wanyu/IteraTeR_v2 huggingface dataset:
Original:  We extracted the structure of  social interactions from the people mentioned in tweets from that area.
Revised:  We extracted the structure of online social interactions from the people mentioned in tweets from that area.
Edit intent: clarity
Original:  We find that at an aggregate level, areas where social media users engage in stronger, less diverse online social interactions are those where they express more negative emotions, like sadness and anger.
Revised:  We find that at an aggregate level, places where social media users engage in stronger, less diverse online social interactions are those where they express more negative emotions, like sadness and anger.
Edit intent: clarity
Original:  We find that at an aggregate level, areas where social media users engage in stronger, less diverse online social interactions are those where they express more negative emotions, like sadness and anger.
Revised:  We find that at an aggregate level, areas where social media users engage more deeply with less diverse social contacts are those where they express more negative emotions, like sadness and anger.
Edit intent: clarity
Original:  With respect to demographics, these areas have larger numbers of Hispanic residents , lower mean household income , and lower education levels.
Revised:  Demographics also has an impact: these places have residents with lower household income and education levels.
Edit intent: clarity
Original:  Conversely, areas with weaker, more diverse online interactions are associated with happier, more positive feelings and also have better educated, younger and higher-earning residents .
Revised:  Conversely, places where people engage less frequently but with diverse contacts have happier, more positive feelings and also have better educated, younger and higher-earning residents .
Edit intent: clarity
Original:  Conversely, areas with weaker, more diverse online interactions are associated with happier, more positive feelings and also have better educated, younger and higher-earning residents .
Revised:  Conversely, areas with weaker, more diverse online interactions are associated with happier, more positive messages posted from them and also have better educated, younger and higher-earning residents .
Edit intent: clarity
Original: In this paper, we propose a  data-driven approach to the problem of detrending fractal and multifractal time series.
Revised: In this paper, we propose a data-driven approach for removing trends (detrending) from nonstationary, fractal and multifractal time series.
Edit intent: clarity
Original:  We consider a time series as the measurements elaborated from a dynamical process over time.
Revised:  We consider real-valued time series relative to measurements of an underlying dynamical system that evolves through time.
Edit intent: clarity
Original:  We assume that such a dynamical process is predictable to a certain degree , by means of a class of recurrent networks called echo state networks.
Revised:  We assume that such a dynamical process is predictable to a certain degree by means of a class of recurrent networks called echo state networks.
Edit intent: fluency
Original:  Such a ( estimated) trend is then removed from the original time series and the residual signal is analyzed with the Multifractal Detrended Fluctuation Analysis for a quantitative verification of the correctness of the proposed detrending procedure.
Revised:  Such a ( estimated) trend is removed from the original time series and the residual signal is analyzed with the Multifractal Detrended Fluctuation Analysis for a quantitative verification of the correctness of the proposed detrending procedure.
Edit intent: coherence
Original:  Such a ( estimated) trend is then removed from the original time series and the residual signal is analyzed with the Multifractal Detrended Fluctuation Analysis for a quantitative verification of the correctness of the proposed detrending procedure.
Revised:  Such a ( estimated) trend is then removed from the original time series and the residual signal is analyzed with the multifractal detrended fluctuation analysis procedure to verify the correctness of the proposed detrending procedure.
Edit intent: clarity
Original:  Such a ( estimated) trend is then removed from the original time series and the residual signal is analyzed with the Multifractal Detrended Fluctuation Analysis for a quantitative verification of the correctness of the proposed detrending procedure.
Revised:  Such a ( estimated) trend is then removed from the original time series and the residual signal is analyzed with the Multifractal Detrended Fluctuation Analysis for a quantitative verification of the correctness of the detrending procedure.
Edit intent: clarity
Original:  We also process a real-world dataset, the sunspot time series, which is well-known for its multifractal features and it has recently gained attention in the complex systems field.
Revised:  We also process a real-world dataset, the sunspot time series, which is well-known for its multifractal features and has recently gained attention in the complex systems field.
Edit intent: fluency
Original:  Results demonstrate the validity and generality of the proposed detrending method based on echo state networks .
Revised:  Results demonstrate the validity and generality of the proposed detrending method based on ESNs .
Edit intent: clarity
Original: Interpreting others' actions in a correct way is fundamental for healthy and successful social relationships.
Edit intent: coherence
Original:  Previous theoretical research suggests that the mere act of considering one's strategic options in a social dilemma will be met with distrust .
Revised:  While previous theoretical research suggests that the mere act of considering one's strategic options in a social dilemma will be met with distrust .
Edit intent: clarity
Original: a small adaptive portion that exhibits divergent control flows and is handled by the CPU  and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Revised: a small adaptive portion that exhibits divergent control flows , and should therefore be handled by the CPU and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Edit intent: coherence
Original: a small adaptive portion that exhibits divergent control flows and is handled by the CPU  and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Revised: a small adaptive portion that exhibits divergent control flows and is handled by the CPU , and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Edit intent: fluency
Original: a small adaptive portion that exhibits divergent control flows and is handled by the CPU  and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Revised: a small adaptive portion that exhibits divergent control flows and is handled by the CPU and a vectorizable portion that can again be sent to GPGPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Edit intent: fluency
Original: a small adaptive portion that exhibits divergent control flows and is handled by the CPU  and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Revised: a small adaptive portion that exhibits divergent control flows and is handled by the CPU and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPGPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Edit intent: fluency
Original: a small adaptive portion that exhibits divergent control flows and is handled by the CPU  and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to speedup the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Revised: a small adaptive portion that exhibits divergent control flows and is handled by the CPU and a vectorizable portion that can again be sent to GPUs . We propose a hybrid algorithm that splits the computation into tasks for CPUs and GPUs . Our method presented in this article is able to reduce the setup time of boundary integral operators by a significant factor of 19-30 for both the Laplace and the Helmholtz equation in 3D when using two consumer GPGPUs compared to a quad-core CPU.
Edit intent: clarity
Original:  Forkable expressions may give rise to non-regular languages, in general, but we identify sufficient conditions on expressions that guarantee finite- ness of the automata construction via derivatives.
Revised:  Forkable expressions may give rise to non-regular languages, in general, but we identify sufficient conditions on expressions that guarantee finiteness of the automata construction via derivatives.
Edit intent: fluency
Original: Sparse linear systems are ubiquitous in various scientific computing applications.
Edit intent: coherence
Original:  Inversion of sparse matrices with standard direct solve schemes are prohibitive for large systems due to their quadratic/cubic complexity .
Revised:  Inversion of sparse matrices with standard direct solve schemes is robust, but computationally expensive .
Edit intent: clarity
Original: Cells  transmit information via signaling pathways , using temporal dynamical patterns .
Revised: Cells use temporal dynamical patterns to transmit information via signaling pathways , using temporal dynamical patterns .
Edit intent: fluency
Original: Cells  transmit information via signaling pathways , using temporal dynamical patterns .
Revised: Cells transmit information via signaling pathways .
Edit intent: clarity
Original:  As optimality with respect to environments is the universal principle in biological systems, organisms have acquired an optimal way of transmitting information.
Revised:  As optimality with respect to the environment is a universal principle in biological systems, organisms have acquired an optimal way of transmitting information.
Edit intent: fluency
Original:  As optimality with respect to environments is the universal principle in biological systems, organisms have acquired an optimal way of transmitting information.
Revised:  As optimality with respect to environments is the universal principle in biological systems, organisms have evolved optimal ways to transmit information.
Edit intent: clarity
Original:  Here we obtain optimal dynamical signal patterns which can transmit information efficiently (low power) and reliably (high accuracy) using the optimal control theory .
Revised:  Here , we use optimal control theory to obtain optimal dynamical signal patterns which can transmit information efficiently (low power) and reliably (high accuracy) using the optimal control theory .
Edit intent: coherence
Original:  Here we obtain optimal dynamical signal patterns which can transmit information efficiently (low power) and reliably (high accuracy) using the optimal control theory .
Revised:  Here we obtain optimal dynamical signal patterns that can transmit information efficiently (low power) and reliably (high accuracy) using the optimal control theory .
Edit intent: fluency
Original:  Here we obtain optimal dynamical signal patterns which can transmit information efficiently (low power) and reliably (high accuracy) using the optimal control theory .
Revised:  Here we obtain optimal dynamical signal patterns which can transmit information efficiently (low power) and reliably (high accuracy) .
Edit intent: clarity
Original:  Adopting an activation-inactivation decoding network, we reproduced several dynamical patterns found in actual signals, such as steep, gradual  and overshooting dynamics.
Revised:  Adopting an activation-inactivation decoding network, we reproduce several dynamical patterns found in actual signals, such as steep, gradual and overshooting dynamics.
Edit intent: fluency
Original:  Adopting an activation-inactivation decoding network, we reproduced several dynamical patterns found in actual signals, such as steep, gradual  and overshooting dynamics.
Revised:  Adopting an activation-inactivation decoding network, we reproduced several dynamical patterns found in actual signals, such as steep, gradual , and overshooting dynamics.
Edit intent: fluency
Original:  Notably, when minimizing the power of the input signal,  optimal signals exhibit the overshootingpattern , which is a biphasic pattern with transient and steady phases;
Revised:  Notably, when minimizing the power of the input signal, the optimal signals exhibit the overshootingpattern , which is a biphasic pattern with transient and steady phases;
Edit intent: fluency
Original:  Notably, when minimizing the power of the input signal,  optimal signals exhibit the overshootingpattern , which is a biphasic pattern with transient and steady phases;
Revised:  Notably, when minimizing the power of the input signal, optimal signals exhibit overshooting , which is a biphasic pattern with transient and steady phases;
Edit intent: fluency
Original:  this pattern is prevalent in actual dynamical patterns as it can be generated by an incoherent feed-forward loop (FFL), a common motif in biochemical networks .
Revised:  this pattern is prevalent in actual dynamical patterns .
Edit intent: clarity
Original:  We also identified conditions when the three patterns , steep, gradual and overshooting, confer advantages.
Revised:  We also identify conditions when these three patterns ( steep, gradual and overshooting, confer advantages.
Edit intent: fluency
Original:  We also identified conditions when the three patterns , steep, gradual and overshooting, confer advantages.
Revised:  We also identified conditions when the three patterns , steep, gradual , and overshooting) confer advantages.
Edit intent: fluency
Original:  As optimality with respect to the environment is a universal principle in biological systems, organisms have evolved optimal ways to transmit information.
Revised:  As optimality with respect to the environment plays a fundamental role in biological systems, organisms have evolved optimal ways to transmit information.
Edit intent: clarity
Original:  Here, we use optimal control theory to obtain  optimal dynamical signal patterns that can transmit information efficiently (low power ) and reliably (high accuracy).
Revised:  Here, we use optimal control theory to obtain the optimal dynamical signal patterns that can transmit information efficiently (low power ) and reliably (high accuracy).
Edit intent: fluency
Original:  Notably, when minimizing the power of the input signal, the optimal signals exhibit overshooting, which is a biphasic pattern with transient and steady phases;
Revised:  Notably, when minimizing the energy of the input signal, the optimal signals exhibit overshooting, which is a biphasic pattern with transient and steady phases;
Edit intent: clarity
Original:  Here, we use optimal control theory to obtain the optimal dynamical signal patterns that can transmit informationefficiently (low energy) and reliably (high accuracy ).
Revised:  Here, we use optimal control theory to obtain the dynamical signal patterns that can transmit informationefficiently (low energy) and reliably (high accuracy ).
Edit intent: fluency
Original:  Here, we use optimal control theory to obtain the optimal dynamical signal patterns that can transmit informationefficiently (low energy) and reliably (high accuracy ).
Revised:  Here, we use optimal control theory to obtain the optimal dynamical signal patterns for the optimal transmission of information, in terms of efficiency (low energy) and reliably (high accuracy ).
Edit intent: clarity
Original:  We also identify conditions when these three patterns (steep, gradual, and overshooting) confer advantages  .
Revised:  We also identify conditions in which these three patterns (steep, gradual, and overshooting) confer advantages .
Edit intent: clarity
Original: Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of  binomial coefficients and also all the sequences with algebraic generating function.
Revised: Multiple binomial sums form a large class of multi-indexed sequences, closed under partial summation, which contains most of the sequences obtained by multiple summation of products of binomial coefficients and also all the sequences with algebraic generating function.
Edit intent: clarity
Original:  Secondly  we propose algorithms that decide the equality of multiple binomial sums and that compute recurrence relations for them.
Revised:  Secondly , we propose algorithms that decide the equality of multiple binomial sums and that compute recurrence relations for them.
Edit intent: fluency
Original:  The process avoids the computation of certificates and the problem of accurate summation that afflicts discrete creative telescoping, both in theory and in practice.
Revised:  The process avoids the computation of certificates and the problem of the appearance of spurious singularities that afflicts discrete creative telescoping, both in theory and in practice.
Edit intent: clarity
Original:  These formulations are based on Hamilton's law of varying action.
Revised:  These methods are based on Hamilton's law of varying action.
Edit intent: clarity
Original:  From the action integral of the continuous system we derive a spatially and temporally weak form of the governing equilibrium equations.
Revised:  From the action of the continuous system we derive a spatially and temporally weak form of the governing equilibrium equations.
Edit intent: clarity
Original:  From the discrete virtual action we finally construct a class of different one-step schemes.
Revised:  From the discrete virtual action we finally construct a class of one-step schemes.
Edit intent: clarity
Original:  Here, we study both linear and nonlinear systems , considering either inherently continuous or discrete structures.
Revised:  Here, we study both linear and nonlinear systems as well as inherently continuous and discrete structures.
Edit intent: clarity
Original:  Thus, especially if high accuracy of the numerical solution is required, this scheme can be more efficient than existing methods .
Revised:  Thus, especially if high accuracy of the numerical solution is required, this scheme can be more efficient than methods of lower order .
Edit intent: clarity
Original:  It further exhibits similar properties as variational integrators: Conservation of linear momentum and, for simple linear systems, symplecticity.
Revised:  It further exhibits , for linear simple problems, properties similar to variational integrators, such as symplecticity.
Edit intent: clarity
Original:  While it remains to be investigated whether our method is symplectic for arbitrary systems, all our numerical results show an excellent long-term energy behavior.
Revised:  While it remains to be investigated whether symplecticity holds for arbitrary systems, all our numerical results show an excellent long-term energy behavior.
Edit intent: clarity
Original: We address the problem of enumeration of seating arrangements of married couples around a circular table such that no spouses seat next to each other and no k consecutive persons are of the same gender.
Revised: We address the problem of enumeration of seating arrangements of married couples around a circular table such that no spouses sit next to each other and no k consecutive persons are of the same gender.
Edit intent: fluency
Original:  While the case of k=2 corresponds to the classical probl\`eme des m\'enages with a well-studied solution, no closed-form expression for number of arrangements is known when k>=3.
Revised:  While the case of k=2 corresponds to the classical probl\`eme des m\'enages with a well-studied solution, no closed-form expression for the number of seating arrangements is known when k>=3.
Edit intent: clarity
Original:  We propose a novel approach to this type of problems based on enumeration of circuits in certain algebraically weighted de Bruijn graphs.
Revised:  We propose a novel approach for this type of problems based on enumeration of circuits in certain algebraically weighted de Bruijn graphs.
Edit intent: fluency
Original:  We propose a novel approach to this type of problems based on enumeration of circuits in certain algebraically weighted de Bruijn graphs.
Revised:  We propose a novel approach to this type of problems based on enumeration of walks in certain algebraically weighted de Bruijn graphs.
Edit intent: clarity
Original:  Our approach leads to a new expression for the menage numbers and their exponential generating function , and allows one to efficiently compute the number of seating arrangements in general cases .
Revised:  Our approach leads to new expressions for the menage numbers and their exponential generating function , and allows one to efficiently compute the number of seating arrangements in general cases .
Edit intent: fluency
Original:  Our approach leads to a new expression for the menage numbers and their exponential generating function , and allows one to efficiently compute the number of seating arrangements in general cases .
Revised:  Our approach leads to a new expression for the menage numbers and their exponential generating function and allows one to efficiently compute the number of seating arrangements in general cases .
Edit intent: fluency