wanyu/IteraTeR_v2 huggingface dataset:
Original:  We explore this connection for general H-colorings and prove that under a well-known condition in statistical physics, known as Dobrushin uniqueness condition, we can learn G in \mathrm{poly {\rm  (d,q)\times O(n^2n) time.
Revised:  We explore this connection for general H-colorings and prove that under a well-known condition in statistical physics, known as Dobrushin uniqueness condition, we can learn G in \mathrm{poly {\rm poly (d,q)\times O(n^2n) time.
Edit intent: fluency
Original: Quantum walks provide a powerful demonstration of the effectiveness of the renormalization group (RG), here applied to find a lower bound on the computational complexity of Grover's quantum search algorithms in low-dimensional networks.
Revised: We establish a lower bound concerning the computational complexity of Grover's quantum search algorithms in low-dimensional networks.
Edit intent: clarity
Original:  It can be characterized in terms of the quantum walk dimension d ^Q_w and the spatial (fractal) dimension d _f, even when translational invariance is broken .
Revised:  The latter is characterized in terms of the quantum walk dimension d ^Q_w and the spatial (fractal) dimension d _f, even when translational invariance is broken .
Edit intent: clarity
Original:  It can be characterized in terms of the quantum walk dimension d ^Q_w and the spatial (fractal) dimension d _f, even when translational invariance is broken .
Revised:  It can be characterized in terms of the quantum walk dimension d ^Q_w and the spatial (fractal) dimension d _{f .
Edit intent: clarity
Original:  The analysis simultaneously determines the optimal time for a quantum measurement and the probability for successfully pin-pointing the sought-after element in the network.
Revised:  The analysis simultaneously determines the optimal time for a quantum measurement and the probability for successfully pin-pointing a marked element in the network.
Edit intent: clarity
Original:  The RG further encompasses an optimization scheme , devised by Tulsi , that allows to tune that probability to certainty .
Revised:  The RG further encompasses an optimization scheme devised by Tulsi , that allows to tune that probability to certainty .
Edit intent: fluency
Original:  The RG further encompasses an optimization scheme , devised by Tulsi , that allows to tune that probability to certainty .
Revised:  The RG further encompasses an optimization scheme , devised by Tulsi that allows to tune that probability to certainty .
Edit intent: fluency
Original:  The RG further encompasses an optimization scheme , devised by Tulsi , that allows to tune that probability to certainty .
Revised:  The RG further encompasses an optimization scheme , devised by Tulsi , that allows to tune this probability to certainty .
Edit intent: fluency
Original:  Our RG considers entire families of problems to be studied, thereby establishing a large universality class for quantum search, here verified with extensive simulations  .
Revised:  Our RG considers entire families of problems to be studied, thereby establishing large universality classes for quantum search, here verified with extensive simulations .
Edit intent: fluency
Original:  Our RG considers entire families of problems to be studied, thereby establishing a large universality class for quantum search, here verified with extensive simulations  .
Revised:  Our RG considers entire families of problems to be studied, thereby establishing a large universality class for quantum search, which we verify with extensive simulations .
Edit intent: coherence
Original: The mathematical modelling of genetic-metabolic networks is of outmost importance in the field of systems biology.
Revised: The mathematical modelling of genetic-metabolic networks is of out most importance in the field of systems biology.
Edit intent: fluency
Original: With the ever increasing penetration of wearable devices into our daily lives, traditional communication networks that are mainly designed for human being oriented applications are facing tremendous challenges.
Revised: As wearable devices become more ingrained in our daily lives, traditional communication networks that are mainly designed for human being oriented applications are facing tremendous challenges.
Edit intent: clarity
Original: With the ever increasing penetration of wearable devices into our daily lives, traditional communication networks that are mainly designed for human being oriented applications are facing tremendous challenges.
Revised: With the ever increasing penetration of wearable devices into our daily lives, traditional communication networks primarily designed for human being oriented applications are facing tremendous challenges.
Edit intent: fluency
Original: With the ever increasing penetration of wearable devices into our daily lives, traditional communication networks that are mainly designed for human being oriented applications are facing tremendous challenges.
Revised: With the ever increasing penetration of wearable devices into our daily lives, traditional communication networks that are mainly designed for human being-oriented applications are facing tremendous challenges.
Edit intent: fluency
Original:  A cloud/edge communication architecture that integrates  cloud radio access network, software defined network, device to device communications, and cloud/edge technology is presentedin this article . Computation offloading enabled by this multi-layer communications architecture can offload computation excessive and latency stringent applications to nearby devices through device to device communications or to nearby edge nodes through cellular or other wireless technologies.
Revised:  A cloud/edge communication architecture that integrates the cloud radio access network, software defined network, device to device communications, and cloud/edge technology is presentedin this article . Computation offloading enabled by this multi-layer communications architecture can offload computation excessive and latency stringent applications to nearby devices through device to device communications or to nearby edge nodes through cellular or other wireless technologies.
Edit intent: fluency
Original:  A cloud/edge communication architecture that integrates  cloud radio access network, software defined network, device to device communications, and cloud/edge technology is presentedin this article . Computation offloading enabled by this multi-layer communications architecture can offload computation excessive and latency stringent applications to nearby devices through device to device communications or to nearby edge nodes through cellular or other wireless technologies.
Revised:  A cloud/edge communication architecture that integrates cloud radio access network, software defined network, device to device communications, and cloud/edge technologies is presented . Computation offloading enabled by this multi-layer communications architecture can offload computation excessive and latency stringent applications to nearby devices through device to device communications or to nearby edge nodes through cellular or other wireless technologies.
Edit intent: clarity
Original:  A cloud/edge communication architecture that integrates  cloud radio access network, software defined network, device to device communications, and cloud/edge technology is presentedin this article . Computation offloading enabled by this multi-layer communications architecture can offload computation excessive and latency stringent applications to nearby devices through device to device communications or to nearby edge nodes through cellular or other wireless technologies.
Revised:  A cloud/edge communication architecture that integrates cloud radio access network, software defined network, device to device communications, and cloud/edge technology is presentedin this article . Computation offloading enabled by this multi-layer communications architecture can offload computation-excessive and latency-stringent applications to nearby devices through device to device communications or to nearby edge nodes through cellular or other wireless technologies.
Edit intent: fluency
Original:  Critical issues faced by wearables communications such as short battery life, limited computing capability, and stringent latency can be greatly alleviated by this cloud/edge architecture.
Revised:  Critical issues faced by wearable communications such as short battery life, limited computing capability, and stringent latency can be greatly alleviated by this cloud/edge architecture.
Edit intent: fluency
Original:  Together with the presented architecture,  transmission and networking technologies such as non-orthogonal multiple access, mobile edge computing, and energy harvesting can further greatly enhance the performance of wearable communication in terms of spectral efficiency, energy efficiency, latency, and connectivity.
Revised:  Together with the presented architecture, current transmission and networking technologies such as non-orthogonal multiple access, mobile edge computing, and energy harvesting can further greatly enhance the performance of wearable communication in terms of spectral efficiency, energy efficiency, latency, and connectivity.
Edit intent: clarity
Original:  Together with the presented architecture,  transmission and networking technologies such as non-orthogonal multiple access, mobile edge computing, and energy harvesting can further greatly enhance the performance of wearable communication in terms of spectral efficiency, energy efficiency, latency, and connectivity.
Revised:  Together with the presented architecture, transmission and networking technologies , including non-orthogonal multiple access, mobile edge computing, and energy harvesting can further greatly enhance the performance of wearable communication in terms of spectral efficiency, energy efficiency, latency, and connectivity.
Edit intent: clarity
Original:  Together with the presented architecture,  transmission and networking technologies such as non-orthogonal multiple access, mobile edge computing, and energy harvesting can further greatly enhance the performance of wearable communication in terms of spectral efficiency, energy efficiency, latency, and connectivity.
Revised:  Together with the presented architecture, transmission and networking technologies such as non-orthogonal multiple access, mobile edge computing, and energy harvesting , can greatly enhance the performance of wearable communication in terms of spectral efficiency, energy efficiency, latency, and connectivity.
Edit intent: clarity
Original:  Our analysis illustrates how, at high dimension, the intuition promoted by a one-dimensional (scalar) notion of fitness becomes structurally incorrect . Specifically, while the low-dimensional picture emphasizes organism cost or efficiency, we exhibit a regime where cost becomes irrelevant for survival, and link this observation to generic properties of high-dimensional geometry.
Revised:  Our analysis illustrates how, at high dimension, the intuition promoted by a one-dimensional (scalar) notion of fitness can become misleading . Specifically, while the low-dimensional picture emphasizes organism cost or efficiency, we exhibit a regime where cost becomes irrelevant for survival, and link this observation to generic properties of high-dimensional geometry.
Edit intent: clarity
Original:  We also discuss the setting in which guards are open (i.e., they are segments without the endpoints), proving that the same results hold even in this more challenging case.
Revised:  We also consider the setting in which guards are open (i.e., they are segments without the endpoints), proving that the same results hold even in this more challenging case.
Edit intent: clarity
Original: Given a large population, it is an intensive task to gather individual preferences over a set of alternatives and arrive at an aggregate preference that reflects the collective preference of the population.
Revised: Given a large population, it is an intensive task to gather individual preferences over a set of alternatives and arrive at an aggregate or collective preference of the population.
Edit intent: clarity
Original:  Using a Facebook dataset that we created, we develop models that capture the spread of preferences among nodes in a typical social network.
Revised:  Using a Facebook dataset that we created, we develop models that capture how preferences are distributed among nodes in a typical social network.
Edit intent: clarity
Original:  We next propose an appropriate objective function for the problem of selecting best representative nodes , and observe that the greedy algorithm exhibits excellent performance.
Revised:  We hence propose an appropriate objective function for the problem of selecting best representative nodes , and observe that the greedy algorithm exhibits excellent performance.
Edit intent: coherence
Original:  Our analysis also suggests that selecting representatives using social network information is advantageous for aggregating preferences related to personal topics , while random polling with a reasonable sample size is good enough for aggregating preferences related to social topics  .
Revised:  Our analysis suggests that selecting representatives using social network information is advantageous for aggregating preferences related to personal topics , while random polling with a reasonable sample size is good enough for aggregating preferences related to social topics .
Edit intent: clarity
Original:  Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses , with implications for the design of wireless communication and control protocols  .
Revised:  Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses . Quantification of temporal correlations has implications for the design of wireless communication and control protocols .
Edit intent: clarity
Original: This article constructs a Turing Machine which can solve for \beta^{'} which is RE-complete.
Revised: This article describes a Turing machine which can solve for \beta^{'} which is RE-complete.
Edit intent: clarity
Original:  We show that the abstractions do not lose precision when the middlebox may reset in any state.
Revised:  We show that the abstractions do not lose precision when middleboxes may reset in any state.
Edit intent: fluency
Original:  At present, this process of identification is brute-force, requiring the manual generation and evaluation of a large number of histograms .
Revised:  At present, this process of identification is brute-force, requiring the manual generation and evaluation of a large number of histogram .
Edit intent: fluency
Original:  We present FastMatch: an end-to-end architecture for interactively retrieving the histogram visualizations that are most similar to a user-specified target, from a large collection of histograms.
Revised:  We present FastMatch: an end-to-end approach for interactively retrieving the histogram visualizations that are most similar to a user-specified target, from a large collection of histograms.
Edit intent: clarity
Original:  While HistSim can be used independently, within FastMatch we couple HistSim with a novel system architecture that is aware of practical considerations, employing  block-based sampling policies and asynchronous statistics and computation , building on lightweight sampling engines developed in recent work.
Revised:  While HistSim can be used independently, within FastMatch we couple HistSim with a novel system architecture that is aware of practical considerations, employing asynchronous block-based sampling policies and asynchronous statistics and computation , building on lightweight sampling engines developed in recent work.
Edit intent: fluency
Original:  While HistSim can be used independently, within FastMatch we couple HistSim with a novel system architecture that is aware of practical considerations, employing  block-based sampling policies and asynchronous statistics and computation , building on lightweight sampling engines developed in recent work.
Revised:  While HistSim can be used independently, within FastMatch we couple HistSim with a novel system architecture that is aware of practical considerations, employing block-based sampling policies , building on lightweight sampling engines developed in recent work.
Edit intent: clarity
Original: In exploratory data analysis, analysts often have a need to identify histograms that possess a specific distribution, among a large class of candidate histograms, e.g., find histograms of countries whose income distribution is most similar to that of Greece.
Revised: In exploratory data analysis, analysts often have a need to identify histograms that possess a specific distribution, among a large class of candidate histograms, e.g., find countries whose income distribution is most similar to that of Greece.
Edit intent: fluency
Original:  At present, this process of identification is brute-force, requiring the manual generation and evaluation of a large number of histogram .
Revised:  At present, this process of identification is brute-force, requiring the manual generation and evaluation of a large number of histograms .
Edit intent: fluency
Original:  We present FastMatch: an end-to-end approach for interactively retrieving the histogram visualizations that are most similar to a user-specified target, from a large collection of histograms.
Revised:  We present FastMatch: an end-to-end approach for interactively retrieving the histogram visualizations most similar to a user-specified target, from a large collection of histograms.
Edit intent: coherence
Original:  In our experiments on several real-world datasets, FastMatch obtains near-perfect accuracy with up to 20\times speedups over less sophisticated approaches .
Revised:  FastMatch obtains near-perfect accuracy with up to 20\times speedups over less sophisticated approaches .
Edit intent: clarity
Original: The problem of interest here is the study of brain functional and effective connectivity based  non-invasive EEG-MEG inverse solution time series.
Revised: The problem of interest here is the study of brain functional and effective connectivity based on non-invasive EEG-MEG inverse solution time series.
Edit intent: fluency
Original:  If q^h-1 has a prime divisor r with r=O((h\log q)^c), then there is a constant 0<\epsilon<1 such that for a ratio at least \frac 1 {q^{  \epsilon h}} of \alpha\in F_{q^{h}} \backslashF_{q}, the set S=\{ \alpha-x^t, x\inF_{q}\} of cardinality O(q^{\frac 12 +\delta_c contains a non-d-th power in F_{q^{\lfloor q^\delta\rfloor}}, where t is the largest power of r such that t<q/h . r^{\min\{v_r(q-1), \lfloorq/2-\log_r h\rfloor\}}.
Revised:  Let r be a prime divisor r with r=O((h\log q)^c), then there is a constant 0<\epsilon<1 such that for a ratio at least \frac 1 {q^{ \epsilon h}} of \alpha\in F_{q^{h}} \backslashF_{q}, the set S=\{ \alpha-x^t, x\inF_{q}\} of cardinality O(q^{\frac 12 +\delta_c contains a non-d-th power in F_{q^{\lfloor q^\delta\rfloor}}, where t is the largest power of r such that t<q/h . r^{\min\{v_r(q-1), \lfloorq/2-\log_r h\rfloor\}}.
Edit intent: clarity
Original:  If q^h-1 has a prime divisor r with r=O((h\log q)^c), then there is a constant 0<\epsilon<1 such that for a ratio at least \frac 1 {q^{  \epsilon h}} of \alpha\in F_{q^{h}} \backslashF_{q}, the set S=\{ \alpha-x^t, x\inF_{q}\} of cardinality O(q^{\frac 12 +\delta_c contains a non-d-th power in F_{q^{\lfloor q^\delta\rfloor}}, where t is the largest power of r such that t<q/h . r^{\min\{v_r(q-1), \lfloorq/2-\log_r h\rfloor\}}.
Revised:  If q^h-1 has a prime divisor r with r=O((h\log q)^c), then there is a constant 0<\epsilon<1 such that for a ratio at least {q^{ \epsilon h}} of \alpha\in F_{q^{h}} \backslashF_{q}, the set S=\{ \alpha-x^t, x\inF_{q}\} of cardinality O(q^{\frac 12 +\delta_c contains a non-d-th power in F_{q^{\lfloor q^\delta\rfloor}}, where t is the largest power of r such that t<q/h . r^{\min\{v_r(q-1), \lfloorq/2-\log_r h\rfloor\}}.
Edit intent: clarity
Original:  If q^h-1 has a prime divisor r with r=O((h\log q)^c), then there is a constant 0<\epsilon<1 such that for a ratio at least \frac 1 {q^{  \epsilon h}} of \alpha\in F_{q^{h}} \backslashF_{q}, the set S=\{ \alpha-x^t, x\inF_{q}\} of cardinality O(q^{\frac 12 +\delta_c contains a non-d-th power in F_{q^{\lfloor q^\delta\rfloor}}, where t is the largest power of r such that t<q/h . r^{\min\{v_r(q-1), \lfloorq/2-\log_r h\rfloor\}}.
Revised:  If q^h-1 has a prime divisor r with r=O((h\log q)^c), then there is a constant 0<\epsilon<1 such that for a ratio at least \frac 1 {q^{ \epsilon h}} of \alpha\in F_{q^{h}} \backslashF_{q}, the set S=\{ \alpha-x^t, x\inF_{q}\} of cardinality 1+\frac{q-1 contains a non-d-th power in F_{q^{\lfloor q^\delta\rfloor}}, where t is the largest power of r such that t<q/h . r^{\min\{v_r(q-1), \lfloorq/2-\log_r h\rfloor\}}.
Edit intent: clarity
Original:  Here r runs thourgh prime divisors and v_r(x) is the r-adic oder of x. } For odd q, the choice of \delta=\frac 12-d, d=o(1)>0 shows that there exists an explicit subset of cardinality q^{1-d}=O(\log^{2+\epsilon'}(q^h)) containing a non-quadratic element in  F_{q^h}.
Revised:  Here r runs thourgh prime divisors and v_r(x) is the r-adic oder of x. } For odd q, the choice of \delta=\frac 12-d, d=o(1)>0 shows that there exists an explicit subset of cardinality q^{1-d}=O(\log^{2+\epsilon'}(q^h)) containing a non-quadratic element in the field F_{q^h}.
Edit intent: clarity
Original:  On the other hand, the choice of h=2 shows that for any odd prime power q, there is an explicit subset of cardinality O(\sqrt{q containing a non-quadratic element in \mathbb{F}_{q^2} , essentially improving a O(q) construction by Coulter and Kosick \cite{CK} \lfloor }\rfloor .
Revised:  On the other hand, the choice of h=2 shows that for any odd prime power q, there is an explicit subset of cardinality O(\sqrt{q containing a non-quadratic element in \mathbb{F}_{q^2} , essentially improving a O(q) construction by Coulter and Kosick \cite{CK} since\lfloor }\rfloor .
Edit intent: fluency
Original: In this article , we derive the calculation of two critical numbers that quantify the capabilities of artificial neural networkswith gating functions, such as sign, sigmoid, or rectified linear units .
Revised: In this article , we derive the calculation of two critical numbers predicting the behavior of perceptron networks .
Edit intent: clarity
Original:  Our derivation of the capacity is embedded into a Shannoncommunication model, which allows measuring the capacities of neural networks in bits.
Revised:  Our derivations are performed by embedding the ideal network into Shannon's communication model which allows to interpret the two points as capacities measured in bits.
Edit intent: clarity
Original:  We then compare our theoretical derivations with experiments using different network configurations, diverse neural network implementations, varying activation functions, and several learning algorithms to confirm our upper bound.
Revised:  We validate our upper bounds with repeatable experiments using different network configurations, diverse neural network implementations, varying activation functions, and several learning algorithms to confirm our upper bound.
Edit intent: clarity
Original:  We then compare our theoretical derivations with experiments using different network configurations, diverse neural network implementations, varying activation functions, and several learning algorithms to confirm our upper bound.
Revised:  We then compare our theoretical derivations with experiments using different network configurations, diverse implementations, varying activation functions, and several learning algorithms to confirm our upper bound.
Edit intent: clarity
Original: By assuming an ideal neural network with gating functions handling the worst case data, we derive the calculation of two critical numbers predicting the behavior of perceptron networks.
Revised: We derive the calculation of two critical numbers predicting the behavior of perceptron networks.
Edit intent: clarity