wanyu/IteraTeR_full_sent huggingface dataset:
Original:  Specifically, in the case of Bernoulli arrivals ,  we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Revised:  Specifically, in the case of Bernoulli arrivals , we show that the heavy-traffic scaled queue length is given by\left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Edit intent: clarity
Original:  Specifically, in the case of Bernoulli arrivals ,  we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Revised:  Specifically, in the case of Bernoulli arrivals , we show that the heavy-traffic scaled queue length is \left(1-\frac{1{2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Edit intent: meaning-changed
Original:  Specifically, in the case of Bernoulli arrivals ,  we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Revised:  Specifically, in the case of Bernoulli arrivals , we show that the heavy-traffic scaled queue length is \left({2n}}\right)||\sigma||^2, where \sigma is the vector of the standard deviations of arrivals to each port in the heavy-traffic limit. In the special case of uniform Bernoulli arrivals, the corresponding formula is given by\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Edit intent: meaning-changed
Original:  Specifically, in the case of Bernoulli arrivals ,  we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Revised:  Specifically, in the case of Bernoulli arrivals , we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Edit intent: coherence
Original:  Specifically, in the case of Bernoulli arrivals ,  we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Revised:  Specifically, in the case of Bernoulli arrivals , we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right). The result shows that the heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Edit intent: fluency
Original:  Specifically, in the case of Bernoulli arrivals ,  we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern.
Revised:  Specifically, in the case of Bernoulli arrivals , we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic scaled queue length has optimal scaling with respect to the size of a switch with a uniform traffic pattern.
Edit intent: clarity
Original:  Specifically, in the case of Bernoulli arrivals ,  we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to the size of a switch with a uniform traffic pattern. This settles the heavy-traffic version of an open conjecture  .
Revised:  Specifically, in the case of Bernoulli arrivals , we show that the heavy-traffic scaled queue length is \left({2n}}\right)\left( n-3{2}+1{2n} . Our result implies that the MaxWeight algorithm has optimal queue-length scaling behavior in the \right) heavy-traffic regime with respect to n, thus settling one version of an open conjecture .
Edit intent: clarity
Original:  This settles the heavy-traffic version of an open conjecture  .
Revised:  This settles the heavy-traffic version of an open conjecture ; in fact, it is shown that the heavy-traffic queue length is at most within a factor of two from the optimal. We then consider certain asymptotic regimes where the load of the system scales simultaneously with the number of ports. We show that the MaxWeight algorithm has optimal queue length scaling behavior provided that the arrival rate approaches capacity sufficiently fast .
Edit intent: meaning-changed
Original: The recent economic crisis has raised a wide awareness that the financial system should be considered as a complex network with financial institutions and financial dependencies respectively as nodes and links between these nodes. Systemic risk is defined as the risk of default of a large portion of financial exposures among institution in the network. Indeed, the structure of this network is an important element to measure systemic risk and there is no widely accepted methodology to determine the systemically important nodes in a large financial network.
Edit intent: coherence
Original:  In this research, we introduce a metric for systemic risk measurement with taking into account both common idiosyncratic shocks as well as contagion through counterparty exposures.
Revised:  In this research, we introduce a robust metric to identify Systemically Important Financial Institution (SIFI) in a financial network by taking into account both common idiosyncratic shocks as well as contagion through counterparty exposures.
Edit intent: meaning-changed
Original:  We applied this technique and studied the performance and convergence behavior of the algorithm with different structure of the financial network  .
Revised:  We applied this technique and studied the performance and convergence behavior of the algorithm with different structure of the financial network are important elements to measure systemic risk and identify SIFIs. Results show that increasing the levels of out- and in-degree connections of an institution can have a diverse impact on its systemic ranking. Additionally, on the empirical side, we investigate the factors which lead to the identification of Global Systemic Important Banks (G-SIB) by using a panel dataset of the largest banks in each country. Our empirical results supports the main findings of the theoretical model .
Edit intent: meaning-changed
Original:  Motivated by this we study models with out-of-equilibrium dynamics that depend on the local density. Our simulations suggest that density-dependent dynamics in which the motion of a molecule slows down in the presence of nearby molecules , tend to cause condensation into an out-of-equilibrium liquidstate. This out-of-equilibrium state behaves like a liquid in the sense that it coexists with a much more dilute phase, droplets coalesce, and the state has a well-defined surface tension --- which we calculate. Liquid /liquid separation appears to be a very general phenomenon that occurs in and out of equilibrium .
Revised:  Motivated by this we consider what sort of simple rules for the dynamics of model mRNA molecules lead to liquid /liquid separation appears to be a very general phenomenon that occurs in and out of equilibrium .
Edit intent: clarity
Original: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts.
Revised: This paper deals with an optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts.
Edit intent: clarity
Original: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts.
Revised: This paper provides the optimal position management problem for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts.
Edit intent: clarity
Original: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts.
Revised: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer order flows in an illiquid market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts.
Edit intent: clarity
Original: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts.
Revised: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading incurs a stochastic linear price impacts.
Edit intent: clarity
Original: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impacts. In addition, it is supposed that the market participants can partially infer the position size held by the market maker and their aggregate reactions affect the security prices. Although the market maker can ask its OTC counterparties to transact a block trade without causing a direct price impact in the exchange, its timing is assumed to be uncertain.
Revised: This paper provides the optimal position management strategy for a market maker who has to face uncertain customer orders in an "illiquid " market, where the market maker's continuous trading through a traditional exchange incurs stochastic linear price impact. Although the execution timing is uncertain, the market maker can also ask its OTC counterparties to transact a block trade without causing a direct price impact in the exchange, its timing is assumed to be uncertain.
Edit intent: meaning-changed
Original:  Although the market maker can ask its OTC counterparties to transact a block trade without causing a direct price impact in the exchange, its timing is assumed to be uncertain. Another important way for the market maker to reduce its position is to match an incoming customer order to the outstanding position being warehoused in its balance sheet .
Revised:  Although the market maker can ask its OTC counterparties to transact a block trade without causing a direct price impact .
Edit intent: clarity
Original:   The solution of the problem is represented by a stochastic Hamilton-Jacobi-Bellman equation, which can be decomposed into three (one non-linear and two linear) backward stochastic differential equations (BSDEs).
Revised:  We adopt quite generic stochastic processes of the securities, order flows, price impacts, quadratic penalties as well as security borrowing/lending rates. The solution of the problem is represented by a stochastic Hamilton-Jacobi-Bellman equation, which can be decomposed into three (one non-linear and two linear) backward stochastic differential equations (BSDEs).
Edit intent: meaning-changed
Original:   The solution of the problem is represented by a stochastic Hamilton-Jacobi-Bellman equation, which can be decomposed into three (one non-linear and two linear) backward stochastic differential equations (BSDEs).
Revised:  The solution of the market maker's optimal position-management strategy is represented by a stochastic Hamilton-Jacobi-Bellman equation, which can be decomposed into three (one non-linear and two linear) backward stochastic differential equations (BSDEs).
Edit intent: clarity
Original:  For a multiple-security case, we use an interesting connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties have been studied by Bismut(1976)  .
Revised:  For a multiple-security case, we make use of the connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties have been studied by Bismut(1976) .
Edit intent: clarity
Original:  For a multiple-security case, we use an interesting connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties have been studied by Bismut(1976)  .
Revised:  For a multiple-security case, we use an interesting connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties were studied by Bismut(1976) .
Edit intent: clarity
Original:  For a multiple-security case, we use an interesting connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties have been studied by Bismut(1976)  .
Revised:  For a multiple-security case, we use an interesting connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties have been studied by Bismut(1976) . We also propose a perturbative approximation scheme for the resultant BSRDE, which only requires a system of linear ODEs to be solved at each expansion order. Its justification and the convergence rate are also given .
Edit intent: meaning-changed
Original:  Jumps, in particular exponential L\'evy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see Tankov for an overview) .
Revised:  Jumps, in particular exponential L\'evy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see \mbox{%DIFAUXCMD Tank for an overview) .
Edit intent: meaning-changed
Original:  Jumps, in particular exponential L\'evy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see Tankov for an overview) . A recent breakthrough was made by Gatheral, Jaisson and Rosenbaum, who proposed to replace the Brownian driver of the instantaneous volatility by a short-memory fractional Brownian motion, which is able to capture the short-maturity steepness while preserving path continuity .
Revised:  Jumps, in particular exponential L\'evy and affine models, which exhibit small-maturity exploding smiles, have historically been proposed to remedy this (see Tankov for an overview) , and more recently rough volatility models \mbox{%DIFAUXCMD AlosLeon, Fukasawa .
Edit intent: meaning-changed
Original:  The range of rates includes behaviours similar to exponential L\'evy models and fractional stochastic volatility models . As a by-product, we make a conjecture on the small-maturity forward smile asymptotics of stochastic volatility models, in exact agreement with the results by Jacquier and Roome for the Heston model .
Revised:  The range of rates includes behaviours similar to exponential L\'evy models and fractional stochastic volatility models .
Edit intent: coherence
Original:  The main focus of the present work is  the expectation of the hitting time (to a given target set) of the process with restart , for which we obtain the explicit formula.Observing that the process with restart is positive Harris recurrent, we obtain the expression of its unique invariant probability. Then we show the equivalence of the following statements: (a) the boundedness (with respect to the initial state) of the expectation of the hitting time ; (b) the finiteness of the expectation of the hitting time for almost all the initial states with respect to the unique invariant probability;
Revised:  The main focus of the present work is the expectation of the hitting time (to a given target set) of the process with restart .The formula is convenient when considering the problem of optimizationof the expected hitting time with respect to the unique invariant probability;
Edit intent: clarity
Original: We aim to obtain explicit representations of locally risk-minimizing  of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein-Uhlenbeck type stochastic volatility models.
Revised: We obtain explicit representations of locally risk-minimizing of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein-Uhlenbeck type stochastic volatility models.
Edit intent: clarity
Original: We aim to obtain explicit representations of locally risk-minimizing  of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein-Uhlenbeck type stochastic volatility models.
Revised: We aim to obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein-Uhlenbeck type stochastic volatility models.
Edit intent: clarity
Original: We aim to obtain explicit representations of locally risk-minimizing  of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein-Uhlenbeck type stochastic volatility models.
Revised: We aim to obtain explicit representations of locally risk-minimizing of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models.
Edit intent: fluency
Original:   Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions by using Malliavin calculus for L\'evy processes.
Revised:  Using Malliavin calculus for Levy processes, Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions by using Malliavin calculus for L\'evy processes.
Edit intent: meaning-changed
Original:   Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions by using Malliavin calculus for L\'evy processes.
Revised:  Arai and Suzuki (2015) obtained a formula for locally risk-minimizing for L\'evy markets under many additional conditions by using Malliavin calculus for L\'evy processes.
Edit intent: coherence
Original:   Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions by using Malliavin calculus for L\'evy processes.
Revised:  Arai and Suzuki (2015) obtained a formula of locally risk-minimizing strategies for Levy markets under many additional conditions by using Malliavin calculus for L\'evy processes.
Edit intent: clarity
Original:   Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions by using Malliavin calculus for L\'evy processes. In this paper, supposing mild conditions, we make sure that the Barndorff-Nielsen and Shephard models satisfy all the conditions imposed in Arai and Suzuki (2015).
Revised:  Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions . Supposing mild conditions, we make sure that the Barndorff-Nielsen and Shephard models satisfy all the conditions imposed in Arai and Suzuki (2015).
Edit intent: clarity
Original: Intracellular calcium is regulated  by the release of Ca^{2+} ions from the endoplasmic reticulum via inisitol-4 ,5-triphosphate receptor channels .
Revised: Intracellular calcium is regulated in part by the release of Ca^{2+} ions from the endoplasmic reticulum via inisitol-4 ,5-triphosphate receptor channels .
Edit intent: meaning-changed
Original: Intracellular calcium is regulated  by the release of Ca^{2+} ions from the endoplasmic reticulum via inisitol-4 ,5-triphosphate receptor channels .
Revised: Intracellular calcium is regulated by the release of Ca^{2+} ions from the endoplasmic reticulum via inositol-4 ,5-triphosphate receptor channels .
Edit intent: fluency
Original: Intracellular calcium is regulated  by the release of Ca^{2+} ions from the endoplasmic reticulum via inisitol-4 ,5-triphosphate receptor channels .
Revised: Intracellular calcium is regulated by the release of Ca^{2+} ions from the endoplasmic reticulum via inisitol-4 ,5-triphosphate receptor (IP_3R) channels (among other possibilities such as RyR and L-type calcium channels) .
Edit intent: meaning-changed
Original:  The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells {\it   . Local fluctuations in the number of calcium ions play a crucial role in the onset of these features.
Revised:  The resulting dynamics are highly diverse, lead to local calcium ``puffs'' as well as global waves propagating through cells {\it . Local fluctuations in the number of calcium ions play a crucial role in the onset of these features.
Edit intent: fluency
Original:  The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells {\it   . Local fluctuations in the number of calcium ions play a crucial role in the onset of these features.
Revised:  The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells , as observed in{\it . Local fluctuations in the number of calcium ions play a crucial role in the onset of these features.
Edit intent: meaning-changed
Original:  The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells {\it   . Local fluctuations in the number of calcium ions play a crucial role in the onset of these features.
Revised:  The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells {\it Xenopus . Local fluctuations in the number of calcium ions play a crucial role in the onset of these features.
Edit intent: meaning-changed
Original:  The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells {\it   . Local fluctuations in the number of calcium ions play a crucial role in the onset of these features.
Revised:  The resulting dynamics are highly diverse, lead to local calcium "puffs" as well as global waves propagating through cells {\it oocytes, neurons, and other cell types . Local fluctuations in the number of calcium ions play a crucial role in the onset of these features.
Edit intent: meaning-changed