wanyu/IteraTeR_v2 huggingface dataset:
Original:  Our approach leads to new expressions for the menage numbers and their exponential generating function and allows one to efficiently compute the number of seating arrangements in general cases, which we illustrate in details for the ternary case of k=3.
Revised:  Our approach leads to new expressions for the menage numbers and their exponential generating function and allows one to efficiently compute the number of seating arrangements in general cases, which we illustrate in detail for the ternary case of k=3.
Edit intent: fluency
Original:  We propose a new method for estimating the  evolutionary distance between two genomes with high accuracy under the fragile breakage model  .
Revised:  We propose a new method for estimating the evolutionary distance between two genomes under the fragile breakage model .
Edit intent: clarity
Original: We study the price of Asian options with floating-strike when the underlying asset price follows a  regime-switching  geometric Brownian motion  .
Revised: We study the price of Asian options with floating-strike when the underlying asset price follows a regime-switching ) geometric Brownian motion .
Edit intent: fluency
Original:  We propose an iterative procedure to compute the option prices without recourse to solving a  PDE system.
Revised:  We propose an iterative procedure that converges to the option prices without recourse to solving a PDE system.
Edit intent: clarity
Original:  We show that global games with noisy sharing of information do not admit an intuitive type of threshold policies which only depends on agents' belief about the underlying \theta.
Revised:  We show that global games with noisy sharing of information do not admit an intuitive type of threshold policy which only depends on agents' belief about the underlying \theta.
Edit intent: fluency
Original:  This is in contrast to the existing results on the threshold policies for the conventional set-up of global games.
Revised:  This is in contrast to the existing results on the threshold policy for the conventional set-up of global games.
Edit intent: fluency
Original:  Nevertheless, such methods have shown lack of precision in phenotypes classification.
Revised:  Nevertheless, such methods have shown lack of accuracy in phenotypes classification.
Edit intent: clarity
Original:  In addition, our method is able to correctly classify sets of tumor samples drawn from TCGA (overall error rate equal to 0.90\%) .
Revised:  In addition, our method is able to correctly classify sets of tumor samples drawn from TCGA .
Edit intent: coherence
Original:  Single molecule studies have uncovered the detailed force kinetics of isolated motor proteins in-vitro , however their behavior in-vivo has been elusivedue to the complex environment inside the cell .
Revised:  Single molecule studies have uncovered the detailed force kinetics of isolated motor proteins in-vitro by single molecule approaches, however, their in-vivo has been elusivedue to the complex environment inside the cell .
Edit intent: clarity
Original:  Single molecule studies have uncovered the detailed force kinetics of isolated motor proteins in-vitro , however their behavior in-vivo has been elusivedue to the complex environment inside the cell .
Revised:  Single molecule studies have uncovered the detailed force kinetics of isolated motor proteins in-vitro , however their behavior in-vivo behavior has remained elusive .
Edit intent: clarity
Original:  We integrate an experimental and theoretical framework to connect mesoscopic measurements of nonequilibrium properties to the underlying molecular-scale force kinetics .
Revised:  We integrate an experimental and theoretical framework to extract molecular-scale force kinetics .
Edit intent: clarity
Original:  The kinetics of molecular motors have been precisely characterized in-vitro by single molecule approaches, however, their in-vivo behavior has remained elusive.
Revised:  The kinetics of molecular motors have been precisely characterized in-vitro by single molecule approaches, however, their in-vivo behavior remains elusive.
Edit intent: fluency
Original:  Our results reveal that measuring in-vivo active fluctuations allows extraction of the underlying molecular motor activity and demonstrates a widely applicable mesoscopic framework to access molecular-scale force kinetics.
Revised:  Our results reveal that measuring in-vivo active fluctuations allows extraction of the underlying molecular motor activity and demonstrates a mesoscopic framework to access molecular-scale force kinetics.
Edit intent: clarity
Original:  Our results reveal that measuring in-vivo active fluctuations allows extraction of the underlying molecular motor activity and demonstrates a widely applicable mesoscopic framework to access molecular-scale force kinetics.
Revised:  Our results reveal that measuring in-vivo active fluctuations allows extraction of the underlying molecular motor activity and demonstrates a widely applicable mesoscopic framework to access force kinetics.
Edit intent: clarity
Original:  The problem has previously been studied by analogy with statistical mechanics: the allele frequency distribution at each time is approximated by the stationary form, which maximises entropy.
Revised:  The problem has previously been studied by analogy with statistical mechanics: the allele frequency distribution at each time is approximated by the stationary form, which maximizes entropy.
Edit intent: fluency
Original:  In these numerical experiments, the PELS approach often produced significant convergence improvements compared to the use of classical Wolfe approximate line searches.
Revised:  In these numerical experiments, the PELS approach produced significant convergence improvements compared to the use of classical Wolfe approximate line searches.
Edit intent: clarity
Original:  In these numerical experiments, the PELS approach often produced significant convergence improvements compared to the use of classical Wolfe approximate line searches.
Revised:  In these numerical experiments, the PELS approach often produced significant convergence improvements compared to the use of classical Wolfe line searches.
Edit intent: clarity
Original:  The new PELS method has the potential to significantly speed up widely-used parallel large-scale regression and factorization computations, and is broadly applicable to important classes of continuous optimization problems with smooth loss functions.
Revised:  The new PELS method has the potential to significantly accelerate large-scale regression and factorization computations, and is broadly applicable to important classes of continuous optimization problems with smooth loss functions.
Edit intent: clarity
Original:  The new PELS method has the potential to significantly speed up widely-used parallel large-scale regression and factorization computations, and is broadly applicable to important classes of continuous optimization problems with smooth loss functions.
Revised:  The new PELS method has the potential to significantly speed up widely-used parallel large-scale regression and factorization computations, and is applicable to continuous optimization problems with smooth loss functions.
Edit intent: clarity
Original:  Recentlyclinical trials demonstrated that blockade of immune checkpoint signals led to dramatic clinic responses in a fraction of cancer patients.
Revised:  Recentlyclinical trials demonstrated that blockade of immune checkpoint signals ) demonstrates therapeutic effects in treatment of human cancer, but only in a fraction of cancer patients.
Edit intent: clarity
Original:  To improve the therapeutic efficacy of regimens aimed to enhance T cell responses to cancers, a predictable mathematical model is needed for designing efficient therapy.
Revised:  Since this therapy is aimed to enhance T cell responses to cancers, a predictable mathematical model is needed for designing efficient therapy.
Edit intent: clarity
Original:  Our model provides a rationale for synergistic treatment combination aimed to defuse resistance and maximize T cell responses against cancers .
Revised:  This model allows us to evaluate strategies in order to enhance antitumor T cell responses against cancers .
Edit intent: clarity
Original:  We also show that the cut polynomials and the perfect matching polynomial (or ``unsigned Pfaffian'' ) are not monotone p-projections of the permanent.
Revised:  We also show that the cut polynomials and the perfect matching polynomial (or "unsigned Pfaffian" ) are not monotone p-projections of the permanent.
Edit intent: fluency
Original: In this short note, we show that the  Hamiltonian Cycle polynomial is not a monotone sub-exponential-size projection of the permanent;
Revised: In this short note, we show that the Hamiltonian Cycle polynomial is not a monotone subexponential-size projection of the permanent;
Edit intent: fluency
Original:  this both rules out a natural attempt at a monotone lower bound on the Boolean permanent, and shows that the permanent is not complete for non-negative polynomials in VNP_{ \mathbb{R } under monotone p-projections.
Revised:  this both rules out a natural attempt at a monotone lower bound on the Boolean permanent, and shows that the permanent is not complete for non-negative polynomials in VNP_{ \mathbb R } under monotone p-projections.
Edit intent: fluency
Original:  We also show that the cut polynomials and the perfect matching polynomial (or "unsigned Pfaffian") are not monotone p-projections of the permanent.
Revised:  2. The cut polynomials and the perfect matching polynomial (or "unsigned Pfaffian") are not monotone p-projections of the permanent.
Edit intent: coherence
Original:  The latter can be interpreted as saying that there is no monotone projection reduction from counting perfect matchings in general graphs to counting perfect matchings in bipartite graphs , putting at least one theorem behind the well-established intuition .
Revised:  The latter can be interpreted as saying that there is no monotone projection reduction from counting perfect matchings in general graphs to perfect matchings in bipartite graphs , putting at least one theorem behind the well-established intuition .
Edit intent: fluency
Original:  The latter can be interpreted as saying that there is no monotone projection reduction from counting perfect matchings in general graphs to counting perfect matchings in bipartite graphs , putting at least one theorem behind the well-established intuition .
Revised:  The latter can be interpreted as saying that there is no monotone projection reduction from counting perfect matchings in general graphs to counting perfect matchings in bipartite graphs .
Edit intent: coherence
Original: We present an algorithm for synthesizing recursive functions that provably satisfy a given specification in the form of a refinement type.
Revised: We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a refinement type.
Edit intent: clarity
Original:  We show that refinement types can be decomposed more effectively than other kinds of specifications, which helps prune the space of candidate programs the synthesizer has to consider.
Revised:  We show that refinement types can be decomposed more effectively than other kinds of specifications, which is the key to pruning the search space of candidate programs the synthesizer has to consider.
Edit intent: clarity
Original:   We have evaluated our prototype implementation on a set of benchmarks and found that it meets or exceeds the state of the art in terms of scalability and conciseness of user input, and also extends the class of programs for which a verified implementation can be synthesized .
Revised:  We have evaluated our prototype implementation on a large set of synthesis problems and found that it meets or exceeds the state of the art in terms of scalability and conciseness of user input, and also extends the class of programs for which a verified implementation can be synthesized .
Edit intent: clarity
Original:   We have evaluated our prototype implementation on a set of benchmarks and found that it meets or exceeds the state of the art in terms of scalability and conciseness of user input, and also extends the class of programs for which a verified implementation can be synthesized .
Revised:  We have evaluated our prototype implementation on a set of benchmarks and found that it exceeds the state of the art in terms of scalability and conciseness of user input, and also extends the class of programs for which a verified implementation can be synthesized .
Edit intent: clarity
Original:  First, they support automatic inference of rich universal invariants , which enables synthesis of nontrivial programswith no additional hints from the user . Second, refinement types can be decomposed more effectively than other kinds of specifications , which is the key to pruning the search space of candidate programs.
Revised:  First, they support automatic inference of rich universal invariants , which enables automatic verification---and hence synthesis---of nontrivial programs . Second, refinement types can be decomposed more effectively than other kinds of specifications , which is the key to pruning the search space of candidate programs.
Edit intent: clarity
Original:  The tool was able to synthesize more complex programs than those reported in prior work (several sorting algorithms , binary-search tree manipulations, red-black tree rotation ), as well as most of the benchmarks tackled by existing synthesizers, often starting from a more concise and intuitive user input.
Revised:  The tool was able to synthesize more complex programs than those reported in prior work (several sorting algorithms and operations on balanced search trees ), as well as most of the benchmarks tackled by existing synthesizers, often starting from a more concise and intuitive user input.
Edit intent: clarity
Original:  More precisely, our problem of interest consists in the optimization , over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs).
Revised:  More precisely, our problem of interest consists in the optimisation , over a set of possibly non-dominated probability measures, of solutions of backward stochastic differential equations (BSDEs).
Edit intent: fluency
Original:  Our first main contribution is to prove a dynamic pro- gramming principle for this control problem in an abstract setting, which we then use to provide a semimartingale characterization of the value function.
Revised:  Our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting, which we then use to provide a semimartingale characterization of the value function.
Edit intent: fluency
Original:  Our first main contribution is to prove a dynamic pro- gramming principle for this control problem in an abstract setting, which we then use to provide a semimartingale characterization of the value function.
Revised:  Our first main contribution is to prove a dynamic pro- gramming principle for this control problem in an abstract setting, which we then use to provide a semi-martingale characterisation of the value function.
Edit intent: fluency
Original:  Finally, we relate, under addi- tional regularity assumptions, the value function to a viscosity solution of an appropriate path-dependent partial differential equation (PPDE).
Revised:  Finally, we relate, under additional regularity assumptions, the value function to a viscosity solution of an appropriate path-dependent partial differential equation (PPDE).
Edit intent: fluency
Original: This paper presents a sociophysics model which incorporates psychological factors as a determinant and as a consequence of social network characteristics.
Revised: This paper presents two models that exemplify psychological factors as a determinant and as a consequence of social network characteristics.
Edit intent: clarity
Original:  There is an endogeneity considered in network formation: while the social experiences have impacts on people, their current psychological states and traits affect the network evolution.
Revised:  There is an endogeneity considered in network formation: while the social experiences have impacts on people, their current psychological states and traits affect network evolution.
Edit intent: fluency
Original:  An agent-based model over Bianconi-Barabasi networks is used to model social psychology phenomena.
Revised:  The first model is an agent-based model over Bianconi-Barabasi networks is used to model social psychology phenomena.
Edit intent: coherence
Original:  The onion spectrum is exactly as easy to compute as the k-cores: it is based on the stages at which each vertex gets removed from a graph in the standard algorithm for computing the k-cores.
Revised:  The onion spectrum is exactly as easy to compute as the k-cores: It is based on the stages at which each vertex gets removed from a graph in the standard algorithm for computing the k-cores.
Edit intent: fluency
Original:  Furthermore, unlike the k-core decomposition, the combined onion-degree spectrum immediately gives a clear local picture of the network around each node which allows the detection of interesting subgraphs whose topological structure differs from the global network organization.
Revised:  Furthermore, unlike the k-core decomposition, the combined degree-onion spectrum immediately gives a clear local picture of the network around each node which allows the detection of interesting subgraphs whose topological structure differs from the global network organization.
Edit intent: fluency
Original:  This local description can also be leveraged to easily generate samples from the ensemble of networks with a given joint onion-degree distribution.
Revised:  This local description can also be leveraged to easily generate samples from the ensemble of networks with a given joint degree-onion distribution.
Edit intent: fluency
Original:  Therefore, we consider a nonlinear infection process, which generalizes the bilinear process arising from the classic mass-action assumption.
Revised:  Therefore, we consider a nonlinear infection process, which generalises the bilinear process arising from the classic mass-action assumption.
Edit intent: fluency
Original:  We then provide empirical evidence that at least some important examples of both naturally occurring and engineered networks are capable of approaching a state of optimal dynamical efficiency, one of the key results of the theory.
Revised:  We then provide empirical evidence that at least some important examples of widely different naturally occurring and engineered networks are capable of approaching a state of optimal dynamical efficiency, one of the key results of the theory.
Edit intent: clarity
Original:  In different ways, we use the theory to investigate properties of pyramidal neurons in biological neural networks in the visual cortex, the prevalence of the small world network topology, and the internet router network  .
Revised:  In different ways, we use the theory to investigate properties of pyramidal neurons in the visual cortex, the prevalence of the small world network topology, and the internet router network .
Edit intent: clarity
Original:  In different ways, we use the theory to investigate properties of pyramidal neurons in biological neural networks in the visual cortex, the prevalence of the small world network topology, and the internet router network  .
Revised:  In different ways, we use the theory to investigate properties of pyramidal neurons in biological neural networks in the visual cortex, and the internet router network .
Edit intent: coherence
Original: The functional and computational power of a network emerges as a property of the system operating as a coherent whole at a global scale, not at the scale of individual nodes.
Revised: The functional and computational power of a network emerges as a prop- erty of the system operating as a coherent whole at a global scale, not at the scale of individual nodes.
Edit intent: fluency
Original:  A natural question to ask is what are the physical principles that allow a collection of nodes to interact in such a way that they produce emergent global network dynamics?
Revised:  A natural question to ask is what are the physical principles that allow a collection of nodes to interact in such away that they produce emergent global network dynamics?
Edit intent: fluency
Original:  There is in general a lack of sufficient theory capable of providing insights into universal physical principles that bridge individual node dynamics to the behavior of the network as a whole in a deterministic way.
Edit intent: coherence
Original:  One of the main theoretical results is the definition of a ratio between the speed of signaling or information flow, which is bounded by the spatial geometry, and the internal time it takes for individual nodes to process incoming signals.
Revised:  One of the main theoretical results is the definition of a ratio between the signaling latencies on the edges of the network and the internal time it takes for individual nodes to process incoming signals.
Edit intent: clarity
Original:  In parallel  the minimal model size is studied with a suitable notion of minimality.
Revised:  In parallel , the minimal model size is studied with a suitable notion of minimality.
Edit intent: fluency
Original:  A sharp dichotomy is shown in terms of complexity and optimal models: Temporal depth one has low expressive power, while temporal depth two is equivalent to full CTL.
Revised:  A sharp dichotomy is shown in terms of complexity and minimal models: Temporal depth one has low expressive power, while temporal depth two is equivalent to full CTL.
Edit intent: clarity
Original: We investigate two novel mixed robust/average-case submodular data partitioning problems that we collectively call Submodular Partitioning .
Revised: We study two mixed robust/average-case submodular data partitioning problems that we collectively call Submodular Partitioning .
Edit intent: clarity
Original: We investigate two novel mixed robust/average-case submodular data partitioning problems that we collectively call Submodular Partitioning .
Revised: We investigate two novel mixed robust/average-case submodular partitioning problems that we collectively call Submodular Partitioning .
Edit intent: clarity
Original: We investigate two novel mixed robust/average-case submodular data partitioning problems that we collectively call Submodular Partitioning .
Revised: We investigate two novel mixed robust/average-case submodular data partitioning problems that we collectively call Submodular Partitioning .
Edit intent: fluency
Original:  These problems generalize  purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Revised:  These problems generalize both purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Edit intent: fluency
Original:  These problems generalize  purely robust instances of the problem , namelymax-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Revised:  These problems generalize purely robust instances of the problem max-min submodular fair allocation (SFA) and \emph{min-max submodular load balancing (SLB) , and also average-case instances , that is the submodular welfare problem (SWP) and \emph{submodular multiway partition (SMP).
Edit intent: clarity