wanyu/IteraTeR_full_sent huggingface dataset:
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:  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 can achieve a revenue that 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: clarity
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:  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 while ensuring that the overdraft or underdraft is O(1/\epsilon) {1+\Delta} fraction of the revenue if \Delta is the percentage error in click-through rate estimation.
Edit intent: clarity
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:  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) , where \epsilon can be arbitrarily small. With a view towards practice, we also show that one can always operate strictly under the budget. Our algorithm also allows us to quantify the effect of errors in click-through rate estimation on the achieved revenue. We show that we lose at most \frac{\Delta{1+\Delta} fraction of the revenue if \Delta is the percentage error in click-through rate estimation.
Edit intent: meaning-changed
Original:  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.
Revised:  Due to the stochastic nature of the arrival process considered here, either temporary "free" service, i.e., service above the specified budget or under-utilization of the budget (which we call "underdraft") is unavoidable.
Edit intent: fluency
Original:  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.
Revised:  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 is unavoidable.
Edit intent: fluency
Original:  Our algorithm also allows us to quantify the effect of errors in click-through rate estimation on the achieved revenue .
Revised:  In addition, we extend our results to a click-through rate maximization model, and also show how our algorithm can be modified to handle non-stationary query arrival processes and clients with short-term contracts. Our algorithm allows us to quantify the effect of errors in click-through rate estimation on the achieved revenue .
Edit intent: meaning-changed
Original:  Our algorithm also allows us to quantify the effect of errors in click-through rate estimation on the achieved revenue . We show that we lose at most \frac{\Delta{1+\Delta} fraction of the revenue if \Delta is the percentage error in click-through rate estimation} .
Revised:  Our algorithm also allows us to quantify the effect of errors in click-through rate estimation on the achieved revenue {1+\Delta} fraction of the revenue if \Delta is the percentage error in click-through rate estimation} .
Edit intent: coherence
Original:  Under appropriate conditions, we show that the lower value function of this game is a viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation , by generalizing the weak dynamic programming principles in 3 .
Revised:  Under appropriate conditions, we show that the game has a value and the value function is the unique viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation , by generalizing the weak dynamic programming principles in 3 .
Edit intent: meaning-changed
Original:  Under appropriate conditions, we show that the lower value function of this game is a viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation , by generalizing the weak dynamic programming principles in 3 .
Revised:  Under appropriate conditions, we show that the lower value function of this game is a viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation 3 .
Edit intent: coherence
Original:  Under appropriate conditions, we show that the lower value function of this game is a viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation , by generalizing the weak dynamic programming principles in 3 .
Revised:  Under appropriate conditions, we show that the lower value function of this game is a viscosity solution to an obstacle problem for a Hamilton-Jacobi-Bellman equation , by generalizing the weak dynamic programming principles in .
Edit intent: coherence
Original:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol  . 1 , 2010)  by a moment generating function computation in the particular case of the Heston model.
Revised:  The results of this paper generalize the ones obtained in Feng , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol . 1 , 2010) by a moment generating function computation in the particular case of the Heston model.
Edit intent: meaning-changed
Original:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol  . 1 , 2010)  by a moment generating function computation in the particular case of the Heston model.
Revised:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% , SIAM Journal on Financial Mathematics, Vol . 1 , 2010) by a moment generating function computation in the particular case of the Heston model.
Edit intent: meaning-changed
Original:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol  . 1 , 2010)  by a moment generating function computation in the particular case of the Heston model.
Revised:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model Forde and Fouque . 1 , 2010) by a moment generating function computation in the particular case of the Heston model.
Edit intent: meaning-changed
Original:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol  . 1 , 2010)  by a moment generating function computation in the particular case of the Heston model.
Revised:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol SIAM J. Financial Math . 1 , 2010) by a moment generating function computation in the particular case of the Heston model.
Edit intent: meaning-changed
Original:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol  . 1 , 2010)  by a moment generating function computation in the particular case of the Heston model.
Revised:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol . 1 ( 2010) by a moment generating function computation in the particular case of the Heston model.
Edit intent: fluency
Original:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol  . 1 , 2010)  by a moment generating function computation in the particular case of the Heston model.
Revised:  The results of this paper generalize the ones obtained in \mbox{%DIFAUXCMD FFF , %DIFDELCMD < {\it %%% Short maturity asymptotic for a fast mean reverting Heston stochastic volatility model , SIAM Journal on Financial Mathematics, Vol . 1 , 2010) 126-141 by a moment generating function computation in the particular case of the Heston model.
Edit intent: meaning-changed
Original:   A weaker sufficient condition than that of \mbox{%DIFAUXCMD \cite[Section V.2]{FlemingS for the continuity of the value function is obtained.
Revised:  The goal is to find an optimal control that minimizes the total cost up to a stochastic exit time. A weaker sufficient condition than that of \mbox{%DIFAUXCMD \cite[Section V.2]{FlemingS for the continuity of the value function is obtained.
Edit intent: meaning-changed
Original: We examine a class of Brownian based models which produce tractable incomplete equilibria. The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income .
Revised: In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income .
Edit intent: clarity
Original:  The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income . The investors can trade continuously on a finite time interval in a money market account as well as a risky security.
Revised:  The models are based on finitely many investors with heterogeneous exponential utilities over intermediate consumption who receive partially unspanned income and can trade continuously on a finite time interval in a money market account as well as a risky security.
Edit intent: clarity
Original:  Besides establishing the existence of an equilibrium, our main result shows that the resulting equilibrium can display a lower risk-free rate and a higher risk premium relative to the usual Pareto efficient equilibrium in complete markets.
Revised:  Besides establishing the existence of an equilibrium, our main result shows that if the investors' unspanned income has stochastic countercyclical volatility, the resulting equilibrium can display a lower risk-free rate and a higher risk premium relative to the usual Pareto efficient equilibrium in complete markets.
Edit intent: meaning-changed
Original:  Besides establishing the existence of an equilibrium, our main result shows that the resulting equilibrium can display a lower risk-free rate and a higher risk premium relative to the usual Pareto efficient equilibrium in complete markets. Consequently, our model can simultaneously help explaining the risk-free rate and equity premium puzzles .
Revised:  Besides establishing the existence of an equilibrium, our main result shows that the resulting equilibrium can display a lower risk-free rate and a higher risk premium relative to the usual Pareto efficient equilibrium in an otherwise identical complete market .
Edit intent: clarity
Original:  This result is consequently generalized and numerically studied for broad return distributions and returns generated by a GARCH process  .
Revised:  This result is consequently generalized and numerically studied for broad return distributions and returns generated by a GARCH process . Finally we study the case when investment is rebalanced only partially and show that this strategy can improve the investment long-term growth rate more than optimization of the rebalancing period .
Edit intent: meaning-changed
Original:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey  away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \varphi and z>0.
Revised:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the {\PaleGrey away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \varphi and z>0.
Edit intent: clarity
Original:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey  away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \varphi and z>0.
Revised:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey density of \nu away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \varphi and z>0.
Edit intent: meaning-changed
Original:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey  away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \varphi and z>0.
Revised:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \phi (x){\bf 1}_{xz} for smooth functions \varphi and z>0.
Edit intent: fluency
Original:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey  away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \varphi and z>0.
Revised:  Small-time expansions, of arbitrary polynomial order, in time-t, are obtained for the tails \bbp(Z_{t}\geq z), z>0, and for the call-option prices \bbe(e^{z+Z_{t}}-1)_{+}, z\neq 0, assuming smoothness conditions on the L\'evy density {\PaleGrey away from the origin and a small-time large deviation principle on U. Our approach allows for a unified treatment of general payoff functions of the form \varphi (x){\bf 1}_{xz} for smooth functions \phi and z>0.
Edit intent: fluency
Original: We present an implementation of a general purpose GPU-Molecular Dynamics code named LAMMPScuda which is based on LAMMPS. It exhibits excellent scaling behavior, allowing for the efficient usage of hundreds of GPUs for a single simulation . At the same time each GPU provides the equivalent performance of approximately 5 modern Quad Core CPUs. By supporting a wide array of force fields LAMMPScuda allows to model many different condensed matter systems including URLanic glasses, polymer systems and molecular fluids. In the paper implementation details are presented as well as performance measurements with a number of different condensed systems .
Revised: We present a GPU implementation of LAMMPS, a number of different condensed systems .
Edit intent: coherence
Original:  In the paper implementation details are presented as well as performance measurements with a number of different condensed systems .
Revised:  In the paper implementation details are presented as well as performance measurements with a widely-used parallel molecular dynamics (MD) software package, and show 5x to 13x single node speedups versus the CPU-only version of LAMMPS. This new CUDA package for LAMMPS also enables multi-GPU simulation on hybrid heterogeneous clusters, using MPI for inter-node communication, CUDA kernels on the GPU for all methods working with particle data, and standard LAMMPS C++ code for CPU execution. Cell and neighbor list approaches are compared for best performance on GPUs, with thread-per-atom and block-per-atom neighbor list variants showing best performance at low and high neighbor counts, respectively. Computational performance results of GPU-enabled LAMMPS are presented for a variety of materials classes (e.g. biomolecules, polymers, metals, semiconductors), along with a speed comparison versus other available GPU-enabled MD software. Finally, we show strong and weak scaling performance on a CPU/GPU cluster using up to 128 dual GPU nodes .
Edit intent: meaning-changed
Original: Based on the temporal distributions of clustered segments in the time series of the ten Dow Jones US (DJUS) economic sector indices, we calculated their cross correlations over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 corresponding segments within the present financial crisis .
Revised: We calculated the cross correlations between the half-hourly times series of the ten Dow Jones US (DJUS) economic sector indices, we calculated their cross correlations over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 corresponding segments within the present financial crisis .
Edit intent: meaning-changed
Original: Based on the temporal distributions of clustered segments in the time series of the ten Dow Jones US (DJUS) economic sector indices, we calculated their cross correlations over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 corresponding segments within the present financial crisis .
Revised: Based on the temporal distributions of clustered segments in the time series of the ten Dow Jones US economic sectors over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 corresponding segments within the present financial crisis .
Edit intent: clarity
Original: Based on the temporal distributions of clustered segments in the time series of the ten Dow Jones US (DJUS) economic sector indices, we calculated their cross correlations over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 corresponding segments within the present financial crisis .
Revised: Based on the temporal distributions of clustered segments in the time series of the ten Dow Jones US (DJUS) economic sector indices, we calculated their cross correlations over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 segments within the present financial crisis .
Edit intent: clarity
Original: Based on the temporal distributions of clustered segments in the time series of the ten Dow Jones US (DJUS) economic sector indices, we calculated their cross correlations over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 corresponding segments within the present financial crisis . From these cross-correlation matrices, we constructed minimal spanning trees (MSTs) of the US economy at the sector level.
Revised: Based on the temporal distributions of clustered segments in the time series of the ten Dow Jones US (DJUS) economic sector indices, we calculated their cross correlations over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 corresponding segments within the present financial crisis , to construct minimal spanning trees (MSTs) of the US economy at the sector level.
Edit intent: clarity
Original:  In all MSTs, a core-fringe structure is found, with CY, IN, and NC consistently making up the core, and BM, EN, HC, TL, UT residing predominantly on the fringe.
Revised:  In all MSTs, a core-fringe structure is found, with consumer goods, consumer services, and the industrials consistently making up the core, and BM, EN, HC, TL, UT residing predominantly on the fringe.
Edit intent: meaning-changed
Original:  In all MSTs, a core-fringe structure is found, with CY, IN, and NC consistently making up the core, and BM, EN, HC, TL, UT residing predominantly on the fringe.
Revised:  In all MSTs, a core-fringe structure is found, with CY, IN, and NC consistently making up the core, and basic materials, oil and gas, healthcare, telecommunications, and utilities residing predominantly on the fringe.
Edit intent: meaning-changed
Original:  More importantly, we find that the MSTs can be classified into two distinct, statistically robust, topologies: (i) star-like, with IN at the center, associated with low-volatility economic growth;
Revised:  More importantly, we find that the MSTs can be classified into two distinct, statistically robust, topologies: (i) star-like, with the industrials at the center, associated with low-volatility economic growth;
Edit intent: meaning-changed