wanyu/IteraTeR_v2 huggingface dataset:
Original:  The methodology is pure dual in the sense that it doesn't require certain (input ) approximations to the Snell envelope.
Revised:  The methodology is pure dual in the sense that it doesn't require certain input approximations to the Snell envelope.
Edit intent: fluency
Original: Much of the genome is expressed in the vertebrate brain  with individual genes exhibiting different spatially-varying patterns of expression.
Revised: Much of the genome is expressed in the vertebrate brain , with individual genes exhibiting different spatially-varying patterns of expression.
Edit intent: fluency
Original:  These correlations have been previously studied quantitatively, particularly for the gene expression atlas of the mouse brain (references) , but the biological meaning of the co-expression patterns remains obscure.
Revised:  These correlations have been previously studied quantitatively, particularly for the gene expression atlas of the mouse brain , but the biological meaning of the co-expression patterns remains obscure.
Edit intent: coherence
Original:  This lemma establishes the connectivity of a certain graph whose nodes correpond to the spanning trees of a 2-vertex-connected graph, and implies the k=2 case of the Gyori-Lov\'asz Theorem on partitioning of k-vertex-connected graphs.
Revised:  This lemma establishes the connectivity of a certain graph whose nodes correspond to the spanning trees of a 2-vertex-connected graph, and implies the k=2 case of the Gyori-Lov\'asz Theorem on partitioning of k-vertex-connected graphs.
Edit intent: fluency
Original: In this paper, we study the performance of greedy scheduling in multihop wireless networks  where the objective is aggregate utility maximization.
Revised: In this paper, we study the performance of greedy scheduling in multihop wireless networks , where the objective is aggregate utility maximization.
Edit intent: fluency
Original:  Optimal scheduling requires selecting independent sets of maximum aggregate price, but this problem is known to be NP-hard.
Revised:  The dual can be solved optimally, only with the knowledge of the maximal independent sets in the network. But computation of maximal independent sets is known to be NP-hard.
Edit intent: clarity
Original:  We propose a distributed greedy heuristic to address the problem of link scheduling.
Revised:  Motivated by this, we propose a distributed greedy heuristic to address the problem of link scheduling.
Edit intent: coherence
Original:  We  give simulation results for the  distributed implementation of  greedy heuristic and find them close to that of centralized optimal algorithm .
Revised:  We give simulation results for the distributed implementation of the greedy heuristic and find them close to that of centralized optimal algorithm .
Edit intent: fluency
Original:  A grid graph is a finite subgraph of the infinite 2D grid .
Revised:  The latter are finite connected subgraphs of the infinite 2D grid .
Edit intent: clarity
Original:  The main contribution of our work however is a proof that shows that, unless P=NP, no FPTAS exists that will compute partitions in which the set sizes are at most (1 +%DIFDELCMD < \eps%%% )n/k for any%DIFDELCMD < \eps %%% > 0. This is true even if the cut size may deviate by a factor of n^c/%DIFDELCMD < \eps%%% ^d from optimum for any constants c and d where, for solid grid graphs, c < 1/2.
Revised:  The main contribution of our work however is a proof that shows that, unless P=NP, no FPTAS exists that will compute partitions in which the %DIFDELCMD < \eps%%% )n/k for any%DIFDELCMD < \eps %%% > 0. This is true even if the cut size may deviate by a factor of n^c/%DIFDELCMD < \eps%%% ^d from optimum for any constants c and d where, for solid grid graphs, c < 1/2.
Edit intent: clarity
Original:  The main contribution of our work however is a proof that shows that, unless P=NP, no FPTAS exists that will compute partitions in which the set sizes are at most (1 +%DIFDELCMD < \eps%%% )n/k for any%DIFDELCMD < \eps %%% > 0. This is true even if the cut size may deviate by a factor of n^c/%DIFDELCMD < \eps%%% ^d from optimum for any constants c and d where, for solid grid graphs, c < 1/2.
Revised:  The main contribution of our work however is a proof that shows that, unless P=NP, no FPTAS exists that will compute partitions in which the set sizes are at most (1 +%DIFDELCMD < \eps%%% %DIFDELCMD < \eps %%% > 0. This is true even if the cut size may deviate by a factor of n^c/%DIFDELCMD < \eps%%% ^d from optimum for any constants c and d where, for solid grid graphs, c < 1/2.
Edit intent: clarity
Original:  The main contribution of our work however is a proof that shows that, unless P=NP, no FPTAS exists that will compute partitions in which the set sizes are at most (1 +%DIFDELCMD < \eps%%% )n/k for any%DIFDELCMD < \eps %%% > 0. This is true even if the cut size may deviate by a factor of n^c/%DIFDELCMD < \eps%%% ^d from optimum for any constants c and d where, for solid grid graphs, c < 1/2.
Revised:  The main contribution of our work however is a proof that shows that, unless P=NP, no FPTAS exists that will compute partitions in which the set sizes are at most (1 +%DIFDELCMD < \eps%%% )n/k for any%DIFDELCMD < \eps %%% > 0. This is true even if the %DIFDELCMD < \eps%%% ^d from optimum for any constants c and d where, for solid grid graphs, c < 1/2.
Edit intent: clarity
Original: Two kinds of approximation algorithms exist for the k-Balanced Partitioning problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow.
Revised: Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow.
Edit intent: fluency
Original:  First we use the framework to show that for both classes it is NP-hard to approximate the optimum number of cut edges within any reasonable ratio.
Revised:  First we use the framework to show that for both classes it is NP-hard to approximate the optimum number of cut edges within any satisfying ratio.
Edit intent: clarity
Original:  In this formalism, the price of the stock and its trend satisfy the generalized uncertainty relation and the corresponding generalized Hamiltonian contains an additional term proportional to the forth power of the trend.
Revised:  In this formalism, the price of the stock and its trend satisfy the generalized uncertainty relation and the corresponding generalized Hamiltonian contains an additional term proportional to the fourth power of the trend.
Edit intent: fluency
Original: Normal surfaces are a key tool in computational knot theory and 3-manifold topology , and have featured in significant computational breakthroughs in recent years . Despite this , there has been little practical progress on algorithmsthat use fundamental normal surfaces , which are described in terms of a Hilbert basis for a pointed rational coneon a high-dimensional integer lattice.
Revised: Computational knot theory and 3-manifold topology , and have featured in significant computational breakthroughs in recent years . Despite this , there has been little practical progress on algorithmsthat use fundamental normal surfaces , which are described in terms of a Hilbert basis for a pointed rational coneon a high-dimensional integer lattice.
Edit intent: clarity
Original: Normal surfaces are a key tool in computational knot theory and 3-manifold topology , and have featured in significant computational breakthroughs in recent years . Despite this , there has been little practical progress on algorithmsthat use fundamental normal surfaces , which are described in terms of a Hilbert basis for a pointed rational coneon a high-dimensional integer lattice.
Revised: Normal surfaces are a key tool in computational knot theory and 3-manifold topology have seen significant breakthroughs in recent years . Despite this , there has been little practical progress on algorithmsthat use fundamental normal surfaces , which are described in terms of a Hilbert basis for a pointed rational coneon a high-dimensional integer lattice.
Edit intent: clarity
Original:  In this paper we developand implement several algorithms to enumerate fundamental normal surfaces, by merging domain-specific techniques from normal surface theory with classical Hilbert basis algorithms.
Revised:  In this paper we developand implement several algorithms to enumerate fundamental normal surfaces, by merging domain-specific techniques with classical Hilbert basis algorithms.
Edit intent: clarity
Original:  A surface finite element method is developed to appropriate the Laplace-Beltremi operators in the partial differential equations (PDEs) of the model.
Revised:  A surface finite element method is developed to appropriate the Laplace-Beltrami operators in the partial differential equations (PDEs) of the model.
Edit intent: fluency
Original:  In 2010, Byrka et al. presented a ln(4)+ \epsilon\ approximation based on a hypergraphic LP relaxation, but surprisingly, their analysis does not provide a matching bound on the integrality gap.
Revised:  In 2010, Byrka et al. presented a ln(4)+ epsilon approximation based on a hypergraphic LP relaxation, but surprisingly, their analysis does not provide a matching bound on the integrality gap.
Edit intent: fluency
Original:  More precisely, we present a deterministic ln(4)+ \epsilon\ approximation that compares against the LP value and therefore proves a matching ln(4) upper bound on the integrality gap.
Revised:  More precisely, we present a deterministic ln(4)+ epsilon approximation that compares against the LP value and therefore proves a matching ln(4) upper bound on the integrality gap.
Edit intent: fluency
Original:  Our formulation is flexible in the sense that it allows the design and comparison of different methods (possibly specialized for different settings) .
Revised:  Our formulation provides a framework in which different approaches can be studied and developed .
Edit intent: clarity
Original:  We first study the simple class of equi-width histograms in our learning framework and present a learning algorithm (EquiHist) that is competitive in many settings and that has formal error guarantees .
Revised:  We first study the simple class of equi-width histograms and present a learning algorithm (EquiHist) that is competitive in many settings and that has formal error guarantees .
Edit intent: clarity
Original:  We first study the simple class of equi-width histograms in our learning framework and present a learning algorithm (EquiHist) that is competitive in many settings and that has formal error guarantees .
Revised:  We first study the simple class of equi-width histograms in our learning framework and present a learning algorithm , EquiHist, that is competitive in many settings and that has formal error guarantees .
Edit intent: fluency
Original:  We then go beyond equi-width histograms and present a novel learning algorithm (SpHist) for estimating general histograms.
Revised:  We then go beyond equi-width histograms and present a novel learning algorithm , SpHist, for estimating general histograms.
Edit intent: fluency
Original:  Here we use Haar wavelets to reduce the problem of learning histograms to a sparse vectory recovery problem .
Revised:  Here we use Haar wavelets to reduce the problem of learning histograms to that of learning a sparse vector .
Edit intent: clarity
Original:  Both algorithms have multiple advantages over existing methods: 1) simple and scalable extensions to multi-dimensional data, 2) scale with number of histogram buckets and size of query feedback, 3) natural extensions to incorporate new feedback and handle database updates.
Revised:  Both algorithms have multiple advantages over existing methods: 1) simple and scalable extensions to multi-dimensional data, 2) scalability with number of histogram buckets and size of query feedback, 3) natural extensions to incorporate new feedback and handle database updates.
Edit intent: clarity
Original:  To resolve these difficulties. we developed CytoITMprobe, a  Cytoscape plugin.
Revised:  To resolve these difficulties. we developed CytoITMprobe, a new Cytoscape plugin.
Edit intent: clarity
Original:  We use our analytical results to show how one can reduce the number of equations and parameters in ODE models of cell signalling cascades, and how delay differential equation models can sometimes be approximated through the use of simple expressions involving the incomplete gamma function.
Revised:  We use our analytical results to show how the output of delay differential equation models can sometimes be approximated through the use of simple expressions involving the incomplete gamma function.
Edit intent: clarity
Original: Activation cascadesare a prevalent feature in cellular mechanisms for signaltransduction .
Revised: Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal .
Edit intent: clarity
Original:  Here we study the classic model of linear activation cascades and obtain analytical solutions in terms of lower incomplete gamma functions .
Revised:  Here we study the classic model of linear activation cascades and obtain analytical solutions for a variety of inputs .
Edit intent: clarity
Original:  Finally, we use our results to show how the output of delay differential equation models can be approximated with the use of simple expressions involving the incomplete gamma function .
Revised:  Finally, we show how the output of delay differential equation models can be approximated with the use of simple expressions involving the incomplete gamma function .
Edit intent: clarity
Original:  Finally, we use our results to show how the output of delay differential equation models can be approximated with the use of simple expressions involving the incomplete gamma function .
Revised:  Finally, we use our results to show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction .
Edit intent: clarity
Original:  However, we show that contrarily to a widely shared belief, the simple and partial Mantel tests are not valid statistical procedures to assess the significance of the correlation between two variables structured in space.
Revised:  However, we show that contrarily to a widely shared belief, partial Mantel tests are not valid statistical procedures to assess the significance of the correlation between two variables structured in space.
Edit intent: coherence
Original:  Here, we construct a neural circuit model informed by behavioral and electrophysiological data collected from multiple domains including response inhibition , switching, salience detection, and volitional control .
Revised:  Here, we construct a neural circuit model informed by behavioral and electrophysiological data collected on various response inhibition paradigms .
Edit intent: clarity
Original:  In turn, these regions act to pause action selection via projections to the subthalamic nucleus , allowing executive control to influence behavior .
Revised:  In turn, these regions act to pause action selection via projections to the subthalamic nucleus .
Edit intent: clarity
Original:  Our model reproduces key patterns of behavioral data in the antisaccade and stop signal tasks, and  their sensitivity to lesions and pharmacological manipulations.
Revised:  Our model reproduces key behavioral and their sensitivity to lesions and pharmacological manipulations.
Edit intent: clarity
Original:  It also captures electrophysiological data in the frontal cortex, basal ganglia, and superior colliculus in these tasks.
Edit intent: coherence
Original:  This model extends a well established model of action selection in the basal ganglia (BG) by including a frontal executive control network which integrates information about sensory input and task rules to facilitate well-informed decision making via the oculomotor system.
Revised:  This model extends a well established model of action selection in the basal ganglia by including a frontal executive control network which integrates information about sensory input and task rules to facilitate well-informed decision making via the oculomotor system.
Edit intent: clarity
Original:  Most related work in the literature focuses on low-level modulations, such as binary phase-shift keying (BPSK) or quadrature phase-shift keying (QPSK).
Edit intent: coherence
Original:  In this paper, we consider DNF-based PNC with high-level modulations, specifically the M-ary quadrature amplitude modulation (M-QAM) . We propose a mapping scheme that maps the superposed M-QAM signal to coded symbols.
Revised:  In this paper, we consider DNF-based PNC with M-ary quadrature amplitude modulation (M-QAM) . We propose a mapping scheme that maps the superposed M-QAM signal to coded symbols.
Edit intent: clarity
Original:  In this paper, we consider DNF-based PNC with high-level modulations, specifically the M-ary quadrature amplitude modulation (M-QAM) . We propose a mapping scheme that maps the superposed M-QAM signal to coded symbols.
Revised:  In this paper, we consider DNF-based PNC with high-level modulations, specifically the M-ary quadrature amplitude modulation (M-QAM) and propose a mapping scheme that maps the superposed M-QAM signal to coded symbols.
Edit intent: coherence
Original:  It also ensures that the expected symbol can be successfully decoded at the destination, while attempting to minimize the size of the coded symbol set.
Edit intent: coherence
Original:  Subsequently, we evaluate the symbol error rate and bit error rate (BER) of M-QAM modulated PNC that uses the proposed mapping scheme , both analytically and with simulations . Afterwards, as an application, a rate adaptation scheme for the DNF method of PNC is proposed.
Revised:  Subsequently, we evaluate the symbol error rate and bit error rate (BER) of M-QAM modulated PNC that uses the proposed mapping scheme . Afterwards, as an application, a rate adaptation scheme for the DNF method of PNC is proposed.
Edit intent: coherence
Original:  Rate adaptation is achieved by selecting the appropriate modulation level, based on the channel status and the BER requirement.
Edit intent: coherence
Original:  Simulation results show that  rate-adaptive PNC is advantageous in various scenarios.
Revised:  Simulation results show that the rate-adaptive PNC is advantageous in various scenarios.
Edit intent: fluency
Original: Dodis and Wichs \mbox{ DW09 introduced the notion of a non-malleable extractor to study the problem of privacy amplification with an active adversary.
Revised: Dodis and Wichs introduced the notion of a non-malleable extractor to study the problem of privacy amplification with an active adversary.
Edit intent: coherence
Original:  Given a weakly-random string x and a uniformly random seed y as the inputs, the non-malleable extractor nmExt has the property that nmExt(x,y) appears uniform even given y as well as nmExt(x,A(y)), for an arbitrary function A with A(y) \neq y. Dodis and Wichs showed that such an object can be used to give optimal privacy amplification protocols with an active adversary.
Edit intent: coherence
Original:  Previously, there are only two known explicit constructions of non-malleable extractors \mbox{ DLWZ11, CRS11 . Both constructions only work for (n, k)-sources with k>n/ 2 and thus they also only achieve optimal privacy amplification protocols for k > n / 2. In this paper, we give the first construction of non-malleable extractors for k < n/2.
Revised:  Previously, there are only two known constructions of non-malleable extractors \mbox{ DLWZ11, CRS11 . Both constructions only work for (n, k)-sources with k>n/ 2 and thus they also only achieve optimal privacy amplification protocols for k > n / 2. In this paper, we give the first construction of non-malleable extractors for k < n/2.
Edit intent: clarity
Original:  Previously, there are only two known explicit constructions of non-malleable extractors \mbox{ DLWZ11, CRS11 . Both constructions only work for (n, k)-sources with k>n/ 2 and thus they also only achieve optimal privacy amplification protocols for k > n / 2. In this paper, we give the first construction of non-malleable extractors for k < n/2.
Revised:  Previously, there are only two known explicit constructions of non-malleable extractors . Both constructions only work for (n, k)-sources with k>n/ 2 and thus they also only achieve optimal privacy amplification protocols for k > n / 2. In this paper, we give the first construction of non-malleable extractors for k < n/2.
Edit intent: coherence
Original:  Previously, there are only two known explicit constructions of non-malleable extractors \mbox{ DLWZ11, CRS11 . Both constructions only work for (n, k)-sources with k>n/ 2 and thus they also only achieve optimal privacy amplification protocols for k > n / 2. In this paper, we give the first construction of non-malleable extractors for k < n/2.
Revised:  Previously, there are only two known explicit constructions of non-malleable extractors \mbox{ DLWZ11, CRS11 . Both constructions only work for (n, k)-sources with k>n/ 2 and thus they also only achieve optimal privacy amplification protocols for k > 1 / 2. In this paper, we give the first construction of non-malleable extractors for k < n/2.
Edit intent: clarity
Original:  Specifically, we give two unconditional constructions for min-entropy k=(1/2-\delta)n for some constant \delta>0, and a conditional  construction that can potentially achieve k=\alpha n for any constant \alpha>0.
Revised:  Specifically, we give an unconditional construction for min-entropy k=(1/2-\delta)n for some constant \delta>0, and a conditional construction that can potentially achieve k=\alpha n for any constant \alpha>0.
Edit intent: clarity
Original:  Using our non-malleable extractor, we also obtain the first optimal privacy amplification protocol for min-entropy k =(1/2-\delta)n, with an active adversary.
Revised:  Finally, despite the lack of explicit non-malleable extractor, we also obtain the first optimal privacy amplification protocol for min-entropy k =(1/2-\delta)n, with an active adversary.
Edit intent: clarity
Original: In applicationssuch as playlist recommendation,  flow analysis in information networks , and itinerary planning, we face the problem of finding the heaviest path(s) in a graph under a given length constraint .
Revised: In applicationssuch as playlist recommendation, and flow analysis in information networks , and itinerary planning, we face the problem of finding the heaviest path(s) in a graph under a given length constraint .
Edit intent: fluency
Original: In applicationssuch as playlist recommendation,  flow analysis in information networks , and itinerary planning, we face the problem of finding the heaviest path(s) in a graph under a given length constraint .
Revised: In applicationssuch as playlist recommendation, flow analysis in information networks is that of finding the heaviest path(s) in a graph under a given length constraint .
Edit intent: clarity
Original: In applicationssuch as playlist recommendation,  flow analysis in information networks , and itinerary planning, we face the problem of finding the heaviest path(s) in a graph under a given length constraint .
Revised: In applicationssuch as playlist recommendation, flow analysis in information networks , and itinerary planning, we face the problem of finding the heaviest path(s) in a graph .
Edit intent: clarity
Original:  More precisely, in these applications , we are given a graph with non-negative edge weights, and a monotone function such as sum, which aggregates edge weights into a single value that defines a path weight .
Revised:  More precisely, we can model these applications as a graph with non-negative edge weights, and a monotone function such as sum, which aggregates edge weights into a single value that defines a path weight .
Edit intent: clarity