wanyu/IteraTeR_v2 huggingface dataset:
Original:  Here, we settle the multiparameterized complexity of under pairs of parameters as \max\{ k,\Delta \ where \Delta=\max_i\{|S_i|\} and \max\{k,f \ =\max_i|\{j | x_i \in S_j\}|.
Revised:  Here, we settle the multiparameterized complexity of under pairs of parameters as ( k,\Delta \ where \Delta=\max_i\{|S_i|\} and \max\{k,f \ =\max_i|\{j | x_i \in S_j\}|.
Edit intent: fluency
Original:  Then, we investigate some similar parameterizations of a satisfiability problem that is linked to in a sense explained in the paper  . Finally, we sketch an enhancement of the classes of the W[\cdot] hierarchy that seems more appropriate for showing completeness of cardinality constrained W[\cdot]-hard problems.
Revised:  Then, we investigate some similar parameterizations of a satisfiability problem in a sense explained in the paper . Finally, we sketch an enhancement of the classes of the W[\cdot] hierarchy that seems more appropriate for showing completeness of cardinality constrained W[\cdot]-hard problems.
Edit intent: clarity
Original:  Recent studies have also found evidence in support of the hourglass effect at the genomic level.
Revised:  Recent studies have found evidence in support of the hourglass effect at the genomic level.
Edit intent: clarity
Original:  Here, we propose an abstract model of regulatory gene interactions during development , and of their evolution .
Revised:  Here, we use an evolutionary model of regulatory gene interactions during development , and of their evolution .
Edit intent: clarity
Original:  It also captures the evolution of a population under random perturbations in the structure of this regulatory network.
Revised:  It also captures the evolution of a population under random perturbations in the structure of that network.
Edit intent: clarity
Original:  Additionally, the evolutionary age of those genes also follows an hourglass pattern, with the oldest genes concentrated at the hourglass waist.
Revised:  Additionally, the evolutionary age of the corresponding genes also follows an hourglass pattern, with the oldest genes concentrated at the hourglass waist.
Edit intent: clarity
Original:  The key condition behind the hourglass effect is that developmental regulators should have an increasingly specific function as development progresses.
Revised:  The key behind the hourglass effect is that developmental regulators should have an increasingly specific function as development progresses.
Edit intent: clarity
Original:  We have confirmed the theoretical predictions of the model with gene expression profiles from Drosophila melanogaster and Arabidopsis thaliana  .
Revised:  Analysis of developmental gene expression profiles from Drosophila melanogaster and Arabidopsis thaliana .
Edit intent: clarity
Original: We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) degree n defined on any compact interval [0,\alpha], where \alpha \ varies in (0,\pi).
Revised: We construct a constrained trivariate extension of the univariate normalized B-basis of the vector space of trigonometric polynomials of arbitrary (finite) order n defined on any compact interval [0,\alpha], where \alpha \ varies in (0,\pi).
Edit intent: clarity
Original:  Our triangular extension is a normalized linearly independent constrained trivariate trigonometric function system of dimension 3n(n+1)+1 that spans the same vector space of functions as the constrained trivariate extension of the canonical basis of truncated Fourier series of degree n over [0,\alpha].
Revised:  Our triangular extension is a normalized linearly independent constrained trivariate trigonometric function system of dimension 3n(n+1)+1 that spans the same vector space of functions as the constrained trivariate extension of the canonical basis of truncated Fourier series of order n over [0,\alpha].
Edit intent: clarity
Original:  As a possible application of our triangular extension, we introduce the notion of (rational) triangular trigonometric patches of degree n and of singularity free parametrization that could be used as control point based modeling tools in CAGD.
Revised:  As a possible application of our triangular extension, we introduce the notion of (rational) triangular trigonometric patches of order n and of singularity free parametrization that could be used as control point based modeling tools in CAGD.
Edit intent: clarity
Original: The minimum amount of resources to recognize a non-regular language is a fundamental research topic in theoretical computer science which has been examined for different kinds of resources and many different models.
Revised: The minimum amount of resources to recognize a nonregular language is a fundamental research topic in theoretical computer science which has been examined for different kinds of resources and many different models.
Edit intent: fluency
Original:  Up to our knowledge, it is still open whether a 2DCA using sublinear space or a bounded-error 2QCFA can recognize a non-regular unary language .
Revised:  It is known that any 2DCA using sublinear space or a bounded-error 2QCFA can recognize a non-regular unary language .
Edit intent: clarity
Original:  In this note, on the other hand, we show that bounded-error 2QCCAs can recognize a non-regular unary language by using logarithmic space on its counters for the members  .
Revised:  In this note, we show that bounded-error 2QCCAs can recognize a non-regular unary language by using logarithmic space on its counters for the members .
Edit intent: coherence
Original:  In this paper we derive a formula for evaluating the function \rho^{ab}(n) explicitly.
Revised:  In this paper we derive an automaton that evaluates the function \rho^{ab}(n) explicitly.
Edit intent: clarity
Original:  The formula uses the representation n=\sum_{j=0^{k} \delta_j T_j, where (T_j)_{j=0}^\infty=}  ( 1,2,4,7,13,\ldots) are Tribonacci numbers and \delta_j\in\{0,1\} for every j=0,1,\ldots,k.
Revised:  The ^{k} \delta_j T_j, where (T_j)_{j=0}^\infty=} ( 1,2,4,7,13,\ldots) are Tribonacci numbers and \delta_j\in\{0,1\} for every j=0,1,\ldots,k.
Edit intent: clarity
Original:  We demonstrate that \rho^{ab}(n) =%DIFDELCMD < \left(%%% A\circ \tau_{\delta_0\circ \delta_1\circ\cdots\circ \delta_{k}}%DIFDELCMD < \right)%%% (0), where \tau_0 and \tau_1 are certain endomorphisms of \{0,1,\ldots,67\} and A is a map \{1,\ldots,67\}%DIFDELCMD < \to%%% \{3,4,5,6,7\ evaluation of \rho^{ab}(n) needs O(\log n) operations, and thus it is fast even for large values of n.
Revised:  We demonstrate that \rho^{ab}(n) %DIFDELCMD < \left(%%% A\circ \tau_{\delta_0\circ \delta_1\circ\cdots\circ \delta_{k}}%DIFDELCMD < \right)%%% (0), where \tau_0 and \tau_1 are certain endomorphisms of \{0,1,\ldots,67\} and A is a map \{1,\ldots,67\}%DIFDELCMD < \to%%% \{3,4,5,6,7\ evaluation of \rho^{ab}(n) needs O(\log n) operations, and thus it is fast even for large values of n.
Edit intent: clarity
Original:  We demonstrate that \rho^{ab}(n) =%DIFDELCMD < \left(%%% A\circ \tau_{\delta_0\circ \delta_1\circ\cdots\circ \delta_{k}}%DIFDELCMD < \right)%%% (0), where \tau_0 and \tau_1 are certain endomorphisms of \{0,1,\ldots,67\} and A is a map \{1,\ldots,67\}%DIFDELCMD < \to%%% \{3,4,5,6,7\ evaluation of \rho^{ab}(n) needs O(\log n) operations, and thus it is fast even for large values of n.
Revised:  We demonstrate that \rho^{ab}(n) =%DIFDELCMD < \left(%%% \circ \delta_1\circ\cdots\circ \delta_{k}}%DIFDELCMD < \right)%%% (0), where \tau_0 and \tau_1 are certain endomorphisms of \{0,1,\ldots,67\} and A is a map \{1,\ldots,67\}%DIFDELCMD < \to%%% \{3,4,5,6,7\ evaluation of \rho^{ab}(n) needs O(\log n) operations, and thus it is fast even for large values of n.
Edit intent: fluency
Original:  We demonstrate that \rho^{ab}(n) =%DIFDELCMD < \left(%%% A\circ \tau_{\delta_0\circ \delta_1\circ\cdots\circ \delta_{k}}%DIFDELCMD < \right)%%% (0), where \tau_0 and \tau_1 are certain endomorphisms of \{0,1,\ldots,67\} and A is a map \{1,\ldots,67\}%DIFDELCMD < \to%%% \{3,4,5,6,7\ evaluation of \rho^{ab}(n) needs O(\log n) operations, and thus it is fast even for large values of n.
Revised:  We demonstrate that \rho^{ab}(n) =%DIFDELCMD < \left(%%% A\circ \tau_{\delta_0\circ \delta_1\circ\cdots\circ \delta_{k}}%DIFDELCMD < \right)%%% (0), where \tau_0 and \tau_1 are certain endomorphisms of \{0,1,\ldots,67\} and A is a map \{1,\ldots,67\}%DIFDELCMD < \to%%% \{3,4,5,6,7\ evaluation of \rho^{ab}(n) uses O(\log n) operations, and thus it is fast even for large values of n.
Edit intent: fluency
Original:  We demonstrate that \rho^{ab}(n) =%DIFDELCMD < \left(%%% A\circ \tau_{\delta_0\circ \delta_1\circ\cdots\circ \delta_{k}}%DIFDELCMD < \right)%%% (0), where \tau_0 and \tau_1 are certain endomorphisms of \{0,1,\ldots,67\} and A is a map \{1,\ldots,67\}%DIFDELCMD < \to%%% \{3,4,5,6,7\ evaluation of \rho^{ab}(n) needs O(\log n) operations, and thus it is fast even for large values of n.
Revised:  We demonstrate that \rho^{ab}(n) =%DIFDELCMD < \left(%%% A\circ \tau_{\delta_0\circ \delta_1\circ\cdots\circ \delta_{k}}%DIFDELCMD < \right)%%% (0), where \tau_0 and \tau_1 are certain endomorphisms of \{0,1,\ldots,67\} and A is a map \{1,\ldots,67\}%DIFDELCMD < \to%%% \{3,4,5,6,7\ evaluation of \rho^{ab}(n) needs O(\log n) operations, it is fast even for large values of n.
Edit intent: coherence
Original:  In addition, the result implies a characterization of those n for which \rho^{\mathrm{ab}}(n)= m in terms of the existence of walks in a certain graph, which de facto solves an open problem proposed by Richomme et al .
Revised:  Our result also leads to a solution of an open problem proposed by Richomme et al. concerning the characterization of those n for which \rho^{\mathrm{ab}}(n)= m in terms of the existence of walks in a certain graph, which de facto solves an open problem proposed by Richomme et al .
Edit intent: clarity
Original: Adjusting the metabolic network organization to the environment by tuning enzyme expression levels is crucial for cellular growth , in particular in a changing environment or during metabolic adaptation .
Revised: The regulation of metabolic activity by tuning enzyme expression levels is crucial for cellular growth , in particular in a changing environment or during metabolic adaptation .
Edit intent: clarity
Original: Adjusting the metabolic network organization to the environment by tuning enzyme expression levels is crucial for cellular growth , in particular in a changing environment or during metabolic adaptation .
Revised: Adjusting the metabolic network organization to the environment by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments .
Edit intent: clarity
Original:  Here , we present a modeling framework combining the metabolic network and the enzyme production costs.
Revised:  Here , we present a dynamic optimization framework that integrates the metabolic network and the enzyme production costs.
Edit intent: clarity
Original:  Based on this model, we propose a dynamic optimization approach to determine reaction fluxes, explicitly taking production costs for enzymes and enzymatic capacity into account .
Revised:  Based on this model, we propose a dynamic optimization approach to determine reaction fluxes, explicitly taking production costs for enzymes and enzymatic capacity .
Edit intent: coherence
Original:  In contrast to the established dynamic flux balance analysis, the proposed approach thereby allows to analyse dynamic changes in both the metabolic fluxes and the detailed biomass composition in situations of metabolic adaptation .
Revised:  In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the detailed biomass composition in situations of metabolic adaptation .
Edit intent: clarity
Original:  The analysis of the algorithm uses an extension of the recompression technique (used in the context of grammar-based string compression) from strings to trees.
Revised:  The analysis of the algorithm uses an extension of the recompression technique from strings to trees.
Edit intent: clarity
Original: Due to the success of Wireless Local Area Networks (WLANs) and the dominance of the downlink traffic , a large number of previous research efforts have been put to enhance the transmission from the Access Point (AP) to stations (STAs).
Revised: Due to the dominance of the downlink traffic in Wireless Local Area Networks (WLANs) and the dominance of the downlink traffic , a large number of previous research efforts have been put to enhance the transmission from the Access Point (AP) to stations (STAs).
Edit intent: clarity
Original: Due to the success of Wireless Local Area Networks (WLANs) and the dominance of the downlink traffic , a large number of previous research efforts have been put to enhance the transmission from the Access Point (AP) to stations (STAs).
Revised: Due to the success of Wireless Local Area Networks (WLANs) , a large number of previous research efforts have been put to enhance the transmission from the Access Point (AP) to stations (STAs).
Edit intent: coherence
Original:  As Peer-to-Peer (P2P) applications and cloud-based storage services get more popular, the need for a higher uplink capacity also becomes inevitable.
Revised:  As Peer-to-Peer (P2P) and telepresence applications get popular, the need for a higher uplink capacity also becomes inevitable.
Edit intent: clarity
Original:  As Peer-to-Peer (P2P) applications and cloud-based storage services get more popular, the need for a higher uplink capacity also becomes inevitable.
Revised:  As Peer-to-Peer (P2P) applications and cloud-based storage services get more popular, the need for a higher uplink capacity has also become inevitable.
Edit intent: clarity
Original:  In this paper, a unified down/up-link Medium Access Control (MAC) protocol called Uni-MUMAC is proposed to improve the performance of IEEE 802.
Revised:  In this paper, a unified down/up-link Medium Access Control (MAC) protocol called Uni-MUMAC is proposed to enhance the performance of IEEE 802.
Edit intent: clarity
Original: 11ac WLANs by utilizing the spatial multiplexing technique, which is enabled by Multi-User Multiple-input Multiple-output (MU-MIMO) . Specifically, in the downlink, the traditional Request-to-Send/Clear-to-Send (RTS/CTS) handshaking scheme is extended to an RTS/multi-CTSs scheme , which allows the AP to  send frames to multiple STAssimultaneously .
Revised: 11ac WLANs by exploring the multi-user spatial multiplexing . Specifically, in the downlink, the traditional Request-to-Send/Clear-to-Send (RTS/CTS) handshaking scheme is extended to an RTS/multi-CTSs scheme , which allows the AP to send frames to multiple STAssimultaneously .
Edit intent: clarity
Original: 11ac WLANs by utilizing the spatial multiplexing technique, which is enabled by Multi-User Multiple-input Multiple-output (MU-MIMO) . Specifically, in the downlink, the traditional Request-to-Send/Clear-to-Send (RTS/CTS) handshaking scheme is extended to an RTS/multi-CTSs scheme , which allows the AP to  send frames to multiple STAssimultaneously .
Revised: 11ac WLANs by utilizing the spatial multiplexing technique, which is enabled by Multi-User Multiple-input Multiple-output (MU-MIMO) . Specifically, in the downlink, we implement an IEEE 802.11ac-compliant MU-MIMO transmission scheme to allow the AP to send frames to multiple STAssimultaneously .
Edit intent: clarity
Original: 11ac WLANs by utilizing the spatial multiplexing technique, which is enabled by Multi-User Multiple-input Multiple-output (MU-MIMO) . Specifically, in the downlink, the traditional Request-to-Send/Clear-to-Send (RTS/CTS) handshaking scheme is extended to an RTS/multi-CTSs scheme , which allows the AP to  send frames to multiple STAssimultaneously .
Revised: 11ac WLANs by utilizing the spatial multiplexing technique, which is enabled by Multi-User Multiple-input Multiple-output (MU-MIMO) . Specifically, in the downlink, the traditional Request-to-Send/Clear-to-Send (RTS/CTS) handshaking scheme is extended to an RTS/multi-CTSs scheme , which allows the AP to simultaneously send frames to multiple STAssimultaneously .
Edit intent: fluency
Original: 11ac WLANs by utilizing the spatial multiplexing technique, which is enabled by Multi-User Multiple-input Multiple-output (MU-MIMO) . Specifically, in the downlink, the traditional Request-to-Send/Clear-to-Send (RTS/CTS) handshaking scheme is extended to an RTS/multi-CTSs scheme , which allows the AP to  send frames to multiple STAssimultaneously .
Revised: 11ac WLANs by utilizing the spatial multiplexing technique, which is enabled by Multi-User Multiple-input Multiple-output (MU-MIMO) . Specifically, in the downlink, the traditional Request-to-Send/Clear-to-Send (RTS/CTS) handshaking scheme is extended to an RTS/multi-CTSs scheme , which allows the AP to send frames to a group of STAs .
Edit intent: clarity
Original:  In the uplink,  the traditional one round channel access contention is extended to two rounds, which synchronize multiple STAs to transmit frames to the AP in parallel.
Revised:  In the uplink, we extend the traditional one round channel access contention is extended to two rounds, which synchronize multiple STAs to transmit frames to the AP in parallel.
Edit intent: clarity
Original:  In the uplink,  the traditional one round channel access contention is extended to two rounds, which synchronize multiple STAs to transmit frames to the AP in parallel.
Revised:  In the uplink, the traditional one round channel access contention to two rounds, which synchronize multiple STAs to transmit frames to the AP in parallel.
Edit intent: clarity
Original:  In the uplink,  the traditional one round channel access contention is extended to two rounds, which synchronize multiple STAs to transmit frames to the AP in parallel.
Revised:  In the uplink, the traditional one round channel access contention is extended to two rounds, which enable multiple STAs to transmit frames to the AP in parallel.
Edit intent: clarity
Original:  In the uplink,  the traditional one round channel access contention is extended to two rounds, which synchronize multiple STAs to transmit frames to the AP in parallel.
Revised:  In the uplink, the traditional one round channel access contention is extended to two rounds, which synchronize multiple STAs to transmit frames towards the AP in parallel.
Edit intent: fluency
Original:  Through analyzing simulation results, we observe that the 2-nd round Contention Window (CW2nd ), a parameter that controls the length of the extra contention round , plays an important role in the uplink performance .
Revised:  Through analyzing simulation results, we observe that the 2-nd round Contention Window (CW2nd ), a parameter that makes the length of the extra contention round , plays an important role in the uplink performance .
Edit intent: clarity
Original:  By properly setting CW2nd and other parameters, a WLAN implementing Uni-MUMAC exhibits that the system not only performs well in the downlink-dominant traffic scenario, but also achieves the balanced down/up-link throughput in the emerging uplink-hungry traffic scenario.
Revised:  By properly setting CW2nd and other parameters, a WLAN implementing Uni-MUMAC exhibits that the system not only performs well in the downlink traffic dominated scenario, but also achieves the balanced down/up-link throughput in the emerging uplink-hungry traffic scenario.
Edit intent: fluency
Original:  By properly setting CW2nd and other parameters, a WLAN implementing Uni-MUMAC exhibits that the system not only performs well in the downlink-dominant traffic scenario, but also achieves the balanced down/up-link throughput in the emerging uplink-hungry traffic scenario.
Revised:  By properly setting CW2nd and other parameters, a WLAN implementing Uni-MUMAC exhibits that the system not only performs well in the downlink-dominant traffic scenario, but it is also able to balance both the downlink and uplink throughput in the emerging uplink-hungry traffic scenario.
Edit intent: clarity
Original:  By properly setting CW2nd and other parameters, a WLAN implementing Uni-MUMAC exhibits that the system not only performs well in the downlink-dominant traffic scenario, but also achieves the balanced down/up-link throughput in the emerging uplink-hungry traffic scenario.
Revised:  By properly setting CW2nd and other parameters, a WLAN implementing Uni-MUMAC exhibits that the system not only performs well in the downlink-dominant traffic scenario, but also achieves the balanced down/up-link throughput in the emerging uplink bandwidth-hungry scenario.
Edit intent: clarity
Original:  IEEE 802.11ac, the amendment for next generation WLANs, will support Multi-User Multiple-Input Multiple-Output (MU-MIMO) in the downlink, which is considered as one of the key techniques leading WLANs to the Gigabit era.
Revised:  The downlink Multi-User Multiple-Input Multiple-Output (MU-MIMO) in the downlink, which is considered as one of the key techniques leading WLANs to the Gigabit era.
Edit intent: clarity
Original:  IEEE 802.11ac, the amendment for next generation WLANs, will support Multi-User Multiple-Input Multiple-Output (MU-MIMO) in the downlink, which is considered as one of the key techniques leading WLANs to the Gigabit era.
Revised:  IEEE 802.11ac, the amendment for next generation WLANs, will support Multi-User Multiple-Input Multiple-Output (MU-MIMO) in the downlink, which is considered as one of the key enhancements leading WLANs to the Gigabit era.
Edit intent: clarity
Original:  However, as cloud-based uploading services, Peer-to-Peer (P2P) and telepresence applications get popular, the need for a higher uplink capacity has also become inevitable.
Revised:  However, as cloud uploading services, Peer-to-Peer (P2P) and telepresence applications get popular, the need for a higher uplink capacity has also become inevitable.
Edit intent: clarity
Original:  However, as cloud-based uploading services, Peer-to-Peer (P2P) and telepresence applications get popular, the need for a higher uplink capacity has also become inevitable.
Revised:  However, as cloud-based uploading services, Peer-to-Peer (P2P) and telepresence applications get popular, the need for a higher uplink capacity becomes inevitable.
Edit intent: clarity
Original: 11ac WLANs by exploring the multi-user spatial multiplexing  . Specifically, in the downlink, we implement an IEEE 802.11ac-compliant MU-MIMO transmission scheme to allow the AP to simultaneously send frames to a group of STAs.
Revised: 11ac WLANs by exploring the multi-user spatial multiplexing technique . Specifically, in the downlink, we implement an IEEE 802.11ac-compliant MU-MIMO transmission scheme to allow the AP to simultaneously send frames to a group of STAs.
Edit intent: clarity
Original:  In the uplink, we extend the traditional one round channel access contention to two rounds, which enable multiple STAs to transmit frames towards the AP in parallel . 2-nd round Contention Window (CW2nd), a parameter that makes the length of the 2-nd contention round elastic according to the traffic condition, is introduced.
Revised:  In the uplink, we extend the traditional one round channel access contention to two rounds, which coordinate multiple STAs to transmit frames towards the AP in parallel . 2-nd round Contention Window (CW2nd), a parameter that makes the length of the 2-nd contention round elastic according to the traffic condition, is introduced.
Edit intent: clarity
Original:  In the uplink, we extend the traditional one round channel access contention to two rounds, which enable multiple STAs to transmit frames towards the AP in parallel . 2-nd round Contention Window (CW2nd), a parameter that makes the length of the 2-nd contention round elastic according to the traffic condition, is introduced.
Revised:  In the uplink, we extend the traditional one round channel access contention to two rounds, which enable multiple STAs to transmit frames to the AP simultaneously . 2-nd round Contention Window (CW2nd), a parameter that makes the length of the 2-nd contention round elastic according to the traffic condition, is introduced.
Edit intent: clarity