wanyu/IteraTeR_v2 huggingface dataset:
Original:  We address this question by observing that edges, not vertices, act as the statistical units in many network datasets , making a theory of edge labeled networks more natural for these applications.
Revised:  We address this question by observing that edges, not vertices, act as the statistical units in networks constructed from interaction data , making a theory of edge labeled networks more natural for these applications.
Edit intent: clarity
Original:  We address this question by observing that edges, not vertices, act as the statistical units in many network datasets , making a theory of edge labeled networks more natural for these applications.
Revised:  We address this question by observing that edges, not vertices, act as the statistical units in many network datasets , making a theory of edge-labeled networks more natural for these applications.
Edit intent: fluency
Original:  We address this question by observing that edges, not vertices, act as the statistical units in many network datasets , making a theory of edge labeled networks more natural for these applications.
Revised:  We address this question by observing that edges, not vertices, act as the statistical units in many network datasets , making a theory of edge labeled networks more natural for many applications.
Edit intent: clarity
Original:  In this context we introduce the new invariance principle of {\em edge exchangeability}, which unlike its vertex exchangeable counterpart admits models for networks with sparse and/or power law structure.
Revised:  In this context we introduce the concept of {\em edge exchangeability}, which unlike its vertex exchangeable counterpart admits models for networks with sparse and/or power law structure.
Edit intent: clarity
Original:  Moreover, we describe algebraic methods targeted to efficiently solve these problems  .
Revised:  Moreover, we describe algebraic methods targeted to solve these problems .
Edit intent: clarity
Original: Several min-max relations in graph theory can be expressed in the framework of  Erdos-P\'osa properties .
Revised: Several min-max relations in graph theory can be expressed in the framework of the Erdos-P\'osa properties .
Edit intent: fluency
Original: Several min-max relations in graph theory can be expressed in the framework of  Erdos-P\'osa properties .
Revised: Several min-max relations in graph theory can be expressed in the framework of Erdos-P\'osa property .
Edit intent: fluency
Original:  Typically, such properties reveal a connection between packing and covering problems on graphs.
Revised:  Typically, this property reveals a connection between packing and covering problems on graphs.
Edit intent: clarity
Original:  We describe some recent techniques for proving such properties that are related to tree-like decompositions.
Revised:  We describe some recent techniques for proving this property that are related to tree-like decompositions.
Edit intent: clarity
Original: Measures for the overall similarity of partitions P =\{P_1,%DIFDELCMD < \dots%%% ,P_{\vert\mathcal{P\vert}\} }  and P' =\{P'_1,%DIFDELCMD < \dots%%% ,P'_{\vert\mathcal{P'\vert}\} of the same set Vdo not provide specifics on how P and P' correspond, e. g., when the union of two parts in P is similar to that of three parts in P '.
Revised: %DIFDELCMD < \dots%%% ,P_{\vert\mathcal{P\vert}\} } and P' =\{P'_1,%DIFDELCMD < \dots%%% ,P'_{\vert\mathcal{P'\vert}\} of the same set Vdo not provide specifics on how P and P' correspond, e. g., when the union of two parts in P is similar to that of three parts in P '.
Edit intent: clarity
Original: Measures for the overall similarity of partitions P =\{P_1,%DIFDELCMD < \dots%%% ,P_{\vert\mathcal{P\vert}\} }  and P' =\{P'_1,%DIFDELCMD < \dots%%% ,P'_{\vert\mathcal{P'\vert}\} of the same set Vdo not provide specifics on how P and P' correspond, e. g., when the union of two parts in P is similar to that of three parts in P '.
Revised: Measures for the overall similarity of partitions P =\{P_1,%DIFDELCMD < \dots%%% \vert}\} } and P' =\{P'_1,%DIFDELCMD < \dots%%% ,P'_{\vert\mathcal{P'\vert}\} of the same set Vdo not provide specifics on how P and P' correspond, e. g., when the union of two parts in P is similar to that of three parts in P '.
Edit intent: fluency
Original: Measures for the overall similarity of partitions P =\{P_1,%DIFDELCMD < \dots%%% ,P_{\vert\mathcal{P\vert}\} }  and P' =\{P'_1,%DIFDELCMD < \dots%%% ,P'_{\vert\mathcal{P'\vert}\} of the same set Vdo not provide specifics on how P and P' correspond, e. g., when the union of two parts in P is similar to that of three parts in P '.
Revised: Measures for the overall similarity of partitions P =\{P_1,%DIFDELCMD < \dots%%% ,P_{\vert\mathcal{P\vert}\} } and P' %DIFDELCMD < \dots%%% ,P'_{\vert\mathcal{P'\vert}\} of the same set Vdo not provide specifics on how P and P' correspond, e. g., when the union of two parts in P is similar to that of three parts in P '.
Edit intent: fluency
Original: Measures for the overall similarity of partitions P =\{P_1,%DIFDELCMD < \dots%%% ,P_{\vert\mathcal{P\vert}\} }  and P' =\{P'_1,%DIFDELCMD < \dots%%% ,P'_{\vert\mathcal{P'\vert}\} of the same set Vdo not provide specifics on how P and P' correspond, e. g., when the union of two parts in P is similar to that of three parts in P '.
Revised: Measures for the overall similarity of partitions P =\{P_1,%DIFDELCMD < \dots%%% ,P_{\vert\mathcal{P\vert}\} } and P' =\{P'_1,%DIFDELCMD < \dots%%% '\vert}\} of the same set Vdo not provide specifics on how P and P' correspond, e. g., when the union of two parts in P is similar to that of three parts in P '.
Edit intent: fluency
Original:  and a low value of }%DIFDELCMD < \vert%%% (\bigcup_{S\in\mathcal{S}S)\triangle(\bigcup_{S'\in\mathcal{S}'}S')}%DIFDELCMD < \vert%%% ,
Revised:  and a low value of }%DIFDELCMD < \vert%%% }S)\triangle(\bigcup_{S'\in\mathcal{S}'}S')}%DIFDELCMD < \vert%%% ,
Edit intent: coherence
Original:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, }  \mathcal{P} \setminus \mathcal{S)
Revised:  where \triangle and%DIFDELCMD < \vert%%% %DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, } \mathcal{P} \setminus \mathcal{S)
Edit intent: coherence
Original:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, }  \mathcal{P} \setminus \mathcal{S)
Revised:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, } \mathcal{P} \setminus \mathcal{S)
Edit intent: coherence
Original:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, }  \mathcal{P} \setminus \mathcal{S)
Revised:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality %DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, } \mathcal{P} \setminus \mathcal{S)
Edit intent: clarity
Original:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, }  \mathcal{P} \setminus \mathcal{S)
Revised:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted %DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, } \mathcal{P} \setminus \mathcal{S)
Edit intent: fluency
Original:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, }  \mathcal{P} \setminus \mathcal{S)
Revised:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% \subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, } \mathcal{P} \setminus \mathcal{S)
Edit intent: coherence
Original:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, }  \mathcal{P} \setminus \mathcal{S)
Revised:  where \triangle and%DIFDELCMD < \vert%%% \cdot%DIFDELCMD < \vert %%% denote symmetric difference and cardinality total weight%DIFDELCMD < ] %%% if the elements of V are unweighted weighted%DIFDELCMD < ]%%% . Such an objective function is essentially one for \mathcal{S\subseteq\mathcal{P} only and yields the weight of the cut (\mathcal{S}, } \mathcal{P} )
Edit intent: fluency
Original:  w. r.t. \mathcal{P}'}%DIFDELCMD < }%%% . Thus, we can derive a hierarchy of the%DIFDELCMD < \vert%%%  \mathcal{P} -1%DIFDELCMD < \vert %%% best correspondences from a minimal and \mathcal{P'} correspond to each other.
Revised:  w. r.t. \mathcal{P}'}%DIFDELCMD < }%%% %DIFDELCMD < \vert%%% \mathcal{P} -1%DIFDELCMD < \vert %%% best correspondences from a minimal and \mathcal{P'} correspond to each other.
Edit intent: clarity
Original:  To this end, we first define natural collections of best correspondences under three constraints }\cone\ctwo\cthree\cone cut basis of \mathcal{P.
Revised:  To this end, we first define natural collections of best correspondences under three constraints }\cone,\ctwo\cthree\cone cut basis of \mathcal{P.
Edit intent: fluency
Original:  To this end, we first define natural collections of best correspondences under three constraints }\cone\ctwo\cthree\cone cut basis of \mathcal{P.
Revised:  To this end, we first define natural collections of best correspondences under three constraints }\cone\ctwo, and\cthree\cone cut basis of \mathcal{P.
Edit intent: coherence
Original:  To this end, we first define natural collections of best correspondences under three constraints }\cone\ctwo\cthree\cone cut basis of \mathcal{P.
Revised:  To this end, we first define natural collections of best correspondences under three constraints }\cone\ctwo\cthree. In case of\cone cut basis of \mathcal{P.
Edit intent: coherence
Original:  To this end, we first define natural collections of best correspondences under three constraints }\cone\ctwo\cthree\cone cut basis of \mathcal{P.
Revised:  To this end, we first define natural collections of best correspondences under three constraints }\cone\ctwo\cthree\cone cut basis of .
Edit intent: coherence
Original:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Revised:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% %DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Edit intent: fluency
Original:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Revised:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% %DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Edit intent: coherence
Original:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Revised:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Edit intent: fluency
Original:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Revised:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% %DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Edit intent: coherence
Original:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% \mathcal{P'}%DIFDELCMD < \vert%%% ).
Revised:  A minimal P_s-P_t cut can be computed in time O(}%DIFDELCMD < \vert %DIFDELCMD < %%% V%DIFDELCMD < \vert%%% +%DIFDELCMD < \vert%%% \mathcal{P }%DIFDELCMD < \vert%%% ^4%DIFDELCMD < \vert%%% '}%DIFDELCMD < \vert%%% ).
Edit intent: fluency
Original:  We also introduce a constraint, }\cfour\cthree branch-and-bound algorithm for finding minimal P_s-P_t cuts .
Revised:  We also introduce a constraint, }\cfour\cthree branch-and-bound algorithms for finding minimum P_s-P_t cuts .
Edit intent: fluency
Original:  When the entire cut basis needs to be computed, the algorithm is feasible up to%DIFDELCMD < \vert%%% \mathcal{P \vert ,%DIFDELCMD < \vert%%% \mathcal{P \vert around 1000.
Revised:  When the entire cut basis needs to be computed, the algorithm is feasible up to%DIFDELCMD < \vert%%% of \mathcal{P \vert ,%DIFDELCMD < \vert%%% \mathcal{P \vert around 1000.
Edit intent: clarity
Original:  When the entire cut basis needs to be computed, the algorithm is feasible up to%DIFDELCMD < \vert%%% \mathcal{P \vert ,%DIFDELCMD < \vert%%% \mathcal{P \vert around 1000.
Revised:  When the entire cut basis needs to be computed, the algorithm is feasible up to%DIFDELCMD < \vert%%% \mathcal{P \vert %DIFDELCMD < \vert%%% \mathcal{P \vert around 1000.
Edit intent: coherence
Original:  When the entire cut basis needs to be computed, the algorithm is feasible up to%DIFDELCMD < \vert%%% \mathcal{P \vert ,%DIFDELCMD < \vert%%% \mathcal{P \vert around 1000.
Revised:  When the entire cut basis needs to be computed, the algorithm is feasible up to%DIFDELCMD < \vert%%% \mathcal{P \vert ,%DIFDELCMD < \vert%%% \mathcal{P \vert around 1000.
Edit intent: fluency
Original:  Finally\ctwo , \cthree\cfour we use  correspondences to gain insight into a parallel community detection algorithm that is non-deterministic due to race conditions and that has an optional refinement phase.
Revised:  Finally\ctwo , \cthree, and\cfour we use correspondences to gain insight into a parallel community detection algorithm that is non-deterministic due to race conditions and that has an optional refinement phase.
Edit intent: coherence
Original:  Finally\ctwo , \cthree\cfour we use  correspondences to gain insight into a parallel community detection algorithm that is non-deterministic due to race conditions and that has an optional refinement phase.
Revised:  Finally\ctwo , \cthree\cfour we use the correspondences to gain insight into a parallel community detection algorithm that is non-deterministic due to race conditions and that has an optional refinement phase.
Edit intent: fluency
Original:  Finally\ctwo , \cthree\cfour we use  correspondences to gain insight into a parallel community detection algorithm that is non-deterministic due to race conditions and that has an optional refinement phase.
Revised:  Finally\ctwo , \cthree\cfour we use correspondences to gain insight into a community detection algorithm that is non-deterministic due to race conditions and that has an optional refinement phase.
Edit intent: clarity
Original:  Through this approach we further show that the presence of a dendritic cable (i) attenuates the somatic subthreshold response to slowly-varying inputs and (ii)mediates spike rate resonance , or equivalently, pronounced spike to field coherence, in the beta and gamma frequency range due to an oscillatory weak electric field.
Revised:  Through this approach we further show that the presence of a dendritic cable (i) attenuates the somatic subthreshold response to slowly-varying inputs and (ii)mediates spike rate resonance in the beta and gamma frequency range due to an oscillatory weak electric field.
Edit intent: clarity
Original:  Our point neuron model extension is simple to implement and well suited for studying the dynamics of populations with heterogeneous neuronal morphologyand the effects of weak electric fieldson population activity .
Revised:  Our point neuron model extension is simple to implement and well suited for application in large populations of coupled neurons with different morphology, exposed to extracellular electric fields .
Edit intent: clarity
Original:  The classifiers are provided with data samples from both an agent and modelsunder observation, and are rewarded for discriminating between them . Conversely, the models are rewarded for 'tricking' the classifiers into categorizing them as the agent . Unlike other methods for system identification, Turing Learning does not require predefined metrics to quantify the difference between the agent and models.
Revised:  The classifiers are provided with data samples from both an agent and modelsunder observation, and are rewarded for discriminating between them . Conversely, the models are rewarded for 'tricking' the classifiers into categorizing their data samples as genuine . Unlike other methods for system identification, Turing Learning does not require predefined metrics to quantify the difference between the agent and models.
Edit intent: clarity
Original:  The classifiers are provided with data samples from both an agent and modelsunder observation, and are rewarded for discriminating between them . Conversely, the models are rewarded for 'tricking' the classifiers into categorizing them as the agent . Unlike other methods for system identification, Turing Learning does not require predefined metrics to quantify the difference between the agent and models.
Revised:  The classifiers are provided with data samples from both an agent and modelsunder observation, and are rewarded for discriminating between them . Conversely, the models are rewarded for 'tricking' the classifiers into categorizing them as the agent . Unlike other methods for system identification, Turing Learning does not require predefined metrics to quantify the difference between the system and its models.
Edit intent: clarity
Original:  The results show that collective behaviors can be directly inferred from motion trajectories of a single agent in the swarm, which may have significant implications for the study of animal collectives  .
Revised:  The results show that collective behaviors can be directly inferred from motion trajectories of individuals in the swarm, which may have significant implications for the study of animal collectives .
Edit intent: clarity
Original:  For constant \delta_k \equiv \delta and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of \delta between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records S.-C. Park et al . ,{\it Phys.
Revised:  For constant \delta_k \equiv \delta and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of \delta between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records (Park et al . ,{\it Phys.
Edit intent: clarity
Original:  For constant \delta_k \equiv \delta and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of \delta between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records S.-C. Park et al . ,{\it Phys.
Revised:  For constant \delta_k \equiv \delta and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of \delta between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records S.-C. Park et al ,{\it Phys.
Edit intent: fluency
Original:  For constant \delta_k \equiv \delta and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of \delta between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records S.-C. Park et al . ,{\it Phys.
Revised:  For constant \delta_k \equiv \delta and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of \delta between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records S.-C. Park et al . 2015{\it Phys.
Edit intent: clarity
Original:  Rev. E 91 : 042707 (2015) .
Revised:  Rev. E 91 042707 (2015) .
Edit intent: coherence
Original:  Rev. E 91 : 042707 (2015) .
Revised:  Rev. E 91 : 042707 ) .
Edit intent: coherence
Original: Multi-agent differential games are important and useful tools for analyzing many practical problems , such as air traffic management and multi-vehicle collision avoidance .
Revised: Multi-agent differential games are important and useful tools for analyzing many practical problems .
Edit intent: clarity
Original: Recently, there has been an immense surge of interest in using unmanned aerial vehicles (UAVs) for civil purposes.
Edit intent: clarity
Original:  Multi-UAV systems are safety-critical, and safety guarantees must be made to ensure no undesirable configurations such as collisions occur.
Revised:  Multi-UAV systems are safety-critical, and guarantees must be made to ensure no undesirable configurations such as collisions occur.
Edit intent: coherence