wanyu/IteraTeR_v2 huggingface dataset:
Original:   OR circuits have OR gates as their computation gates, as well as the usual input, output and constant  gates.
Revised:  As their name suggests, OR circuits have OR gates as their computation gates, as well as the usual input, output and constant gates.
Edit intent: clarity
Original:  As usual, our Boolean circuits have multiple sink gates  which implies that an OR circuit computes an OR function on some subset of its input variables.
Revised:  As is the norm for Boolean circuits, our circuits have multiple sink gates which implies that an OR circuit computes an OR function on some subset of its input variables.
Edit intent: clarity
Original:  As usual, our Boolean circuits have multiple sink gates  which implies that an OR circuit computes an OR function on some subset of its input variables.
Revised:  As usual, our Boolean circuits have multiple sink gates , which implies that an OR circuit computes an OR function on some subset of its input variables.
Edit intent: fluency
Original:  Determining that subset amounts to solving a number of reachability questions on a polynomial-size directed graph (which input gates are connected to the output gate?)  taken from a very sparse set , for which it is not obvious whether or not they can be solved by say uniform AC0 circuits .
Revised:  Determining that subset amounts to solving a number of reachability questions on a polynomial-size directed graph (which input gates are connected to the output gate?) , taken from a very sparse set , for which it is not obvious whether or not they can be solved by say uniform AC0 circuits .
Edit intent: fluency
Original:  Determining that subset amounts to solving a number of reachability questions on a polynomial-size directed graph (which input gates are connected to the output gate?)  taken from a very sparse set , for which it is not obvious whether or not they can be solved by say uniform AC0 circuits .
Revised:  Determining that subset amounts to solving a number of reachability questions on a polynomial-size directed graph (which input gates are connected to the output gate?) taken from a very sparse set of graphs. However, it is not obvious whether or not they can be solved by say uniform AC0 circuits .
Edit intent: coherence
Original:  Determining that subset amounts to solving a number of reachability questions on a polynomial-size directed graph (which input gates are connected to the output gate?)  taken from a very sparse set , for which it is not obvious whether or not they can be solved by say uniform AC0 circuits .
Revised:  Determining that subset amounts to solving a number of reachability questions on a polynomial-size directed graph (which input gates are connected to the output gate?) taken from a very sparse set , for which it is not obvious whether or not this (restricted) reachability problem can be solved by say uniform AC0 circuits .
Edit intent: clarity
Original:  Our goal is the systematic characterization of uniform polynomial-size OR circuits  and AND circuits  in terms of known uniform machine-based complexity classes.
Revised:  Our goal is the systematic characterization of uniform polynomial-size OR circuits , and AND circuits in terms of known uniform machine-based complexity classes.
Edit intent: fluency
Original:  Our goal is the systematic characterization of uniform polynomial-size OR circuits  and AND circuits  in terms of known uniform machine-based complexity classes.
Revised:  Our goal is the systematic characterization of uniform polynomial-size OR circuits and AND circuits , in terms of known uniform machine-based complexity classes.
Edit intent: fluency
Original:  In particular, we consider the languages reducible to such uniform families of OR circuits  and AND circuits  under a variety of reduction types.
Revised:  In particular, we consider the languages reducible to such uniform families of OR circuits , and AND circuits under a variety of reduction types.
Edit intent: fluency
Original:  In particular, we consider the languages reducible to such uniform families of OR circuits  and AND circuits  under a variety of reduction types.
Revised:  In particular, we consider the languages reducible to such uniform families of OR circuits and AND circuits , under a variety of reduction types.
Edit intent: fluency
Original:  Specifically, for a variety of types of reductions (many-one, conjunctive and disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL . Some of these OR and AND classes are shown to coincide  and some are proven to be distinct.
Revised:  Specifically, for a variety of types of reductions (many-one, conjunctive truth table, disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL . Some of these OR and AND classes are shown to coincide and some are proven to be distinct.
Edit intent: coherence
Original:  Specifically, for a variety of types of reductions (many-one, conjunctive and disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL . Some of these OR and AND classes are shown to coincide  and some are proven to be distinct.
Revised:  Specifically, for a variety of types of reductions (many-one, conjunctive and disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL classes. Then, some of these OR and AND classes are shown to coincide and some are proven to be distinct.
Edit intent: coherence
Original:  Specifically, for a variety of types of reductions (many-one, conjunctive and disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL . Some of these OR and AND classes are shown to coincide  and some are proven to be distinct.
Revised:  Specifically, for a variety of types of reductions (many-one, conjunctive and disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL . Some of these OR classes are shown to coincide and some are proven to be distinct.
Edit intent: clarity
Original:  Specifically, for a variety of types of reductions (many-one, conjunctive and disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL . Some of these OR and AND classes are shown to coincide  and some are proven to be distinct.
Revised:  Specifically, for a variety of types of reductions (many-one, conjunctive and disjunctive truth table, truth table, Turing) we give characterizations of languages reducible to OR circuit classes in terms of languages reducible to tallyNL . Some of these OR and AND classes are shown to coincide , and some are proven to be distinct.
Edit intent: fluency
Original:   Finally, for many of our OR circuit classes ( and analogous AND circuit classes ) we prove whether or not the two classes coincide, although we leave one such inclusion open.
Revised:  Finally, for many of our OR circuit classes , and analogous AND circuit classes ) we prove whether or not the two classes coincide, although we leave one such inclusion open.
Edit intent: fluency
Original:   Finally, for many of our OR circuit classes ( and analogous AND circuit classes ) we prove whether or not the two classes coincide, although we leave one such inclusion open.
Revised:  Finally, for many of our OR circuit classes ( and analogous AND circuit classes , we prove whether or not the two classes coincide, although we leave one such inclusion open.
Edit intent: fluency
Original:  We show how to derive these diffeomorphic modes and observe, fortunately, that such modes typically span a very low-dimensional subspace  .
Revised:  We show how to derive these diffeomorphic modes and observe, fortunately, that such modes typically span a very low-dimensional subspace of parameter space .
Edit intent: clarity
Original:  A system of interest, when exposed to a stimulus S, adopts a deterministic response R of which a  noisy measurement M is made.
Revised:  When exposed to a stimulus S, adopts a deterministic response R of which a noisy measurement M is made.
Edit intent: clarity
Original:  Given a large number of measurements and corresponding stimuli , we wish to identify the correct " response function " relating R to S . However the "noise function" relating M to R is unknown a priori.
Revised:  Given a large number of signals and measurements , we wish to identify the correct " response function " relating R to S . However the "noise function" relating M to R is unknown a priori.
Edit intent: clarity
Original:  Given a large number of measurements and corresponding stimuli , we wish to identify the correct " response function " relating R to S . However the "noise function" relating M to R is unknown a priori.
Revised:  Given a large number of measurements and corresponding stimuli , we wish to infer the " response function " relating R to S . However the "noise function" relating M to R is unknown a priori.
Edit intent: clarity
Original:  Given a large number of measurements and corresponding stimuli , we wish to identify the correct " response function " relating R to S . However the "noise function" relating M to R is unknown a priori.
Revised:  Given a large number of measurements and corresponding stimuli , we wish to identify the correct " filter " relating R to S . However the "noise function" relating M to R is unknown a priori.
Edit intent: clarity
Original:  Moreover, if the correct response function is in the class of models being explored, maximizing mutual information becomes equivalent to simultaneously maximizing every dependence measure that satisfies the Data Processing Inequality.
Revised:  Moreover, if the correct filter lies within the space of filters being explored, maximizing mutual information becomes equivalent to simultaneously maximizing every dependence measure that satisfies the Data Processing Inequality.
Edit intent: clarity
Original:  By restricting m=O( log n), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m= sqrt k] n for a fixed k.
Revised:  By restricting m=O( log n), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m= sqrt k] n for a fixed k.
Edit intent: fluency
Original:  Finally, if the number of negative entries in Q is fixed, BQP01 is shown to be polynomially solvable whereas it is NP-hard if this number is O( sqrt k] n ) for a fixed k.
Revised:  Finally, if the number of negative entries in Q is fixed, BQP01 is shown to be polynomially solvable whereas it is NP-hard if this number is O( \sqrt[ k] n ) for a fixed k.
Edit intent: coherence
Original:  Finally, if the number of negative entries in Q is fixed, BQP01 is shown to be polynomially solvable whereas it is NP-hard if this number is O( sqrt k] n ) for a fixed k.
Revised:  Finally, if the number of negative entries in Q is fixed, BQP01 is shown to be polynomially solvable whereas it is NP-hard if this number is O( sqrt k] n ) for a fixed k.
Edit intent: fluency
Original:  The complexity of this algorithm is quasi-polynomial if rank of Q is O(\log^k n) for a fixed k.
Edit intent: coherence
Original:  By restricting m=O(\log n), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m=  \sqrt[k]{n}  for a fixed k.
Revised:  By restricting m=O(\log n), we obtain yet another polynomially solvable case of BQP01 but the problem remains MAX SNP hard if m= \sqrt[k]{n} ) for a fixed k.
Edit intent: fluency
Original:  Finally, if the number of negative entries in Q is fixed, BQP01 is shown to be polynomially solvable whereas it is NP-hard if this number is O(\sqrt[k]{n}) for a fixed k.
Revised:  Finally, if the number of negative entries in Q is fixed, BQP01 polynomially solvable but it is NP-hard if this number is O(\sqrt[k]{n}) for a fixed k.
Edit intent: coherence
Original:  This can be posed as a vertex graph coloring problem, and the configurations attainable under these constraints through coordinated algorithms (e.g. aiming at using the least amount of colors) are well characterized  .
Revised:  This can be posed as a vertex graph coloring problem, and the configurations attainable under these constraints through coordinated algorithms (e.g. aiming at using the least amount of colors) are well characterizedglobal .
Edit intent: fluency
Original:  This can be posed as a vertex graph coloring problem, and the configurations attainable under these constraints through coordinated algorithms (e.g. aiming at using the least amount of colors) are well characterized  .
Revised:  This can be posed as a vertex graph coloring problem, and the configurations attainable under these constraints through coordinated algorithms (e.g. aiming at using the least amount of colors) are well characterized metric .
Edit intent: fluency
Original:  This solves an open problem and explains the failure of previous proposed methods using potential functions.
Revised:  This solves an open problem, and explains the failure of previous proposed methods using potential functions.
Edit intent: fluency
Original:  Our results extend to variants where nodes join multiple groups , have asymmetrical weights, and utility goes beyond pairwise relationship  . Finally, we show these games create a tension between stability and efficiency, as collusions and using multiple colors both have a beneficial effect on the price of anarchy \emph{  .
Revised:  Our results extend to variants where nodes join multiple groups , have asymmetrical weights, and utility goes beyond pairwise relationship . Finally, we prove that collusions have a significant and effect on the price of anarchy \emph{ .
Edit intent: clarity
Original:  Our results extend to variants where nodes join multiple groups , have asymmetrical weights, and utility goes beyond pairwise relationship  . Finally, we show these games create a tension between stability and efficiency, as collusions and using multiple colors both have a beneficial effect on the price of anarchy \emph{  .
Revised:  Our results extend to variants where nodes join multiple groups , have asymmetrical weights, and utility goes beyond pairwise relationship . Finally, we show these games create a tension between stability and efficiency, as collusions and using multiple colors both have a beneficial effect on the \emph{ .
Edit intent: clarity
Original:  Our results extend to variants where nodes join multiple groups , have asymmetrical weights, and utility goes beyond pairwise relationship  . Finally, we show these games create a tension between stability and efficiency, as collusions and using multiple colors both have a beneficial effect on the price of anarchy \emph{  .
Revised:  Our results extend to variants where nodes join multiple groups , have asymmetrical weights, and utility goes beyond pairwise relationship . Finally, we show these games create a tension between stability and efficiency, as collusions and using multiple colors both have a beneficial effect on the price of anarchy \emph{efficiency .
Edit intent: fluency
Original:  Analytic and numeric results are presented to inspect general conditions for synchronization and in particular,  the possibility of inphase synchronization and near inphase synchronization is studied when a source of inhomogeneity (in the neurons or in the couplings parameters) is present.
Revised:  Analytic and numeric results are presented to inspect general conditions for synchronization and in particular, we have studied the possibility of inphase synchronization and near inphase synchronization is studied when a source of inhomogeneity (in the neurons or in the couplings parameters) is present.
Edit intent: clarity
Original: In principle coupled oscillators can overcome mismatch in intrinsic firing rates and match their frequencies, but with a nonzero phase lag . Delay in communication, on the other hand, can exert phase shifts in the concerted activity of the coupled oscillators.
Revised: In principle coupled oscillators can overcome mismatch in intrinsic rates and match their frequencies, but with a nonzero phase lag . Delay in communication, on the other hand, can exert phase shifts in the concerted activity of the coupled oscillators.
Edit intent: clarity
Original: In principle coupled oscillators can overcome mismatch in intrinsic firing rates and match their frequencies, but with a nonzero phase lag . Delay in communication, on the other hand, can exert phase shifts in the concerted activity of the coupled oscillators.
Revised: In principle coupled oscillators can overcome mismatch in intrinsic firing rates and match their frequencies, but with a nonzero phase lag . Delay in communication, on the other hand, can exert phase shift in the activity of the coupled oscillators.
Edit intent: clarity
Original:  We show that while any single source of inhomogeneity violates exact isochronous synchrony, it is possible to maintain synchrony if multiple sources of inhomogeneity are present in the system .
Revised:  We have shown that while any single source of inhomogeneity violates exact isochronous synchrony, it is possible to maintain synchrony if multiple sources of inhomogeneity are present in the system .
Edit intent: style
Original:  We show that while any single source of inhomogeneity violates exact isochronous synchrony, it is possible to maintain synchrony if multiple sources of inhomogeneity are present in the system .
Revised:  We show that while any single source of inhomogeneity can violate isochronous synchrony, it is possible to maintain synchrony if multiple sources of inhomogeneity are present in the system .
Edit intent: clarity
Original:  We show that while any single source of inhomogeneity violates exact isochronous synchrony, it is possible to maintain synchrony if multiple sources of inhomogeneity are present in the system .
Revised:  We show that while any single source of inhomogeneity violates exact isochronous synchrony, multiple sources of inhomogeneity are present in the system .
Edit intent: clarity
Original:  An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the instrinsic structure of the neural code.
Revised:  An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code.
Edit intent: fluency
Original:  Our main finding is that these objects can be expressed in a "canonical form" that directly translates to a minimal description of the receptive field structure intrinsic to the neural code.
Revised:  Our main finding is that these objects can be expressed in a "canonical form" that directly translates to a minimal description of the receptive field structure intrinsic to the code.
Edit intent: clarity
Original:  QBOP is strongly NP-hard even if the family of feasible solutions have a very simple structure.
Revised:  QBOP is strongly NP-hard even if the family of feasible solutions has a very simple structure.
Edit intent: fluency
Original:  We address this question by providing a widely-applicable link between network characteristics on two scales.
Revised:  We address this question by linking network characteristics on two scales.
Edit intent: clarity
Original:  On the global scale we consider the coherence of overall network activity .
Revised:  On the global scale we consider the coherence of overall network dynamics .
Edit intent: clarity
Original:  We show that such global coherence  can often be predicted from the local structure of the network.
Revised:  We show that such global coherence in activity can often be predicted from the local structure of the network.
Edit intent: clarity
Original:  To characterize this local structure we introduce motif cumulants, which measure the deviation of pathway counts from those expected in a minimal probabilistic network model.
Revised:  To characterize local network structure we use " motif cumulants, which measure the deviation of pathway counts from those expected in a minimal probabilistic network model.
Edit intent: clarity
Original:  To characterize this local structure we introduce motif cumulants, which measure the deviation of pathway counts from those expected in a minimal probabilistic network model.
Revised:  To characterize this local structure we introduce motif cumulants, " a measure of the deviation of pathway counts from those expected in a minimal probabilistic network model.
Edit intent: coherence
Original:  Importantly, this link between global  dynamics and local  architecture is strongly affected by heterogeneity in the network connectivity.
Revised:  Importantly, this link between global network dynamics and local architecture is strongly affected by heterogeneity in the network connectivity.
Edit intent: fluency
Original:  Importantly, this link between global  dynamics and local  architecture is strongly affected by heterogeneity in the network connectivity.
Revised:  Importantly, this link between global dynamics and local network architecture is strongly affected by heterogeneity in the network connectivity.
Edit intent: fluency
Original:  Importantly, this link between global  dynamics and local  architecture is strongly affected by heterogeneity in the network connectivity.
Revised:  Importantly, this link between global dynamics and local architecture is strongly affected by heterogeneity in network connectivity.
Edit intent: fluency
Original:  We show that such global coherence \emph{ in activity can often be predicted from the local structure of the network.
Revised:  We show that such \emph{ in activity can often be predicted from the local structure of the network.
Edit intent: clarity
Original:  We show that such global coherence \emph{ in activity can often be predicted from the local structure of the network.
Revised:  We show that such global coherence \emph{global coherence in activity can often be predicted from the local structure of the network.
Edit intent: clarity
Original:  We show that such global coherence \emph{ in activity can often be predicted from the local structure of the network.
Revised:  We show that such global coherence \emph{ in activity can often be predicted from the local structure of the network.
Edit intent: fluency
Original:  Our contributions are threefold: First, we give a new combinatorial formulation of motif cumulants that connects with the allied concept in probability theory.
Revised:  Our contributions are threefold: First, we give a new combinatorial formulation of motif cumulants that relates to the allied concept in probability theory.
Edit intent: clarity
Original:  Third, for a particular set of models we generalize the underlying theory to treat dynamical coherence at arbitrary orders (i.e. triplet correlations, and beyond) , and show that at any order only a highly restricted set of motifs impact dynamical correlations.
Revised:  Third, for a particular set of models we generalize the underlying theory to treat dynamical coherence at arbitrary orders (i.e. triplet correlations, and beyond) . We show that at any order only a highly restricted set of motifs impact dynamical correlations.
Edit intent: coherence
Original: We employ a simple modification to the conventional time of flight mass spectrometry (TOFMS) where a variable and (pseudo) random pulsing rate is used which allows for traces from different pulses to overlap.
Revised: We study a simple modification to the conventional time of flight mass spectrometry (TOFMS) where a variable and (pseudo) random pulsing rate is used which allows for traces from different pulses to overlap.
Edit intent: clarity