wanyu/IteraTeR_v2 huggingface dataset:
Original:  The main features of this approach are that both mergings and splittings  are purely localized phenomenon, which allow a transparent and continuous use of the involved subtrees (as far as no higher-level communication is concerned).
Revised:  The main features of this approach is that both are purely localized phenomenon, which allow a transparent and continuous use of the involved subtrees (as far as no higher-level communication is concerned).
Edit intent: clarity
Original:  We do both here, and provide analytical expressions of the expected merging time of two given trees .
Revised:  We do both here, and provide analytical expressions of the expected merging time for two given trees .
Edit intent: clarity
Original:  The pattern is acheived by the sequential interaction of two signaling pathways.
Revised:  The pattern is achieved by the sequential interaction of two signaling pathways.
Edit intent: fluency
Original: We develop a technique that predicts the probability and attack rate of epidemics as well as the size distribution of non-epidemic outbreaks and the growth rate in networks with a specific form of clustering.
Revised: The social networks that infectious diseases spread along are typically clustered. Because of the growth rate in networks with a specific form of clustering.
Edit intent: clarity
Original:  In this paper we present an approximating algorithm for counting triangles in graphs within a (1%DIFDELCMD < \pm %%% \epsilon) factor with high probability.
Revised:  In this paper we present an approximating algorithm for counting triangles in graphs %DIFDELCMD < \pm %%% \epsilon) factor with high probability.
Edit intent: clarity
Original:  Note: in this version a reference to "beats" on the bottom of page two is incorrect and should instead be "nonlinear mixing".
Edit intent: coherence
Original: We study distributed storage problems for large-scale wireless sensor networks .
Revised: We consider large-scale wireless sensor networks .
Edit intent: clarity
Original:  Due to limited energy and hostile environment, sensors are vulnerable, and it is therefore desirable to disseminate the acquired information throughout the network so that each of the n sensors stores one (possibly coded)
Revised:  Due to limited energy and hostile environment, it is desirable to disseminate the acquired information throughout the network so that each of the n sensors stores one (possibly coded)
Edit intent: clarity
Original:  Due to limited energy and hostile environment, sensors are vulnerable, and it is therefore desirable to disseminate the acquired information throughout the network so that each of the n sensors stores one (possibly coded)
Revised:  Due to limited energy and hostile environment, sensors are vulnerable, and it is therefore desirable to disseminate the acquired information throughout the network so that each of the n nodes stores one (possibly coded)
Edit intent: clarity
Original:  packet and the original source information can be recovered later in a computationally simple way from any k(1 + \epsilon) of nodes for some small \epsilon > 0. To accomplish this, we propose two distributed algorithms--LTCDS and RCDS--based on random walks and Fountain codes . Both algorithms employ simple random walks to disseminate source information, but use different coding schemes.
Revised:  packet so that the original k source packets can be recovered later in a computationally simple way from any k(1 + \epsilon) of nodes for some small \epsilon > 0. To accomplish this, we propose two distributed algorithms--LTCDS and RCDS--based on random walks and Fountain codes . Both algorithms employ simple random walks to disseminate source information, but use different coding schemes.
Edit intent: clarity
Original:  packet and the original source information can be recovered later in a computationally simple way from any k(1 + \epsilon) of nodes for some small \epsilon > 0. To accomplish this, we propose two distributed algorithms--LTCDS and RCDS--based on random walks and Fountain codes . Both algorithms employ simple random walks to disseminate source information, but use different coding schemes.
Revised:  packet and the original source information can be recovered , locally and in a computationally simple way from any k(1 + \epsilon) of nodes for some small \epsilon > 0. To accomplish this, we propose two distributed algorithms--LTCDS and RCDS--based on random walks and Fountain codes . Both algorithms employ simple random walks to disseminate source information, but use different coding schemes.
Edit intent: clarity
Original:  packet and the original source information can be recovered later in a computationally simple way from any k(1 + \epsilon) of nodes for some small \epsilon > 0. To accomplish this, we propose two distributed algorithms--LTCDS and RCDS--based on random walks and Fountain codes . Both algorithms employ simple random walks to disseminate source information, but use different coding schemes.
Revised:  packet and the original source information can be recovered later in a computationally simple way from any k(1 + \epsilon) nodes for some small \epsilon > 0. To accomplish this, we propose two distributed algorithms--LTCDS and RCDS--based on random walks and Fountain codes . Both algorithms employ simple random walks to disseminate source information, but use different coding schemes.
Edit intent: clarity
Original:  Unlike all previously developed schemes, both algorithms are truly distributed .
Revised:  Unlike all previously developed schemes, our algorithms are truly distributed .
Edit intent: clarity
Original:  We establish tight bounds for the corresponding degree vectors, as well as precise domains where these concentrate ;
Revised:  We establish tight bounds for all corresponding degree vectors, as well as precise domains where these concentrate ;
Edit intent: clarity
Original:  We establish tight bounds for the corresponding degree vectors, as well as precise domains where these concentrate ;
Revised:  We establish tight bounds for the corresponding degree vectors, and specify domains that will surely contain such vectors ;
Edit intent: clarity
Original:  these include a new type of Sylvester-type matrix as well as Bezout-type matrices, which we call partial Bezoutians.
Revised:  these include a new type of Sylvester-type matrix as well as Bezout-type matrices, known as partial Bezoutians.
Edit intent: clarity
Original:  In order to highlight this feature, we introduce the  local risk decomposition  (LRD) formalism, where dynamical information about a strategy's performance is retained.
Revised:  In order to highlight this feature, we introduce the ' local risk decomposition (LRD) formalism, where dynamical information about a strategy's performance is retained.
Edit intent: fluency
Original:  In order to highlight this feature, we introduce the  local risk decomposition  (LRD) formalism, where dynamical information about a strategy's performance is retained.
Revised:  In order to highlight this feature, we introduce the local risk decomposition ' (LRD) formalism, where dynamical information about a strategy's performance is retained.
Edit intent: fluency
Original:  This framework, motivated by the multi-scaling techniques used in complex system theory, is particularly suitable for high-frequency trading systems and can be applied into problems of portfolio optimization.
Revised:  This framework, motivated by the multi-scaling techniques used in complex system theory, is particularly suitable for high-frequency trading systems and can be applied into problems of strategy optimization.
Edit intent: clarity
Original:  We test this model in the context of an agent based microscopic stochastic order book model that was recently proposed by Bovier, Cern\'{y} and Hryniv .
Revised:  We apply these strategies to an agent-based stochastic order book model that was recently proposed by Bovier, Cern\'{y} and Hryniv .
Edit intent: clarity
Original:  In particular, from our simulations the recovery speed of the market after a large order is clearly depended on the order size, whereas the ASS model assumes the speed to be given by a constant .
Revised:  In particular, from our simulations the recovery speed of the market after a large order is clearly dependent on the order size, whereas the ASS model assumes the speed to be given by a constant .
Edit intent: fluency
Original:  In particular, from our simulations the recovery speed of the market after a large order is clearly depended on the order size, whereas the ASS model assumes the speed to be given by a constant .
Revised:  In particular, from our simulations the recovery speed of the market after a large order is clearly depended on the order size, whereas the AFS model assumes a constant speed .
Edit intent: clarity
Original:  For this reason, we propose a generalisation of the model of ASS that incorporates this dependency, and derive the optimal investment strategies.
Revised:  For this reason, we propose a generalisation of the model of ASS that incorporates this dependency, and prove the optimal investment strategies.
Edit intent: clarity
Original:  We show that within our artificial market, correct fitting of this parameter leads to optimal hedging strategies that reduce the trading costs, compared to the ones produced by ASS . Finally, we show that the costs of applying the optimal strategies of the improved ASS model to the artificial market  still differ significantly from the model predictions, indicating that even the improved model does not capture all of the relevant details of a real market.
Revised:  We show that within our artificial market, correct fitting of this parameter leads to optimal hedging strategies that reduce the trading costs, compared to the ones produced by ASS . Finally, we show that the costs of applying the optimal strategies of the improved ASS model to the artificial market environment still differ significantly from the model predictions, indicating that even the improved model does not capture all of the relevant details of a real market.
Edit intent: clarity
Original:  On the basis of this, succinct equations describing the backoff distribution as a function of the collision probability \gamma are derived , which also shed light on a controversy in the field .
Revised:  On the basis of this, succinct equations describing the backoff distribution as a function of the collision probability \gamma are derived .
Edit intent: coherence
Original:  However, it is also found that the %DIFDELCMD < {\it %DIFDELCMD < %%% collision effect between nodes prevails over the %DIFDELCMD < {\it %%% Poissonian aggregation effect in spite of its tendency to increase with the number of nodes.
Revised:  However, it is also found that the %DIFDELCMD < {\it %DIFDELCMD < %%% collision effect between nodes prevails over the %DIFDELCMD < {\it %%% Poissonian aggregation effect in spite of its tendency to increase with the number of nodes.
Edit intent: fluency
Original:  This reveals that the  backoff process is heavy-tailed in the strict sense for m^2 \gamma>1 , essentially due to collision.
Revised:  This reveals that the backoff process is heavy-tailed in the strict sense for \gamma>1 , essentially due to collision.
Edit intent: clarity
Original: We present  a simple algorithm that produces a so called growing Ramified Random Apollonian Networks ( R-RAN ) in any dimension d.
Revised: We present a simple algorithm that produces so called growing Ramified Random Apollonian Networks ( R-RAN ) in any dimension d.
Edit intent: fluency
Original:  To characterize further the structure of R-RAN , we introduce new parameters that we refer to as the parallel degree and the ramification coefficient, that determine locally and in average the number of vertices inside the (d+1)-cliques composing the network.
Revised:  To characterize further the structure of R-RAN , we introduce new parameters that we refer to as the parallel degree and the parallel coefficient, that determine locally and in average the number of vertices inside the (d+1)-cliques composing the network.
Edit intent: clarity
Original:  We provide analytical derivations for the computation of the degree and parallel degree distributions, ramification and clustering coefficients.
Revised:  We provide analytical derivations for the computation of the degree and parallel degree distributions, parallel and clustering coefficients.
Edit intent: clarity
Original: This paper introduces a robust point-to-point transmission scheme , Tetrys, that relies on a novel on-the-fly erasure coding concept in order to reduce the delay for recovering lost data at the receiver side.
Revised: This paper introduces a robust point-to-point transmission scheme : Tetrys, that relies on a novel on-the-fly erasure coding concept in order to reduce the delay for recovering lost data at the receiver side.
Edit intent: fluency
Original: This paper introduces a robust point-to-point transmission scheme , Tetrys, that relies on a novel on-the-fly erasure coding concept in order to reduce the delay for recovering lost data at the receiver side.
Revised: This paper introduces a robust point-to-point transmission scheme , Tetrys, that relies on a novel on-the-fly erasure coding concept which reduces the delay for recovering lost data at the receiver side.
Edit intent: coherence
Original:  There is a significant difference between the expressibilities of decision problems and optimization problems.
Revised:  There is a significant difference between the expressibilities of decision problems and optimisation problems.
Edit intent: clarity
Original:  for example, a 2SAT Horn formula can be satisfied in polynomial time, whereas the optimization version in NP-hard.
Revised:  for example, a 2SAT Horn formula can be satisfied in polynomial time, whereas the optimisation version in NP-hard.
Edit intent: fluency
Original:  Gr\"{adel \mbox{ gradel91 }0pt proved }  that all polynomially solvable decision problems can be expressed as  universal (\Pi_1) Horn sentences  .
Revised:  del \mbox{ gradel91 }0pt proved } that all polynomially solvable decision problems can be expressed as universal (\Pi_1) Horn sentences .
Edit intent: coherence
Original:  Gr\"{adel \mbox{ gradel91 }0pt proved }  that all polynomially solvable decision problems can be expressed as  universal (\Pi_1) Horn sentences  .
Revised:  Gr\"{adel \mbox{ gradel91 }0pt proved } It is known that all polynomially solvable decision problems can be expressed as universal (\Pi_1) Horn sentences .
Edit intent: clarity
Original:  We show here that, on the other hand, optimization problems defy such a simple characterization , by demonstrating that even a simple \Pi_0 formula is unable to guarantee polynomial time solvability.
Revised:  We show here that, on the other hand, optimization problems defy such a characterisation , by demonstrating that even a simple \Pi_0 formula is unable to guarantee polynomial time solvability.
Edit intent: clarity
Original: Given a set of n blue and n red points in general position in the plane , a line \ell determined by them is said to be balanced if  each open half-plane bounded by \ell contains precisely the same number of blue points as red points .
Revised: Given a set of n blue and n red points in general position in the plane . A line \ell determined by them is said to be balanced if each open half-plane bounded by \ell contains precisely the same number of blue points as red points .
Edit intent: fluency
Original: Given a set of n blue and n red points in general position in the plane , a line \ell determined by them is said to be balanced if  each open half-plane bounded by \ell contains precisely the same number of blue points as red points .
Revised: Given a set of n blue and n red points in general position in the plane , a line \ell determined by them is said to be balanced if in each open half-plane bounded by \ell contains precisely the same number of blue points as red points .
Edit intent: clarity
Original:  On the number of balanced lines,Discrete and Computational Geometry , 25 (2001), 611--628%DIFDELCMD < ]%%% : Every set as above has at least n balanced lines .
Revised:  On the number of balanced lines, , 25 (2001), 611--628%DIFDELCMD < ]%%% : Every set as above has at least n balanced lines .
Edit intent: coherence
Original:  On the number of balanced lines,Discrete and Computational Geometry , 25 (2001), 611--628%DIFDELCMD < ]%%% : Every set as above has at least n balanced lines .
Revised:  On the number of balanced lines,Discrete and Computational Geometry %DIFDELCMD < ]%%% : Every set as above has at least n balanced lines .
Edit intent: coherence
Original: Distributed fault-tolerance can mask the effect of a limited number of per- manent faults, while self-stabilization provides forward recovery after an arbitrary number of transient fault hit the system.
Revised: Distributed fault-tolerance can mask the effect of a limited number of permanent faults, while self-stabilization provides forward recovery after an arbitrary number of transient fault hit the system.
Edit intent: fluency
Original:  Unison can be seen as a local clock syn- chronisation problem as neighbors must maintain digital clocks at most one time unit away from each other, and increment their own clock value infinitely often.
Revised:  Unison can be seen as a local clock synchronization problem as neighbors must maintain digital clocks at most one time unit away from each other, and increment their own clock value infinitely often.
Edit intent: fluency
Original:  We present many im- possiblity results for this difficult problem and propose a FTSS solution when the problem is solvable that exhibits optimal fault containment.
Revised:  We present many impossibility results for this difficult problem and propose a FTSS solution when the problem is solvable that exhibits optimal fault containment.
Edit intent: fluency
Original:  Analysis of the price process shows that the bond volatility is determined by prices of certain weighted perpetual annuities.
Revised:  Analysis of the bond price dynamics shows that the bond volatility is determined by prices of certain weighted perpetual annuities.
Edit intent: clarity
Original:  Selection by individuals' fitness,  the basic driving force of neo-Darwinian evolution, then quickly eliminates cooperators.
Revised:  Selection by individuals' fitness, usually the basic driving force of neo-Darwinian evolution, then quickly eliminates cooperators.
Edit intent: coherence
Original:  Selection by individuals' fitness,  the basic driving force of neo-Darwinian evolution, then quickly eliminates cooperators.
Revised:  Selection by individuals' fitness, the basic driving force of evolution, quickly eliminates cooperators.
Edit intent: clarity
Original:  By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging ` edge of neutral evolution' which delineates regimes of neutral and neo-Darwinian evolution.
Revised:  By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging ' edge of neutral evolution' which delineates regimes of neutral and neo-Darwinian evolution.
Edit intent: fluency
Original:  By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging ` edge of neutral evolution' which delineates regimes of neutral and neo-Darwinian evolution.
Revised:  By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging ` edge of neutral evolution' that delineates regimes of neutral and neo-Darwinian evolution.
Edit intent: fluency
Original:  By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging ` edge of neutral evolution' which delineates regimes of neutral and neo-Darwinian evolution.
Revised:  By studying the mean extinction times of cooperators and defectors, a variable sensitive to fluctuations, we are able to identify and quantify an emerging ` edge of neutral evolution' which delineates regimes of neutral and Darwinian evolution.
Edit intent: clarity
Original:  In contrast, the classical predictions of evolutionary game theory, where defectors beat cooperators, are recovered in the neo-Darwinian regimes.
Revised:  In contrast, the classical predictions of evolutionary game theory, where defectors beat cooperators, are recovered in the Darwinian regimes.
Edit intent: clarity
Original:  This improves a result by Moon (1971) who showed upper and lower bounds of 1.7170^n and 1.4757^n on the maximum number of minimal feedback vertex sets in tournaments .
Revised:  This improves and extends the bounds of Moon (1971) who showed upper and lower bounds of 1.7170^n and 1.4757^n on the maximum number of minimal feedback vertex sets in tournaments .
Edit intent: clarity
Original:  We prove that every tournament on n vertices has at most 1.6740^n minimal feedback vertex sets  and that there is an infinite family of tournaments, all having at least 1.5448^n minimal feedback vertex sets.
Revised:  We prove that every tournament on n vertices has at most 1.6740^n minimal feedback vertex sets , and that there is an infinite family of tournaments, all having at least 1.5448^n minimal feedback vertex sets.
Edit intent: fluency
Original:  Our main findings are: 1 -fast oscillations are always supercritical for realistic transfer functions (sigmoidal or power-law with power greater than one) . 2 - Traveling waves are preferred over standing waves given realistic patterns of local connectivity.
Revised:  Our main findings are: 1 - fast oscillations are always supercritical for realistic transfer functions (sigmoidal or power-law with power greater than one) . 2 - Traveling waves are preferred over standing waves given realistic patterns of local connectivity.
Edit intent: fluency
Original:  Our main findings are: 1 -fast oscillations are always supercritical for realistic transfer functions (sigmoidal or power-law with power greater than one) . 2 - Traveling waves are preferred over standing waves given realistic patterns of local connectivity.
Revised:  Our main findings are: 1 -fast oscillations are always supercritical for realistic transfer functions . 2 - Traveling waves are preferred over standing waves given realistic patterns of local connectivity.
Edit intent: clarity
Original:  Our main findings are: 1 -fast oscillations are always supercritical for realistic transfer functions (sigmoidal or power-law with power greater than one) . 2 - Traveling waves are preferred over standing waves given realistic patterns of local connectivity.
Revised:  Our main findings are: 1 -fast oscillations are always supercritical for realistic transfer functions (sigmoidal or power-law with power greater than one) . 2 - Traveling waves are preferred over standing waves given plausible patterns of local connectivity.
Edit intent: clarity
Original:  Previous work has shown that such delays , which play an important role in shaping the dynamics of networks of large numbers of spiking neuronswith continuous synaptic kinetics, can be taken into account with a rate model through the addition of an explicit, fixed delay  .
Revised:  Previous work has shown that such delays , which play an important role in shaping the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model through the addition of an explicit, fixed delay .
Edit intent: clarity
Original:  While this dependence is, in general, nontrivial, we make use of the smallness of the ratio in the delay in neuronal interactions to the effective time constant of integration to arrive at two general observations of physiological relevance  .
Revised:  We arrive at two general observations of physiological relevance .
Edit intent: clarity