wanyu/IteraTeR_v2 huggingface dataset:
Original: As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering.
Revised: As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, reinforcement learning techniques may be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering.
Edit intent: clarity
Original: As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering.
Revised: As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering.
Edit intent: clarity
Original: As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering.
Revised: As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Efficiency may be dramatically improved by guiding light transport paths by an approximate solution to the integral equation that is learned during rendering.
Edit intent: clarity
Original: As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution to the integral equation that is learned during rendering.
Revised: As both light transport simulation and reinforcement learning are ruled by the same Fredholm integral equation of the second kind, machine learning techniques can be used for efficient photorealistic image synthesis: Light transport paths are guided by an approximate solution of the integral equation that is learned during rendering.
Edit intent: fluency
Original:  In analogy to recent advances in reinforcement learning for playing games, we investigate the training of neural networks to represent this approximate solution in the context of Monte Carlo and quasi-Monte Carlo methods in order to compute functionals of integral equations .
Revised:  In the light of the recent advances in reinforcement learning for playing games, we investigate the training of neural networks to represent this approximate solution in the context of Monte Carlo and quasi-Monte Carlo methods in order to compute functionals of integral equations .
Edit intent: clarity
Original:  European Journal of Combinatorics, 66, 160--167, 2017 . Furthermore, we show that an open conjecture of Neumann-Lara holds for all planar graphs on at most 26 vertices  .
Revised:  European Journal of Combinatorics, 66, 160--167, 2017 and show that the conjecture of Neumann-Lara holds for all planar graphs on at most 26 vertices .
Edit intent: clarity
Original:  In this paper, we present a quantum algorithm to decide whether a Boolean equation system F has a solution and compute one if F does have solutions with any given success probability.
Revised:  In this paper, we present a quantum algorithm to decide whether a Boolean equation system FS has a solution and compute one if F does have solutions with any given success probability.
Edit intent: fluency
Original:  In this paper, we present a quantum algorithm to decide whether a Boolean equation system F has a solution and compute one if F does have solutions with any given success probability.
Revised:  In this paper, we present a quantum algorithm to decide whether a Boolean equation system F has a solution and compute one if FS does have solutions with any given success probability.
Edit intent: fluency
Original:  The  complexity of the algorithm is polynomial in the size of F and the condition number of F . As a consequence, we have achieved exponential speedup for solving sparse Boolean equation systems if their condition numbers are small  .
Revised:  The complexity of the algorithm is polynomial in the size of F and the condition number of FS . As a consequence, we have achieved exponential speedup for solving sparse Boolean equation systems if their condition numbers are small .
Edit intent: clarity
Original:  The  complexity of the algorithm is polynomial in the size of F and the condition number of F . As a consequence, we have achieved exponential speedup for solving sparse Boolean equation systems if their condition numbers are small  .
Revised:  The complexity of the algorithm is polynomial in the size of F and the condition number of F . As a consequence, we have achieved exponential speedup for solving sparse Boolean equation systems if their condition numbers are small , say polynomial in the size of FS .
Edit intent: clarity
Original:  We apply the quantum algorithm to the cryptanalysis of  the stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, and the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the condition numbers of the corresponding equation systems are large  .
Revised:  We apply the quantum algorithm to the cryptanalysis of several important cryptosystems: the stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, and the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the condition numbers of the corresponding equation systems are large .
Edit intent: clarity
Original:  We apply the quantum algorithm to the cryptanalysis of  the stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, and the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the condition numbers of the corresponding equation systems are large  .
Revised:  We apply the quantum algorithm to the cryptanalysis of the stream cipher Trivum, the block cipher AES, the hash function SHA-3/Keccak, and the multivariate public key cryptosystems, and show that they are secure under quantum algebraic attack only if the condition numbers of the corresponding equation systems are large . This leads to a new criterion for designing cryptosystems that can against the attack of quantum computers: their corresponding equation systems must have large condition numbers .
Edit intent: coherence
Original: Inductive inductive k-independent graphs are a generalization of chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling.
Revised: Inductive k-independent graphs are a generalization of chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling.
Edit intent: clarity
Original:  We investigate the parameterized complexity of this problem on inductive inductive k-independent graphs.
Revised:  We investigate the parameterized complexity of this problem on inductive k-independent graphs.
Edit intent: fluency
Original:  Aside from this, we survey other graph classes between inductive inductive 1-independent and inductive inductive 2-independent graphs with applications in scheduling.
Revised:  Aside from this, we survey other graph classes between inductive 1-independent and inductive inductive 2-independent graphs with applications in scheduling.
Edit intent: fluency
Original:  Aside from this, we survey other graph classes between inductive inductive 1-independent and inductive inductive 2-independent graphs with applications in scheduling.
Revised:  Aside from this, we survey other graph classes between inductive inductive 1-independent and inductive 2-independent graphs with applications in scheduling.
Edit intent: fluency
Original: Inductive k-independent graphs are a generalization of chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling.
Revised: Inductive k-independent graphs generalize chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling.
Edit intent: coherence
Original:  On the contrary , we prove that the more general Maximum c-Colorable Subgraph problem is fixed-parameter tractable on edge-wise unions of cluster and chordal graphs, which are 2-simplicial.
Revised:  In contrast , we prove that the more general Maximum c-Colorable Subgraph problem is fixed-parameter tractable on edge-wise unions of cluster and chordal graphs, which are 2-simplicial.
Edit intent: coherence
Original:  Aside from this, we survey other graph classes between inductive 1-independent and inductive 2-independent graphs with applications in scheduling.
Revised:  Aside from this, we survey other graph classes between inductive 1-inductive and inductive 2-inductive graphs with applications in scheduling.
Edit intent: fluency
Original:  To this end, we design new network architectures that can be trained using the AVC task for these functionalities: for cross-modal retrieval , and for localizing the source of a sound in an image  .
Revised:  To this end, we design new network architectures that can be trained for cross-modal retrieval , and for localizing the source of a sound in an image .
Edit intent: clarity
Original:  To this end, we design new network architectures that can be trained using the AVC task for these functionalities: for cross-modal retrieval , and for localizing the source of a sound in an image  .
Revised:  To this end, we design new network architectures that can be trained using the AVC task for these functionalities: for cross-modal retrieval and localizing the sound source in an image .
Edit intent: coherence
Original:  To this end, we design new network architectures that can be trained using the AVC task for these functionalities: for cross-modal retrieval , and for localizing the source of a sound in an image  .
Revised:  To this end, we design new network architectures that can be trained using the AVC task for these functionalities: for cross-modal retrieval , and for localizing the source of a sound in an image , by using the AVC task .
Edit intent: coherence
Original:  We make the following contributions: (i) show that audio and visual embedding can be learnt that enable both within-mode (e.g. audio-to-audio) and between-mode retrieval;
Revised:  We make the following contributions: (i) show that audio and visual embeddings can be learnt that enable both within-mode (e.g. audio-to-audio) and between-mode retrieval;
Edit intent: fluency
Original:  and (iv) give a cautionary tale in how to avoid undesirable shortcuts in the data preparation.
Revised:  and (iv) give a cautionary tale on how to avoid undesirable shortcuts in the data preparation.
Edit intent: fluency
Original:  [{\it Israel J. Math.} {\bf 193} (2013), 359--398], using tools from additive combinatorics and group theory, proved necessary and sufficient conditions under which the linear congruence a_1x_1+\cdots +a_kx_k\equiv b n, where a_1,\ldots,a_k,b,n (n\geq 1) are arbitrary integers, has a solution \langle x_1,\ldots,x_k \rangle \in n^k with all x_i distinct modulo n . So, it would be an interesting problem to give an explicit formula for the number of such solutions.
Revised:  [{\it Israel J. Math.} {\bf 193} (2013), 359--398], using tools from additive combinatorics and group theory, proved necessary and sufficient conditions under which the linear congruence a_1x_1+\cdots +a_kx_k\equiv b n, where a_1,\ldots,a_k,b,n (n\geq 1) are arbitrary integers, has a solution \langle x_1,\ldots,x_k \rangle \in n^k with all x_i distinct . So, it would be an interesting problem to give an explicit formula for the number of such solutions.
Edit intent: clarity
Original:  Math.} {\bf 1839} (1839), 231--243] proved an explicit formula for the number of such solutions when b=0, n=p a prime, and i=1^k a_i \equiv 0 p but i \in I a_i \not\equiv 0 p for all \not I\varsubsetneq \lbrace 1, \ldots, k\rbrace.
Revised:  Math.} {\bf 1839} (1839), 231--243] proved an explicit formula for the number of such solutions when b=0, n=p a prime, and i=1^k a_i \equiv 0 p but i \in I a_i \not\equiv 0 p for all \not= I\varsubsetneq \lbrace 1, \ldots, k\rbrace.
Edit intent: clarity
Original:  In this paper, we generalize Sch\"{o}nemann's theorem using a result on the number of solutions of linear congruences due to D. N. Lehmer and also a result on graph enumeration recently obtained by Ardila et al.
Revised:  In this paper, we generalize Sch\"{o}nemann's theorem using a result on the number of solutions of linear congruences due to D. N. Lehmer and also a result on graph enumeration 
Edit intent: coherence
Original:  Math. Res. Not.%DIFDELCMD < } {\bf %%% 2015 (2015), 3830--3877 .
Revised:  Math. Res. Not.%DIFDELCMD < } {\bf %%% (2015), 3830--3877 .
Edit intent: fluency
Original:  Math. Res. Not.%DIFDELCMD < } {\bf %%% 2015 (2015), 3830--3877 .
Revised:  Math. Res. Not.%DIFDELCMD < } {\bf %%% 2015 .
Edit intent: clarity
Original:  We have developed a new deep neural network tailored to estimating the binding affinity of ligand-receptor complexes.
Revised:  We have developed a novel deep neural network tailored to estimating the binding affinity of ligand-receptor complexes.
Edit intent: clarity
Original:  We have developed a new deep neural network tailored to estimating the binding affinity of ligand-receptor complexes.
Revised:  We have developed a new deep neural network estimating the binding affinity of ligand-receptor complexes.
Edit intent: clarity
Original:  Our network was tested on the CASF "scoring power" benchmark and Astex diverse set and outperformed classical scoring functions.
Revised:  Our network was tested on the CASF "scoring power" benchmark and Astex Diverse Set and outperformed classical scoring functions.
Edit intent: fluency
Original:  This is in part due to their nonlinear dynamics  and a strong dependence on the circuit topology.
Revised:  This is in part due to their nonlinear dynamics , and a strong dependence on the circuit topology.
Edit intent: fluency
Original:  We show that a Lyapunov function, polynomial in the internal memory parameters , exists for the case of DC controlled memristors.
Revised:  In the present paper we show that a Lyapunov function, polynomial in the internal memory parameters , exists for the case of DC controlled memristors.
Edit intent: coherence
Original:  We show that a Lyapunov function, polynomial in the internal memory parameters , exists for the case of DC controlled memristors.
Revised:  We show that a polynomial Lyapunov function in the memory parameters exists for the case of DC controlled memristors.
Edit intent: clarity
Original:  This  shows a direct parallel between memristive circuits and the Hopfield-Little model.
Revised:  This also shows a direct parallel between memristive circuits and the Hopfield-Little model.
Edit intent: clarity
Original:  In the case of Erdos-Renyi random circuits, we provide numerical evidence that the distribution of the matrix elements of the couplings can be roughly approximated by a Gaussian distribution, and that they scale with the inverse square root of the number of elements.
Revised:  In the case of Erdos-Renyi random circuits, we show numerically that the distribution of the matrix elements of the couplings can be roughly approximated by a Gaussian distribution, and that they scale with the inverse square root of the number of elements.
Edit intent: clarity
Original:  In the case of Erdos-Renyi random circuits, we provide numerical evidence that the distribution of the matrix elements of the couplings can be roughly approximated by a Gaussian distribution, and that they scale with the inverse square root of the number of elements.
Revised:  In the case of Erdos-Renyi random circuits, we provide numerical evidence that the distribution of the matrix elements of the projectors can be roughly approximated by a Gaussian distribution, and that they scale with the inverse square root of the number of elements.
Edit intent: clarity
Original:  In the case of Erdos-Renyi random circuits, we provide numerical evidence that the distribution of the matrix elements of the couplings can be roughly approximated by a Gaussian distribution, and that they scale with the inverse square root of the number of elements.
Revised:  In the case of Erdos-Renyi random circuits, we provide numerical evidence that the distribution of the matrix elements of the couplings can be roughly approximated with a Gaussian distribution, and that they scale with the inverse square root of the number of elements.
Edit intent: fluency
Original:  In the case of Erdos-Renyi random circuits, we provide numerical evidence that the distribution of the matrix elements of the couplings can be roughly approximated by a Gaussian distribution, and that they scale with the inverse square root of the number of elements.
Revised:  In the case of Erdos-Renyi random circuits, we provide numerical evidence that the distribution of the matrix elements of the couplings can be roughly approximated by a Gaussian distribution, and that it scales with the inverse square root of the number of elements.
Edit intent: clarity
Original:  This provides an approximated but direct connection to the physics of disordered system and, in particular, of mean field spin glasses.
Revised:  This provides an approximated but direct connection with the physics of disordered system and, in particular, of mean field spin glasses.
Edit intent: fluency
Original:  Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit , we estimate the number of stationary points of the Lyapunov function, and provide a scaling formula as an upper bound in terms of the circuit topology only .
Revised:  Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit . We estimate the number of stationary points of the Lyapunov function, and provide a scaling formula as an upper bound in terms of the circuit topology only .
Edit intent: fluency
Original:  Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit , we estimate the number of stationary points of the Lyapunov function, and provide a scaling formula as an upper bound in terms of the circuit topology only .
Revised:  Using this and the fact that the interaction is controlled by a projector operator on the loop space of the circuit , we estimate the number of stationary points of the approximate Lyapunov function and provide a scaling formula as an upper bound in terms of the circuit topology only .
Edit intent: clarity
Original:  However, perfect storage of all experiences is not possible .
Revised:  However, perfect storage of all experiences is not feasible .
Edit intent: coherence
Original:  A limitation of this approach is that  although events in the buffer are represented with perfect accuracy, the resources necessary to represent information at a particular time scale go up rapidly.
Revised:  A limitation of this approach is that , although events in the buffer are represented with perfect accuracy, the resources necessary to represent information at a particular time scale go up rapidly.
Edit intent: fluency
Original:  This representation covers an exponentially large period of time in the past at the cost of sacrificing temporal accuracy for events further in the past.
Revised:  This representation covers an exponentially large period of time at the cost of sacrificing temporal accuracy for events further in the past.
Edit intent: fluency
Original:  The form of this decay is scale-invariant and can be shown to be optimal  in that it is able to respond to worlds with a wide range of  time scales.
Revised:  The form of this decay is scale-invariant and can be shown to be optimal , in that it is able to respond to worlds with a wide range of time scales.
Edit intent: fluency
Original:  Whereas the buffer performs well as long as the temporal dependencies can be represented within the buffer, SITH performs well over a much larger range of time scales for the same amount of resources.
Revised:  Whereas the buffer performs well as long as the temporal dependencies can be represented within the buffer, SITH performs well over a much larger range of time scales with the same amount of resources.
Edit intent: clarity
Original:  One possibility, utilized in many applications,  is to retain information about the past in a buffer.
Revised:  One approach utilized in many applications, is to retain information about the past in a buffer.
Edit intent: clarity
Original:  Here we present a neurally-plausible, compressed, scale-free memory representation we call Scale-Invariant Temporal History (SITH)  . This representation covers an exponentially large period of time at the cost of sacrificing temporal accuracy for events further in the past.
Revised:  Here we introduce a neurally-plausible, compressed, scale-free memory representation we call Scale-Invariant Temporal History (SITH) . This representation covers an exponentially large period of time at the cost of sacrificing temporal accuracy for events further in the past.
Edit intent: clarity
Original:  Here we present a neurally-plausible, compressed, scale-free memory representation we call Scale-Invariant Temporal History (SITH)  . This representation covers an exponentially large period of time at the cost of sacrificing temporal accuracy for events further in the past.
Revised:  Here we present a neurally-plausible, scale-free memory representation we call Scale-Invariant Temporal History (SITH) . This representation covers an exponentially large period of time at the cost of sacrificing temporal accuracy for events further in the past.
Edit intent: clarity
Original:  Here we present a neurally-plausible, compressed, scale-free memory representation we call Scale-Invariant Temporal History (SITH)  . This representation covers an exponentially large period of time at the cost of sacrificing temporal accuracy for events further in the past.
Revised:  Here we present a neurally-plausible, compressed, scale-free memory representation we call Scale-Invariant Temporal History (SITH) . This representation covers an exponentially large period of time by sacrificing temporal accuracy for events further in the past.
Edit intent: clarity
Original:  The form of this decay is scale-invariant and can be shown to be optimal, in that it is able to respond to worlds with a wide range of relevant time scales.
Edit intent: coherence
Original: We consider the problem of approximating the output of a parametric electromagnetic field model in the presence of a large number of uncertain input parameters.
Revised: We consider the problem of quantifying uncertainty regarding the output of a parametric electromagnetic field model in the presence of a large number of uncertain input parameters.
Edit intent: clarity
Original: We consider the problem of approximating the output of a parametric electromagnetic field model in the presence of a large number of uncertain input parameters.
Revised: We consider the problem of approximating the output of an electromagnetic field problem in the presence of a large number of uncertain input parameters.
Edit intent: clarity