wanyu/IteraTeR_v2 huggingface dataset:
Original:  The results  indicate that the optimal performance depends on the way of balancing the input strength with the recurrent activity, which also has an influence on the network with regard to the quality of  the short term prediction versus prediction that accounts for influences that date back a long time in the input history.
Revised:  The results indicate that the optimal performance depends on the way of balancing the input strength with the recurrent activity, which also has an influence on the network with regard to the quality of inference from the short term prediction versus prediction that accounts for influences that date back a long time in the input history.
Edit intent: clarity
Original:  The results  indicate that the optimal performance depends on the way of balancing the input strength with the recurrent activity, which also has an influence on the network with regard to the quality of  the short term prediction versus prediction that accounts for influences that date back a long time in the input history.
Revised:  The results indicate that the optimal performance depends on the way of balancing the input strength with the recurrent activity, which also has an influence on the network with regard to the quality of the short term input history versus inference that accounts for influences that date back a long time in the input history.
Edit intent: clarity
Original:  Finally, sensitivity of such networks against noise / finite accuracy of network states in the recurrent layer is investigated.
Revised:  Finally, sensitivity of such networks against noise and the finite accuracy of network states in the recurrent layer is investigated.
Edit intent: fluency
Original:  Finally, sensitivity of such networks against noise / finite accuracy of network states in the recurrent layer is investigated.
Revised:  Finally, sensitivity of such networks against noise / finite accuracy of network states in the recurrent layer are investigated.
Edit intent: fluency
Original:  In addition a measure that bases on mutual information is introduced in order to best quantify the performance of the network with the time series .
Revised:  In addition , a measure based on mutual information is introduced in order to best quantify the performance of the network with the time series .
Edit intent: fluency
Original: The digital exhaust left by flows of physical and digital commodities provides a rich measure of the nature, strength and significance of relationships between The digital exhaust left by flows of physical and digital commodities provides a rich measure of the nature, strength and significance of relationships between countries in the global network.
Revised: The digital exhaust left by flows of physical and digital commodities provides a rich measure of the nature, strength and significance of relationships between countries in the global network.
Edit intent: fluency
Original: The two-parameter Poisson-Dirichlet diffusion, recently introduced by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman's one-parameter Poisson-Dirichlet distribution and to certain Fleming-Viot processes.
Revised: The two-parameter Poisson-Dirichlet diffusion, recently introduced by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman's one-parameter Poisson--Dirichlet distribution and to certain Fleming-Viot processes.
Edit intent: fluency
Original: The two-parameter Poisson-Dirichlet diffusion, recently introduced by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman's one-parameter Poisson-Dirichlet distribution and to certain Fleming-Viot processes.
Revised: The two-parameter Poisson-Dirichlet diffusion, recently introduced by Petrov, extends the infinitely-many-neutral-alleles diffusion model, related to Kingman's one-parameter Poisson-Dirichlet distribution and to certain Fleming--Viot processes.
Edit intent: fluency
Original:  Here we shed some light on these dynamics by formulating a K-allele Wright-Fisher model for a population of size N, involving a uniform parent-independent mutation pattern and a specific state-dependent immigration kernel . Suitably scaled, this process converges in distribution to a K-dimensional diffusion process as N\to\infty.
Revised:  Here we shed some light on these dynamics by formulating a K-allele Wright--Fisher model for a population of size N, involving a uniform parent-independent mutation pattern and a specific state-dependent immigration kernel . Suitably scaled, this process converges in distribution to a K-dimensional diffusion process as N\to\infty.
Edit intent: fluency
Original:  Here we shed some light on these dynamics by formulating a K-allele Wright-Fisher model for a population of size N, involving a uniform parent-independent mutation pattern and a specific state-dependent immigration kernel . Suitably scaled, this process converges in distribution to a K-dimensional diffusion process as N\to\infty.
Revised:  Here we shed some light on these dynamics by formulating a K-allele Wright-Fisher model for a population of size N, involving a uniform mutation pattern and a specific state-dependent immigration kernel . Suitably scaled, this process converges in distribution to a K-dimensional diffusion process as N\to\infty.
Edit intent: clarity
Original:  Here we shed some light on these dynamics by formulating a K-allele Wright-Fisher model for a population of size N, involving a uniform parent-independent mutation pattern and a specific state-dependent immigration kernel . Suitably scaled, this process converges in distribution to a K-dimensional diffusion process as N\to\infty.
Revised:  Here we shed some light on these dynamics by formulating a K-allele Wright-Fisher model for a population of size N, involving a uniform parent-independent mutation pattern and a specific state-dependent migration mechanism . Suitably scaled, this process converges in distribution to a K-dimensional diffusion process as N\to\infty.
Edit intent: clarity
Original:  Moreover, the descending order statistics of the K-dimensional diffusion converge in distribution to the two-parameter Poisson-Dirichlet diffusion as K\to\infty.
Revised:  Moreover, the descending order statistics of the K-dimensional diffusion converge in distribution to the two-parameter Poisson--Dirichlet diffusion as K\to\infty.
Edit intent: fluency
Original:  The choice of the immigration kernel depends on a delicate balance between reinforcement and redistributive effects.
Revised:  The choice of the migration mechanism depends on a delicate balance between reinforcement and redistributive effects.
Edit intent: clarity
Original:  Our strategy for overcoming this complication is to prove a priori that in the limit there is no "loss of mass", i.e., that, for each limit point of the  finite-dimensional diffusions (after a reordering of components by size), allele frequencies sum to one.
Revised:  Our strategy for overcoming this complication is to prove a priori that in the limit there is no "loss of mass", i.e., that, for each limit point of the sequence of finite-dimensional diffusions (after a reordering of components by size), allele frequencies sum to one.
Edit intent: clarity
Original:  Using data about physics publications and US patents, we show that our method allows to reveal , using a quantitative approach, that being more interdisciplinary causes -- in the Granger sense -- benefits in scientific productivity and impact .
Revised:  Using data about physics publications and US patents, we show that our method allows to reward , using a quantitative approach, that being more interdisciplinary causes -- in the Granger sense -- benefits in scientific productivity and impact .
Edit intent: clarity
Original:  Using data about physics publications and US patents, we show that our method allows to reveal , using a quantitative approach, that being more interdisciplinary causes -- in the Granger sense -- benefits in scientific productivity and impact .
Revised:  Using data about physics publications and US patents, we show that our method allows to reveal , using a quantitative approach, scholars and institutions that have carried out interdisciplinary work and have had an impact in different scientific areas .
Edit intent: clarity
Original:  Furthermore, for these channels, we have the Blahut-Arimoto algorithm that allows to efficiently solve the optimization problem and compute the capacity.
Revised:  Furthermore, for these channels, we have the Blahut-Arimoto algorithm that efficiently solves the optimization problem and compute the capacity.
Edit intent: coherence
Original:  Furthermore, for these channels, we have the Blahut-Arimoto algorithm that allows to efficiently solve the optimization problem and compute the capacity.
Revised:  Furthermore, for these channels, we have the Blahut-Arimoto algorithm that allows to efficiently solve the optimization problem and computes the capacity.
Edit intent: fluency
Original:  Observations are made relating HTM to well known algorithms such as competitive learning and attribute bagging.
Revised:  Observations are made relating HTM to well-known algorithms such as competitive learning and attribute bagging.
Edit intent: fluency
Original:  Uniform substitutions make it possible to rely on concrete axioms rather than axiom schemata,  substantially simplifying implementations.
Revised:  Uniform substitutions make it possible to use axioms instead of axiom schemata, substantially simplifying implementations.
Edit intent: clarity
Original:  Uniform substitutions make it possible to rely on concrete axioms rather than axiom schemata,  substantially simplifying implementations.
Revised:  Uniform substitutions make it possible to rely on concrete axioms rather than axiom schemata, thereby substantially simplifying implementations.
Edit intent: coherence
Original:  Instead of subtle schema variables and soundness-critical side conditions on the occurrence patterns of logical variables to restrict their infinitely many schema instances to sound ones, the resulting calculus adopts only a finite number of ordinary dL formulas as axioms, which uniform substitutions instantiate soundly.
Revised:  Instead of subtle schema variables and soundness-critical side conditions on the occurrence patterns of logical variables to restrict infinitely many axiom schema instances to sound ones, the resulting calculus adopts only a finite number of ordinary dL formulas as axioms, which uniform substitutions instantiate soundly.
Edit intent: clarity
Original:  In addition to sound uniform substitutions, this article introduces differential forms for differential dynamic logic that make it possible to internalize differential invariants, differential substitutions, and derivations as first-class axioms to reason about differential equations .
Revised:  In addition to sound uniform substitutions, this article introduces differential forms for differential dynamic logic that make it possible to internalize differential invariants, differential substitutions, and derivatives as first-class axioms to reason about differential equations .
Edit intent: clarity
Original: We investigate centrality properties and the existence of a finite confidence set for the root node in growing random tree models .
Revised: We investigate centrality and root-inference properties in a class of growing random graphs known as sublinear preferential attachment trees .
Edit intent: clarity
Original:  Furthermore, we show that the same centrality criterion produces a  finite-sized 1 - \epsilon confidence set for the root node, for any \epsilon > 0.
Revised:  Furthermore, we show that the same centrality criterion produces a finite-sized 1- \epsilon confidence set for the root node, for any \epsilon > 0.
Edit intent: fluency
Original: Let A be a non-empty alphabet and the symbol \diamond%DIFDELCMD < \not%%% \in A . A partial word (or pword){\em   of length n is{\em  \notin  u= u_1\cdots u_n where u_i\in A \cup\{\diamond\}.
Revised: %DIFDELCMD < \not%%% \in A . A partial word (or pword){\em of length n is{\em \notin u= u_1\cdots u_n where u_i\in A \cup\{\diamond\}.
Edit intent: coherence
Original: Let A be a non-empty alphabet and the symbol \diamond%DIFDELCMD < \not%%% \in A . A partial word (or pword){\em   of length n is{\em  \notin  u= u_1\cdots u_n where u_i\in A \cup\{\diamond\}.
Revised: Let A be a non-empty alphabet and the symbol \diamond%DIFDELCMD < \not%%% A{\em of length n is{\em \notin u= u_1\cdots u_n where u_i\in A \cup\{\diamond\}.
Edit intent: clarity
Original: Let A be a non-empty alphabet and the symbol \diamond%DIFDELCMD < \not%%% \in A . A partial word (or pword){\em   of length n is{\em  \notin  u= u_1\cdots u_n where u_i\in A \cup\{\diamond\}.
Revised: Let A be a non-empty alphabet and the symbol \diamond%DIFDELCMD < \not%%% \in A . A partial word (or pword){\em universal word of length n is{\em \notin u= u_1\cdots u_n where u_i\in A \cup\{\diamond\}.
Edit intent: fluency
Original: Let A be a non-empty alphabet and the symbol \diamond%DIFDELCMD < \not%%% \in A . A partial word (or pword){\em   of length n is{\em  \notin  u= u_1\cdots u_n where u_i\in A \cup\{\diamond\}.
Revised: Let A be a non-empty alphabet and the symbol \diamond%DIFDELCMD < \not%%% \in A . A partial word (or pword){\em of length n is{\em partial \notin u= u_1\cdots u_n where u_i\in A \cup\{\diamond\}.
Edit intent: fluency
Original:  A word u=u_1\cdots u_n\in A^n occurs in a word v=v_1\cdots v_m\in A_\diamond^m as a factor for m\geq n, if there exists i such that u_j=v_{i+j for  1 \leq j\leq n whenever v_{i+j\in A. A universal word for A^n is a word w such that all factors of w of length nare distinct and the set of these factors coincides with A^n.
Revised:  A word u=u_1\cdots u_n\in A^n occurs in a word v=v_1\cdots v_m\in A_\diamond^m as a factor for m\geq n, if there exists i such that u_j=v_{i+j for 1 \in A. A universal word for A^n is a word w such that all factors of w of length nare distinct and the set of these factors coincides with A^n.
Edit intent: clarity
Original: A %DIFDELCMD < {\em %%% universal word for a finite alphabet A and some integer n\geq 1 is a word over A such that every word of length n appears exactly once as a (consecutive)subword .
Revised: A %DIFDELCMD < {\em %%% universal word for a finite alphabet A and some integer n\geq 1 is a word over A such that every word of length n appears exactly once as a (consecutive)subword .
Edit intent: fluency
Original: A %DIFDELCMD < {\em %%% universal word for a finite alphabet A and some integer n\geq 1 is a word over A such that every word of length n appears exactly once as a (consecutive)subword .
Revised: A %DIFDELCMD < {\em %%% universal word for a finite alphabet A and some integer n\geq 1 is a word over A such that every word in A^n appears exactly once as a (consecutive)subword .
Edit intent: clarity
Original:  In this work we initiate the systematic study of universal %DIFDELCMD < {\em %%% partial words.
Revised:  In this work we initiate the systematic study of universal %DIFDELCMD < {\em %%% partial words.
Edit intent: fluency
Original:  We present several result on the existence and non-existence of  universal partial words in different situations (depending on the number of \Diamonds and their positions), including various explicit constructions.
Revised:  We present results on the existence and non-existence of universal partial words in different situations (depending on the number of \Diamonds and their positions), including various explicit constructions.
Edit intent: clarity
Original:  We present examples of logically consistent non-causal circuits outperforming all causal ones;
Revised:  We present examples of logically consistent non- causal circuits outperforming all causal ones;
Edit intent: fluency
Original:  We propose the problem of robust influence maximization, which maximizes the worse-case ratio between the influence spread of the chosen seed set and the optimal seed set, given the uncertainty of the parameter input.
Revised:  We propose the problem of robust influence maximization, which maximizes the worst-case ratio between the influence spread of the chosen seed set and the optimal seed set, given the uncertainty of the parameter input.
Edit intent: fluency
Original:  For the case of two symmetric clusters, we show that the spectral approaches are asymptotically optimal in that they detect the clusters as soon as it is information theoretically possible to do so.
Revised:  For the case of two symmetric clusters, we conjecture that these algorithms are asymptotically optimal in that they detect the clusters as soon as it is information theoretically possible to do so.
Edit intent: clarity
Original: Based on the transport model of Sorensen et al. (1999), an improved mathematical model describing the process of thrombus deposition and growth was developed . Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus  phase.
Revised: In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus . Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus phase.
Edit intent: clarity
Original:  The transport and reactions of 10 chemical and biological species are modeled using a system of coupled convection-reaction-diffusion (CRD) equations .
Revised:  The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations .
Edit intent: clarity
Original:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and  thrombus deposition in a small (  125 x 95 micros)crevice observed in vitro { { {  . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Revised:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and thrombus deposition in a small ( 125 x 95 micros)crevice observed in vitro { { { . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Edit intent: clarity
Original:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and  thrombus deposition in a small (  125 x 95 micros)crevice observed in vitro { { {  . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Revised:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and in vitro thrombus deposition in a small ( 125 x 95 micros)crevice observed in vitro { { { . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Edit intent: fluency
Original:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and  thrombus deposition in a small (  125 x 95 micros)crevice observed in vitro { { {  . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Revised:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and thrombus deposition in micro-channels ( 125 x 95 micros)crevice observed in vitro { { { . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Edit intent: clarity
Original:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and  thrombus deposition in a small (  125 x 95 micros)crevice observed in vitro { { {  . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Revised:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and thrombus deposition in a small ( 125 x 95 micros)crevice observed in vitro {\mu { { . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Edit intent: fluency
Original:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and  thrombus deposition in a small (  125 x 95 micros)crevice observed in vitro { { {  . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Revised:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and thrombus deposition in a small ( 125 x 95 micros)crevice observed in vitro { {\mu { . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Edit intent: fluency
Original:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and  thrombus deposition in a small (  125 x 95 micros)crevice observed in vitro { { {  . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Revised:  Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: mural thrombus growth in an injured blood vessel and thrombus deposition in a small ( 125 x 95 micros)crevice observed in vitro { { {\mu . For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally.
Edit intent: fluency
Original:  These promising results encourage further simulations to investigate clinical conditions and design factors that affect the risk of thrombosis in blood-wetted  devices.
Revised:  Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices.
Edit intent: clarity
Original:  Gerber's lemma twice in different directions to a Markov chain to show gains in privacy-leakage  as compared to assuming a noise-free  identifier at the encoder  .
Revised:  Gerber's lemma twice in different directions to a Markov chain to show gains in privacy-leakage as compared to a noise-free identifier at the encoder .
Edit intent: clarity
Original: Information-related measures are important tools of multi-variable data analysis, as measures of dependence among variables and the description of order in biological and physical systems.
Revised: Information related measures are useful tools for multi variable data analysis, as measures of dependence among variables and the description of order in biological and physical systems.
Edit intent: clarity