wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Our results show that the throughput of Geometric Retransmission is unstable for large n  while the throughput  of Exponential Backoff still exists for n -> infinity .
Revised:  Our results show that the throughput of Geometric Retransmission (K = 1) is inherently unstable for large n while the throughput of Exponential Backoff still exists for n -> infinity .
Edit intent: meaning-changed
Original:  Our results show that the throughput of Geometric Retransmission is unstable for large n  while the throughput  of Exponential Backoff still exists for n -> infinity .
Revised:  Our results show that the throughput of Geometric Retransmission is unstable for large n since its stable throughput region vanishes as the number of nodes n -> infinity; while the throughput of Exponential Backoff still exists for n -> infinity .
Edit intent: meaning-changed
Original:  The input buffer of each access node is modeled as a Geo/G/1 queue, and the service time distribution of each individual head-of-line packet is derived from the Markov chain of  underlying scheduling algorithm , from which we obtain stable regions of the retransmission factor that ensures the throughput stability of the system and bounded mean delay of input packets .
Revised:  The input buffer of each access node is modeled as a Geo/G/1 queue, and the service time distribution of each individual head-of-line packet is derived from the Markov chain of the underlying scheduling algorithm , from which we obtain stable regions of the retransmission factor that ensures the throughput stability of the system and bounded mean delay of input packets .
Edit intent: fluency
Original:  The input buffer of each access node is modeled as a Geo/G/1 queue, and the service time distribution of each individual head-of-line packet is derived from the Markov chain of  underlying scheduling algorithm , from which we obtain stable regions of the retransmission factor that ensures the throughput stability of the system and bounded mean delay of input packets .
Revised:  The input buffer of each access node is modeled as a Geo/G/1 queue, and the service time distribution of each individual head-of-line packet is derived from the Markov chain of underlying scheduling algorithm . From the queuing model, we derive the characteristic equation of network throughput and obtain the stable throughput and bounded delay regions with respect to the retransmission factor .
Edit intent: meaning-changed
Original:  Our results show that the throughput of Geometric Retransmission (K = 1) is inherently unstable for large n since its stable throughput region vanishes as the number of nodes n -> infinity; while the throughput stable region of Exponential Backoff still exists even for an infinite population.
Revised:  Our results show that the throughput of Geometric Retransmission (K = 1) is inherently unstable for large n since its stable throughput region of the exponential backoff scheme exists even for an infinite population.
Edit intent: clarity
Original:  Moreover, we find that the bounded delay region of Geometric Retransmission is the same as its stable throughput region; but that of Exponential Backoff is only a sub-set of its stable throughput region due to the capture effect, which causes large variances of the service time of input packets  .
Revised:  Moreover, we find that the bounded delay region of exponential backoff is only a sub-set of its stable throughput region due to the capture effect, which causes large variances of the service time of input packets .
Edit intent: coherence
Original:  but that of Exponential Backoff is only a sub-set of its stable throughput region due to the capture effect, which causes large variances of the service time of input packets  .
Revised:  but that of Exponential Backoff is only a sub-set of its stable throughput region due to the capture effect, which causes large variances of the service time of input packets caused by the capture effect .
Edit intent: meaning-changed
Original:  We show that the no-arbitrage of second kind property (NA2 in short), introduced by \mbox{%DIFAUXCMD ras09 markets, allows  to provide a closure property for the set of attainable claims in a very natural way, under a suitable efficient friction condition.
Revised:  We show that the no-arbitrage of second kind property (NA2 in short), recently introduced by Rasonyi for finite-dimensional markets, allows to provide a closure property for the set of attainable claims in a very natural way, under a suitable efficient friction condition.
Edit intent: meaning-changed
Original:  We show that the no-arbitrage of second kind property (NA2 in short), introduced by \mbox{%DIFAUXCMD ras09 markets, allows  to provide a closure property for the set of attainable claims in a very natural way, under a suitable efficient friction condition.
Revised:  We show that the no-arbitrage of second kind property (NA2 in short), introduced by \mbox{%DIFAUXCMD ras09 markets, allows us to provide a closure property for the set of attainable claims in a very natural way, under a suitable efficient friction condition.
Edit intent: coherence
Original:  We start with the interpretation of the generator of a backward stochastic differential equation as an infinitesimal pricing rule or an instantaneous utility. With this interpretation the generator has an economic meaning and describes the subjective views of the investor concerning the expected change in the price or the utility. We give a motivation for considering non-Markovian generators of BSDEs which leads us to{t}\int_0^tY(s)ds, 1{t}\int_0^tZ(s)ds).
Revised:  We start with the interpretation of the generator of a backward stochastic differential equations with time-delayed generators of a moving average type. The classical and well-known framework with linear generators depending on (Y(t),Z(t)) is extended and we investigate linear generators depending on (\frac{1{t}\int_0^tY(s)ds, 1{t}\int_0^tZ(s)ds).
Edit intent: meaning-changed
Original:  We investigate two pricing principles and recursive utilities which are derived from time-delayed BSDEs with generators of a moving average type .
Revised:  We investigate two pricing principles and recursive utilities which are derived from time-delayed BSDEs and we investigate in detail some properties of the solutions. In particular, these solutions are linear, time-consistent, continuous, non-monotonic and not conditionally invariant with respect to a terminal condition. A motivation for dealing with generators of a moving average type .
Edit intent: meaning-changed
Original:  We investigate two pricing principles and recursive utilities which are derived from time-delayed BSDEs with generators of a moving average type . They might be useful in the case of an individual valuation of a pay-off. A non-Markovian generator arises when the local valuation rule of the investor depends on the past values of prices, volatilities or utilities. Some properties of our new pricing principles and recursive utilities are considered and we show that they are fundamentally different from the properties which hold for prices and utilities based on classical BSDEs.
Revised:  We investigate two pricing principles and recursive utilities which are derived from time-delayed BSDEs with generators of a moving average type in the context of dynamic pricing and recursive utilities are considered and we show that they are fundamentally different from the properties which hold for prices and utilities based on classical BSDEs.
Edit intent: clarity
Original:  The classical and well-known framework with linear generators depending on (Y(t),Z(t)) is extended and we investigate linear generators depending on (1{t}\int_0^tY(s)ds, 1{t}\int_0^tZ(s)ds).
Revised:  The classical framework with linear generators depending on (Y(t),Z(t)) is extended and we investigate linear generators depending on (1{t}\int_0^tY(s)ds, 1{t}\int_0^tZ(s)ds).
Edit intent: clarity
Original:  We propose a new direction in modelling of investors' preferencesand behaviors .
Revised:  We argue that such equations may arise when we face the problem of dynamic modelling of non-monotone preferences. We model a disappointment effect under which the present pay-off is compared with the past expectations and a volatility aversion which causes the present pay-off to be penalized by the past exposures to the volatility risk .
Edit intent: meaning-changed
Original:  For about two decades, knowledge based potentials based on pairwise distances -- so-called `` potentials of mean force '' (PMFs) -- have been at the central stage in the prediction and design of protein structure and the simulation of protein folding.
Revised:  For about two decades, knowledge based potentials based on pairwise distances -- so-called " potentials of mean force '' (PMFs) -- have been at the central stage in the prediction and design of protein structure and the simulation of protein folding.
Edit intent: fluency
Original:  For about two decades, knowledge based potentials based on pairwise distances -- so-called `` potentials of mean force '' (PMFs) -- have been at the central stage in the prediction and design of protein structure and the simulation of protein folding.
Revised:  For about two decades, knowledge based potentials based on pairwise distances -- so-called `` potentials of mean force " (PMFs) -- have been at the central stage in the prediction and design of protein structure and the simulation of protein folding.
Edit intent: fluency
Original:  For about two decades, knowledge based potentials based on pairwise distances -- so-called `` potentials of mean force '' (PMFs) -- have been at the central stage in the prediction and design of protein structure and the simulation of protein folding.
Revised:  For about two decades, knowledge based potentials based on pairwise distances -- so-called `` potentials of mean force '' (PMFs) -- have been center stage in the prediction and design of protein structure and the simulation of protein folding.
Edit intent: clarity
Original:  However, the validity, scope and limitations of these potentials are still vigorously debated  , and the optimal choice of the reference state -- a necessary component of these potentials -- is an unsolved problem.
Revised:  However, the validity, scope and limitations of these potentials are still vigorously debated and disputed , and the optimal choice of the reference state -- a necessary component of these potentials -- is an unsolved problem.
Edit intent: clarity
Original:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise interactions to arbitrary features of protein structure  and it becomes clear for which purposes the use of these potentials is justified.
Revised:  We call these quantities reference ratio distributions deriving from the application of the reference ratio method. This new view is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise interactions to arbitrary features of protein structure and it becomes clear for which purposes the use of these potentials is justified.
Edit intent: meaning-changed
Original:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise interactions to arbitrary features of protein structure  and it becomes clear for which purposes the use of these potentials is justified.
Revised:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise interactions to arbitrary features of protein structure and it becomes clear for which purposes the use of these potentials is justified.
Edit intent: meaning-changed
Original:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise interactions to arbitrary features of protein structure  and it becomes clear for which purposes the use of these potentials is justified.
Revised:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise distances to arbitrary features of protein structure and it becomes clear for which purposes the use of these potentials is justified.
Edit intent: clarity
Original:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise interactions to arbitrary features of protein structure  and it becomes clear for which purposes the use of these potentials is justified.
Revised:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise interactions to arbitrary features of protein structure ; and it becomes clear for which purposes the use of these potentials is justified.
Edit intent: fluency
Original:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise interactions to arbitrary features of protein structure  and it becomes clear for which purposes the use of these potentials is justified.
Revised:  This justification is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined by the probability distributions involved, PMFs can be generalized beyond pairwise interactions to arbitrary features of protein structure and it becomes clear for which purposes the use of these quantities is justified.
Edit intent: clarity
Original:  Molecular biology assumes that function is explained by structure, the complementary geometries of molecules and weak intermolecular hydrogen bonds. However, both this assumption and its converse are possible URLanic molecules and quantum circuits/protocols are considered as hardware and software of living systems that are co-optimized during evolution.
Revised:  Organic molecules and quantum circuits/protocols are considered as hardware and software of living systems that are co-optimized during evolution.
Edit intent: coherence
Original:  Then, base pairing occurs by swapping intrabase entanglements with interbase entanglements  .
Revised:  Then, base pairing occurs by swapping intrabase entanglements with interbase entanglements . We examine possible realizations of quantum circuits to be used to obtain intrabase entanglement and swapping protocols to be employed to obtain interbase entanglement. Finally, we discuss possible ways for computational and experimental verification of the model .
Edit intent: meaning-changed
Original:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action  whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved .  After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
Revised:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action functional whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved . After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
Edit intent: fluency
Original:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action  whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved .  After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
Revised:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action whose potential term is an exponential function . After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
Edit intent: coherence
Original:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action  whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved .  After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
Revised:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved . This path integral is evaluated by use of the Feynman-Kac theorem. After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
Edit intent: meaning-changed
Original:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action  whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved .  After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
Revised:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved . After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion for the value of an Asian option .
Edit intent: clarity
Original:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action  whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved .  After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of an Asian option .
Revised:  By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action whose potential term is an exponential function , i. e. the Liouville Hamiltonian, which can be explicitly solved . After working out some auxiliary integrations involving Bessel and Whittaker functions, we arrive at the spectral expansion expression of the value of Asian options .
Edit intent: fluency
Original: We extend the groupoid formalism of coupled cell networks as developed by Golubitsky, Stewart and their collaborators by recasting it in a categorical language .
Revised: We develop a new framework for the study of complex continuous time dynamical systems based on viewing them as collections of interacting control modules. This framework is inspired by and builds upon the groupoid formalism of Golubitsky, Stewart and their collaborators by recasting it in a categorical language .
Edit intent: clarity
Original: We extend the groupoid formalism of coupled cell networks as developed by Golubitsky, Stewart and their collaborators by recasting it in a categorical language .
Revised: We extend the groupoid formalism of coupled cell networks as developed by Golubitsky, Stewart and their collaborators . Our approach uses the tools and --- more importantly ---the stance of category theory. This enables us to put the groupoid formalism in a coordinate-free setting and to extend it from ordinary differential equations to vector fields on manifolds .
Edit intent: meaning-changed
Original:  In particular we develop a combinatorial models for the categories of modular continuous time dynamical systems on manifolds .
Revised:  In particular we develop a combinatorial models for the categories of modular continuous time dynamical systems . Each such model, as a category, is a fibration over an appropriate category of labeled directed graphs. This makes precise the relation between dynamical systems living on networks and the combinatorial structure of the underlying directed graphs, allowing us to exploit the relation in new and interesting ways .
Edit intent: meaning-changed
Original:  Under some suitable assumptions, we show that any accumulation point of the sequence generated by our method when applied to the rank constrained minimization problem is a stationary point of a nonlinear reformulation of the problem .
Revised:  Under some suitable assumptions, we show that any accumulation point of the sequence generated by the penalty decomposition methods satisfies the first-order optimality conditions of a nonlinear reformulation of the problem .
Edit intent: meaning-changed
Original:  Under some suitable assumptions, we show that any accumulation point of the sequence generated by our method when applied to the rank constrained minimization problem is a stationary point of a nonlinear reformulation of the problem .
Revised:  Under some suitable assumptions, we show that any accumulation point of the sequence generated by our method when applied to the rank constrained minimization problem is a stationary point of a nonlinear reformulation of the problems .
Edit intent: fluency
Original:  With a small customizable parameter \epsilon which is the step size used in each iteration of the online algorithm, we have shown that our online algorithm achieves a long-term average revenue which is within O(\epsilon) of the optimal revenue and the overdraft level of this algorithm is upper-bounded by O(1/\epsilon) {1+\Delta} fraction of the revenue if \Delta is the percentage error in click-through rate estimation.
Revised:  Unlike prior models, we do not assume that the number of query arrivals is known. Due to the stochastic nature of the arrival process considered here, either temporary "free" service, i.e., service above the specified budget (which we call "overdraft") or under-utilization of the budget (which we call "underdraft") is unavoidable. We prove that our online algorithm achieves a long-term average revenue which is within O(\epsilon) of the optimal revenue and the overdraft level of this algorithm is upper-bounded by O(1/\epsilon) {1+\Delta} fraction of the revenue if \Delta is the percentage error in click-through rate estimation.
Edit intent: meaning-changed