wanyu/IteraTeR_v2 huggingface dataset:
Original:  for any k \geq 2, it is possible to detect efficiently communities whenever SNR>1 (the KS bound ), whereas for k\geq 5, it is possible to detect communities information-theoretically for some \mathrm{SNR<1. Massouli\'e, Mossel et al.\ and Bordenave et al.\ succeeded in proving that the KS bound is efficiently achievable for k=2, while Mossel et al.\ proved that the KS bound cannot be crossed information-theoretically for k=2.
Revised:  for any k \geq 2, it is possible to detect efficiently communities whenever SNR>1 (the KS threshold ), whereas for k\geq 5, it is possible to detect communities information-theoretically for some \mathrm{SNR<1. Massouli\'e, Mossel et al.\ and Bordenave et al.\ succeeded in proving that the KS bound is efficiently achievable for k=2, while Mossel et al.\ proved that the KS bound cannot be crossed information-theoretically for k=2.
Edit intent: clarity
Original:  Specifically, an acyclic belief propagation (ABP) algorithm is developed and proved to detect communities for any k whenever \mathrm{SNR}>1, i.e., } <1.
Revised:  Specifically, an acyclic belief propagation (ABP) algorithm is developed and proved to detect communities for any k whenever \mathrm{SNR}>1, i.e., } \mathrm{SNR<1.
Edit intent: coherence
Original:  For the efficient part, an acyclic belief propagation (ABP) algorithm is developed and proved to detect communities for any k } down the KS bound, with a complexity of O(n \log n).
Revised:  For the efficient part, an acyclic belief propagation (ABP) algorithm is developed and proved to detect communities for any k } down the KS threshold in time O(n \log n).
Edit intent: clarity
Original:  Further , a non-efficient algorithm sampling a typical clustering is shown to break down the KS bound at k=5.
Revised:  Further , a non-efficient algorithm sampling a typical clustering is shown to break down the KS threshold at k=5.
Edit intent: clarity
Original:  The gap between the KS bound and the information-theoretic bound is shown to be large in some cases;
Revised:  The emerging gap is shown to be large in some cases;
Edit intent: clarity
Original:  if a=0, the KS bound reads b \gtrsim k^2 whereas the information-theoretic bound reads b \gtrsim k \ln(k)  . The results extend to general SBMs.
Revised:  if a=0, the KS threshold reads b \gtrsim k^2 whereas the information-theoretic bound reads b \gtrsim k \ln(k) . The results extend to general SBMs.
Edit intent: clarity
Original:  if a=0, the KS bound reads b \gtrsim k^2 whereas the information-theoretic bound reads b \gtrsim k \ln(k)  . The results extend to general SBMs.
Revised:  if a=0, the KS bound reads b \gtrsim k^2 whereas the IT bound reads b \gtrsim k \ln(k) . The results extend to general SBMs.
Edit intent: clarity
Original: In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed up Mossel et al., made a fascinating conjecture: Denote by k the number of balanced communities, a/n the probability of connecting inside communities and b/n across, and set SNR= | a-b | / \sqrt{k(a+(k-1)b) ;
Revised: In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed by Mossel et al., made a fascinating conjecture: Denote by k the number of balanced communities, a/n the probability of connecting inside communities and b/n across, and set SNR= | a-b | / \sqrt{k(a+(k-1)b) ;
Edit intent: fluency
Original: In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed up Mossel et al., made a fascinating conjecture: Denote by k the number of balanced communities, a/n the probability of connecting inside communities and b/n across, and set SNR= | a-b | / \sqrt{k(a+(k-1)b) ;
Revised: In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed up Mossel et al., made a fascinating conjecture: Denote by k the number of balanced communities, a/n the probability of connecting inside communities and b/n across, and set SNR= ( a-b | / \sqrt{k(a+(k-1)b) ;
Edit intent: fluency
Original:  For the efficient part, an acyclic belief propagation (ABP) algorithm is developed and proved to detect communities for any k down  the KS threshold in time O(n \log n).
Revised:  For the efficient part, an acyclic belief propagation (ABP) algorithm is developed and proved to detect communities for any k down to the KS threshold in time O(n \log n).
Edit intent: fluency
Original:  Achieving this requires showing optimality of BP in the presence of cycles and random initialization , a challenge in the realm of graphical models.
Revised:  Achieving this requires showing optimality of BP in the presence of cycles , a challenge in the realm of graphical models.
Edit intent: clarity
Original:  The paper also connects ABP to a power iteration method on a r-nonbacktracking operator , formalizing the  message passing and spectral interplay.
Revised:  The paper further connects ABP to a power iteration method on a r-nonbacktracking operator , formalizing the message passing and spectral interplay.
Edit intent: clarity
Original:  The paper also connects ABP to a power iteration method on a r-nonbacktracking operator , formalizing the  message passing and spectral interplay.
Revised:  The paper also connects ABP to a power iteration method on a r-nonbacktracking operator , formalizing the interplay between message passing and spectral interplay.
Edit intent: clarity
Original: In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed by Mossel et al., made a fascinating conjecture: Denote by k the number of balanced communities, a/n the probability of connecting inside communities and b/n across, and set SNR=(a-b)^2/(k(a+(k-1)b);
Revised: In a paper that initiated the modern study of the stochastic block model, Decelle et al., backed by Mossel et al., made the following conjecture: Denote by k the number of balanced communities, a/n the probability of connecting inside communities and b/n across, and set SNR=(a-b)^2/(k(a+(k-1)b);
Edit intent: clarity
Original:  This paper proves this conjecture, and further extends the efficient detection to non-symmetrical SBMs with a generalized notion of detection and KS threshold.
Revised:  This paper proves this conjecture, further extending the efficient detection to non-symmetrical SBMs with a generalized notion of detection and KS threshold.
Edit intent: coherence
Original:  Achieving this requires showing optimality of ABP in the presence of cycles, a challenge in the realm of graphical models .
Revised:  Achieving this requires showing optimality of ABP in the presence of cycles, a challenge for message passing algorithms .
Edit intent: clarity
Original:  Interestingly, oscillation amplitude may be volitionally controlled with the aid of an electroencephalogram (EEG) brain-computer interface, utilizing a closed neurofeedback  loop.
Revised:  Oscillation amplitude may be volitionally controlled with the aid of an electroencephalogram (EEG) brain-computer interface, utilizing a closed neurofeedback loop.
Edit intent: coherence
Original:  However, despite emerging clinical applications, the nature of neurofeedback 's impact on brain function remains controversial and poorly understood.
Revised:  However, despite emerging clinical applications, the nature of NFB 's impact on brain function remains controversial and poorly understood.
Edit intent: clarity
Original:  By uncovering a substantially independent mechanism of action, our findings offer a novel framework for motivating research and clinical applications of neurofeedback , encompassing brain disorders with perturbed LRTCs
Revised:  By uncovering a novel mechanism of action, our findings offer a novel framework for motivating research and clinical applications of neurofeedback , encompassing brain disorders with perturbed LRTCs
Edit intent: clarity
Original:  By uncovering a substantially independent mechanism of action, our findings offer a novel framework for motivating research and clinical applications of neurofeedback , encompassing brain disorders with perturbed LRTCs
Revised:  By uncovering a substantially independent mechanism of action, our findings offer a novel framework for motivating research and clinical applications of neurofeedback .
Edit intent: clarity
Original: The amplitude dynamics of neuronal oscillations , namely their scale-free, long-range temporal correlations (LRTCs), are considered supporting evidence for criticality in the brain , a balanced state between order and disorder theoretically optimal for information processing.
Revised: Brain oscillations exhibit long-range temporal correlations (LRTCs), are considered supporting evidence for criticality in the brain , a balanced state between order and disorder theoretically optimal for information processing.
Edit intent: clarity
Original:  Interestingly, neurofeedback rescued LRTCs in regions that were abnormally low in value (i.e., increased randomness) compared to a healthy control sample . Lastly, we identified an inverse-U relationship between strength of LRTC and alpha amplitude, suggesting a gradual breakdown of long-range dependence at high/low synchronization extremes, in line with computational work.
Revised:  Notably, regions manifesting abnormally low LRTCs (i.e., increased randomness) compared to a healthy control sample . Lastly, we identified an inverse-U relationship between strength of LRTC and alpha amplitude, suggesting a gradual breakdown of long-range dependence at high/low synchronization extremes, in line with computational work.
Edit intent: clarity
Original:  Interestingly, neurofeedback rescued LRTCs in regions that were abnormally low in value (i.e., increased randomness) compared to a healthy control sample . Lastly, we identified an inverse-U relationship between strength of LRTC and alpha amplitude, suggesting a gradual breakdown of long-range dependence at high/low synchronization extremes, in line with computational work.
Revised:  Interestingly, neurofeedback rescued LRTCs in regions that were abnormally low in value (i.e., increased randomness) compared to a healthy control sample . Lastly, we observed an inverse-U relationship between strength of LRTC and alpha amplitude, suggesting a gradual breakdown of long-range dependence at high/low synchronization extremes, in line with computational work.
Edit intent: clarity
Original:  Interestingly, neurofeedback rescued LRTCs in regions that were abnormally low in value (i.e., increased randomness) compared to a healthy control sample . Lastly, we identified an inverse-U relationship between strength of LRTC and alpha amplitude, suggesting a gradual breakdown of long-range dependence at high/low synchronization extremes, in line with computational work.
Revised:  Interestingly, neurofeedback rescued LRTCs in regions that were abnormally low in value (i.e., increased randomness) compared to a healthy control sample . Lastly, we identified an inverse-U relationship between strength of LRTC and oscillation amplitude, suggesting a gradual breakdown of long-range dependence at high/low synchronization extremes, in line with computational work.
Edit intent: clarity
Original:  Interestingly, neurofeedback rescued LRTCs in regions that were abnormally low in value (i.e., increased randomness) compared to a healthy control sample . Lastly, we identified an inverse-U relationship between strength of LRTC and alpha amplitude, suggesting a gradual breakdown of long-range dependence at high/low synchronization extremes, in line with computational work.
Revised:  Interestingly, neurofeedback rescued LRTCs in regions that were abnormally low in value (i.e., increased randomness) compared to a healthy control sample . Lastly, we identified an inverse-U relationship between strength of LRTC and alpha amplitude, suggesting a breakdown of long-range dependence at high/low synchronization extremes, in line with computational work.
Edit intent: clarity
Original:  By uncovering a novel mechanism of action , our findings offer a broader framework for framework for motivating research and clinical applications of neurofeedback .
Revised:  By uncovering a novel mechanism of action , our findings offer a broader mechanistic framework for motivating research and clinical applications of neurofeedback .
Edit intent: clarity
Original:  However, epidemic spread across multiple hosts has been little studied in a network context .
Revised:  However, little is known regarding the spread of epidemics across networks representing populations of multiple hosts .
Edit intent: clarity
Original:  We explored cross-species transmission in a multilayer network in which layers represent populations of two distinct hosts, and in which a disease can spread across intralayer (within-host) and interlayer (between-host) edges.
Revised:  We explored cross-species transmission in a multilayer network where layers represent populations of two distinct hosts, and in which a disease can spread across intralayer (within-host) and interlayer (between-host) edges.
Edit intent: fluency
Original:  We explored cross-species transmission in a multilayer network in which layers represent populations of two distinct hosts, and in which a disease can spread across intralayer (within-host) and interlayer (between-host) edges.
Revised:  We explored cross-species transmission in a multilayer network in which layers represent populations of two distinct hosts, and disease can spread across intralayer (within-host) and interlayer (between-host) edges.
Edit intent: coherence
Original:  Using an agent-based SIR simulation model , we examined the effect of (i) source of infection and (ii) between-host asymmetry in infection probabilities on epidemic size (proportion of individuals infected) and probability (probability to infect at least 10\% of individuals) in a focal host  represented by one network layer.
Revised:  We developed an analytic framework for the SIR epidemic model to examine the effect of (i) source of infection and (ii) between-host asymmetry in infection probabilities on epidemic size (proportion of individuals infected) and probability (probability to infect at least 10\% of individuals) in a focal host represented by one network layer.
Edit intent: clarity
Original:  Using an agent-based SIR simulation model , we examined the effect of (i) source of infection and (ii) between-host asymmetry in infection probabilities on epidemic size (proportion of individuals infected) and probability (probability to infect at least 10\% of individuals) in a focal host  represented by one network layer.
Revised:  Using an agent-based SIR simulation model , we examined the effect of (i) source of infection and (ii) between-host asymmetry in infection probabilities , on disease risk. We measured risk as outbreak probability and outbreak size in a focal host represented by one network layer.
Edit intent: clarity
Original:  Using an agent-based SIR simulation model , we examined the effect of (i) source of infection and (ii) between-host asymmetry in infection probabilities on epidemic size (proportion of individuals infected) and probability (probability to infect at least 10\% of individuals) in a focal host  represented by one network layer.
Revised:  Using an agent-based SIR simulation model , we examined the effect of (i) source of infection and (ii) between-host asymmetry in infection probabilities on epidemic size (proportion of individuals infected) and probability (probability to infect at least 10\% of individuals) in a focal host , represented by one network layer.
Edit intent: fluency
Original: We shall discuss the use of Discontinuous Galerkin (DG) Finite Element Methods to solve Boltzmann - Poisson (BP) models of electron transport in semiconductor devices at nano scales .
Revised: We shall discuss the use of Discontinuous Galerkin (DG) Finite Element Methods to solve Boltzmann - Poisson (BP) models of electron transport in semiconductor device modelling at nano scales .
Edit intent: clarity
Original:  We study the specular, diffusive and mixed reflection BC on physical boundaries of the device for  the modeling of surface roughness, comparing the influence of these different reflection cases in the computational prediction of moments close to the boundaries and their associated scale.
Revised:  We study these BC on the physical boundaries of the device for the modeling of surface roughness, comparing the influence of these different reflection cases in the computational prediction of moments close to the boundaries and their associated scale.
Edit intent: clarity
Original:  We study the specular, diffusive and mixed reflection BC on physical boundaries of the device for  the modeling of surface roughness, comparing the influence of these different reflection cases in the computational prediction of moments close to the boundaries and their associated scale.
Revised:  We study the specular, diffusive and mixed reflection BC on physical boundaries of the device for ). We compare the modeling of surface roughness, comparing the influence of these different reflection cases in the computational prediction of moments close to the boundaries and their associated scale.
Edit intent: coherence
Original:  We study the specular, diffusive and mixed reflection BC on physical boundaries of the device for  the modeling of surface roughness, comparing the influence of these different reflection cases in the computational prediction of moments close to the boundaries and their associated scale.
Revised:  We study the specular, diffusive and mixed reflection BC on physical boundaries of the device for the computational prediction of moments close to the boundaries and their associated scale.
Edit intent: clarity
Original:  We observe in our preliminary numerical simulations an effect due to diffusivity at the reflection boundaries over the kinetic moments of the probability density function, whose influence is not restricted to the boundaries but rather over the position space domain .
Revised:  We observe in our preliminary numerical simulations an effect due to diffusivity at the reflection boundaries over the kinetic moments over the whole domain in position space .
Edit intent: clarity
Original:  Here, we consider two flow algorithms (max-flow and uniform-flow) , and two more realistic congestion control schemes (max-min fairness and proportional fairness) .
Revised:  Here, we consider two flow algorithms (max-flow and uniform-flow) and two realistic (max-min fairness and proportional fairness) .
Edit intent: clarity
Original:  We analyse how the algorithms and network topology affect throughput, fairness and the location of bottleneck edges.
Revised:  We analyse how the algorithms and network structure affect throughput, fairness and the location of bottleneck edges.
Edit intent: clarity
Original:  We analyse how the algorithms and network topology affect throughput, fairness and the location of bottleneck edges.
Revised:  We analyse how the algorithms and network topology affect throughput, the fairness of flow allocation, and the location of bottleneck edges.
Edit intent: clarity
Original:  Our results show that on large random networks a network operator can implement the trade-off (proportional fairness ) instead of the fair allocation ( max-min fairness ) with little sacrifice in throughput.
Revised:  The more realistic proportional fairness and max-min fairness ) with little sacrifice in throughput.
Edit intent: clarity
Original:  Finally, we found that links with high edge betweenness centrality are good candidates for bottleneck edges .
Revised:  Finally, we show that the number of paths passing through an edge characterises the location of a wide range of bottleneck edges in these algorithms. Such identification of bottlenecks could provide a bridge between the two fields of complex networks and congestion control .
Edit intent: clarity
Original: Cryo-electron tomography enables 3D visualization of cells in a near native state to molecular resolution.
Revised: Cryo-electron tomography enables 3D visualization of cells in a near native state at molecular resolution.
Edit intent: fluency
Original:  Here, we formulate the task of extracting the information as a reference-free pattern mining problem , and propose a set of novel analysis methods and integrate these methods into a software system to support proteome-scale mining of 3D structures from cellular tomograms .
Revised:  Here, we formulate a template-free visual proteomics analysis as a de novo pattern mining problem , and propose a set of novel analysis methods and integrate these methods into a software system to support proteome-scale mining of 3D structures from cellular tomograms .
Edit intent: clarity
Original:  Here, we formulate the task of extracting the information as a reference-free pattern mining problem , and propose a set of novel analysis methods and integrate these methods into a software system to support proteome-scale mining of 3D structures from cellular tomograms .
Revised:  Here, we formulate the task of extracting the information as a reference-free pattern mining problem and propose a set of novel analysis methods and integrate these methods into a software system to support proteome-scale mining of 3D structures from cellular tomograms .
Edit intent: fluency
Original:  Our tests on simulated and experimental tomograms show that the methods are promising for visual proteomics analysis.
Revised:  Our tests on simulated and experimental tomograms show that our method is a promising tool for template-free visual proteomics analysis.
Edit intent: clarity
Original:  However, extracting this information is very challenging and no method exist to date to tackle this problem without the use of template structures .
Revised:  However, extracting this information is very challenging and current methods usually rely on templates of known structure .
Edit intent: clarity
Original: We propose a Laplace approximation that closely links any smooth monotonic activation function to its stochastic counterpart using Gaussian noise.
Revised: We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function to its stochastic counterpart using Gaussian noise.
Edit intent: clarity
Original: We propose a Laplace approximation that closely links any smooth monotonic activation function to its stochastic counterpart using Gaussian noise.
Revised: We propose a Laplace approximation that closely links any smooth monotonic activation function , using only Gaussian noise.
Edit intent: clarity
Original:  We investigate the application of this  approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences.
Revised:  This paper investigates the application of this approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences.
Edit intent: clarity
Original:  This family -- exponential family RBM (Exp-RBM) -- is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearities for neurons . Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBMs can learn useful representations using novel stochastic units.
Revised:  This family , that we call exponential family RBM (Exp-RBM) -- is a subset of the exponential family Harmoniums that expresses family members through a choice of smooth monotonic non-linearities for neurons . Using contrastive divergence along with our Gaussian approximation, we show that Exp-RBMs can learn useful representations using novel stochastic units.
Edit intent: clarity