wanyu/IteraTeR_v2 huggingface dataset:
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A %DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: clarity
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D %DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M %DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E Extra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% orwein line search technique (PADMM-EBB).
Edit intent: fluency
Original:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B orwein line search technique (PADMM-EBB).
Revised:  yielding a new algorithm, namely nonsymmetric %DIFDELCMD < {\bf %%% P roximal%DIFDELCMD < {\bf %DIFDELCMD < %%% A lternating%DIFDELCMD < {\bf %%% D irection%DIFDELCMD < {\bf %%% M ethod of%DIFDELCMD < {\bf %%% M ultipliers with a preconditioned %DIFDELCMD < {\bf %%% E xtra-gradient step in which the preconditioned metric is generated by a blockwise %DIFDELCMD < {\bf %%% B arzilai-%DIFDELCMD < {\bf %%% B Barzilai-Borwein line search technique (PADMM-EBB).
Edit intent: clarity
Original:  Motivated by the problem of shape sealing whose goal is to seal an object using as little resourcesas possible, we investigate how a particle system can self-organize to form an object's convex hull.
Revised:  Motivated by the problem of sealing an object using as little resourcesas possible, we investigate how a particle system can self-organize to form an object's convex hull.
Edit intent: clarity
Original:  Motivated by the problem of shape sealing whose goal is to seal an object using as little resourcesas possible, we investigate how a particle system can self-organize to form an object's convex hull.
Revised:  Motivated by the problem of shape sealing whose goal is to seal an object using minimal resources, we show how a particle system can self-organize to form an object's convex hull.
Edit intent: clarity
Original:  We give a fully distributed, local algorithm for convex hull formation and prove that it runs in O(B + H\log H ) asynchronous rounds, where B is the length of the object's boundary and H is the length of the object's convex hull.
Revised:  We give a distributed, local algorithm for convex hull formation and prove that it runs in O(B + H\log H ) asynchronous rounds, where B is the length of the object's boundary and H is the length of the object's convex hull.
Edit intent: clarity
Original:  It is formally defined both declaratively as an acyclicity axiom, and operationally as a concurrent algorithm with memory bearing timestamps.
Revised:  Its semantics is formally defined both declaratively as an acyclicity axiom, and operationally as a concurrent algorithm with memory bearing timestamps.
Edit intent: clarity
Original:  In this paper, we develop two simpler equivalent operational definitions of SI as lock-based reference implementations that do not use timestamps.
Revised:  We develop two simpler equivalent operational definitions of SI as lock-based reference implementations that do not use timestamps.
Edit intent: coherence
Original: This paper studies the fundamental problem of how to reroute k unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner and fast .
Revised: This paper studies the fundamental problem of how to reroute k unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner and fast .
Edit intent: fluency
Original:  However, existing algorithms for this problem either have a super-polynomial runtime or only compute feasible schedules, which do not provide any guarantees on the length of the rerouting schedule.
Revised:  However, existing algorithms for this problem either have a super-polynomial runtime or only compute feasible schedules, which do not provide any guarantees on the length of the rerouting schedule.
Edit intent: fluency
Original:  We contribute an almost tight characterization of the polynomial-time tractability of the problem: We present the first polynomial-time solution for this problem for two flows, but also show that even the question whether a feasible update schedule exists, is already NP-hard for six flows.
Revised:  We contribute an almost tight characterization of the polynomial-time tractability of the problem: We present the first polynomial-time solution for this problem for two flows, but also show that even the question whether a feasible update schedule exists, is already NP-hard for six flows.
Edit intent: fluency
Original:  In fact, the presented algorithm runs in linear time and is hence not only optimal in terms of scheduling but also asymptotically optimal in terms of runtime.
Revised:  In fact, the presented algorithm runs in linear time and is hence not only optimal in terms of scheduling but also asymptotically optimal in terms of runtime.
Edit intent: fluency
Original:  This scheduling problem has applications in traffic engineering in communication networks and has recently received much attention in software-defined networks, in which updates are distributed over an asynchronously network by a software controller.
Revised:  This scheduling problem has applications in traffic engineering in communication networks and has recently received much attention in software-defined networks, in which updates are distributed over an asynchronous network by a software controller.
Edit intent: fluency
Original:  Using randomization techniques recently developed in BDT17 , we can transform the original problem into a frictionless market framework, however, with the extra probability uncertainty on an enlarged space.
Revised:  The randomization techniques recently developed in BDT17 , we can transform the original problem into a frictionless market framework, however, with the extra probability uncertainty on an enlarged space.
Edit intent: fluency
Original:  Using randomization techniques recently developed in BDT17 , we can transform the original problem into a frictionless market framework, however, with the extra probability uncertainty on an enlarged space.
Revised:  Using randomization techniques recently developed in BDT17 allow us to transform the original problem into a frictionless market framework, however, with the extra probability uncertainty on an enlarged space.
Edit intent: clarity
Original:  This allows us to prove all together the existence of the optimal strategy,  the auxiliary dynamic programming principle as well as the convex duality theorem in our context with transaction costs.
Revised:  This allows us to prove all together the existence of the optimal strategy, convex duality theorem as well as the auxiliary dynamic programming principle as well as the convex duality theorem in our context with transaction costs.
Edit intent: fluency
Original:  This allows us to prove all together the existence of the optimal strategy,  the auxiliary dynamic programming principle as well as the convex duality theorem in our context with transaction costs.
Revised:  This allows us to prove all together the existence of the optimal strategy, the auxiliary dynamic programming principle in our context with transaction costs.
Edit intent: coherence
Original: We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a  semi-static utility maximization for the case of exponential utility preference.
Revised: We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a semi-static utility maximization problem with an exponential utility preference.
Edit intent: clarity
Original:  The randomization techniques recently developed in BDT17 allow us to transform the original problem into a frictionless market framework, however, with the extra probability uncertainty on an enlarged space.
Revised:  The randomization techniques recently developed in BDT17 allow us to transform the original problem into a frictionless counterpart on an enlarged space.
Edit intent: clarity
Original:  As an application of the duality representation, some important features of utility indifference prices are investigated in the robust setting .
Revised:  As an application of the duality representation, some basic features of utility indifference prices are investigated in the robust setting .
Edit intent: clarity
Original:  We introduce a novel class of multi-rate Adams-Bashforth (MRAB) schemes that offer significant stability improvements and computational efficiencies for SBP-SAT methods.
Revised:  We introduce a class of multi-rate Adams-Bashforth (MRAB) schemes that offer significant stability improvements and computational efficiencies for SBP-SAT methods.
Edit intent: clarity
Original:  We present numerical results that confirm the numerical efficacy of MRAB integrators, outline a number of outstanding implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB.
Revised:  We present numerical results that confirm the efficacy of MRAB integrators, outline a number of outstanding implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB.
Edit intent: clarity
Original:  We present numerical results that confirm the numerical efficacy of MRAB integrators, outline a number of outstanding implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB.
Revised:  We present numerical results that confirm the numerical efficacy of MRAB integrators, outline a number of implementation challenges, and demonstrate a reduction in computational cost enabled by MRAB.
Edit intent: clarity
Original:  The present paper attempts to provide a new approach of dimension-ing 5G NR radio resource (number of Physical Resource Blocks) considering its congestion probability, qualified as a relevant metric for QoS evaluation.
Revised:  The present paper attempts to provide a new approach of radio resources dimensioning considering the congestion probability, qualified as a relevant metric for QoS evaluation.
Edit intent: clarity
Original:  Moreover, 5G users are assumed to be distributed in roads modeled by Poisson Line Process (PLP) instead of the widely-used 2D-Poisson Point Process .
Revised:  Users are assumed to be distributed in roads modeled by Poisson Line Process (PLP) instead of the widely-used 2D-Poisson Point Process .
Edit intent: coherence
Original: High data rates, low latencies, and a widespread availability are the key elements why current cellular network technologies are used for many different applications.
Revised: High data rates, low latencies, and a widespread availability are the key properties why current cellular network technologies are used for many different applications.
Edit intent: clarity
Original:  Particularly in the context of time-critical and highly-dynamic Cyber Physical Systems (CPS) and Vehicle-to-Everything (V2X) applications, the compliance with deadlines and therefore the efficient allocation of scarce mobile radio resources is of high importance.
Revised:  Particularly in the context of time-critical and highly dynamic Cyber Physical Systems (CPS) and Vehicle-to-Everything (V2X) applications, the compliance with deadlines and therefore the efficient allocation of scarce mobile radio resources is of high importance.
Edit intent: fluency
Original:  Hence, scheduling solutions are required offering a good trade-off between the compliance with deadlines and a resource-efficient allocation of rare resources in mobile networks.
Revised:  Hence, scheduling solutions are required offering a good trade-off between the compliance with deadlines and a spectrum-efficient allocation of resources in mobile networks.
Edit intent: clarity
Original:  In this paper, we present the results of an experimental validation of the Payload-Size and Deadline-Aware (PayDA) scheduling algorithm using a Software-Defined Radio (SDR)-based eNodeB.
Revised:  In this paper, we present the results of an experimental validation of the Payload-size and Deadline-aware (PayDA) scheduling algorithm using a Software-Defined Radio (SDR)-based eNodeB.
Edit intent: fluency
Original:  The results of the experimental validation prove the high efficiency of the proposed PayDA scheduling algorithm for time-critical applications in both miscellaneous and homogeneous data traffic  .
Revised:  The results of the experimental validation prove the high efficiency of the proposed PayDA scheduling algorithm for time-critical applications in both miscellaneous and homogeneous data traffic scenarios .
Edit intent: clarity
Original:  Several illustrations are provided .
Revised:  We also illustrate the potential use of the framework for out-of-sample predictions .
Edit intent: clarity
Original: Motivated by recent results relating synchronizing automata and primitive sets, we tackle the synchronization process and the related longstanding C ern\'y conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns.
Revised: Motivated by recent results relating synchronizing automata and primitive sets, we tackle the synchronization process and the related longstanding C ern\'{y conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns.
Edit intent: fluency
Original:  We report numerical results and supported by them we state a conjecture that, if true, would imply an upper bound of n(n-1) on the reset threshold of a certain (broad) class of automata.
Revised:  We report numerical results and supported by them we state a conjecture that, if true, would imply an upper bound of n(n-1) on the reset threshold of a certain class of automata.
Edit intent: clarity
Original: Motivated by recent results relating synchronizing automata and primitive sets, we tackle the synchronization process and the related longstanding Cern\'{y} conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns.
Revised: Motivated by recent results relating synchronizing DFAs and primitive sets, we tackle the synchronization process and the related longstanding Cern\'{y} conjecture by studying the primitivity phenomenon for sets of nonnegative matrices having neither zero-rows nor zero-columns.
Edit intent: clarity
Original:  We report numerical results and supported by them we state a conjecture that, if true, would imply an upper bound of n(n-1) on the reset threshold of a certain class of automata.
Revised:  We report numerical results and supported by them we state a conjecture that, if true, would imply an upper bound of n(n-1) on the reset threshold of a new class of automata.
Edit intent: clarity