wanyu/IteraTeR_v2 huggingface dataset:
Original:  The core contribution is to propose a probabilistic forecast-driven strategy, modeled as a min-max-min robust optimization problem with recourse , and solved using a Benders-dual cutting plane algorithm  in a tractable manner.
Revised:  The core contribution is to propose a probabilistic forecast-driven strategy, modeled as a min-max-min robust optimization problem with recourse . It is solved using a Benders-dual cutting plane algorithm in a tractable manner.
Edit intent: coherence
Original:  As a direct consequence, we get a general lower bound FC_{w}(4)\geq4(4^{n}-1) where 2n is the period of the sequence w.
Revised:  As a direct consequence, we obtain a general lower bound FC_{w}(4)\geq4(4^{n}-1) where 2n is the period of the sequence w.
Edit intent: fluency
Original:  By taking a and b to be several types of known binary sequences with ideal autocorrelation (m-sequences, twin-prime, Legendre, Hall sequences and their complement, shift or sample sequences), we compute the exact values of FC_{w}(4), w=w(a, b) . The results show that in most cases FC_{w}(4) reaches or nearly reaches the maximum value 4(4^{2n}-1)  .
Revised:  By taking a and b to be several types of known binary sequences with ideal autocorrelation (m-sequences, twin-prime, Legendre, Hall sequences and their complement, shift or sample sequences), we compute the exact values of FC_{w}(4), w=w(a, b) and show that in most cases FC_{w}(4) reaches or nearly reaches the maximum value 4(4^{2n}-1) .
Edit intent: coherence
Original: Let a set of nodes \mathcal X in the plain be n-independent, i.e., each node has a fundamental polynomial of degree n. Assume that \#\mathcal X=d(n,k)+3= (n+1)+n+\cdots+(n-k+5)+3 and 4 \le k\le n-1.
Revised: Let a set of nodes \mathcal X in the plane be n-independent, i.e., each node has a fundamental polynomial of degree n. Assume that \#\mathcal X=d(n,k)+3= (n+1)+n+\cdots+(n-k+5)+3 and 4 \le k\le n-1.
Edit intent: clarity
Original: Asset pricing crucially depends on an averaging time interval {\Delta} of the market trade time-series .
Revised: We consider the time interval {\Delta} of the market trade time-series .
Edit intent: clarity
Original: Asset pricing crucially depends on an averaging time interval {\Delta} of the market trade time-series .
Revised: Asset pricing crucially depends on an averaging time interval {\Delta} during which the market trade time-series .
Edit intent: clarity
Original:  The choice of {\Delta} changes the basic pricing equation and determines Taylor series of investor's utility functions over current and future values of consumption.
Revised:  The choice of {\Delta} determines Taylor series of investor's utility functions over current and future values of consumption.
Edit intent: clarity
Original:  The choice of {\Delta} changes the basic pricing equation and determines Taylor series of investor's utility functions over current and future values of consumption.
Revised:  The choice of {\Delta} changes the basic pricing equation and determines Taylor series of investor's utility over current and future values of consumption.
Edit intent: clarity
Original:  We present  current and future values of random consumption as sums of the mean values during the interval {\Delta} and perturbations determined by random variations of the price at current moment t and  the payoff at day t+1.
Revised:  We present consumption at current and future values of random consumption as sums of the mean values during the interval {\Delta} and perturbations determined by random variations of the price at current moment t and the payoff at day t+1.
Edit intent: clarity
Original:  We present  current and future values of random consumption as sums of the mean values during the interval {\Delta} and perturbations determined by random variations of the price at current moment t and  the payoff at day t+1.
Revised:  We present current and future moments as sums of the mean values during the interval {\Delta} and perturbations determined by random variations of the price at current moment t and the payoff at day t+1.
Edit intent: clarity
Original:  We present  current and future values of random consumption as sums of the mean values during the interval {\Delta} and perturbations determined by random variations of the price at current moment t and  the payoff at day t+1.
Revised:  We present current and future values of random consumption as sums of their mean values and perturbations during {\Delta} and perturbations determined by random variations of the price at current moment t and the payoff at day t+1.
Edit intent: clarity
Original:  We present  current and future values of random consumption as sums of the mean values during the interval {\Delta} and perturbations determined by random variations of the price at current moment t and  the payoff at day t+1.
Revised:  We present current and future values of random consumption as sums of the mean values during the interval {\Delta} of the price at current moment t and the payoff at day t+1.
Edit intent: clarity
Original:  We present  current and future values of random consumption as sums of the mean values during the interval {\Delta} and perturbations determined by random variations of the price at current moment t and  the payoff at day t+1.
Revised:  We present current and future values of random consumption as sums of the mean values during the interval {\Delta} and perturbations determined by random variations of the price at current moment t and perturbations of the payoff at day t+1.
Edit intent: clarity
Original:  Linear and quadratic Taylor series ' approximations of the basic pricing equation describe mean price, mean payoff, their volatilities, skewness and the amount of asset {\xi}_{max} that delivers max to investor's utility.
Revised:  For linear and quadratic Taylor series ' approximations of the basic pricing equation describe mean price, mean payoff, their volatilities, skewness and the amount of asset {\xi}_{max} that delivers max to investor's utility.
Edit intent: fluency
Original:  Linear and quadratic Taylor series ' approximations of the basic pricing equation describe mean price, mean payoff, their volatilities, skewness and the amount of asset {\xi}_{max} that delivers max to investor's utility.
Revised:  Linear and quadratic Taylor series approximations of the basic pricing equation describe mean price, mean payoff, their volatilities, skewness and the amount of asset {\xi}_{max} that delivers max to investor's utility.
Edit intent: fluency
Original:  Linear and quadratic Taylor series ' approximations of the basic pricing equation describe mean price, mean payoff, their volatilities, skewness and the amount of asset {\xi}_{max} that delivers max to investor's utility.
Revised:  Linear and quadratic Taylor series ' approximations of the basic equation we obtain new relations on mean price, mean payoff, their volatilities, skewness and the amount of asset {\xi}_{max} that delivers max to investor's utility.
Edit intent: clarity
Original:  Linear and quadratic Taylor series ' approximations of the basic pricing equation describe mean price, mean payoff, their volatilities, skewness and the amount of asset {\xi}_{max} that delivers max to investor's utility.
Revised:  Linear and quadratic Taylor series ' approximations of the basic pricing equation describe mean price, mean payoff, their volatilities, skewness and amount of asset {\xi}_{max} that delivers max to investor's utility.
Edit intent: fluency
Original:  We believe that the stochasticity of the market trade time-series must define the random properties of the  } price and introduce the new price probability measure entirely determined by the probability measures of trading value and volume.
Revised:  The stochasticity of market trade time-series must define the random properties of the } price and introduce the new price probability measure entirely determined by the probability measures of trading value and volume.
Edit intent: coherence
Original:  We believe that the stochasticity of the market trade time-series must define the random properties of the  } price and introduce the new price probability measure entirely determined by the probability measures of trading value and volume.
Revised:  We believe that the stochasticity of the market trade time-series defines random properties of the } price and introduce the new price probability measure entirely determined by the probability measures of trading value and volume.
Edit intent: clarity
Original:  We believe that the stochasticity of the market trade time-series must define the random properties of the  } price and introduce the new price probability measure entirely determined by the probability measures of trading value and volume.
Revised:  We believe that the stochasticity of the market trade time-series must define the random properties of the } price probability measure entirely determined by the probability measures of trading value and volume.
Edit intent: coherence
Original:  We believe that the stochasticity of the market trade time-series must define the random properties of the  } price and introduce the new price probability measure entirely determined by the probability measures of trading value and volume.
Revised:  We believe that the stochasticity of the market trade time-series must define the random properties of the } price and introduce the new price probability measure entirely determined by the probability measures of the market trade value and volume.
Edit intent: fluency
Original: We propose differentiable artificial reverberation (DAR), a family of artificial reverberation ( AR) models implemented in a deep learning framework.
Revised: Artificial reverberation ( AR) models implemented in a deep learning framework.
Edit intent: coherence
Original:  Combined with the modern deep neural networks (DNNs) , the differentiable structure of DAR allows training loss gradients to be back-propagated in an end-to-end manner.
Revised:  Combined with the modern deep neural networks (DNNs) , the differentiable structure of DAR allows training loss gradients to be back-propagated end-to-end manner.
Edit intent: fluency
Original:  Most of the AR models bottleneck training speed when implemented "as is" in the time domain and executed with a parallel processor like GPU due to their infinite impulse response (IIR) filter components.
Revised:  Most of the AR models bottleneck training speed when implemented "as is" in the time domain and executed with a parallel processor like GPU due to their infinite impulse response (IIR) components.
Edit intent: clarity
Original:  In benchmarks against state-of-the-art methods on multiple public datasets, our frame-work outperforms other optimization methods and achieves competitive accuracy against regression methods. 
Revised:  In benchmarks against state-of-the-art methods on multiple public datasets, our framework outperforms other optimization methods and achieves competitive accuracy against regression methods. 
Edit intent: clarity
Original: Nature has found one method of organizing living matter, but maybe there are also other options -- not yet discovered -- on how to create life.
Revised: Nature has found one method of organizing living matter, but maybe other options exist -- not yet discovered -- on how to create life.
Edit intent: clarity
Original:  To study the life  as it could be  is the objective of an interdisciplinary field called Artificial Life (commonly abbreviated as ALife).
Revised:  To study the life " as it could be is the objective of an interdisciplinary field called Artificial Life (commonly abbreviated as ALife).
Edit intent: fluency
Original:  To study the life  as it could be  is the objective of an interdisciplinary field called Artificial Life (commonly abbreviated as ALife).
Revised:  To study the life as it could be " is the objective of an interdisciplinary field called Artificial Life (commonly abbreviated as ALife).
Edit intent: fluency
Original:  The results might be completely unlike natural forms of life, not only because of their chemical composition, but even some computer programs exhibiting life-like behaviours interest ALife researchers .
Revised:  The artificial life forms might be completely unlike natural forms of life, not only because of their chemical composition, but even some computer programs exhibiting life-like behaviours interest ALife researchers .
Edit intent: clarity
Original:  The results might be completely unlike natural forms of life, not only because of their chemical composition, but even some computer programs exhibiting life-like behaviours interest ALife researchers .
Revised:  The results might be completely unlike natural forms of life, with different chemical compositions, and even computer programs exhibiting life-like behaviours interest ALife researchers .
Edit intent: clarity
Original:  The results might be completely unlike natural forms of life, not only because of their chemical composition, but even some computer programs exhibiting life-like behaviours interest ALife researchers .
Revised:  The results might be completely unlike natural forms of life, not only because of their chemical composition, but even some computer programs exhibiting life-like behaviours .
Edit intent: clarity
Original: We present deterministic O(\log^2 \log n) time sublinear Massively Parallel Computation (MPC) algorithms for 3-coloring, maximal independent set and maximal matching in trees with n nodes.
Revised: We present O(\log^2 \log n) time sublinear Massively Parallel Computation (MPC) algorithms for 3-coloring, maximal independent set and maximal matching in trees with n nodes.
Edit intent: clarity
Original: We present deterministic O(\log^2 \log n) time sublinear Massively Parallel Computation (MPC) algorithms for 3-coloring, maximal independent set and maximal matching in trees with n nodes.
Revised: We present deterministic O(\log^2 \log n) time 3-coloring, maximal independent set and maximal matching in trees with n nodes.
Edit intent: clarity
Original:  The key ingredient of our 3-coloring algorithm is an O(\log^2 \log n) time MPC implementation of a variant of the rake-and-compress tree decomposition used by Chang and Pettie [FOCS'17], which is closely related to the H-partition by Barenboim and Elkin PODC'08 . When restricting  to trees of constant maximum degree, we bring the runtime down to O(\log \log n).
Revised:  The key ingredient of our 3-coloring algorithm is an O(\log^2 \log n) time adaptation of the rake-and-compress tree decomposition used by Chang and Pettie [FOCS'17], which is closely related to the H-partition by Barenboim and Elkin PODC'08 . When restricting to trees of constant maximum degree, we bring the runtime down to O(\log \log n).
Edit intent: clarity
Original:  The key ingredient of our 3-coloring algorithm is an O(\log^2 \log n) time MPC implementation of a variant of the rake-and-compress tree decomposition used by Chang and Pettie [FOCS'17], which is closely related to the H-partition by Barenboim and Elkin PODC'08 . When restricting  to trees of constant maximum degree, we bring the runtime down to O(\log \log n).
Revised:  The key ingredient of our 3-coloring algorithm is an O(\log^2 \log n) time MPC implementation of a variant of the rake-and-compress tree decomposition used by Chang and Pettie [FOCS'17], PODC'08 . When restricting to trees of constant maximum degree, we bring the runtime down to O(\log \log n).
Edit intent: coherence
Original:  The key ingredient of our 3-coloring algorithm is an O(\log^2 \log n) time MPC implementation of a variant of the rake-and-compress tree decomposition used by Chang and Pettie [FOCS'17], which is closely related to the H-partition by Barenboim and Elkin PODC'08 . When restricting  to trees of constant maximum degree, we bring the runtime down to O(\log \log n).
Revised:  The key ingredient of our 3-coloring algorithm is an O(\log^2 \log n) time MPC implementation of a variant of the rake-and-compress tree decomposition used by Chang and Pettie [FOCS'17], which is closely related to the H-partition by Barenboim and Elkin PODC'08 . When restricting our attention to trees of constant maximum degree, we bring the runtime down to O(\log \log n).
Edit intent: clarity
Original:  HTM stores memories by dividing the past into chunks, and recalls by first performing high-level attention over coarse summaries of the chunks, and then performing detailed attention within only the most relevant chunks.
Revised:  HCAM stores memories by dividing the past into chunks, and recalls by first performing high-level attention over coarse summaries of the chunks, and then performing detailed attention within only the most relevant chunks.
Edit intent: clarity
Original:  Agents with HTM can extrapolate to task sequences an order of magnitude longer than they were trained on, and can even generalize zero-shot from a meta-learning setting to maintaining knowledge across episodes.
Revised:  Agents with HTM can extrapolate to task sequences much longer than they were trained on, and can even generalize zero-shot from a meta-learning setting to maintaining knowledge across episodes.
Edit intent: clarity
Original:  HTM improves agent sample efficiency, generalization, and generality (by solving tasks that previously required specialized architectures).
Revised:  HCAM improves agent sample efficiency, generalization, and generality (by solving tasks that previously required specialized architectures).
Edit intent: clarity
Original: Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, \omega \dagger%DIFDELCMD < }%%% H and S. All of these gates have matrix entries in the ring \mathbb Z[ \frac{1 ,i], the smallest subring of the complex numbers containing \frac{1 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in \mathbb Z[ \frac{1 ,i] can be realized by a quantum circuit over the above gate set using at most one ancilla.
Revised: Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, \dagger%DIFDELCMD < }%%% H and S. All of these gates have matrix entries in the ring \mathbb Z[ \frac{1 ,i], the smallest subring of the complex numbers containing \frac{1 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in \mathbb Z[ \frac{1 ,i] can be realized by a quantum circuit over the above gate set using at most one ancilla.
Edit intent: clarity
Original: Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, \omega \dagger%DIFDELCMD < }%%% H and S. All of these gates have matrix entries in the ring \mathbb Z[ \frac{1 ,i], the smallest subring of the complex numbers containing \frac{1 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in \mathbb Z[ \frac{1 ,i] can be realized by a quantum circuit over the above gate set using at most one ancilla.
Revised: Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, \omega %DIFDELCMD < }%%% H and S. All of these gates have matrix entries in the ring \mathbb Z[ \frac{1 ,i], the smallest subring of the complex numbers containing \frac{1 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in \mathbb Z[ \frac{1 ,i] can be realized by a quantum circuit over the above gate set using at most one ancilla.
Edit intent: clarity
Original: Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, \omega \dagger%DIFDELCMD < }%%% H and S. All of these gates have matrix entries in the ring \mathbb Z[ \frac{1 ,i], the smallest subring of the complex numbers containing \frac{1 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in \mathbb Z[ \frac{1 ,i] can be realized by a quantum circuit over the above gate set using at most one ancilla.
Revised: Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, \omega \dagger%DIFDELCMD < }%%% H and S. All of these gates have matrix entries in the ring Z[ \frac{1 ,i], the smallest subring of the complex numbers containing \frac{1 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in \mathbb Z[ \frac{1 ,i] can be realized by a quantum circuit over the above gate set using at most one ancilla.
Edit intent: fluency
Original: Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, \omega \dagger%DIFDELCMD < }%%% H and S. All of these gates have matrix entries in the ring \mathbb Z[ \frac{1 ,i], the smallest subring of the complex numbers containing \frac{1 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in \mathbb Z[ \frac{1 ,i] can be realized by a quantum circuit over the above gate set using at most one ancilla.
Revised: Consider the universal gate set for quantum computing consisting of the gates X, CX, CCX, \omega \dagger%DIFDELCMD < }%%% H and S. All of these gates have matrix entries in the ring \mathbb Z[ \frac{1 ,i], the smallest subring of the complex numbers containing \frac{1 and i. Amy, Glaudell, and Ross proved the converse, i.e., any unitary matrix with entries in Z[ \frac{1 ,i] can be realized by a quantum circuit over the above gate set using at most one ancilla.
Edit intent: fluency
Original:  In this paper, we give a finite presentation by generators and relations of U_n( \mathbb Z[ \frac{1 ,i]), the group of unitary n\times n-matrices with entries in \mathbb Z[ \frac{1 ,i].
Revised:  In this paper, we give a finite presentation by generators and relations of U_n( Z[ \frac{1 ,i]), the group of unitary n\times n-matrices with entries in \mathbb Z[ \frac{1 ,i].
Edit intent: fluency
Original:  In this paper, we give a finite presentation by generators and relations of U_n( \mathbb Z[ \frac{1 ,i]), the group of unitary n\times n-matrices with entries in \mathbb Z[ \frac{1 ,i].
Revised:  In this paper, we give a finite presentation by generators and relations of U_n( \mathbb Z[ \frac{1 ,i]), the group of unitary n\times n-matrices with entries in Z[ \frac{1 ,i].
Edit intent: fluency
Original: Despite recent, independent progress in model-based reinforcement learning and integrated symbolic-geometric robotic planning , synthesizing these techniques remains challenging because of their disparate assumptions and strengths .
Revised: In robotic domains, learning and planning are complicated by continuous state spaces, continuous action spaces, and long task horizons .
Edit intent: clarity
Original:  In this work, we take a step toward bridging this gap with Neuro-Symbolic Relational Transition Models (NSRTs), a novel class of transition models that are data-efficient to learn, compatible with powerful robotic planning methods, and generalizable over objects.
Revised:  In this work, we address these challenges with Neuro-Symbolic Relational Transition Models (NSRTs), a novel class of transition models that are data-efficient to learn, compatible with powerful robotic planning methods, and generalizable over objects.
Edit intent: clarity
Original:  In this work, we take a step toward bridging this gap with Neuro-Symbolic Relational Transition Models (NSRTs), a novel class of transition models that are data-efficient to learn, compatible with powerful robotic planning methods, and generalizable over objects.
Revised:  In this work, we take a step toward bridging this gap with Neuro-Symbolic Relational Transition Models (NSRTs), a novel class of models that are data-efficient to learn, compatible with powerful robotic planning methods, and generalizable over objects.
Edit intent: fluency
Original:  Experiments in four robotic planning domains show that NSRTs can be learned after only tens or hundreds of training episodes, and then used for fast planning in new tasks that require up to 60 actions to reach the goal and involve many more objects than were seen during training.
Revised:  Experiments in four robotic planning domains show that NSRTs can be learned after only tens or hundreds of training episodes, and then used for fast planning in new tasks that require up to 60 actions and involve many more objects than were seen during training.
Edit intent: clarity