wanyu/IteraTeR_v2 huggingface dataset:
Original:  Considering all the non-redundant protein structures across all the major structural classes, the present study attempts to find the probabilistic distributions that describe several facets of the occurrence of these rare secondary structures in proteins.
Revised:  Considering all the non-redundant protein structures across all the major structural classes, present study identified the probabilistic characteristics that describe several facets of the occurrence of these rare secondary structures in proteins.
Edit intent: clarity
Original:  Probabilistic profiling of the occurrence of 3-10 and Pi-helices reveal their presence to follow Poisson flow on the sequence.
Revised:  Probabilistic profiling of the occurrence of 3-10 and Pi-helices revealed that, their presence follows Poisson flow on the sequence.
Edit intent: coherence
Original:  Alongside these unexpected and significant results } , a new algorithm to differentiate between related sequences is proposed here that reliably studies evolutionary distance with respect to protein secondary structures.
Revised:  Alongside these unexpected and significant results } , a new algorithm to differentiate between related sequences is proposed , which reliably studies evolutionary distance with respect to protein secondary structures.
Edit intent: coherence
Original:  This bound is an improvement for all d even over the worst-case bound on the combinatorial complexity of the convex hull of a point set where we impose no restriction on the points' configuration, and is shown to be tight for d= 4. Finally, we discuss algorithms for computing the convex hull in the context of the two problems we consider, i.e., when we have:
Revised:  This bound is an improvement for all d even over the worst-case bound on the combinatorial complexity of the convex hull of a point set where we impose no restriction on the points' configuration, and is shown to be tight for all even d 4. Finally, we discuss algorithms for computing the convex hull in the context of the two problems we consider, i.e., when we have:
Edit intent: clarity
Original: Given a set \Sigma of n hyperspheres in \mathbb{E 3, having m distinct radii, we show that the worst-case combinatorial complexity of the convex hull CH_d(\Sigma) of \Sigma is O(m n^{\lfloord{2\rfloor}).
Revised:  3, having m distinct radii, we show that the worst-case combinatorial complexity of the convex hull CH_d(\Sigma) of \Sigma is O(m n^{\lfloord{2\rfloor}).
Edit intent: coherence
Original:  (1) a set of m convex polytopes lying on m parallel hyperplanes of E^d, with a total of n vertices, where d 4 and d even, or (2) a set of n hyperspheres in E^d with m distinct radii, where d%DIFDELCMD < %%% 3 and d odd.
Revised:  (1) a set of m convex polytopes lying on m parallel hyperplanes of E^d, with a total of n vertices, where d %DIFDELCMD < %%% 3 and d odd.
Edit intent: coherence
Original:  The solution to the associated optimal stopping problem can be characterised in terms of an optimal exercise boundary which, in contrast to the case when there are no dividends, is no longer monotone.
Revised:  The solution to the associated optimal stopping problem can be characterised in terms of an optimal exercise boundary which, in contrast to the case when there are no dividends, may no longer be monotone.
Edit intent: clarity
Original:  We also show that the exercise boundary is continuous and a high contact principle holds in such a neighbourhood when the dividend function is moreover linearin a neighbourhood of 0.
Revised:  We also show that the exercise boundary and a high contact principle holds in such a neighbourhood when the dividend function is moreover linearin a neighbourhood of 0.
Edit intent: clarity
Original:  Alternatively, the Differential TR (DTR) scheme offers 3dB performance gain compared to conventional TR structures and double data rates since the previously transmitted data pulse is used as a reference .
Revised:  Alternatively, the Differential TR (DTR) schemes have attracted researchers attention .
Edit intent: clarity
Original:  In this paper we introduce a less complex , energy-efficient TR scheme, called Self Reference (SR) UWB system , which uses as reference an elaborated replica of the received signal .
Revised:  In this letter, we introduce an alternative, less complex scheme, called Self Reference (SR) UWB system , which uses as reference an elaborated replica of the received signal .
Edit intent: clarity
Original:  In this paper we introduce a less complex , energy-efficient TR scheme, called Self Reference (SR) UWB system , which uses as reference an elaborated replica of the received signal .
Revised:  In this paper we introduce a less complex , energy-efficient TR scheme, called Self Reference (SR) UWB transceiver , which uses as reference an elaborated replica of the received signal .
Edit intent: clarity
Original:  In this paper we introduce a less complex , energy-efficient TR scheme, called Self Reference (SR) UWB system , which uses as reference an elaborated replica of the received signal .
Revised:  In this paper we introduce a less complex , energy-efficient TR scheme, called Self Reference (SR) UWB system , which uses a modified replica of the received signal .
Edit intent: clarity
Original:  In 2001 Zorin and Schroeder were able to prove C^1-continuity for midpoint subdivision surfaces analytically up to degree 9.
Revised:  In 2001 Zorin and Schroeder were able to prove C1-continuity for midpoint subdivision surfaces analytically up to degree 9.
Edit intent: clarity
Original:  Here, we develop a general geometric analysis method and show that the limiting surfaces under midpoint subdivision of any degree %DIFDELCMD < \ge %%%  2 are C^1-continuous at their extraordinary points.
Revised:  Here, we develop a general geometric analysis method and show that the limiting surfaces under midpoint subdivision of any degree %DIFDELCMD < \ge %%% 2 are C1-continuous at their extraordinary points.
Edit intent: clarity
Original: Midpoint subdivision generalizes the Lane-Riesenfeld algorithm for uniform tensor product splines and can be applied also to non regular meshes.
Revised: Midpoint subdivision generalizes the Lane-Riesenfeld algorithm for uniform tensor product splines and can also be applied to non regular meshes.
Edit intent: fluency
Original:  In 2001  Zorin and Schroeder were able to prove C1-continuity for midpoint subdivision surfaces analytically up to degree 9.
Revised:  In 2001 , Zorin and Schroeder were able to prove C1-continuity for midpoint subdivision surfaces analytically up to degree 9.
Edit intent: fluency
Original:  Here, we develop a general geometric analysis method and show that the limiting surfaces under midpoint subdivision of any degree >= 2 are C1-continuous at their extraordinary points.
Revised:  Here, we develop general analysis tools to show that the limiting surfaces under midpoint subdivision of any degree >= 2 are C1-continuous at their extraordinary points.
Edit intent: clarity
Original: This paper deals with multiphase models for the growth of tumor masses in interaction with a surrounding tissue  .
Revised: This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue .
Edit intent: clarity
Original: We study the question of whether the value of mathematical programs such as linear and semidefinite programming hierarchies on a graph G, is preserved when taking a small random subgraph G'
Revised: We initiate a study of when the value of mathematical programs such as linear and semidefinite programming hierarchies on a graph G, is preserved when taking a small random subgraph G'
Edit intent: clarity
Original: We study the question of whether the value of mathematical programs such as linear and semidefinite programming hierarchies on a graph G, is preserved when taking a small random subgraph G'
Revised: We study the question of whether the value of mathematical relaxations such as linear and semidefinite programming hierarchies on a graph G, is preserved when taking a small random subgraph G'
Edit intent: clarity
Original:  of G. We show that the value of the Goemans-Williamson (1995) semidefinite program (SDP) for%DIFDELCMD < \maxcut %%% of G' is approximately equal to the SDP value of G. Moreover, this holds even if the SDP is augmented with any constraint from a large natural family C of constraints that includes all constraints from the hierarchy of Lasserre (2001).
Revised:  of G. We show that the value of the %DIFDELCMD < \maxcut %%% of G' is approximately equal to the SDP value of G. Moreover, this holds even if the SDP is augmented with any constraint from a large natural family C of constraints that includes all constraints from the hierarchy of Lasserre (2001).
Edit intent: clarity
Original:  In contrast, we showthat for linear programsthis isnot the case, and there are graphs G that have small value for the%DIFDELCMD < \maxcut %%% LP with triangle inequalities, but for which a random subgraph G' has value 1-o( 1 ) even for \pm  the LP augmented with n^{\epsilon Sherali-Adams hierarchy.
Revised:  In contrast, we showthat for linear programsthis is the case, and there are graphs G that have small value for the%DIFDELCMD < \maxcut %%% LP with triangle inequalities, but for which a random subgraph G' has value 1-o( 1 ) even for \pm the LP augmented with n^{\epsilon Sherali-Adams hierarchy.
Edit intent: fluency
Original:  In contrast, we showthat for linear programsthis isnot the case, and there are graphs G that have small value for the%DIFDELCMD < \maxcut %%% LP with triangle inequalities, but for which a random subgraph G' has value 1-o( 1 ) even for \pm  the LP augmented with n^{\epsilon Sherali-Adams hierarchy.
Revised:  In contrast, we showthat for linear programsthis isnot %DIFDELCMD < \maxcut %%% LP with triangle inequalities, but for which a random subgraph G' has value 1-o( 1 ) even for \pm the LP augmented with n^{\epsilon Sherali-Adams hierarchy.
Edit intent: clarity
Original:  In contrast, we showthat for linear programsthis isnot the case, and there are graphs G that have small value for the%DIFDELCMD < \maxcut %%% LP with triangle inequalities, but for which a random subgraph G' has value 1-o( 1 ) even for \pm  the LP augmented with n^{\epsilon Sherali-Adams hierarchy.
Revised:  In contrast, we showthat for linear programsthis isnot the case, and there are graphs G that have small value for the%DIFDELCMD < \maxcut %%% LP with triangle inequalities, but for which a random subgraph G' has value 1-o( 1 \pm the LP augmented with n^{\epsilon Sherali-Adams hierarchy.
Edit intent: clarity
Original:  Such a result can be considered more or less folklore in thedense case, where S is large enough to form a close approximation of the sphere, but requires quite different techniques to demonstrate in the sparse case.
Revised:  Such a result can be considered more or less folklore in the case, where S is large enough to form a close approximation of the sphere, but requires quite different techniques to demonstrate in the sparse case.
Edit intent: fluency
Original:  The power of our theory is demonstrated for prototypical models of cooperation dilemmas . Comparing our predictions with those of the Fokker-Planck equation and numerical results, we show that our theory is superior to the Fokker-Planck approach and has a broader applicability for {\it finite} w.
Revised:  The power of our theory is demonstrated on prototypical models of cooperation dilemmas . Comparing our predictions with those of the Fokker-Planck equation and numerical results, we show that our theory is superior to the Fokker-Planck approach and has a broader applicability for {\it finite} w.
Edit intent: clarity
Original:  The power of our theory is demonstrated for prototypical models of cooperation dilemmas . Comparing our predictions with those of the Fokker-Planck equation and numerical results, we show that our theory is superior to the Fokker-Planck approach and has a broader applicability for {\it finite} w.
Revised:  The power of our theory is demonstrated for prototypical models of cooperation dilemmas with multiple absorbing states. Our predictions compare excellently with numerical simulations, and we show that our theory is superior to the Fokker-Planck approach and has a broader applicability for {\it finite} w.
Edit intent: clarity
Original:  The power of our theory is demonstrated for prototypical models of cooperation dilemmas . Comparing our predictions with those of the Fokker-Planck equation and numerical results, we show that our theory is superior to the Fokker-Planck approach and has a broader applicability for {\it finite} w.
Revised:  The power of our theory is demonstrated for prototypical models of cooperation dilemmas . Comparing our predictions with those of the Fokker-Planck equation and numerical results, we show that our method is superior to the Fokker-Planck approach and has a broader applicability for {\it finite} w.
Edit intent: clarity
Original:  Here, we formulate a WKB (Wentzel-Kramers-Brillouin) based theory to study fixation in evolutionary games under non-vanishing selection .
Revised:  Here, we generalize a recent WKB-based theory to study fixation in evolutionary games under non-vanishing selection .
Edit intent: clarity
Original:  Within this approach, we accurately account for large fluctuations and compute the mean times and probability of fixation for finite selection intensity w,beyond the weak selection limit.
Revised:  Within this approach, we accurately account for large fluctuations and beyond the weak selection limit.
Edit intent: coherence
Original:  The power of our theory is demonstrated on prototypical models of cooperation dilemmas with multiple absorbing states.
Revised:  The power of the theory is demonstrated on prototypical models of cooperation dilemmas with multiple absorbing states.
Edit intent: clarity
Original:  Our predictions compare excellently with numerical simulations , andwe show that our method is superior to the Fokker-Planck approach and has a broader applicability for%DIFDELCMD < {\it %%% finite w .
Revised:  Our predictions compare excellently with numerical simulations , andwe show that our method is superior to the Fokker-Planck %DIFDELCMD < {\it %%% finite w .
Edit intent: clarity
Original: An optical flow gradient algorithm was applied to spontaneously forming networks of neurons and glia in culture imaged by fluorescence optical microscopy in order to map functional calcium signaling with single pixel resolution.
Revised: An optical flow gradient algorithm was applied to spontaneously forming net- works of neurons and glia in culture imaged by fluorescence optical microscopy in order to map functional calcium signaling with single pixel resolution.
Edit intent: fluency
Original:  Computed vector field outputs by the algorithm were able to track the spatiotemporal dynamics of calcium signaling patterns .
Revised:  Computed vector field outputs by the algorithm were able to track the spatiotemporal dynamics of calcium signaling pat- terns .
Edit intent: fluency
Original:  We begin by briefly reviewing the mathematics of the optical flow algorithm,  describe how to solve for the displacement vectors , and how to measure their reliability.
Revised:  We begin by briefly reviewing the mathematics of the optical flow algorithm, and then describe how to solve for the displacement vectors , and how to measure their reliability.
Edit intent: coherence
Original:  We begin by briefly reviewing the mathematics of the optical flow algorithm,  describe how to solve for the displacement vectors , and how to measure their reliability.
Revised:  We begin by briefly reviewing the mathematics of the optical flow algorithm, describe how to solve for the displacement vectors and how to measure their reliability.
Edit intent: fluency
Original: Many applications in network analysis require efficient algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence.
Revised: Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence.
Edit intent: clarity
Original:  For the case of directed graphs, we also explain in this paper why a popular switching algorithm fails in general to sample uniformly at random but characterize under which efficiently checkable conditions it will provable succeed in polynomial time .
Revised:  For the case of directed graphs, we also explain in this paper why a popular switching algorithm fails in general to sample uniformly at random but characterize under which efficiently checkable conditions it will provable succeed .
Edit intent: clarity
Original:  For the case of directed graphs, we also explain in this paper why a popular switching algorithm fails in general to sample uniformly at random but characterize under which efficiently checkable conditions itwill provable succeed .
Revised:  For the case of directed graphs, we also explain in this paper that a popular switching algorithm fails in general to sample uniformly at random but characterize under which efficiently checkable conditions itwill provable succeed .
Edit intent: fluency
Original:  All of the above mentioned spiking neural P systems suffer from an exponential slow down when simulating Turing machine . Using a more relaxed encoding technique we get a universal spiking neural P system that has only 14 neurons and another that has extended rules with only 4 neurons.
Revised:  All of the above mentioned spiking neural P systems suffer from an exponential slow down when simulating Turing machines . Using a more relaxed encoding technique we get a universal spiking neural P system that has only 14 neurons and another that has extended rules with only 4 neurons.
Edit intent: fluency
Original:  All of the above mentioned spiking neural P systems suffer from an exponential slow down when simulating Turing machine . Using a more relaxed encoding technique we get a universal spiking neural P system that has only 14 neurons and another that has extended rules with only 4 neurons.
Revised:  All of the above mentioned spiking neural P systems suffer from an exponential slow down when simulating Turing machine . Using a more relaxed encoding technique we get a universal spiking neural P system that has extended rules with only 4 neurons.
Edit intent: clarity
Original:  These latter two spiking neural P systems simulate 2-counter machines in linear time and thus suffer from a double exponential time overhead when simulating Turing machines.
Revised:  This latter spiking neural P systems simulate 2-counter machines in linear time and thus suffer from a double exponential time overhead when simulating Turing machines.
Edit intent: clarity
Original:  These latter two spiking neural P systems simulate 2-counter machines in linear time and thus suffer from a double exponential time overhead when simulating Turing machines.
Revised:  These latter two spiking neural P system simulates 2-counter machines in linear time and thus suffer from a double exponential time overhead when simulating Turing machines.
Edit intent: fluency
Original:  We  demonstrate that in terms of two dominant factors, shipments lead production by four months.
Revised:  We also demonstrate that in terms of two dominant factors, shipments lead production by four months.
Edit intent: clarity
Original:  Furthermore, out-of-sample test demonstrates that the model stands the 2008-09 recession.
Revised:  Furthermore, out-of-sample test demonstrates that the model holds up even under the 2008-09 recession.
Edit intent: clarity
Original: In this paper, we consider a dual-hop MIMO relay wireless network, in which a source-destination pair both equipped with multiple antennas communicates through a large number of half-duplex amplifyand- forward relay terminals.
Revised: In this paper, we consider a dual-hop MIMO relay wireless network, in which a source-destination pair both equipped with multiple antennas communicates through a large number of half-duplex amplify-and-forward (AF) relay terminals.
Edit intent: clarity
Original: We prove a uniformly computable version of de Finetti's theorem on exchangeable sequences of real random variables.
Revised: We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables.
Edit intent: clarity
Original:  As a consequence, exchangeable stochastic processes  in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state.
Revised:  As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state.
Edit intent: clarity
Original:  The pandemic of influenza A (H1N1) is a serious on-going global public crisis.
Revised: Background: The pandemic of influenza A (H1N1) is a serious on-going global public crisis.
Edit intent: coherence
Original:  In this paper, we investigate the spreading patterns of influenza A and find the Zipf's law of the distributions of confirmed cases in different levels . Similar scaling properties are also observed for severe acute respiratory syndrome (SARS) and bird cases of avian influenza ( H5N1 ).
Revised:  In this paper, we investigate the spreading patterns of influenza A and find the Zipf's law of the distributions of confirmed cases in different levels . Similar scaling properties were also observed for severe acute respiratory syndrome (SARS) and bird cases of avian influenza ( H5N1 ).
Edit intent: fluency
Original:  In this paper, we investigate the spreading patterns of influenza A and find the Zipf's law of the distributions of confirmed cases in different levels . Similar scaling properties are also observed for severe acute respiratory syndrome (SARS) and bird cases of avian influenza ( H5N1 ).
Revised:  In this paper, we investigate the spreading patterns of influenza A and find the Zipf's law of the distributions of confirmed cases in different levels . Similar scaling properties are also observed for severe acute respiratory syndrome (SARS) and bird cases of H5N1 ).
Edit intent: clarity
Original:  Although strict control measures for interregional travelers are helpful to delay the outbreak in the regions without local cases, our analysis suggests that the focus should be turned to local prevention after the outbreak of local cases.
Revised:  Although strict control measures for interregional travelers could delay the outbreak in the regions without local cases, our analysis suggests that the focus should be turned to local prevention after the outbreak of local cases.
Edit intent: clarity
Original:  Although strict control measures for interregional travelers are helpful to delay the outbreak in the regions without local cases, our analysis suggests that the focus should be turned to local prevention after the outbreak of local cases.
Revised:  Although strict control measures for interregional travelers are helpful to delay the outbreak in the regions without local cases, the focus should be turned to local prevention after the outbreak of local cases.
Edit intent: clarity
Original:  This work provides not only a deeper understanding of the generic mechanisms underlying the spread of infectious diseases, but also an indispensable tool to decision makers to adopt suitable control strategies.
Revised:  This work provides not only a deeper understanding of the generic mechanisms underlying the spread of infectious diseases, but also some practical guidelines for decision makers to adopt suitable control strategies.
Edit intent: clarity
Original: The "mind-brain supervenience" theorem suggests that all mental properties (e.g. consciousness, intelligence, personality, etc.) are derived from the physical properties of the brain.
Revised: The "mind-brain supervenience" conjecture suggests that all mental properties (e.g. consciousness, intelligence, personality, etc.) are derived from the physical properties of the brain.
Edit intent: clarity