both of these results, we also prove stability of the corresponding extremal constructions .
Revised:  For k%DIFDELCMD < \ge3%%% , we adapt the approach to show that\ge n-vertex graphs with more than n^2/4 edges contain at least\lfloor4}\rfloor\lfloor6}\rfloor\lfloor6}\rfloor 2n^2/ 9-o(n^2)edges that occur in C_{2k+1 . For both results, we also prove stability of the corresponding extremal constructions .
Edit intent: fluency
Original:  For example, this new formulation dramatically simplifies the classic Erdos-Renyi graph, reducing the overall graph behavior to a simple proportional feedback wrapped around the dynamics of a single node.
Revised:  For example, this new formulation dramatically simplifies the classic Erdos-Renyi graph, reducing the overall network behavior to one proportional feedback wrapped around the dynamics of a single node.
Edit intent: clarity
Original:  Rich connections between structure and function are developed for networks with random input and output weights, and those composed from nodes with distinct dynamics and connectivity .
Revised:  The theory also extends to networks composed from heterogeneous nodes with distinct dynamics and connectivity .
Edit intent: clarity
Original:  These simple statistical descriptions provide a powerful theoretical framework to understand the functionality of real-world network systems, as we illustrate for the mouse brain connectome.
Revised:  These simple statistical descriptions provide a powerful theoretical framework to understand the functionality of real-world network systems, as we illustrate with examples including the mouse brain connectome.
Edit intent: clarity
Original:  In this paper, we propose to interpolate between these two extremes, and show how to perform cheap iterations along non-sparse search directions, provided that these directions admit a new kind of sparse factorization.
Revised:  In this paper, we propose to interpolate between these two extremes, and show how to perform cheap iterations along non-sparse search directions, provided that these directions can be extracted from a new kind of sparse factorization.
Edit intent: clarity
Original:  The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent "respectively safe" investment portfolios with low variability.
Revised:  The purpose of this research is to develop the cumulant based algorithm and use it to determine eigenvectors that represent investment portfolios with low variability.
Edit intent: clarity
Original: Solving inverse problems with iterative algorithms such as stochastic gradient descent is a populartechnique , especially for large data.
Revised: Solving inverse problems with iterative algorithms is popular , especially for large data.
Edit intent: clarity
Original:  In applications, due to time constraints, the number of iterations one may apply is usually limited, consequently limiting the accuracy achievable by certain methods.
Revised:  Due to time constraints, the number of iterations one may apply is usually limited, consequently limiting the accuracy achievable by certain methods.
Edit intent: clarity
Original:  In applications, due to time constraints, the number of iterations one may apply is usually limited, consequently limiting the accuracy achievable by certain methods.
Revised:  In applications, due to time constraints, the number of possible iterations is usually limited, consequently limiting the accuracy achievable by certain methods.
Edit intent: clarity
Original:  Given a reconstruction error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain a faster convergence to a minimizer with the allowed error  . Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set leads to faster convergence to an error related to the accuracy of the set approximation.
Revised:  Given a reconstruction error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain faster convergence to a minimizer with the allowed error . Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set leads to faster convergence to an error related to the accuracy of the set approximation.
Edit intent: fluency
Original:  Given a reconstruction error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain a faster convergence to a minimizer with the allowed error  . Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set leads to faster convergence to an error related to the accuracy of the set approximation.
Revised:  Given a reconstruction error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain a faster convergence to a minimizer achieving the allowed error . Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set leads to faster convergence to an error related to the accuracy of the set approximation.
Edit intent: clarity
Original:  Given a reconstruction error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain a faster convergence to a minimizer with the allowed error  . Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set leads to faster convergence to an error related to the accuracy of the set approximation.
Revised:  Given a reconstruction error one is willing to tolerate, an important question is whether it is possible to modify the original iterations to obtain a faster convergence to a minimizer with the allowed error . Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set may lead to a faster convergence at the cost of an additional error in the reconstruction related to the accuracy of the set approximation.
Edit intent: clarity
Original:  Our theory ties to recent advances in sparse recovery, compressed sensing  and deep learning.
Revised:  Our theory ties to recent advances in sparse recovery, compressed sensing , and deep learning.
Edit intent: fluency
Original:  In particular, it provides an explanation for the successful approximation of the ISTA solution by neural networks with layers representing iterations  .
Revised:  Particularly, it may provide a possible explanation to the successful approximation of the ISTA solution by neural networks with layers representing iterations .
Edit intent: clarity
Original:  Due to time constraints, the number of possible iterations is usually limited, potentially limiting the achievable accuracy.
Revised:  Due to time constraints, the number of possible iterations is usually limited, potentially affecting the achievable accuracy.
Edit intent: clarity
Original:  Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set may lead to a faster convergence at the cost of an additional error in the reconstruction related to the accuracy of the set approximation.
Revised:  Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set may lead to faster convergence at the cost of an additional error in the reconstruction related to the accuracy of the set approximation.
Edit intent: fluency
Original:  Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set may lead to a faster convergence at the cost of an additional error in the reconstruction related to the accuracy of the set approximation.
Revised:  Relying on recent recovery techniques developed for settings in which the desired signal belongs to some low-dimensional set, we show that using a coarse estimate of this set may lead to a faster convergence at the cost of an additional reconstruction error related to the accuracy of the set approximation.
Edit intent: clarity
Original:  Particularly, it may provide a possible explanation to the successful approximation of the l_1-minimization solution by neural networks with layers representing iterations, as practiced in the learned iterative shrinkage-thresholding algorithm (LISTA).
Revised:  Particularly, it may provide a possible explanation to the successful approximation of the l1-minimization solution by neural networks with layers representing iterations, as practiced in the learned iterative shrinkage-thresholding algorithm (LISTA).
Edit intent: fluency
Original:  Differently from previous work , we focus on the control traffic exchanged among the controllers , in addition to the Openflow control traffic exchanged between controllers and switches.
Revised:  Besides the Openflow control traffic exchanged between controllers and switches , we focus on the control traffic exchanged among the controllers , in addition to the Openflow control traffic exchanged between controllers and switches.
Edit intent: clarity
Original:  We develop an analytical model to estimate the reaction time perceived at the switches due to the inter-controller communications, based on the data-ownership model adopted in the cluster.
Revised:  We develop an analytical model to estimate the reaction time perceived by the switches depending on the data-ownership model adopted in the cluster.
Edit intent: clarity
Original:  The model is then accurately validated in an operational Software Defined WAN (SDWAN).
Revised:  The model is accurately validated in an operational Software Defined WAN (SDWAN).
Edit intent: coherence
Original:  We advocate a careful placement of the controllers, taking into account the two above kinds of control traffic.
Revised:  We advocate a careful placement of the controllers, that should take into account both the above kinds of control traffic.
Edit intent: clarity
Original:  We evaluate, for some real ISP network topologies, the possible delay tradeoffs for the controllers placement problem and we propose a novel evolutionary algorithm to find the corresponding Pareto frontier.
Revised:  We evaluate, for some real ISP network topologies, the delay tradeoffs for the controllers placement problem and we propose a novel evolutionary algorithm to find the corresponding Pareto frontier.
Edit intent: clarity
Original:  Our work provides novel quantitative tools to optimize the plan and the design of the network supporting the control plane of SDN networks, especially when the network is very large and in-band control plane is adopted.
Revised:  Our work provides novel quantitative tools to optimize the planning and the design of the network supporting the control plane of SDN networks, especially when the network is very large and in-band control plane is adopted.
Edit intent: fluency
Original:  We also show that for operational distributed controllers (e.g. OpenDaylight and ONOS), the location of the leader controller adopted in the background consensus algorithm has a strong impact on the reactivity perceived by switches.
Revised:  We also show that for operational distributed controllers (e.g. OpenDaylight and ONOS), the location of the controller which acts as a leader in the consensus algorithm has a strong impact on the reactivity perceived by switches.
Edit intent: clarity
Original:  We develop two novel ideas, interleaved LCPs and {\em  {\em precomputed document lists , that yield highly compressed indexes solving the problem of document listing (find all the documents where a string appears), top-k document retrieval (find the k documents where a string appears most often), and document counting (count the number of documents where a string appears).
Revised:  We develop two novel ideas, {\em {\em precomputed document lists , that yield highly compressed indexes solving the problem of document listing (find all the documents where a string appears), top-k document retrieval (find the k documents where a string appears most often), and document counting (count the number of documents where a string appears).
Edit intent: coherence