wanyu/IteraTeR_v2 huggingface dataset:
Original: We study a (possibly infinite-dimensional) dynamical system model for mutation and selection in the presence of recombination . Some features of the model, such as existence and uniqueness of solutions and convergence to the dynamical system of an approximating sequence of discrete time models, were presented in earlier work by Evans, Steinsaltz, and Wachter for quite general selection costs.
Revised: We study a (possibly infinite-dimensional) dynamical system model for mutation and selection in the presence of recombination . Some features of the model, such as existence and uniqueness of solutions and convergence to the dynamical system of an approximating sequence of discrete time models, were presented in earlier work by Evans, Steinsaltz, and Wachter for quite general selective costs.
Edit intent: fluency
Original:  Here we  establish that the phenomenon of mutation-selection balance occurs in the special case of ``polynomial'' selection costs under mild conditions.
Revised:  Here we establish that the phenomenon of mutation-selection balance occurs for such selection costs under mild conditions.
Edit intent: clarity
Original: We experimentally compare the outcomes of MR with those of the optimal #8220;full search #8221;
Revised: We experimentally compare the outcomes of MR with those of the optimal #8221;
Edit intent: clarity
Original: We experimentally compare the outcomes of MR with those of the optimal #8220;full search #8221;
Revised: We experimentally compare the outcomes of MR with those of the optimal #8220;full search "full search"
Edit intent: clarity
Original: We consider the problem of computing a triangulation of the real projective plane \mathbb{P , given a finite point set \mathcal{P = \{p_1, p_2 ,..., p_n\ as input.
Revised: We consider the problem of computing a triangulation of the real projective plane \mathbb{P , given a finite point set \mathcal{P = p1, p2 ,..., p_n\ as input.
Edit intent: fluency
Original: We consider the problem of computing a triangulation of the real projective plane \mathbb{P , given a finite point set \mathcal{P = \{p_1, p_2 ,..., p_n\ as input.
Revised: We consider the problem of computing a triangulation of the real projective plane \mathbb{P , given a finite point set \mathcal{P = \{p_1, p_2 ,..., pn as input.
Edit intent: clarity
Original:  We prove that a triangulation of \mathbb{P always exists if at least six points in \mathcal{P are in }%DIFDELCMD < {\it %%% general position , i.e., no three of them are collinear.
Revised:  We prove that a triangulation of \mathbb{P always exists if at least six points in are in }%DIFDELCMD < {\it %%% general position , i.e., no three of them are collinear.
Edit intent: fluency
Original:  We also design a worst-case time O(n^2) algorithm for triangulating \mathbb{P if this necessary condition holds.
Revised:  We also design an algorithm for triangulating \mathbb{P if this necessary condition holds.
Edit intent: clarity
Original:  We use the RAM model of computation for estimating the time complexity of our algorithm.
Edit intent: coherence
Original:  As far as we know, this seems to be the first computational result on the real projective plane.
Revised:  As far as we know, this is the first computational result on the real projective plane.
Edit intent: coherence
Original:  Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical interest -- they can be used to construct phylogenetic trees.
Revised:  Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical interest--they can be used to construct phylogenetic trees.
Edit intent: fluency
Original:  The embedding optimally preserves the local functional coupling between fMRI time series , and provides a low-dimensional coordinate system for detecting activated voxels.
Revised:  The embedding optimally preserves the local functional coupling between fMRI time series and provides a low-dimensional coordinate system for detecting activated voxels.
Edit intent: fluency
Original:  To compute the embedding, we build a network of functionally connected voxels and represent it with a graph.
Revised:  To compute the embedding, we build a graph of functionally connected voxels and represent it with a graph.
Edit intent: clarity
Original:  After embedding the dataset in low dimensions, coherent structures emerge that can be interpreted as task-related hemodynamic responses, and non-task-related physiological artifacts .
Revised:  After embedding the dataset in low dimensions, coherent structures emerge that can be easily interpreted .
Edit intent: clarity
Original:  We performed an extensive evaluation of our method comparing it to linear and nonlinear techniques using synthetic datasets and %DIFDELCMD < {\em %%% in vivo datasets .
Revised:  We performed an extensive evaluation of our method comparing it to linear and nonlinear techniques using synthetic datasets and %DIFDELCMD < {\em %%% datasets .
Edit intent: clarity
Original: We report the first example of a dynamical system that naturally exhibits two unstable (Milnor) attractors that are completely enclosed by each others basin volume.
Revised: We present a dynamical system that naturally exhibits two unstable (Milnor) attractors that are completely enclosed by each others basin volume.
Edit intent: clarity
Original: We report the first example of a dynamical system that naturally exhibits two unstable (Milnor) attractors that are completely enclosed by each others basin volume.
Revised: We report the first example of a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume.
Edit intent: clarity
Original: We find that discrete noise of inhibiting (signal) molecules can greatly delay the extinction of a regulated component in a prototypical biochemical regulatory network.
Revised: We find that discrete noise of inhibiting (signal) molecules can greatly delay the extinction of plasmids in a plasmid replication system: a prototypical biochemical regulatory network.
Edit intent: clarity
Original: Kwa\'sniewski 's cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition.
Revised: Kwasniewski 's cobweb posets uniquely represented by directed acyclic graphs are such a generalization of the Fibonacci tree that allows joint combinatorial interpretation for all of them under admissibility condition.
Edit intent: fluency
Original:  This leads us to propose a model where spikes are effective at times multiple of a characteristic time scale \delta, where \delta can be mathematically arbitrary small  .
Revised:  This leads us to propose a model where spikes are effective at times multiple of a characteristic time scale \delta, where \delta can be arbitrary .
Edit intent: clarity
Original:  The asymptotic dynamics is composed by finitely many  periodic orbits, whose number and period can be arbitrary large and  diverge in a region of the parameters space, traditionally called the ``edge of chaos'', a notion mathematically well defined in the present paper.
Revised:  The asymptotic dynamics is composed by finitely many periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the parameters space, traditionally called the ``edge of chaos'', a notion mathematically well defined in the present paper.
Edit intent: fluency
Original:  Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the spikes raster plot.
Revised:  Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot.
Edit intent: clarity
Original:  As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy  providing a relevant characterization of the computational capabilities of the network.
Revised:  As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy , providing a relevant characterization of the computational capabilities of the network.
Edit intent: fluency
Original:  This allows us to compare the computational capabilities of leaky and integrate and fire models and conductance based models.
Revised:  This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models.
Edit intent: fluency
Original:  The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the `` edge of chaos '' , a notion mathematically well defined in the present paper.
Revised:  The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the " edge of chaos '' , a notion mathematically well defined in the present paper.
Edit intent: fluency
Original:  The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the `` edge of chaos '' , a notion mathematically well defined in the present paper.
Revised:  The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the `` edge of chaos " , a notion mathematically well defined in the present paper.
Edit intent: fluency
Original:  This shows that the neural code is entirely `` in the spikes '' in this case.
Revised:  This shows that the neural code is entirely " in the spikes '' in this case.
Edit intent: fluency
Original:  This shows that the neural code is entirely `` in the spikes '' in this case.
Revised:  This shows that the neural code is entirely `` in the spikes " in this case.
Edit intent: fluency
Original: In this paper, we compare the performance of different agent's investment strategies in an investment scenario with periodic returns and different types and levels of noise.
Revised: In this paper, we present an adaptive investment strategy for environments with periodic returns and different types and levels of noise.
Edit intent: clarity
Original:  We consider an investment model , where an agent decides the percentage of budget to risk at each time step . Afterwards, agent's investment is evaluated in the market via a  return on investment  (RoI), which we assume is a stochastic process with unknown periodicities and different levels of noise.
Revised:  We consider an investment model where the agent decides at every time step the proportion of wealth to invest in a risky asset, keeping the rest of the budget in a risk-free asset. Every investment is evaluated in the market via a return on investment (RoI), which we assume is a stochastic process with unknown periodicities and different levels of noise.
Edit intent: clarity
Original:  We consider an investment model , where an agent decides the percentage of budget to risk at each time step . Afterwards, agent's investment is evaluated in the market via a  return on investment  (RoI), which we assume is a stochastic process with unknown periodicities and different levels of noise.
Revised:  We consider an investment model , where an agent decides the percentage of budget to risk at each time step . Afterwards, agent's investment is evaluated in the market via a return on investment function (RoI), which we assume is a stochastic process with unknown periodicities and different levels of noise.
Edit intent: clarity
Original:  We consider an investment model , where an agent decides the percentage of budget to risk at each time step . Afterwards, agent's investment is evaluated in the market via a  return on investment  (RoI), which we assume is a stochastic process with unknown periodicities and different levels of noise.
Revised:  We consider an investment model , where an agent decides the percentage of budget to risk at each time step . Afterwards, agent's investment is evaluated in the market via a return on investment (RoI), which is modeled by a stochastic process with unknown periodicities and different levels of noise.
Edit intent: clarity
Original:  We consider an investment model , where an agent decides the percentage of budget to risk at each time step . Afterwards, agent's investment is evaluated in the market via a  return on investment  (RoI), which we assume is a stochastic process with unknown periodicities and different levels of noise.
Revised:  We consider an investment model , where an agent decides the percentage of budget to risk at each time step . Afterwards, agent's investment is evaluated in the market via a return on investment (RoI), which we assume is a stochastic process with unknown periodicities and levels of noise.
Edit intent: clarity
Original:  In our comparison , we also consider two reference strategies for zero-knowledge and complete-knowledge behaviors, respectively.
Revised:  In our comparison , we also consider two reference strategies which represent the case of agents with zero-knowledge and complete-knowledge behaviors, respectively.
Edit intent: clarity
Original:  To this end , we perform some computer experiments , where for each strategy the budget obtained after a certain number of time steps is averaged over a large number of trials.
Revised:  To this end , we perform some computer experiments to calculate the average budget that can be obtained with them over a certain number of time steps is averaged over a large number of trials.
Edit intent: clarity
Original:  Afterwards, we compare the performance of these strategies for RoIs with different  levels of noise and different periodicities .
Revised:  Afterwards, we compare the performance of these strategies for RoIs with different levels of noise .
Edit intent: clarity
Original:  Using this theory and parameters based on known values of neuronal oscillation frequencies and firing rates, the calculated probability distribution of dominance duration of rival states in binocular rivalry under various conditions is  in good agreement with available experimental data.
Revised:  Using this theory and parameters based on known values of neuronal oscillation frequencies and firing rates, the calculated probability distribution of dominance duration of rival states in binocular rivalry under various conditions is found to be in good agreement with available experimental data.
Edit intent: clarity
Original:  This theory naturally explains recently observed marked increase in dominance duration in binocular rivalry upon periodic interruption of stimulus and yields testable predictions for the distribution of perceptual alteration in time.
Revised:  This theory naturally explains an observed marked increase in dominance duration in binocular rivalry upon periodic interruption of stimulus and yields testable predictions for the distribution of perceptual alteration in time.
Edit intent: clarity
Original: We examine an evolutionary naming-game model where communicating agents are equipped with an evolutionary selected learning ability.
Revised: We examine an evolutionary naming-game model where communicating agents are equipped with an evolutionarily selected learning ability.
Edit intent: clarity
Original:  Namely, to the classical Sharing X Lin abstract domain and to the more precise ShLin^2 abstract domain by Andy King.
Revised:  Namely, to the classical Sharing X Lin abstract domain and to the more precise ShLin-2 abstract domain by Andy King.
Edit intent: clarity
Original: We develop a network-based algorithm to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network.
Revised: We develop a matrix-based approach to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network.
Edit intent: clarity
Original:  The essence of the method is to extend the transitivity of indirect regulations ( i.e.
Revised:  The essence of the method is to extend the transitivity of indirect regulations ( e.g.
Edit intent: coherence
Original:  A regulates B and B regulates C implies A regulates C) to longer cascades and effectively take care of the signs of the regulations.
Revised:  A regulates B and B regulates C often implies that A regulates C) to longer cascades and effectively take care of the signs of the regulations.
Edit intent: clarity
Original: Untangling is reconfiguring by vertex moves a geometric planar graph with possible crossings into a geometric planar graph with no crossings.
Revised: To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings.
Edit intent: clarity
Original:  Geom., 2002] , asked if every n-vertex planar geometric graph can be untangled while keeping at least n^\epsilon vertices fixed.
Revised:  Geom., 2002] asked if every n-vertex planar geometric graph can be untangled while keeping at least n^\epsilon vertices fixed.
Edit intent: fluency
Original:  Geom., 2002] , asked if every n-vertex planar geometric graph can be untangled while keeping at least n^\epsilon vertices fixed.
Revised:  Geom., 2002] , asked if every n-vertex geometric planar graph can be untangled while keeping at least n^\epsilon vertices fixed.
Edit intent: fluency
Original:  We answer this question in  affirmative with \epsilon=1/4.
Revised:  We answer this question in the affirmative with \epsilon=1/4.
Edit intent: fluency
Original:  We } answer a question of Spillner and Wolff [  0709.0170 , 2007] , by closing the gap for untangling trees.
Revised:  We } answer a question of Spillner and Wolff [ 0709.0170 2007] , by closing the gap for untangling trees.
Edit intent: fluency
Original:  We } answer a question of Spillner and Wolff [  0709.0170 , 2007] , by closing the gap for untangling trees.
Revised:  We } answer a question of Spillner and Wolff [ 0709.0170 , 2007] by closing this gap for untangling trees.
Edit intent: clarity
Original:  We explore the process of uniformly at random deleting vertices of a \beta-expander  with probability n^{-\alpha} for some constant \alpha> 0.
Revised:  In this work we explore the process of uniformly at random deleting vertices of a \beta-expander with probability n^{-\alpha} for some constant \alpha> 0.
Edit intent: clarity
Original:  We explore the process of uniformly at random deleting vertices of a \beta-expander  with probability n^{-\alpha} for some constant \alpha> 0.
Revised:  We explore the process of deleting vertices of a \beta-expander with probability n^{-\alpha} for some constant \alpha> 0.
Edit intent: clarity
Original:  Our main result implies that as n tends to infinity, the deletion process performed on a \beta-expander graph of bounded degree will result with high probability in a graph composed of a giant component containing n-o(n) vertices which is itself an expander graph, and small constant size components.
Revised:  Our main result states that as n tends to infinity, the deletion process performed on a \beta-expander graph of bounded degree will result with high probability in a graph composed of a giant component containing n-o(n) vertices which is itself an expander graph, and small constant size components.
Edit intent: clarity
Original:  Our main result implies that as n tends to infinity, the deletion process performed on a \beta-expander graph of bounded degree will result with high probability in a graph composed of a giant component containing n-o(n) vertices which is itself an expander graph, and small constant size components.
Revised:  Our main result implies that as n tends to infinity, the deletion process performed on a \beta-expander graph of bounded degree will result with high probability in a graph composed of a giant component containing n-o(n) vertices that is in itself an expander graph, and small constant size components.
Edit intent: clarity
Original:  Our main result implies that as n tends to infinity, the deletion process performed on a \beta-expander graph of bounded degree will result with high probability in a graph composed of a giant component containing n-o(n) vertices which is itself an expander graph, and small constant size components.
Revised:  Our main result implies that as n tends to infinity, the deletion process performed on a \beta-expander graph of bounded degree will result with high probability in a graph composed of a giant component containing n-o(n) vertices which is itself an expander graph, and constant size components.
Edit intent: clarity
Original:  In the particular case of (n,d,\lambda)-graphs, which are such expanders, we compute the values of \alpha, under additional constraints on the graph, for which with high probability the resulting graph will stay connected, or will be composed of a giant component and isolated vertices.
Revised:  In the particular case of (n,d,\lambda)-graphs, that are such expanders, we compute the values of \alpha, under additional constraints on the graph, for which with high probability the resulting graph will stay connected, or will be composed of a giant component and isolated vertices.
Edit intent: fluency
Original:  As a graph sampled from the uniform probability space of d-regular graphs with hight probability meets all of these constraints, this result strengthens a recent result due to Greenhill, Holt , and Wormald who prove a similar theorem for%DIFDELCMD < \Gnd%%%  . We conclude by showing that performing the deletion process with the prescribed deletion probability on expander graphs that expand sub-linear sets by an unbounded expansion ratio, with high probability results in an expander graph.
Revised:  As a graph sampled from the uniform probability space of d-regular graphs with hight probability meets all of these constraints, this result strengthens a recent result due to Greenhill, Holt %DIFDELCMD < \Gnd%%% . We conclude by showing that performing the deletion process with the prescribed deletion probability on expander graphs that expand sub-linear sets by an unbounded expansion ratio, with high probability results in an expander graph.
Edit intent: coherence
Original:  As a graph sampled from the uniform probability space of d-regular graphs with hight probability meets all of these constraints, this result strengthens a recent result due to Greenhill, Holt , and Wormald who prove a similar theorem for%DIFDELCMD < \Gnd%%%  . We conclude by showing that performing the deletion process with the prescribed deletion probability on expander graphs that expand sub-linear sets by an unbounded expansion ratio, with high probability results in an expander graph.
Revised:  As a graph sampled from the uniform probability space of d-regular graphs with hight probability meets all of these constraints, this result strengthens a recent result due to Greenhill, Holt , and Wormald who prove a similar theorem for%DIFDELCMD < \Gnd%%% . We conclude by showing that performing the deletion process with the prescribed deletion probability on expander graphs that expand sub-linear sets by an unbounded expansion ratio, with high probability results in a connected expander graph.
Edit intent: clarity
Original:  Increasingly more complex models have been used by estimation of distribution algorithms (EDAs), what often results better effectiveness on finding the global optima for hard optimization problems.
Revised:  Increasingly more complex models have been used by estimation of distribution algorithms (EDAs), which often result better effectiveness on finding the global optima for hard optimization problems.
Edit intent: coherence