wanyu/IteraTeR_v2 huggingface dataset:
Original: We introduce a family of  norms \| \cdot \|_{1,2,s} on R^n and define a distribution over random matrices \Phi_s \in R^{m \times n} parametrized by sparsity level s such that for a fixed set X of n points in R^n, we have for m \geq C s \log( n) that with high probability, 1{2} \| x \|_{1,2,s} \leq \| \Phi_s (x) \|_1 \leq 2 \| x\|_{1,2,s} for all x\in X. Several existing results in the literature reduce to special cases of this result at different values of s:
Revised: We introduce a family of norms \| \cdot \|_{1,2,s} on R^n and define a distribution over random matrices \Phi_s \in R^{m \times n} parametrized by sparsity level s such that for a fixed set X of n points in R^n, if m \geq C s \log( n) that with high probability, 1{2} \| x \|_{1,2,s} \leq \| \Phi_s (x) \|_1 \leq 2 \| x\|_{1,2,s} for all x\in X. Several existing results in the literature reduce to special cases of this result at different values of s:
Edit intent: clarity
Original: We introduce a family of  norms \| \cdot \|_{1,2,s} on R^n and define a distribution over random matrices \Phi_s \in R^{m \times n} parametrized by sparsity level s such that for a fixed set X of n points in R^n, we have for m \geq C s \log( n) that with high probability, 1{2} \| x \|_{1,2,s} \leq \| \Phi_s (x) \|_1 \leq 2 \| x\|_{1,2,s} for all x\in X. Several existing results in the literature reduce to special cases of this result at different values of s:
Revised: We introduce a family of norms \| \cdot \|_{1,2,s} on R^n and define a distribution over random matrices \Phi_s \in R^{m \times n} parametrized by sparsity level s such that for a fixed set X of n points in R^n, we have for m \geq C s \log( K) then with high probability, 1{2} \| x \|_{1,2,s} \leq \| \Phi_s (x) \|_1 \leq 2 \| x\|_{1,2,s} for all x\in X. Several existing results in the literature reduce to special cases of this result at different values of s:
Edit intent: clarity
Original: Although greedy layer-wise pre-training has achieved a lot of success in training deep neural networks, due to the locality of the method higher layer of the network may not learn representation that are useful for the original input.
Revised: Although greedy layer-wise pre-training has achieved a lot of success in deep neural networks, due to the locality of the method higher layer of the network may not learn representation that are useful for the original input.
Edit intent: clarity
Original: Although greedy layer-wise pre-training has achieved a lot of success in training deep neural networks, due to the locality of the method higher layer of the network may not learn representation that are useful for the original input.
Revised: Although greedy layer-wise pre-training has achieved a lot of success in training deep neural networks, due to the locality of the method , higher layers of the network may not learn representation that are useful for the original input.
Edit intent: fluency
Original: Although greedy layer-wise pre-training has achieved a lot of success in training deep neural networks, due to the locality of the method higher layer of the network may not learn representation that are useful for the original input.
Revised: Although greedy layer-wise pre-training has achieved a lot of success in training deep neural networks, due to the locality of the method higher layer of the network may not learn representations that are useful for the original input.
Edit intent: fluency
Original:  In this work, a simple joint method that tries to integrate multiple single layer training objective into one global objective is proposed.
Revised:  In this work, a simple joint method that tries to integrate multiple single layer training objectives into one global objective is proposed.
Edit intent: fluency
Original:  It not only mimics the layer-wise training scheme locally, but also adjust all the weights together based on the reconstruction loss from end-to-end.
Revised:  It not only mimics the layer-wise training scheme locally, but also adjusts all the weights together based on the reconstruction loss from end-to-end.
Edit intent: fluency
Original:  Preliminary results show that it extract more representative features  in the unsupervised setting, and also achieved comparable performance in the supervised setting as compared to the greedy layer-wise approach  .
Revised:  Results show that it extract more representative features in the unsupervised setting, and also achieved comparable performance in the supervised setting as compared to the greedy layer-wise approach .
Edit intent: clarity
Original:  Preliminary results show that it extract more representative features  in the unsupervised setting, and also achieved comparable performance in the supervised setting as compared to the greedy layer-wise approach  .
Revised:  Preliminary results show that it extracts more representative features in the unsupervised setting, and also achieved comparable performance in the supervised setting as compared to the greedy layer-wise approach .
Edit intent: fluency
Original:  Preliminary results show that it extract more representative features  in the unsupervised setting, and also achieved comparable performance in the supervised setting as compared to the greedy layer-wise approach  .
Revised:  Preliminary results show that it extract more representative features in the unsupervised setting, and also achieves comparable performance in the supervised setting as compared to the greedy layer-wise approach .
Edit intent: fluency
Original:  But due to the greedy scheme of the layerwise training technique, the parameters of the bottom layers are fixed after training .
Revised:  But due to the greedy scheme of the layerwise training technique, the parameters of lower layers are fixed after training .
Edit intent: fluency
Original:  We therefore propose a novel method for training deep autoencoders, where the architecture is viewed as one stack of two or more single-layer autoencoders.
Revised:  We therefore investigate joint training of deep autoencoders, where the architecture is viewed as one stack of two or more single-layer autoencoders.
Edit intent: clarity
Original:  A single global reconstruction objective is proposed and jointly optimized, such that the objective for the single autoencoders at each layer acts as a local, layer-level regularizer.
Revised:  A single global reconstruction objective is jointly optimized, such that the objective for the single autoencoders at each layer acts as a local, layer-level regularizer.
Edit intent: clarity
Original:  We here investigate and model the effect of revisits on popularity.
Revised:  We here investigate the effect of revisits on popularity.
Edit intent: clarity
Original:  (2) applicable, the model is effective for predicting future popularity values of time series .
Revised:  (2) applicable, the model is effective for predicting future popularity values of objects .
Edit intent: clarity
Original: Many of the classic problem of coding theory are highly symmetric, which makes it easy to derive sphere-packing upper bounds and sphere-covering lower bounds on the size of codes.
Revised: Many of the classic problems of coding theory are highly symmetric, which makes it easy to derive sphere-packing upper bounds and sphere-covering lower bounds on the size of codes.
Edit intent: fluency
Original: There is an increasing interest in executing rich and complex analysis tasks over large-scale graphs, many of which require processing and reasoning about a large number of multi-hop neighborhoods or subgraphs in the graph.
Revised: There is an increasing interest in executing complex analyses over large graphs, many of which require processing and reasoning about a large number of multi-hop neighborhoods or subgraphs in the graph.
Edit intent: clarity
Original: There is an increasing interest in executing rich and complex analysis tasks over large-scale graphs, many of which require processing and reasoning about a large number of multi-hop neighborhoods or subgraphs in the graph.
Revised: There is an increasing interest in executing rich and complex analysis tasks over large-scale graphs, many of which require processing a large number of multi-hop neighborhoods or subgraphs in the graph.
Edit intent: clarity
Original:  Examples of such tasks include ego network analysis, motif counting, finding social circles, personalized recommendations, analyzing influence cascades, etc .
Revised:  Examples of such tasks include ego network analysis, motif counting, personalized recommendations, analyzing influence cascades, etc .
Edit intent: clarity
Original:  Examples of such tasks include ego network analysis, motif counting, finding social circles, personalized recommendations, analyzing influence cascades, etc .
Revised:  Examples of such tasks include ego network analysis, motif counting, finding social circles, personalized recommendations, and others .
Edit intent: clarity
Original:  These tasks are not well served by the existing vertex-centric graph processing frameworks, whose computation, execution models limit the user program to directly access the state of a single vertex ;
Revised:  These tasks are not well served by existing vertex-centric graph processing frameworks, whose computation, execution models limit the user program to directly access the state of a single vertex ;
Edit intent: fluency
Original:  These tasks are not well served by the existing vertex-centric graph processing frameworks, whose computation, execution models limit the user program to directly access the state of a single vertex ;
Revised:  These tasks are not well served by the existing vertex-centric graph processing frameworks, where user programs are only able to directly access the state of a single vertex ;
Edit intent: clarity
Original:  It features GEL, a novel graph extraction and loading phase, that extracts the relevant portions of the graph and utilizes a cost-based optimizer to partition and load the graph onto distributed memory using as few machines as possible to minimize the communication cost.
Revised:  It features GEL, a novel graph extraction and packing (GEP) module that utilizes a cost-based optimizer to partition and load the graph onto distributed memory using as few machines as possible to minimize the communication cost.
Edit intent: clarity
Original:   Our experimental results show orders-of-magnitude improvements in performance , and drastic reductions in the cost of analytics , over vertex-centric approaches.
Revised:  Our experimental results show orders-of-magnitude improvements in performance and drastic reductions in the cost of analytics , over vertex-centric approaches.
Edit intent: fluency
Original:   Our experimental results show orders-of-magnitude improvements in performance , and drastic reductions in the cost of analytics , over vertex-centric approaches.
Revised:  Our experimental results show orders-of-magnitude improvements in performance , and drastic reductions in the cost of analytics compared to vertex-centric approaches.
Edit intent: clarity
Original: The paper comments on "Quantifying Long-term Scientific Impact ".
Revised: The paper comments on "Quantifying long-term scientific impact ".
Edit intent: fluency
Original:  It indicates that there is a mistake of [D. S. Wang , C. Song, A. L. Barabasi, Quantifying Long-term Scientific Impact , Science 342, 127 (2013), arXiv:1306.3293].
Revised:  It indicates that there is a mistake of [D. S. Wang , C. Song, A. L. Barabasi, Quantifying long-term scientific impact , Science 342, 127 (2013), arXiv:1306.3293].
Edit intent: fluency
Original: Phenotypic differences between species may be attributable to natural selection.
Revised: Trait differences between species may be attributable to natural selection.
Edit intent: clarity
Original:  However, it is a difficult task to quantify the strength of evidence for selection acting on a particular trait  .
Revised:  However, quantifying the strength of evidence for selection acting on a particular trait .
Edit intent: clarity
Original:  Here we develop a population-genetic test for selection acting on a quantitative trait , which is based on multiple-line crosses.
Revised:  Here we develop a population-genetic test for selection acting on a quantitative trait which is based on multiple-line crosses.
Edit intent: fluency
Original:  First, a test based on three or more lines detects selection on a quantitative trait with strongly increased statistical significance, which is quantified by our analysis .
Revised:  First, a test based on three or more lines detects selection with strongly increased statistical significance, which is quantified by our analysis .
Edit intent: clarity
Original:  Second, a multiple-line test allows to distinguish selection from neutral evolution as well as lineage-specific selection from selection under uniform selection strength.
Revised:  Second, a multiple-line test allows to distinguish different lineage-specific selection from selection under uniform selection strength.
Edit intent: clarity
Original:  We  apply the multiple-line test to QTL data on floral character traits in plant species of the Mimulus genus and on photoperiodic traits in different maize strains .
Revised:  We then apply the multiple-line test to QTL data on floral character traits in plant species of the Mimulus genus and on photoperiodic traits in different maize strains .
Edit intent: coherence
Original:  In both cases, we find a signature of lineage-specific selection that is not seen in a two-line test .
Revised:  In both cases, we find a signatures of lineage-specific selection that is not seen in a two-line test .
Edit intent: fluency
Original:  In both cases, we find a signature of lineage-specific selection that is not seen in a two-line test .
Revised:  In both cases, we find a signature of lineage-specific selection not seen in a two-line test .
Edit intent: clarity
Original:  The state-of-the-art in solving DCOPs relies on the use of ad-hoc infrastructures and ad-hoc constraint solving procedures.
Revised:  The state of the art in solving DCOPs relies on the use of ad-hoc infrastructures and ad-hoc constraint solving procedures.
Edit intent: fluency
Original:  The preliminary experiments show that logic programming provides benefits over a state-of-the-art DCOP system, in terms of performance and scalability, opening the doors to the use of more advanced technology (e.g., search strategies , complex constraints) for solving DCOPs.
Revised:  The preliminary experiments show that logic programming provides benefits over a state-of-the-art DCOP system, in terms of performance and scalability, opening the doors to the use of more advanced technology (e.g., search strategies and complex constraints) for solving DCOPs.
Edit intent: fluency
Original: We consider the spatial patterns provided by mean field numerical simulations for two competing species .
Revised: We consider systems with two competing species .
Edit intent: clarity
Original:  As all individuals have the same rate of mobility, reproduction and competition , interfaces of empty spaces separating domains of single species are formed by a spontaneous process of symmetry breaking.
Revised:  As all individuals have the same rate of mobility, reproduction and competition , interfaces of empty spaces separating domains of single species are formed by spontaneous symmetry breaking.
Edit intent: clarity
Original:  We construct a Lagrangian formalism for studying the static profile of such interfaces by means of a scalar field theory framework.
Revised:  We propose a theoretical formalism for describing the static profile of such interfaces by means of a scalar field theory framework.
Edit intent: clarity
Original: Device-to-Device (D2D ) communications underlaying cellular networks bring numerous benefits including the proximity gain, the reuse gain, and the hop gain, etc.
Revised: The introduction of device-to-device (D2D ) communications underlaying cellular networks bring numerous benefits including the proximity gain, the reuse gain, and the hop gain, etc.
Edit intent: clarity
Original:  However, the introduction of D2D into cellular networks poses many new challenges in the resource allocation design due to the co-channel interference caused by spectrum reuse and limited battery life of User Equipments (UEs).
Revised:  However, the introduction of D2D into cellular networks poses many new challenges in the resource allocation design due to the co-channel interference caused by spectrum reuse and limited battery life of user equipments (UEs).
Edit intent: fluency
Original:  Most of the previous studies mainly focus on how to maximize the Spectral Efficiency (SE) and ignore the energy consumption of UEs.
Edit intent: coherence
Original:  In this paper, we propose a distributed interference-aware energy-efficient resource allocation algorithm to maximize each UE's Energy Efficiency (EE) subject to its specific Quality of Service (QoS) and maximum transmission power constraints.
Revised:  In this paper, we propose a distributed interference-aware energy-efficient resource allocation algorithm to maximize each UE's energy efficiency (EE) subject to its specific Quality of Service (QoS) and maximum transmission power constraints.
Edit intent: fluency
Original:  In this paper, we propose a distributed interference-aware energy-efficient resource allocation algorithm to maximize each UE's Energy Efficiency (EE) subject to its specific Quality of Service (QoS) and maximum transmission power constraints.
Revised:  In this paper, we propose a distributed interference-aware energy-efficient resource allocation algorithm to maximize each UE's Energy Efficiency (EE) subject to its specific quality of service (QoS) and maximum transmission power constraints.
Edit intent: fluency
Original:  In this paper, we model and analyze cognitive and energy harvesting-based device-to-device ( D2D ) communication in cellular networks .
Revised:  In this paper, we model and analyze cognitive and energy harvesting-based D2D ) communication in cellular networks .
Edit intent: clarity
Original:  We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid and best ask prices , both modelled by arbitrary functions of incoming market and limit orders .
Revised:  We take the exchange to be an order-driven market and propose a continuous-time setup for the best bid and best ask prices , both modelled by functions of the market activity .
Edit intent: clarity
Original:  In the situation where the trades take place only in the exchange, we find that the optimal execution strategy depends significantly on the resilience of the limit order book.
Revised:  In the situation where the trades take place only in the exchange, we find that the optimal execution strategy depends significantly on the dynamics of the limit order book.
Edit intent: clarity
Original:  We allow for partial trade executions in the dark pool, and we find the optimal order-size placement in both venues.
Revised:  We allow for partial trade executions in the dark pool, and we find the optimal trading strategy in both venues.
Edit intent: clarity
Original:  Since the mid-price is taken from the exchange, the resilience of the limit order book also affects the optimal allocation of shares in the dark pool.
Revised:  Since the mid-price is taken from the exchange, the dynamics of the limit order book also affects the optimal allocation of shares in the dark pool.
Edit intent: clarity
Original:  We propose a general objective function and we show that, subject to suitable technical conditions, the value function can be characterised by the unique continuous viscosity solution to the associated system of partial integro differential equations .
Revised:  We propose a general objective function and we show that, subject to suitable technical conditions, the value function can be characterised by the unique continuous viscosity solution to the associated partial integro differential equations .
Edit intent: clarity
Original:  We propose a general objective function and we show that, subject to suitable technical conditions, the value function can be characterised by the unique continuous viscosity solution to the associated system of partial integro differential equations .
Revised:  We propose a general objective function and we show that, subject to suitable technical conditions, the value function can be characterised by the unique continuous viscosity solution to the associated system of partial integro differential equation .
Edit intent: fluency
Original: We consider an optimal execution problem over a finite period of time during which an investor has access to both a standard exchange and a dark pool.
Revised: We consider an optimal trading problem over a finite period of time during which an investor has access to both a standard exchange and a dark pool.
Edit intent: clarity
Original:  In a former paper URL  we proved that CAA's wave-based attack is unphysical.
Revised:  In a former paper URL , we proved that CAA's wave-based attack is unphysical.
Edit intent: fluency
Original: Recently  Gunn, Allison and Abbott (GAA) 1 proposed a new scheme to utilize electromagnetic waves for eavesdropping on the Kirchhoff-law-Johnson-noise (KLJN) secure key distribution.
Revised: Recently , Gunn, Allison and Abbott (GAA) 1 proposed a new scheme to utilize electromagnetic waves for eavesdropping on the Kirchhoff-law-Johnson-noise (KLJN) secure key distribution.
Edit intent: fluency
Original:  In a former paper 2 , we proved that the wave claims in the GAA's attack are heavily unphysical, since the quasi-static limit holds for the KLJN scheme, implying that physical waves do not exist in the wire channel.
Revised:  We proved in a former paper 2 , we proved that the wave claims in the GAA's attack are heavily unphysical, since the quasi-static limit holds for the KLJN scheme, implying that physical waves do not exist in the wire channel.
Edit intent: fluency
Original:  In a former paper 2 , we proved that the wave claims in the GAA's attack are heavily unphysical, since the quasi-static limit holds for the KLJN scheme, implying that physical waves do not exist in the wire channel.
Revised:  In a former paper , we proved that the wave claims in the GAA's attack are heavily unphysical, since the quasi-static limit holds for the KLJN scheme, implying that physical waves do not exist in the wire channel.
Edit intent: coherence
Original:  In a former paper 2 , we proved that the wave claims in the GAA's attack are heavily unphysical, since the quasi-static limit holds for the KLJN scheme, implying that physical waves do not exist in the wire channel.
Revised:  In a former paper 2 URL that GAA's attack are heavily unphysical, since the quasi-static limit holds for the KLJN scheme, implying that physical waves do not exist in the wire channel.
Edit intent: clarity
Original:  Here we analyze GAA's cracking scheme and show that in the cable loss free case it serves less eavesdropping information than the old mean-square based attack , while in the loss-dominated case ] it offers no information  .
Revised:  Here we analyze GAA's cracking scheme and show that , in the case of a loss-free cable, it provides less eavesdropping information than the old mean-square based attack , while in the loss-dominated case ] it offers no information .
Edit intent: clarity
Original:  Here we analyze GAA's cracking scheme and show that in the cable loss free case it serves less eavesdropping information than the old mean-square based attack , while in the loss-dominated case ] it offers no information  .
Revised:  Here we analyze GAA's cracking scheme and show that in the cable loss free case it serves less eavesdropping information than in the loss-dominated case ] it offers no information .
Edit intent: clarity