wanyu/IteraTeR_full_sent huggingface dataset:
Original:  If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ). The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992).
Revised:  If the gain results from receiving a side message, this gain, when averaged over the ensemble of possible side messages, is precisely the pragmatic information defined in Weinberger ( 2002 ) as "the amount of information actually used in making a decision". Because a study of information rates led to the Noiseless and Noisy Coding Theorems, two of the most important results of Shannon's theory, we begin the paper by defining a pragmatic information rate, showing that all of the relevant limits make sense, and interpreting them as the improvement in compression obtained from using the correct distribution of transmitted symbols. The first of two applications of the theory extends the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992).
Edit intent: meaning-changed
Original:  The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, an analysis of securities market trading strategies presented in Cover and Thomas (1992). We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races.
Revised:  The relative information result proven herein can be used to extend the information theoretic analysis of the Kelly Criterion, and its generalization, the horse race, to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races.
Edit intent: coherence
Original:  We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some ergodic process, including, but not limited to the history of previous races.
Revised:  We show, in particular, that their results for statistically independent horse races also apply to a series of races where the stochastic process of winning horses, payoffs, and strategies depend on some stationary process, including, but not limited to the history of previous races.
Edit intent: meaning-changed
Original:  Both the theorem proven herein and the application to trading make a compelling case for Weinberger's definition of pragmatic information .
Revised:  A second application is to the question of market efficiency. An efficient market is, by definition, a market in which the pragmatic information of the "tradable past" with respect to current prices is zero. Under this definition, markets whose returns are characterized by a GARCH(1,1) process cannot be efficient. Finally, a pragmatic informational analogue to Shannon's Noisy Coding Theorem suggests that a cause of market inefficiency is that the underlying fundamentals are changing so fast that the price discovery mechanism simply cannot keep up. This may happen most readily in the run-up to a financial bubble, where investors' willful ignorance degrade the information processing capabilities of the market .
Edit intent: meaning-changed
Original:  In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the " optimal mean field " ). Convergence also holds for optimal policies.
Revised:  In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the `` optimal mean field " ). Convergence also holds for optimal policies.
Edit intent: fluency
Original:  In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the " optimal mean field " ). Convergence also holds for optimal policies.
Revised:  In the finite horizon case or with a discounted cost and an infinite horizon, we show that when the number of particles becomes large, the optimal cost of the system converges almost surely to the optimal cost of a discrete deterministic system (the " optimal mean field '' ). Convergence also holds for optimal policies.
Edit intent: fluency
Original:  Inverse of the average dwell time satisfies a `` Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle.
Revised:  Inverse of the average dwell time satisfies a " Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle.
Edit intent: fluency
Original:  Inverse of the average dwell time satisfies a `` Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle.
Revised:  Inverse of the average dwell time satisfies a `` Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle.
Edit intent: fluency
Original:  Inverse of the average dwell time satisfies a " Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle.
Revised:  Inverse of the average dwell time satisfies a `` Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle.
Edit intent: fluency
Original:  Inverse of the average dwell time satisfies a " Michaelis-Menten-like " equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle.
Revised:  Inverse of the average dwell time satisfies a " Michaelis-Menten-like '' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle.
Edit intent: fluency
Original:  We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved between several families: the power law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid.
Revised:  We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved among several families: the power law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid.
Edit intent: fluency
Original:  We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved between several families: the power law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid.
Revised:  We investigate the distribution among species using bipartite networks, and find that two heterogeneous distributions are conserved between several families: the power-law distributions of the number of flavonoids in a species and the number of shared species of a particular flavonoid.
Edit intent: fluency
Original: Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition .
Revised: Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions , which ultimately generate the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition .
Edit intent: fluency
Original: Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition .
Revised: Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cells . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition .
Edit intent: fluency
Original: Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition .
Revised: Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transitions .
Edit intent: fluency
Original:  Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability,  branching, exclusivity, directionality, and promiscuous expression.
Revised:  Here, we construct a generic minimal model of the genetic regulatory network controlling cell fate determination, which exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, directionality, and promiscuous expression.
Edit intent: clarity
Original:  Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability,  branching, exclusivity, directionality, and promiscuous expression.
Revised:  Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, directionality, branching, exclusivity, directionality, and promiscuous expression.
Edit intent: fluency
Original:  We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Revised:  We argue that a modular architecture comprising repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Edit intent: fluency
Original:  We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Revised:  We argue that a modular architecture comprised of repeated network elements reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Edit intent: coherence
Original:  We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Revised:  We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by sequentially repressing selected modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Edit intent: meaning-changed
Original:  We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Revised:  We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence restricting the dynamics to lower dimensional subspaces of the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Edit intent: clarity
Original:  We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace .
Revised:  We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional state space .
Edit intent: clarity
Original:  We implement our model both with ordinary differential equations (ODEs)  to explore the role of bifurcations in producing the one-way character of differentiation  and with stochastic differential equations (SDEs)  to demonstrate the effect of noise on the system in simulations .
Revised:  We implement our model both with ordinary differential equations (ODEs) , to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations .
Edit intent: fluency
Original:  We implement our model both with ordinary differential equations (ODEs)  to explore the role of bifurcations in producing the one-way character of differentiation  and with stochastic differential equations (SDEs)  to demonstrate the effect of noise on the system in simulations .
Revised:  We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation , and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations .
Edit intent: fluency
Original:  We implement our model both with ordinary differential equations (ODEs)  to explore the role of bifurcations in producing the one-way character of differentiation  and with stochastic differential equations (SDEs)  to demonstrate the effect of noise on the system in simulations .
Revised:  We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) , to demonstrate the effect of noise on the system in simulations .
Edit intent: fluency
Original:  We implement our model both with ordinary differential equations (ODEs)  to explore the role of bifurcations in producing the one-way character of differentiation  and with stochastic differential equations (SDEs)  to demonstrate the effect of noise on the system in simulations .
Revised:  We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system .
Edit intent: clarity
Original:  In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes  we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices.
Revised:  In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices.
Edit intent: coherence
Original:  In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes  we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices.
Revised:  In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes , we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices.
Edit intent: fluency
Original:  In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes  we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices.
Revised:  In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a time-homogeneous stock price model which reproduces the given option prices.
Edit intent: clarity
Original: Here we propose an objective scheme to quantify the precise amount of negative entropy, present in an extremely important biochemical pathway; namely, the TCA cycle. Our approach is based on the computational implementation of two-person non-cooperative finite zero-sum game between positive entropy and negative entropy .
Revised: Biological systems possess negative entropy. In them, one form of order produces another, URLanized form of order. We propose a formal scheme to calculate robustness of an entire biological system by quantifying the negative entropy present in it. Our Methodology is based upon a computational implementation of two-person non-cooperative finite zero-sum game between positive entropy and negative entropy .
Edit intent: meaning-changed
Original:  Biochemical analogue of Nash equilibrium condition between these positive and negative entropy, could unambiguously provide a quantitative marker that describes the 'edge of life' for TCA cycle . Difference between concentration-profiles prevalent at the 'edge of life' and biologically observed TCA cycle, could quantitatively express the precise amount of negative entropy present in a typical biochemical network. We show here that it is not the existence of mere order, but the synchronization profile between ordered fluctuations, which accounts for biological robustness. An exhaustive sensitivity analysis could identify the concentrations, for which slightest perturbation can account for enormous increase in positive entropy. Since our algorithm is general, the same analysis can as well be performed on larger networks and (ideally) for an entire cell, if numerical data for concentration is available .
Revised:  Biochemical analogue of Nash equilibrium , proposed here, could measure the robustness in TCA cycle in exact numeric terms, whereas the mixed strategy game between these entropies could quantitate the progression of stages of biological adaptation. Synchronization profile amongst macromolecular concentrations (even under environmental perturbations) is found to account for negative entropy and biological robustness. Emergence of synchronization profile was investigated with dynamically varying metabolite concentrations. Obtained results were verified with that from the deterministic simulation methods. Categorical plans to apply this algorithm in Cancer studies and anti-viral therapies are proposed alongside. From theoretical perspective, this work proposes a general, rigorous and alternative view of immunology .
Edit intent: clarity
Original: The mitotic spindle is an important intermediate structure in eucaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell.
Revised: The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell.
Edit intent: fluency
Original:  We present a complete analytical formulation of this problem, in the case of a single fixed target and for arbitrary cell size. We derive a set of Green's functions for the microtubule dynamics and an associated set of first passage quantities. An implicit analytical expression for the probability distribution of the search time is then obtained , with appropriate boundary conditions at the outer cell membrane. We extract the conditions of optimized search from our formalism. Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it   .
Revised:  Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In{\it .
Edit intent: meaning-changed
Original:  Our approach is based on stochastic differential equations (SDEs)  like the HJM-equation or the Black-Scholes equation  governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs.
Revised:  Our approach is based on stochastic differential equations (SDEs) , like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs.
Edit intent: fluency