wanyu/IteraTeR_v2 huggingface dataset:
Original:  So far this was explored for the case that verifiers are%DIFDELCMD < {\em %DIFDELCMD < %%% two-way probabilistic finite automata (Dwork and Stockmayer, 1990) and%DIFDELCMD < {\em %DIFDELCMD < %%% one-way quantum finite automata as well as%DIFDELCMD < {\em %%% two-way quantum finite automata (Nishimura and Yamakami, 2009).
Revised:  So far this was explored for the case that verifiers are%DIFDELCMD < {\em %DIFDELCMD < %%% two-way probabilistic finite automata %DIFDELCMD < {\em %DIFDELCMD < %%% one-way quantum finite automata as well as%DIFDELCMD < {\em %%% two-way quantum finite automata (Nishimura and Yamakami, 2009).
Edit intent: coherence
Original:  So far this was explored for the case that verifiers are%DIFDELCMD < {\em %DIFDELCMD < %%% two-way probabilistic finite automata (Dwork and Stockmayer, 1990) and%DIFDELCMD < {\em %DIFDELCMD < %%% one-way quantum finite automata as well as%DIFDELCMD < {\em %%% two-way quantum finite automata (Nishimura and Yamakami, 2009).
Revised:  So far this was explored for the case that verifiers are%DIFDELCMD < {\em %DIFDELCMD < %%% two-way probabilistic finite automata (Dwork and Stockmayer, 1990) and%DIFDELCMD < {\em %DIFDELCMD < %%% as well as%DIFDELCMD < {\em %%% two-way quantum finite automata (Nishimura and Yamakami, 2009).
Edit intent: fluency
Original:  So far this was explored for the case that verifiers are%DIFDELCMD < {\em %DIFDELCMD < %%% two-way probabilistic finite automata (Dwork and Stockmayer, 1990) and%DIFDELCMD < {\em %DIFDELCMD < %%% one-way quantum finite automata as well as%DIFDELCMD < {\em %%% two-way quantum finite automata (Nishimura and Yamakami, 2009).
Revised:  So far this was explored for the case that verifiers are%DIFDELCMD < {\em %DIFDELCMD < %%% two-way probabilistic finite automata (Dwork and Stockmayer, 1990) and%DIFDELCMD < {\em %DIFDELCMD < %%% one-way quantum finite automata %DIFDELCMD < {\em %%% two-way quantum finite automata (Nishimura and Yamakami, 2009).
Edit intent: coherence
Original:  So far this was explored for the case that verifiers are%DIFDELCMD < {\em %DIFDELCMD < %%% two-way probabilistic finite automata (Dwork and Stockmayer, 1990) and%DIFDELCMD < {\em %DIFDELCMD < %%% one-way quantum finite automata as well as%DIFDELCMD < {\em %%% two-way quantum finite automata (Nishimura and Yamakami, 2009).
Revised:  So far this was explored for the case that verifiers are%DIFDELCMD < {\em %DIFDELCMD < %%% two-way probabilistic finite automata (Dwork and Stockmayer, 1990) and%DIFDELCMD < {\em %DIFDELCMD < %%% one-way quantum finite automata as well as%DIFDELCMD < {\em %%% (Nishimura and Yamakami, 2009).
Edit intent: fluency
Original:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Revised:  In this paper we explore the power of %DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Edit intent: coherence
Original:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Revised:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Edit intent: clarity
Original:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Revised:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization %DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Edit intent: coherence
Original:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Revised:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Edit intent: clarity
Original:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Revised:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems AM for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Edit intent: clarity
Original:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Revised:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) --introduced by Ambainis and Watrous in 2002 and the communications are classical.
Edit intent: fluency
Original:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002 and the communications are classical.
Revised:  In this paper we explore the power of special type of IP in which verifiers uses%DIFDELCMD < {\em %%% public randomization , namely so called%DIFDELCMD < {\em %%% Arthur-Merlin proof systems (AM ), for the case that verifiers are {\em two-way finite automata with quantum and classical states} (2QCFA) introduced by Ambainis and Watrous in 2002--and the communications are classical.
Edit intent: fluency
Original:  It is of interest to consider AM with such "semi-quantum" verifiers because 2QCFA use only limited quantum resources.
Revised:  It is of interest to consider AM with such "semi-quantum" verifiers because they use only limited quantum resources.
Edit intent: clarity
Original:  Our main result is that such Quantum Arthur-Merlin proof systems (QAM(2QCFA) are asymptotically more powerful than in the case verifiers are two-way probabilistic finite automata (AM(2PFA)) and that there is an NP-complete language , modeling the 0-1 knapsack problem, that can be recognized by  QAM(2QCFA)  .
Revised:  Our main result is that such Quantum Arthur-Merlin proof systems (QAM(2QCFA) are asymptotically more powerful than in the case verifiers are two-way probabilistic finite automata (AM(2PFA)) and that there is an NP-complete language , modeling the 0-1 knapsack problem, that can be recognized by a QAM(2QCFA) .
Edit intent: fluency
Original:  Typically  such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data.
Revised:  Typically , such mathematical models involve networks of coupled jump stochastic processes with a large number of parameters that need to be suitably calibrated against experimental data.
Edit intent: fluency
Original:  In this direction, the  sensitivity analysis of the reaction network's parameters is a crucial mathematical and computational tool since it allows to infer information about the robustness and the identifiability of the model 's parameters.
Revised:  In this direction, the sensitivity analysis of reaction networks is an essential mathematical and computational tool since it allows to infer information about the robustness and the identifiability of the model 's parameters.
Edit intent: clarity
Original:  In this direction, the  sensitivity analysis of the reaction network's parameters is a crucial mathematical and computational tool since it allows to infer information about the robustness and the identifiability of the model 's parameters.
Revised:  In this direction, the sensitivity analysis of the reaction network's parameters is a crucial mathematical and computational tool , yielding information regarding the robustness and the identifiability of the model 's parameters.
Edit intent: clarity
Original:  We develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a high number of parameters.
Revised:  We develop a sensitivity analysis methodology suitable for complex stochastic reaction networks with a large number of parameters.
Edit intent: clarity
Original:  The proposed approach is based on Information Theory  and relies on the quantification of information loss due to parameter perturbations between time-series distributions , hence referred to as "pathwise".
Revised:  The proposed approach is based on Information Theory methods and relies on the quantification of information loss due to parameter perturbations between time-series distributions , hence referred to as "pathwise".
Edit intent: clarity
Original:  A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantify the parameter sensitivities.
Revised:  A key aspect of the method is that an associated pathwise Fisher Information Matrix (FIM) is defined, which in turn constitutes a gradient-free approach to quantifying parameter sensitivities.
Edit intent: fluency
Original:  The study of the structure of the FIM which turns out to be block-diagonal reveals hidden parameter dependencies and sensitivities in reaction networks .
Revised:  The structure of the FIM which turns out to be block-diagonal reveals hidden parameter dependencies and sensitivities in reaction networks .
Edit intent: clarity
Original:  The study of the structure of the FIM which turns out to be block-diagonal reveals hidden parameter dependencies and sensitivities in reaction networks .
Revised:  The study of the structure of the FIM turns out to be block-diagonal reveals hidden parameter dependencies and sensitivities in reaction networks .
Edit intent: coherence
Original:  The study of the structure of the FIM which turns out to be block-diagonal reveals hidden parameter dependencies and sensitivities in reaction networks .
Revised:  The study of the structure of the FIM which turns out to be block-diagonal , revealing hidden parameter dependencies and sensitivities in reaction networks .
Edit intent: fluency
Original:  We prove that for several basic and commonly used rational relations, the intersection problem with regular relations is either undecidable (e.g., for subword or su?x , and some generalizations), or decidable with non-primitive-recursive complexity (e.g., for subsequence and its generalizations).
Revised:  We prove that for several basic and commonly used rational relations, the intersection problem with regular relations is either undecidable (e.g., for subword or suffix , and some generalizations), or decidable with non-primitive-recursive complexity (e.g., for subsequence and its generalizations).
Edit intent: fluency
Original:  We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classi?es them into either e?ciently checkable or undecidable cases.
Revised:  We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classifies them into either e?ciently checkable or undecidable cases.
Edit intent: fluency
Original:  We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classi?es them into either e?ciently checkable or undecidable cases.
Revised:  We then prove a dichotomy result for logics combining regular conditions on individual paths and rational relations on paths, by showing that the syntactic form of formulae classi?es them into either efficiently checkable or undecidable cases.
Edit intent: fluency
Original:  However, recent research shows that carefully synthesized false-data injection attacks can bypass the security system and thus introduce arbitrary errors to state estimates.
Revised:  However, recent research shows that carefully synthesized false-data injection attacks can bypass the security system and introduce arbitrary errors to state estimates.
Edit intent: coherence
Original:  By protecting carefully selected meter measurements and (or) power network topological information, we show that no false-data injection attack can be formulated to compromise any set of state estimates.
Revised:  By protecting carefully selected meter measurements , no false data injection attack can be formulated to compromise any set of state estimates.
Edit intent: coherence
Original:  By protecting carefully selected meter measurements and (or) power network topological information, we show that no false-data injection attack can be formulated to compromise any set of state estimates.
Revised:  By protecting carefully selected meter measurements and (or) power network topological information, we show that no false-data injection attack can be launched to compromise any set of state estimates.
Edit intent: clarity
Original:  By securing carefully selected meter measurements, no false data injection attack can be launched to compromise any set of state estimates .
Revised:  By securing carefully selected meter measurements, no false data injection attack can be launched to compromise any set of state variables .
Edit intent: clarity
Original:  We characterize the optimal protection problem, which protects the state estimates with minimum number of measurements, as a variant Steiner tree problem in a graph.
Revised:  We characterize the optimal protection problem, which protects the state variables with minimum number of measurements, as a variant Steiner tree problem in a graph.
Edit intent: clarity
Original:  Mitigating parameter bias induced by finite sampling is important to any scientific endeavor aiming for high accuracy, but correcting for bias is a also an important step in the construction of optimal parameter estimates.
Revised:  Mitigating parameter bias induced by finite sampling is important to any scientific endeavor aiming for high accuracy, but correcting for bias is also often an important step in the construction of optimal parameter estimates.
Edit intent: coherence
Original: Let s be a point source of light inside a simple polygon P of n vertices.
Revised: Let s be a source point and t be a destination point inside an n-vertex simple polygon P of n vertices.
Edit intent: clarity
Original:  A path from s to some point t inside P is called a %DIFDELCMD < {\it %%% diffuse reflection path if the turning points of the path lie in the interiors of the boundary edges of P.
Revised:  A path from a light source s to t inside P is called a %DIFDELCMD < {\it %%% diffuse reflection path if the turning points of the path lie in the interiors of the boundary edges of P.
Edit intent: clarity
Original:  A diffuse reflection path is said to be %DIFDELCMD < {\it %%% optimal if it has the minimum number of turning points amongst all diffuse reflection paths between s and t.
Revised:  A diffuse reflection path is said to be %DIFDELCMD < {\it %%% optimal if it has the minimum number of turning points amongst all diffuse reflection paths between s and t.
Edit intent: fluency
Original:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t  . For computing a  constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Revised:  The minimum diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t . For computing a constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Edit intent: fluency
Original:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t  . For computing a  constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Revised:  A diffuse reflection path %DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t . For computing a constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Edit intent: clarity
Original:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t  . For computing a  constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Revised:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t . For computing a constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Edit intent: clarity
Original:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t  . For computing a  constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Revised:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple , (ii) it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t . For computing a constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Edit intent: coherence
Original:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t  . For computing a  constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Revised:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t . For computing a constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Edit intent: fluency
Original:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t  . For computing a  constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Revised:  A diffuse reflection path between s and t inside P is said to be%DIFDELCMD < {\it %%% constrained if the path is simple and it intersects only the %DIFDELCMD < {\it %%% eaves of the Euclidean shortest path between s and t . For computing a minimum constrained diffuse reflection path from s to t having the minimum number of turns amongst all such paths , we present an O(n ^22^e) time algorithm, where e\geq 0 is the number of eaves.
Edit intent: fluency
Original: Methods to recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise are developed.
Revised: We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise are developed.
Edit intent: clarity
Original:  Analytical results (existence of minimizers, complexity) on inverse Potts problems are obtained and relations to sparsity problems are provided.
Revised:  Analytical results (existence of minimizers, complexity) on inverse Potts functionals and provide relations to sparsity problems are provided.
Edit intent: clarity
Original:  It is shown in a series of experiments  that the proposed method yields very satisfactory jump-sparse and sparse reconstructions, respectively.
Revised:  It is shown in a series of experiments shows that the proposed method yields very satisfactory jump-sparse and sparse reconstructions, respectively.
Edit intent: fluency