wanyu/IteraTeR_v2 huggingface dataset:
Original:  Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system are formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs).
Revised:  Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs).
Edit intent: fluency
Original:  In the existing approaches, the optimization feasibility and the system safety cannot be enhanced at the same time theoretically.
Revised:  In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically.
Edit intent: clarity
Original:  Relaxing variables are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same.
Revised:  Slack variables with relaxing technique are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same.
Edit intent: clarity
Original:  We define a synthesis algorithm that, given an alphabet P of observable actions and a regular timed correctness property e, returns a monitor that enforces the property e during the execution of any (potentially corrupted) controller with alphabet P, and complying with the property e.
Revised:  We define a synthesis algorithm that, given an alphabet P of observable actions and a timed correctness property e, returns a monitor that enforces the property e during the execution of any (potentially corrupted) controller with alphabet P, and complying with the property e.
Edit intent: clarity
Original:  The objective is to understand the neuronal population dynamics that underlie phase entrainment . Phase and frequency entrainment of brain oscillations by external stimuli are used as therapeutic treatment in neurological disorders, for example in Parkinsonian tremor.
Revised:  The objective is to understand the neuronal population dynamics that underlie phase entrainment of brain oscillations by external stimuli are used as therapeutic treatment in neurological disorders, for example in Parkinsonian tremor.
Edit intent: clarity
Original:  The objective is to understand the neuronal population dynamics that underlie phase entrainment . Phase and frequency entrainment of brain oscillations by external stimuli are used as therapeutic treatment in neurological disorders, for example in Parkinsonian tremor.
Revised:  The objective is to understand the neuronal population dynamics that underlie phase entrainment . Phase and frequency entrainment of brain oscillations by external stimuli , which is used for therapeutic treatment in neurological disorders, for example in Parkinsonian tremor.
Edit intent: coherence
Original:  And yet , the neuronal dynamics underpinning such entrainment is not fully understood.
Revised:  Yet , the neuronal dynamics underpinning such entrainment is not fully understood.
Edit intent: coherence
Original:  Rhythmic sensory stimulation is one way of studying phase synchronisation in the brain.
Revised:  Rhythmic sensory stimulation is one way of studying phase synchronization in the brain.
Edit intent: fluency
Original:  A recent experimental study has shown phase entrainment of brain oscillations during steady state visually evoked potentials (SSVEP), which are scalp electroencephalogram corresponding to periodic rhythmic stimuli.
Revised:  A recent experimental study has reported phase entrainment of brain oscillations during steady state visually evoked potentials (SSVEP), which are scalp electroencephalogram corresponding to periodic rhythmic stimuli.
Edit intent: clarity
Original:  A recent experimental study has shown phase entrainment of brain oscillations during steady state visually evoked potentials (SSVEP), which are scalp electroencephalogram corresponding to periodic rhythmic stimuli.
Revised:  A recent experimental study has shown phase entrainment of brain oscillations during steady state visually evoked potentials (SSVEP), which are scalp electroencephalogram corresponding to periodic stimuli.
Edit intent: clarity
Original:  We have used phase locking values, normalised Shannon entropy and conditional probability as synchronisation indices showing relative phase synchrony between the neuronal populations as well with the input.
Revised:  We have used phase locking values, normalised Shannon entropy and conditional probability as synchronisation indices to show phase synchrony in the neuronal populations as well with the input.
Edit intent: clarity
Original:  Thus, it may be inferred that the phase synchronisation implies entrainment of the network response by the periodic input.
Revised:  Thus, the phase synchronisation implies entrainment of the network response by the periodic input.
Edit intent: clarity
Original:  Overall, our study shows the plausibility of using biologically inspired in silico models, validated with experimental works, to understand and make testable predictions on brain entrainment as a therapeutic treatment in specific neurological disorders.
Revised:  Overall, our study shows the plausibility of using biologically inspired in silico models, validated by experimental works, to understand and make testable predictions on brain entrainment as a therapeutic treatment in specific neurological disorders.
Edit intent: clarity
Original:  In order to be used in "industrial grade" applications, we give implementations for these models that are extremely time efficient, solving large instances, with n = 2000, in one hour on a PC, even for a two-sided matching market.
Revised:  In order to be used in "industrial grade" applications, we demonstrate very fast implementations for these models that are extremely time efficient, solving large instances, with n = 2000, in one hour on a PC, even for a two-sided matching market.
Edit intent: clarity
Original:  In order to be used in "industrial grade" applications, we give implementations for these models that are extremely time efficient, solving large instances, with n = 2000, in one hour on a PC, even for a two-sided matching market.
Revised:  In order to be used in "industrial grade" applications, we give implementations for these models . These are able to solve large instances, with n = 2000, in one hour on a PC, even for a two-sided matching market.
Edit intent: clarity
Original:  Our approach yields a rich collection of models , not only for one-sided , but also two-sided , markets.
Revised:  Our approach yields a rich collection of models : for one-sided , but also two-sided , markets.
Edit intent: coherence
Original:  Our approach yields a rich collection of models , not only for one-sided , but also two-sided , markets.
Revised:  Our approach yields a rich collection of models , not only for one-sided as well as two-sided , markets.
Edit intent: clarity
Original:  We transform \bot_B(e) into a corresponding "bottom-graph" that can be processed for use by standard GNN implementations.
Revised:  We represent \bot_B(e) into a corresponding "bottom-graph" that can be processed for use by standard GNN implementations.
Edit intent: clarity
Original:  We transform \bot_B(e) into a corresponding "bottom-graph" that can be processed for use by standard GNN implementations.
Revised:  We transform \bot_B(e) by a "bottom-graph" that can be processed for use by standard GNN implementations.
Edit intent: clarity
Original:  We transform \bot_B(e) into a corresponding "bottom-graph" that can be processed for use by standard GNN implementations.
Revised:  We transform \bot_B(e) into a corresponding "bottom-graph" that can be converted into a form suitable for GNN implementations.
Edit intent: clarity
Original:  In a separate paper we report a model checking procedure for POTL and experimental results based on a prototype tool developed therefor.
Revised:  In a companion paper we report a model checking procedure for POTL and experimental results based on a prototype tool developed therefor.
Edit intent: clarity
Original:  This allows us to learn the CNN centralized at the base station (BS).
Revised:  This allows to learn the CNN centralized at the base station (BS).
Edit intent: clarity
Original:  This circumvents the necessity of an infeasible amount of feedback, the acquisition of training data at the user, and the offline training phase at each MT. Numerical results show that the CNN which is trained solely  on UL data performs equally well as the network trained  on DL data.
Revised:  This circumvents the necessity of an infeasible amount of feedback, i.e., acquisition of training data at the user, and the offline training phase at each MT. Numerical results show that the CNN which is trained solely on UL data performs equally well as the network trained on DL data.
Edit intent: clarity
Original:  This circumvents the necessity of an infeasible amount of feedback, the acquisition of training data at the user, and the offline training phase at each MT. Numerical results show that the CNN which is trained solely  on UL data performs equally well as the network trained  on DL data.
Revised:  This circumvents the necessity of an infeasible amount of feedback, the acquisition of training data at the user, and the offline training phase at each MT. Numerical results show that the CNN which is trained solely based on UL data performs equally well as the network trained on DL data.
Edit intent: clarity
Original:  This circumvents the necessity of an infeasible amount of feedback, the acquisition of training data at the user, and the offline training phase at each MT. Numerical results show that the CNN which is trained solely  on UL data performs equally well as the network trained  on DL data.
Revised:  This circumvents the necessity of an infeasible amount of feedback, the acquisition of training data at the user, and the offline training phase at each MT. Numerical results show that the CNN which is trained solely on UL data performs equally well as the network trained based on DL data.
Edit intent: clarity
Original: We investigate the algebraic and compositional properties of multiway (non-deterministic) abstract rewriting systems, which are the archetypical structures underlying the formalism of the so-called Wolfram model.
Revised: We investigate algebraic and compositional properties of multiway (non-deterministic) abstract rewriting systems, which are the archetypical structures underlying the formalism of the so-called Wolfram model.
Edit intent: fluency
Original: We investigate the algebraic and compositional properties of multiway (non-deterministic) abstract rewriting systems, which are the archetypical structures underlying the formalism of the so-called Wolfram model.
Revised: We investigate the algebraic and compositional properties of abstract multiway rewriting systems, which are the archetypical structures underlying the formalism of the so-called Wolfram model.
Edit intent: clarity
Original: We investigate the algebraic and compositional properties of multiway (non-deterministic) abstract rewriting systems, which are the archetypical structures underlying the formalism of the so-called Wolfram model.
Revised: We investigate the algebraic and compositional properties of multiway (non-deterministic) abstract rewriting systems, which are archetypical structures underlying the formalism of the so-called Wolfram model.
Edit intent: fluency
Original: We investigate the algebraic and compositional properties of multiway (non-deterministic) abstract rewriting systems, which are the archetypical structures underlying the formalism of the so-called Wolfram model.
Revised: We investigate the algebraic and compositional properties of multiway (non-deterministic) abstract rewriting systems, which are the archetypical structures underlying the formalism of the Wolfram model.
Edit intent: clarity
Original:  We demonstrate the existence of higher homotopies in this class of rewriting systems, where these homotopic maps are induced by the inclusion of appropriate rewriting rules taken from an abstract rulial space of all possible such rules.
Revised:  We demonstrate the existence of higher homotopies in this class of rewriting systems, where homotopical maps are induced by the inclusion of appropriate rewriting rules taken from an abstract rulial space of all possible such rules.
Edit intent: clarity
Original:  We conclude with some comments on how this computational framework of multiway rewriting systems may potentially be used for making formal connections to homotopy spaces upon which models of physics can be instantiated.
Revised:  We conclude with some comments on how this computational framework of homotopical multiway systems may potentially be used for making formal connections to homotopy spaces upon which models of physics can be instantiated.
Edit intent: clarity
Original:  We conclude with some comments on how this computational framework of multiway rewriting systems may potentially be used for making formal connections to homotopy spaces upon which models of physics can be instantiated.
Revised:  We conclude with some comments on how this computational framework of multiway rewriting systems may potentially be used for making formal connections to homotopy spaces upon which models relevant to physics may be instantiated.
Edit intent: clarity
Original:  Rather, our interest in parameters is motivated by parameter uncertainty, as reaction rates are typically either measures with limited precision or estimated.
Revised:  Rather, our interest in parameters is motivated by parameter uncertainty, as reaction rates are typically either measured with limited precision or estimated.
Edit intent: fluency
Original:  We aim at detecting toricity and shifted toricity, using a framework that has been recently introduced and studied for the non-parametric case over both the reals and the complex numbers.
Revised:  We aim at detecting toricity and shifted toricity, using a framework that has been recently introduced and studied for the non-parametric case over both the real and the complex numbers.
Edit intent: fluency
Original:  Roughly speaking, a register is some mutable part of the program state , e. g., mutable classical variables and quantum registers and wires in quantum circuits are examples of this.
Revised:  Roughly speaking, a register is some mutable part of the program state . Mutable classical variables and quantum registers and wires in quantum circuits are examples of this.
Edit intent: coherence
Original:  However, real-time constraints frequently limit the accuracy of online tests , especially in scenarios where realistic robot-terrain interactions are complex to model.
Revised:  However, real-time constraints frequently limit the accuracy of online tests especially in scenarios where realistic robot-terrain interactions are complex to model.
Edit intent: fluency
Original:  In this context, we propose a deep learning framework , trained in an end-to-end fashion from elevation maps and trajectories , to estimate the occurrence of failure events.
Revised:  In this context, we propose a deep learning framework trained in an end-to-end fashion from elevation maps and trajectories , to estimate the occurrence of failure events.
Edit intent: fluency
Original:  In this context, we propose a deep learning framework , trained in an end-to-end fashion from elevation maps and trajectories , to estimate the occurrence of failure events.
Revised:  In this context, we propose a deep learning framework , trained in an end-to-end fashion from elevation maps and trajectories to estimate the occurrence of failure events.
Edit intent: fluency
Original:  Adding a register results in a concurrent extension of the calculus of signal flow graphs, powerful enough to capture continuous Petri nets.
Edit intent: coherence
Original:  SPARQ achieves minor accuracy degradation , 2x speedup over widely used hardware architectures, and a practical hardware implementation.
Revised:  SPARQ achieves minor accuracy degradation and a practical hardware implementation.
Edit intent: clarity
Original:  In this work we develop a straightforward entropy regularised splitting scheme for degenerate non-local non-gradient systems.
Revised:  In this work we develop a natural operator-splitting variational scheme for a general class of non-local non-gradient systems.
Edit intent: clarity
Original:  We illustrate the generality of our work by providing a number of examples, including the Regularized Vlasov-Poisson-Fokker-Planck equation , to which our results applicable .
Revised:  We illustrate the generality of our work by providing a number of examples, including the Regularized Vlasov-Poisson-Fokker-Planck equation .
Edit intent: clarity
Original:  We propose a more general class of EGDs, which we call ``harmless'' , that subsume separable EGDs and allow to model a much broader class of problems.
Revised:  We propose a more general class of EGDs, which we call "harmless" , that subsume separable EGDs and allow to model a much broader class of problems.
Edit intent: fluency
Original: The formation of new vascular networks is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development.
Revised: Neovascularisation is essential for tissue development and regeneration, in addition to playing a key role in pathological settings such as ischemia and tumour development.
Edit intent: clarity
Original:  Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, known as cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo.
Revised:  Experimental findings in the past two decades have led to the identification of a new mechanism of neovascularisation, cluster-based vasculogenesis, during which endothelial progenitor cells (EPCs) mobilised from the bone marrow are capable of bridging distant vascular beds in a variety of hypoxic settings in vivo.
Edit intent: clarity
Original:  In order to achieve this, we propose a  mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of non-local partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion.
Revised:  In order to achieve this, we propose a novel mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of non-local partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion.
Edit intent: clarity
Original:  In order to achieve this, we propose a  mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of non-local partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion.
Revised:  In order to achieve this, we propose a mathematical model of the early stages of cluster-based vasculogenesis, comprising of a system of nonlocal partial differential equations including key mechanisms such as endogenous chemotaxis, matrix degradation, cell proliferation and cell-to-cell adhesion.
Edit intent: fluency
Original:  Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation and topology of clusters, indicating promising, fruitful future modelling and experimental research perspectives .
Revised:  Our results, which qualitatively compare with data from in vitro experiments, elucidate the complementary role played by endogenous chemotaxis and matrix degradation in the formation of clusters, indicating promising, fruitful future modelling and experimental research perspectives .
Edit intent: clarity
Original:  This limits the full use of capabilities of both the  technology and EDA tools.
Revised:  This limits the full use of capabilities of both the process technology and EDA tools.
Edit intent: clarity
Original: In computer science, the "Subset Sum problem" is a very well known NP-complete problem.
Revised: The "Subset Sum problem" is a very well known NP-complete problem.
Edit intent: clarity
Original: In computer science, the "Subset Sum problem" is a very well known NP-complete problem.
Revised: In computer science, the "Subset Sum problem" is a very well-known NP-complete problem.
Edit intent: fluency
Original:  In this article, we consider its top-k variation - the " Top-k Subset Sums problem" that has wide application in recommendation systems, where instead of k best objects they require k best subsets of objects with  lowest (or highest) overall scores . Given any input set R of n real numbers , and a positive integer k, our target is to generate the k best subsets (top-k Subset Sums) of R , whose sum of elements is minimized.
Revised:  In this work, a top-k variation - the " Top-k Subset Sums problem" that has wide application in recommendation systems, where instead of k best objects they require k best subsets of objects with lowest (or highest) overall scores . Given any input set R of n real numbers , and a positive integer k, our target is to generate the k best subsets (top-k Subset Sums) of R , whose sum of elements is minimized.
Edit intent: clarity
Original:  In this article, we consider its top-k variation - the " Top-k Subset Sums problem" that has wide application in recommendation systems, where instead of k best objects they require k best subsets of objects with  lowest (or highest) overall scores . Given any input set R of n real numbers , and a positive integer k, our target is to generate the k best subsets (top-k Subset Sums) of R , whose sum of elements is minimized.
Revised:  In this article, we consider its top-k variation of the " Top-k Subset Sums problem" that has wide application in recommendation systems, where instead of k best objects they require k best subsets of objects with lowest (or highest) overall scores . Given any input set R of n real numbers , and a positive integer k, our target is to generate the k best subsets (top-k Subset Sums) of R , whose sum of elements is minimized.
Edit intent: fluency
Original:  In this article, we consider its top-k variation - the " Top-k Subset Sums problem" that has wide application in recommendation systems, where instead of k best objects they require k best subsets of objects with  lowest (or highest) overall scores . Given any input set R of n real numbers , and a positive integer k, our target is to generate the k best subsets (top-k Subset Sums) of R , whose sum of elements is minimized.
Revised:  In this article, we consider its top-k variation - the " Subset Sum problem" that has wide application in recommendation systems, where instead of k best objects they require k best subsets of objects with lowest (or highest) overall scores . Given any input set R of n real numbers , and a positive integer k, our target is to generate the k best subsets (top-k Subset Sums) of R , whose sum of elements is minimized.
Edit intent: fluency