wanyu/IteraTeR_v2 huggingface dataset:
Original:  From the phenomenological viewpoint, any initial genotype frequency of a closed system will eventually approach a stable fixed point.
Revised:  From the phenomenological viewpoint, any initial parameter of genotype frequencies of a closed system will eventually approach a stable fixed point.
Edit intent: clarity
Original:  To demonstrate the experimental evidence  , as an example, we show a mapping from the  blood type genotype frequencies of world ethnic groups to our stable fixed-point solutions.
Revised:  To demonstrate the experimental evidence for our theory , as an example, we show a mapping from the blood type genotype frequencies of world ethnic groups to our stable fixed-point solutions.
Edit intent: clarity
Original:  To demonstrate the experimental evidence  , as an example, we show a mapping from the  blood type genotype frequencies of world ethnic groups to our stable fixed-point solutions.
Revised:  To demonstrate the experimental evidence , as an example, we show a mapping from the data of blood type genotype frequencies of world ethnic groups to our stable fixed-point solutions.
Edit intent: clarity
Original:  From the mathematical viewpoint, the equilibrium solutions consist of a base manifoldas a global stable attractor , attracting any initial point in a Euclidean fiber bundle to the fixed point where the fiber is attached.
Revised:  From the mathematical viewpoint, the equilibrium solutions consist of a base manifoldas a global stable attractor , attracting any initial point in a Euclidean fiber bundle to the fixed point where this fiber is attached.
Edit intent: clarity
Original:  In addition, the modification of our theory under the process of natural selection and mutation is addressed.
Revised:  The modification of our theory under the process of natural selection and mutation is addressed.
Edit intent: coherence
Original: Traditionally, numerous simple models such as preferential attachment have been put forward to reveal the evolution mechanisms of real networks.
Revised: Numerous concise models such as preferential attachment have been put forward to reveal the evolution mechanisms of real networks.
Edit intent: clarity
Original:  However, previous simulations show that real networks usually are driven by various features instead of  single pure mechanism.
Revised:  However, previous simulations show that real networks usually are driven by various features instead of a single pure mechanism.
Edit intent: fluency
Original:  In this paper , we introduce two methods which can tackle this problem: one is based on link prediction model, and the other is based on likelihood analysis.
Revised:  In this study , we introduce two methods which can tackle this problem: one is based on link prediction model, and the other is based on likelihood analysis.
Edit intent: clarity
Original: We show theoretically that networks of membrane memcapacitive systems - capacitors with memory made out of membrane materials - can be used to perform a complete set of logic gates in a massively parallel way by simply changing the external input amplitudes, but not the topology of the network.
Revised: We show theoretically that networks of membrane memcapacitive systems -- capacitors with memory made out of membrane materials - can be used to perform a complete set of logic gates in a massively parallel way by simply changing the external input amplitudes, but not the topology of the network.
Edit intent: fluency
Original: We show theoretically that networks of membrane memcapacitive systems - capacitors with memory made out of membrane materials - can be used to perform a complete set of logic gates in a massively parallel way by simply changing the external input amplitudes, but not the topology of the network.
Revised: We show theoretically that networks of membrane memcapacitive systems - capacitors with memory made out of membrane materials -- can be used to perform a complete set of logic gates in a massively parallel way by simply changing the external input amplitudes, but not the topology of the network.
Edit intent: fluency
Original:  This electronic polymorphism is an important characteristic of memcomputing (computing with memories) that closely reproduces one of the main features of the brain.
Revised:  This polymorphism is an important characteristic of memcomputing (computing with memories) that closely reproduces one of the main features of the brain.
Edit intent: clarity
Original:  A practical realization of these membrane memcapacitive systems, using, e.g., graphene or other 2D flexible materials, would be a step forward towards a solid-state realization of memcomputing with passive devices.
Revised:  A practical realization of these membrane memcapacitive systems, using, e.g., graphene or other 2D materials, would be a step forward towards a solid-state realization of memcomputing with passive devices.
Edit intent: clarity
Original:  These discrete analogues are obtained from simple random walks (SRWs) on D^{(k)}:=D\cap 2^{-k}Z^d  .
Revised:  These discrete analogues are obtained from random walks on D^{(k)}:=D\cap 2^{-k}Z^d .
Edit intent: clarity
Original:  We prove weak convergence of the joint law of the SRWs and the proposed analogues to the joint law of RBM and its boundary local time.
Revised:  We prove weak convergence of the joint law of the random walks and the proposed analogues to the joint law of RBM and its boundary local time.
Edit intent: clarity
Original:  The key of proof is the local limit theorem for RBMs recently established in 6 .
Revised:  A cornerstone in the proof is the local limit theorem for RBMs recently established in 6 .
Edit intent: clarity
Original:  The key of proof is the local limit theorem for RBMs recently established in 6 .
Revised:  The key of proof is the local limit theorem for 6 .
Edit intent: clarity
Original: For an arbitrary bounded Lipschitz domain D, we propose a class of discrete analogues for the boundary local time of reflected diffusions in D.
Revised: We propose a discrete analogue for the boundary local time of reflected diffusions in D.
Edit intent: clarity
Original:  A cornerstone in the proof is the local  limit theorem for reflected diffusions  ] .
Revised:  A cornerstone of the proof is the local limit theorem for reflected diffusions ] .
Edit intent: clarity
Original:  The lazy approach allows  to break the barrier of 1/2, which is the best competitive ratio that can be guaranteed by any deterministic algorithm in the classical on-line matching.
Revised:  The lazy approach allows us to break the barrier of 1/2, which is the best competitive ratio that can be guaranteed by any deterministic algorithm in the classical on-line matching.
Edit intent: coherence
Original: We extend the exploration regarding dynamic approach of macroeconomic variables by tackling systematically expenditure using Statistical Physics models (for the first time to the best of our knowledge).
Revised: We extend the exploration regarding dynamical approach of macroeconomic variables by tackling systematically expenditure using Statistical Physics models (for the first time to the best of our knowledge).
Edit intent: clarity
Original:  Also, using polynomial distribution which characterizes the behavior of dynamic systems in certain situations, we extend also our analysis to mean income data from the UK that span for a time interval of 35 years.
Revised:  Also, using polynomial distribution which characterizes the behavior of dynamical systems in certain situations, we extend also our analysis to mean income data from the UK that span for a time interval of 35 years.
Edit intent: fluency
Original: Polynomial distribution can be applied to dynamic systems in certain situations.
Revised: Polynomial distribution can be applied to dynamical systems in certain situations.
Edit intent: fluency
Original: We investigate the efficient transmission and processing of weak signals (subthreshold ) in a realistic neural medium in the presence of different levels of the underlying noise.
Revised: We investigate the efficient transmission and processing of weak , subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise.
Edit intent: fluency
Original:  Assuming Hebbian weights for maximal synaptic conductances - that naturally balances the network with excitatory and inhibitory synapses - and considering short-term synaptic plasticity affecting such conductances, we found different dynamical phases in the system.
Revised:  Assuming Hebbian weights for maximal synaptic conductances -- that naturally balances the network with excitatory and inhibitory synapses - and considering short-term synaptic plasticity affecting such conductances, we found different dynamical phases in the system.
Edit intent: fluency
Original:  Assuming Hebbian weights for maximal synaptic conductances - that naturally balances the network with excitatory and inhibitory synapses - and considering short-term synaptic plasticity affecting such conductances, we found different dynamical phases in the system.
Revised:  Assuming Hebbian weights for maximal synaptic conductances - that naturally balances the network with excitatory and inhibitory synapses -- and considering short-term synaptic plasticity affecting such conductances, we found different dynamical phases in the system.
Edit intent: fluency
Original:  Assuming Hebbian weights for maximal synaptic conductances - that naturally balances the network with excitatory and inhibitory synapses - and considering short-term synaptic plasticity affecting such conductances, we found different dynamical phases in the system.
Revised:  Assuming Hebbian weights for maximal synaptic conductances - that naturally balances the network with excitatory and inhibitory synapses - and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system.
Edit intent: clarity
Original:  When a weak stimulus input is applied to each neuron and increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases and therefore for quite well defined and different levels of stochasticity in the system.
Revised:  When a weak stimulus input is applied to each neuron , increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases and therefore for quite well defined and different levels of stochasticity in the system.
Edit intent: coherence
Original:  When a weak stimulus input is applied to each neuron and increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases and therefore for quite well defined and different levels of stochasticity in the system.
Revised:  When a weak stimulus input is applied to each neuron and increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system.
Edit intent: coherence
Original:  We proved that this intriguing phenomenon is quite robust  in different situations , including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies including diluted networks and complex topologies such as scale-free and small-world networks.
Revised:  We proved that this intriguing phenomenon is quite robust , as it occurs in different situations , including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies including diluted networks and complex topologies such as scale-free and small-world networks.
Edit intent: coherence
Original:  We proved that this intriguing phenomenon is quite robust  in different situations , including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies including diluted networks and complex topologies such as scale-free and small-world networks.
Revised:  We proved that this intriguing phenomenon is quite robust in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies including diluted networks and complex topologies such as scale-free and small-world networks.
Edit intent: fluency
Original:  We proved that this intriguing phenomenon is quite robust  in different situations , including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies including diluted networks and complex topologies such as scale-free and small-world networks.
Revised:  We proved that this intriguing phenomenon is quite robust in different situations , including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies , namely, diluted networks and complex topologies such as scale-free and small-world networks.
Edit intent: clarity
Original:  We conclude that the robustness of the phenomenon in different realistic scenarios including the case of spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it also could appear in actual neural systems as recent psychophysical experiments suggest.
Revised:  We conclude that the robustness of the phenomenon in different realistic scenarios , including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it also could appear in actual neural systems as recent psychophysical experiments suggest.
Edit intent: clarity
Original:  We conclude that the robustness of the phenomenon in different realistic scenarios including the case of spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it also could appear in actual neural systems as recent psychophysical experiments suggest.
Revised:  We conclude that the robustness of the phenomenon in different realistic scenarios including the case of spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psychophysical experiments suggest.
Edit intent: clarity
Original:  The investigated parameterization is  temporal depth and  pathwidth.
Revised:  The investigated parameterization is the sum of temporal depth and pathwidth.
Edit intent: clarity
Original:  The only real operator fragments which is in FPT is the fragment containing solely AX.
Revised:  The only real operator fragment which is confirmed to be in FPT is the fragment containing solely AX.
Edit intent: clarity
Original:  Also we prove a generalization of Courcelle's theorem to infinite signatures which will be used to proof the FPT-membership cases .
Revised:  Also we prove a generalization of Courcelle's theorem to infinite signatures which will be used to proof the FPT-membership case .
Edit intent: fluency
Original:  The proposed implementations with both CUDA and OpenCL are freely available in ViennaCL and achieve up to three-fold performance gains when compared to other solver packages for graphics processing units.
Revised:  The proposed implementations with both CUDA and OpenCL are freely available in ViennaCL and are shown to be competitive with or even superior to other solver packages for graphics processing units.
Edit intent: clarity
Original:  Highest performance gains are obtained for small to medium-sized systems, while our implementations remain competitive with vendor-tuned implementations for very large systems.
Revised:  Highest performance gains are obtained for small to medium-sized systems, while our implementations are on par with vendor-tuned implementations for very large systems.
Edit intent: clarity
Original: The paper deals with some generalizations of Fibonacci and Lucas sequences, arising from powers of paths , and cycles, respectively.
Revised: The paper deals with some generalizations of Fibonacci and Lucas sequences, arising from powers of paths and cycles, respectively.
Edit intent: fluency
Original:  In the first part of the work we provide a formula for the number of edges of the Hasse diagram of the independent subsets of the h-th power of a path ordered by inclusion.
Revised:  In the first part of the work we provide a formula for the number of edges of the Hasse diagram of the independent sets of the h-th power of a path ordered by inclusion.
Edit intent: clarity
Original:  Consequently, we derive a generalized notion of Fibonacci sequence, we call h-Fibonacci sequence.
Revised:  Consequently, we derive a generalized notion of Fibonacci sequence, called h-Fibonacci sequence.
Edit intent: fluency
Original:  We evaluate the number of edges of the Hasse diagram of the independent subsets of the h-th power of a cycle ordered by inclusion.
Revised:  We evaluate the number of edges of the Hasse diagram of the independent sets of the hth power of a cycle ordered by inclusion.
Edit intent: clarity
Original:  We derive then a generalized version of the Lucas sequence, we call h-Lucas sequence.
Revised:  We derive then a generalized version of the Lucas sequence, called h-Lucas sequence.
Edit intent: clarity
Original: We propose a new method for network reconstruction by the stationary distribution data of Markov chains on this network.
Revised: It is known that the stationary distribution data of Markov chains on this network.
Edit intent: clarity
Original: We prove that for any convex pentagon in the plane there are two disks, among the five disks having a side of the pentagon as diameter  , that do not intersect.
Revised: We prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter , that do not intersect.
Edit intent: clarity
Original: We prove that for any convex pentagon there are two disks, among the five disks having a side of the pentagon as diameter and the midpoint of the side as its center , that do not intersect .
Revised: We prove that for any convex pentagon there are two disks, among the five disks having a side of the polygon as diameter and the midpoint of the side as its center , that do not intersect .
Edit intent: fluency
Original:  We introduce a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any generalized hypertree decomposition (GHD) of a query of width w and depth d, and computes the query in O(d \linebreakO ) rounds and O(n (\mathrm{IN^w + OUT)^2}{M}) communication cost, where M is the memory available per machine in the cluster and IN and OUT are the sizes of input and output of the query, respectively.
Revised:  We introduce a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any generalized hypertree decomposition (GHD) of a query of width w and depth d, and computes the query in \linebreakO ) rounds and O(n (\mathrm{IN^w + OUT)^2}{M}) communication cost, where M is the memory available per machine in the cluster and IN and OUT are the sizes of input and output of the query, respectively.
Edit intent: clarity
Original:  We introduce a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any generalized hypertree decomposition (GHD) of a query of width w and depth d, and computes the query in O(d \linebreakO ) rounds and O(n (\mathrm{IN^w + OUT)^2}{M}) communication cost, where M is the memory available per machine in the cluster and IN and OUT are the sizes of input and output of the query, respectively.
Revised:  We introduce a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any generalized hypertree decomposition (GHD) of a query of width w and depth d, and computes the query in O(d \linebreakO ) rounds and O(n \frac{(\mathrm{IN^w + OUT)^2}{M}) communication cost, where M is the memory available per machine in the cluster and IN and OUT are the sizes of input and output of the query, respectively.
Edit intent: fluency
Original:  We describe another general technique to construct  even shorter depth GHDs with longer widths, effectively showing a spectrum of tradeoffs one can make between communication and computation and the number of rounds of MapReduce .
Revised:  We describe another general technique to construct GHDs with even shorter depth GHDs with longer widths, effectively showing a spectrum of tradeoffs one can make between communication and computation and the number of rounds of MapReduce .
Edit intent: fluency
Original:  We describe another general technique to construct  even shorter depth GHDs with longer widths, effectively showing a spectrum of tradeoffs one can make between communication and computation and the number of rounds of MapReduce .
Revised:  We describe another general technique to construct even shorter depth and longer widths, effectively showing a spectrum of tradeoffs one can make between communication and computation and the number of rounds of MapReduce .
Edit intent: clarity
Original:  We describe another general technique to construct  even shorter depth GHDs with longer widths, effectively showing a spectrum of tradeoffs one can make between communication and computation and the number of rounds of MapReduce .
Revised:  We describe another general technique to construct even shorter depth GHDs with longer widths, effectively showing a spectrum of tradeoffs one can make between communication and the number of rounds of MapReduce .
Edit intent: clarity
Original:  We introduce a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any generalized hypertree decomposition (GHD) of a query of width w and depth d, and computes the query in %DIFDELCMD < \linebreakO%%%  (d + \log(n)) rounds and O(n(\mathrm{IN^w + OUT)^2}{M}) communication cost, where M is the memory available per machine in the cluster and IN and OUT are the sizes of input and output of the query, respectively.
Revised:  We introduce a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any generalized hypertree decomposition (GHD) of a query , having width w and depth d, and computes the query in %DIFDELCMD < \linebreakO%%% (d + \log(n)) rounds and O(n(\mathrm{IN^w + OUT)^2}{M}) communication cost, where M is the memory available per machine in the cluster and IN and OUT are the sizes of input and output of the query, respectively.
Edit intent: clarity
Original:  We introduce a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any generalized hypertree decomposition (GHD) of a query of width w and depth d, and computes the query in %DIFDELCMD < \linebreakO%%%  (d + \log(n)) rounds and O(n(\mathrm{IN^w + OUT)^2}{M}) communication cost, where M is the memory available per machine in the cluster and IN and OUT are the sizes of input and output of the query, respectively.
Revised:  We introduce a distributed and generalized version of Yannakakis's algorithm, called GYM. GYM takes as input any generalized hypertree decomposition (GHD) of a query of width w and depth d, and computes the query in %DIFDELCMD < \linebreakO%%% O (d + \log(n)) rounds and O(n(\mathrm{IN^w + OUT)^2}{M}) communication cost, where M is the memory available per machine in the cluster and IN and OUT are the sizes of input and output of the query, respectively.
Edit intent: fluency
Original:  M is assumed to be IN^{1{\epsilon}} , for some constant \epsilon > 1. Using GYM we achieve two main results: (1) Every width-w query can be computed in O(n) rounds of MapReduce with O(n(\mathrm{IN^w + OUT)^2}{M}) cost;
Revised:  M is assumed to be IN^{1{\epsilon}} for some constant \epsilon > 1. Using GYM we achieve two main results: (1) Every width-w query can be computed in O(n) rounds of MapReduce with O(n(\mathrm{IN^w + OUT)^2}{M}) cost;
Edit intent: fluency