wanyu/IteraTeR_full_sent huggingface dataset:
Original: We consider a stochastic game-theoretic model of an investment market in continuous time where investors compete for dividend income from several assets . Asset prices are determined endogenously from the equality of supply and demand .
Revised: We consider a stochastic game-theoretic model of an investment market in continuous time with short-lived assets and study strategies, called survival, which guarantee that the relative wealth of an investor who uses such a strategy remains bounded away from zero .
Edit intent: meaning-changed
Original:  The main results are related to the question in what proportions the total capital will be distributed among the investors, and what will be the prices of the assets asymptotically on the infinite time horizon depending on the strategies of the investors. We prove that there exists a strategy with the following properties: the proportion of its capital on the entire time horizon is separated from zero with probability 1 regardless of the strategies of competitors; the relative asset prices are asymptotically determined by it; the proportion of capital of investors who follow essentially different strategies tends to zero. We also show that investors who follow this strategy will accumulate capital faster than their competitorsunder several definitions of the speed of capital growth .
Revised:  The main results consist in obtaining a sufficient condition for a strategy to be survival and showing that all survival strategies are asymptotically close to each other. It is also proved that a survival strategy allows an investor to accumulate wealth in a certain sense faster than competitors .
Edit intent: clarity
Original: We provide an approach to utilize topological priors to reconstruct the surface of a point scan. In particular, we learn parameters for the basis functions that are used for surface reconstruction, satisfying predefined topological constraints.
Revised: We provide an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints.
Edit intent: clarity
Original:  These requirements are captured by persistence diagrams , and these are used to inform the optimization process that learns the parameters. We obtain parameters to build a likelihood function over the reconstruction domain. This novel topology-aware technique is useful to weed out topological noise from point scans, apart from capturing certain nuanced properties of the underlying shape , that could otherwise be lost while performing direct surface reconstruction.
Revised:  These requirements are captured by persistence diagrams which are incorporated in the optimization algorithm promote the correct topology. The result is a novel topology-aware technique is useful to weed out topological noise from point scans, apart from capturing certain nuanced properties of the underlying shape , that could otherwise be lost while performing direct surface reconstruction.
Edit intent: clarity
Original:  This novel topology-aware technique is useful to weed out topological noise from point scans, apart from capturing certain nuanced properties of the underlying shape , that could otherwise be lost while performing direct surface reconstruction.
Revised:  This novel topology-aware technique which can: 1.) weed out topological noise from point scans, apart from capturing certain nuanced properties of the underlying shape , that could otherwise be lost while performing direct surface reconstruction.
Edit intent: clarity
Original:  This novel topology-aware technique is useful to weed out topological noise from point scans, apart from capturing certain nuanced properties of the underlying shape , that could otherwise be lost while performing direct surface reconstruction.
Revised:  This novel topology-aware technique is useful to weed out topological noise from point scans, and 2.) capture certain nuanced properties of the underlying shape , that could otherwise be lost while performing direct surface reconstruction.
Edit intent: coherence
Original: Motivated by the financial problem of building financial portfolios which outperform the market,Pal and Wong considered optimal transport on the probability simplex \triangle^n where the cost function is induced by the free energy. We study the regularity of this problemand find that the associated MTW tensor is non-negative definite and in fact constant on \triangle^n \times \triangle^n. We further find^n equipped with probability measures \mu and \nu, respectively.
Revised: Let X and Y be domains of \mathbb{R^n equipped with probability measures \mu and \nu, respectively.
Edit intent: meaning-changed
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y }\to  of the form c(x,y)= \Psi(x-y) for some convex function \Psi.
Revised:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y }\to \mathbb{R of the form c(x,y)= \Psi(x-y) for some convex function \Psi.
Edit intent: meaning-changed
Original:  We also show } that relative c-convexity corresponds to the standard notion of convexity in the probability simplex. Hence, we are able to use standard results in optimal transport to establish regularity for the optimal transport maps considered by Pal and Wong. We also provide several new examples of costs satisfying the MTW(0) condition  .
Revised:  We also show } that relative c-convexity geometrically corresponds to geodesic convexity with respect to a dual affine connection. Taken together, these results provide a geometric framework for optimal transport which is complementary to the pseudo-Riemannian theory of Kim and McCann. We provide several applications of this work. In particular, we find a complete K\"ahler surface with non-negative orthogonal bisectional curvature that is not a Hermitian symmetric space or biholomorphic to \mathbb{C .
Edit intent: meaning-changed
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of optimal transport from \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: clarity
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of transporting \mu to \nu with respect to a cost function c: X \times Y \to R of the form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: clarity
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R . To ensure that the solution to this problem is smooth, it is necessary to make several assumptions about the structure of the domains and the cost function. In particular, Ma, Trudinger, and Wang established regularity estimates when the domains are strongly form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: meaning-changed
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of therelatively c-convex form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: meaning-changed
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the with respect to each other and cost function has non-negative form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: meaning-changed
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the MTW tensor form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: meaning-changed
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the  form c(x,y)= \Psi(x-y) for some convex function \Psi .
Revised:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the . For cost functions of the form c(x,y)= \Psi(x-y) for some convex function \Psi .
Edit intent: clarity
Original:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the  form c(x,y)= \Psi(x-y) for some convex function \Psi . For this problem , we find an associated K\"ahler manifold whose orthogonal holomorphic bisectional curvature is proportional to the so-called MTW tensor, which was introduced by Ma, Trudinger, and Wang and plays an essential role in the regularity theory of optimal transport .
Revised:  We consider the problem of transporting \mu to \nu in a way that minimizes a cost c: X \times Y \to R of the form c(x,y)= \Psi(x-y) for some convex function \Psi , we find an associated K\"ahler manifold whose orthogonal holomorphic bisectional curvature is proportional to the so-called MTW tensor, which was introduced by Ma, Trudinger, and Wang and plays an essential role in the regularity theory of optimal transport .
Edit intent: coherence
Original:  For this problem , we find an associated K\"ahler manifold whose orthogonal holomorphic bisectional curvature is proportional to the so-called MTW tensor, which was introduced by Ma, Trudinger, and Wang and plays an essential role in the regularity theory of optimal transport .
Revised:  For this problem , we find an associated K\"ahler manifold whose orthogonal holomorphic bisectional curvature is proportional to the MTW tensor .
Edit intent: coherence
Original: Distributed ledger technologies rely on consensus protocols confronting traders with random waiting times until the transfer of ownership is accomplished. This time-consuming settlement process exposes arbitrageurs to price risk and imposes limits to arbitrage.
Revised: Distributed ledger technologies rely on consensus protocols confronting traders with random waiting times until the transfer of ownership . This settlement latency exposes cross-market arbitrageurs to price risk and imposes limits to arbitrage.
Edit intent: clarity
Original:  This time-consuming settlement process exposes arbitrageurs to price risk and imposes limits to arbitrage. We derive theoretical arbitrage boundaries under general assumptions and show that they increase with expected latency, latency uncertainty, spot volatility , and risk aversion.
Revised:  This time-consuming settlement process exposes arbitrageurs to price risk . We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, spot volatility , and risk aversion.
Edit intent: clarity
Original:  Using high-frequency data from the Bitcoin network , we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, covering 88 percent of the observed cross-exchange price differences.
Revised:  Using high-frequency data from the Bitcoin network , we estimate arbitrage boundaries due to settlement latency of on average 121 basis points, covering 88 percent of the observed cross-exchange price differences.
Edit intent: meaning-changed
Original:  Using high-frequency data from the Bitcoin network , we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, covering 88 percent of the observed cross-exchange price differences.
Revised:  Using high-frequency data from the Bitcoin network , we estimate arbitrage boundaries due to settlement latency of on average 124 basis points, explaining 91\% of the observed cross-exchange price differences.
Edit intent: meaning-changed
Original:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate  arbitrage bounds of on average 121 basis points, explaining 91\% of the observed cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Revised:  We theoretically derive arbitrage bounds induced by settlement latency . Using Bitcoin orderbook and network data, we estimate arbitrage bounds of on average 121 basis points, explaining 91\% of the observed cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Edit intent: clarity
Original:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate  arbitrage bounds of on average 121 basis points, explaining 91\% of the observed cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Revised:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate average arbitrage bounds of on average 121 basis points, explaining 91\% of the observed cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Edit intent: fluency
Original:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate  arbitrage bounds of on average 121 basis points, explaining 91\% of the observed cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Revised:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate arbitrage bounds of 121 basis points, explaining 91\% of the observed cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Edit intent: clarity
Original:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate  arbitrage bounds of on average 121 basis points, explaining 91\% of the observed cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Revised:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate arbitrage bounds of on average 121 basis points, explaining 91\% of the cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Edit intent: clarity
Original:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate  arbitrage bounds of on average 121 basis points, explaining 91\% of the observed cross-market price differences . Consistent with our theory, periods of high latency-implied price risk exhibit large price differences, while asset flows chase arbitrage opportunities.
Revised:  We theoretically derive arbitrage bounds that increase with expected latency, latency uncertainty, volatility and risk aversion . Using Bitcoin orderbook and network data, we estimate arbitrage bounds of on average 121 basis points, explaining 91\% of the observed cross-market price differences , and demonstrate that asset flows chase arbitrage opportunities.
Edit intent: coherence
Original:  Benchmarking studies aim to rigorously compare the performance of different methods using well-characterized benchmark datasets, to determine the strengths of each method or to provide recommendations regarding the best choice of method for an analysis.
Revised:  Benchmarking studies aim to rigorously compare the performance of different methods using well-characterized benchmark datasets, to determine the strengths of each method or to provide recommendations regarding suitable choices of methods for an analysis.
Edit intent: clarity
Original:  The dynamic system and subsystem partitioning enable the determination of the distribution of environmental inputs and intercompartmental system flows  as well as URLanization of the associated storages generated by these inputs and flows individually and separately within the system.
Revised:  The dynamic system and subsystem partitioning enable tracking the evolution of the initial stocks, environmental inputs, and intercompartmental system flows as well as URLanization of the associated storages generated by these inputs and flows individually and separately within the system.
Edit intent: clarity
Original:  The dynamic system and subsystem partitioning enable the determination of the distribution of environmental inputs and intercompartmental system flows  as well as URLanization of the associated storages generated by these inputs and flows individually and separately within the system.
Revised:  The dynamic system and subsystem partitioning enable the determination of the distribution of environmental inputs and intercompartmental system flows , as well as URLanization of the associated storages generated by these inputs and flows individually and separately within the system.
Edit intent: fluency
Original:  The dynamic system and subsystem partitioning enable the determination of the distribution of environmental inputs and intercompartmental system flows  as well as URLanization of the associated storages generated by these inputs and flows individually and separately within the system.
Revised:  The dynamic system and subsystem partitioning enable the determination of the distribution of environmental inputs and intercompartmental system flows as well as the associated storages generated by these inputs and flows individually and separately within the system.
Edit intent: clarity
Original:  The dynamic system and subsystem partitioning enable the determination of the distribution of environmental inputs and intercompartmental system flows  as well as URLanization of the associated storages generated by these inputs and flows individually and separately within the system.
Revised:  The dynamic system and subsystem partitioning enable the determination of the distribution of environmental inputs and intercompartmental system flows as well as URLanization of the associated storages derived from these stocks, inputs, and flows individually and separately within the system.
Edit intent: clarity
Original:  Major flow- and stock-related concepts and quantities of the current static network analyses are also extended to nonlinear dynamic settings and integrated with the proposed dynamic measures and indices within the proposed unifying mathematical framework.
Revised:  Further, the article develops a dynamic technique based on the diact transactions for the quantitative classification of interspecific interactions and the determination of their strength within food webs. Major concepts and quantities of the current static network analyses are also extended to nonlinear dynamic settings and integrated with the proposed dynamic measures and indices within the proposed unifying mathematical framework.
Edit intent: meaning-changed
Original:  Furthermore, we establish constructions, again based on the stratified ancestral selection graph, that allow to trace back the ancestral lines into the distant past and obtain explicit results about the ancestral population in the case of unidirectional mutation.
Revised:  Furthermore, with the help of the stratified ancestral selection graph, that allow to trace back the ancestral lines into the distant past and obtain explicit results about the ancestral population in the case of unidirectional mutation.
Edit intent: clarity
Original:  Furthermore, we establish constructions, again based on the stratified ancestral selection graph, that allow to trace back the ancestral lines into the distant past and obtain explicit results about the ancestral population in the case of unidirectional mutation.
Revised:  Furthermore, we establish constructions, again based on the stratified ancestral selection graph, that allow to trace back the ancestral lines into the distant past and obtain explicit results about the ancestral type distribution in the case of unidirectional mutation.
Edit intent: clarity
Original: The research community has observed a massive success of convolutional neural networks ( CNN) in visual recognition tasks. Such powerful CNNs , however, do not generalize well to arbitrary-shaped mainfold domains. Thus, still many visual recognition problems  defined on arbitrary manifolds cannot benefit much from the success of CNNs, if at all .
Revised: The research community has observed a massive success of convolutional neural networks ( CNNs) have been shown to possess a promising capability of extracting and codifying features from visual information. However, the application of such capable CNNs has been quite limited to mostly computer vision problems where the visual information is inherently given on a grid-like structure. This, unfortunately, was not the case for the geometry processing community, where many visual recognition problems defined on arbitrary manifolds cannot benefit much from the success of CNNs, if at all .
Edit intent: meaning-changed
Original:  Technical difficulties hindering  generalization of CNNs  are rooted in the lack of a canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.
Revised:  Technical difficulties hindering generalization of CNNs to arbitrary-shaped manifold are rooted in the lack of a canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain.
Edit intent: meaning-changed
Original:  We also prove that a rotation of a convolution kernel equates to a  2 by 2 rotation matrix applied to Zernike polynomial coefficients, which can be critical in manifold domains.
Revised:  We also prove that a rotation of a convolution kernel equates to a set of 2 by 2 rotation matrix applied to Zernike polynomial coefficients, which can be critical in manifold domains.
Edit intent: clarity