wanyu/IteraTeR_v2 huggingface dataset:
Original:  We also demonstrate that the simple Markov model cannot really be improved upon  : First, a window length of I/\epsilon (I/\epsilon^2) is information-theoretically necessary for KL error ( \ell_1 error ) . Second, the d^{\Theta(I/\epsilon)} samples required to accurately estimate the Markov model when observations are drawn from an alphabet of size d is in fact necessary for any computationally tractable  algorithm, assuming the hardness of strongly refuting a certain class of CSPs.
Revised:  We also demonstrate that the simple Markov model cannot really be improved upon : First, a window length of I/\epsilon (I/\epsilon^2) is information-theoretically necessary for KL error ( \ell_1 error ) . Second, the d^{\Theta(I/\epsilon)} samples required to accurately estimate the Markov model when observations are drawn from an alphabet of size d is in fact necessary for any computationally tractable learning/prediction algorithm, assuming the hardness of strongly refuting a certain class of CSPs.
Edit intent: clarity
Original:  We show that for  any distribution over observations, if the mutual information between past observations and future observations is upper bounded by I, then a simple Markov model over the most recent I/\epsilon observations obtains expected KL error \epsilon --and hence \ell_1 error \epsilon --with respect to the optimal predictor that has access to the entire past  .
Revised:  We show that for any distribution over observations, if the mutual information between past observations and future observations is upper bounded by I, then a simple Markov model over the most recent I/\epsilon observations obtains expected KL error \epsilon ---and hence \ell_1 error \epsilon --with respect to the optimal predictor that has access to the entire past .
Edit intent: fluency
Original:  We show that for  any distribution over observations, if the mutual information between past observations and future observations is upper bounded by I, then a simple Markov model over the most recent I/\epsilon observations obtains expected KL error \epsilon --and hence \ell_1 error \epsilon --with respect to the optimal predictor that has access to the entire past  .
Revised:  We show that for any distribution over observations, if the mutual information between past observations and future observations is upper bounded by I, then a simple Markov model over the most recent I/\epsilon observations obtains expected KL error \epsilon --and hence \ell_1 error \epsilon ---with respect to the optimal predictor that has access to the entire past .
Edit intent: fluency
Original:  We also establish that this result cannot be improved upon,  in the following  senses: First,  a window length of I /\epsilon is information-theoretically necessary for expected KL error \epsilon, or \ell_1 error \epsilon.
Revised:  We also establish that this result cannot be improved upon, in the following senses: First, a window length of I /\epsilon is information-theoretically necessary to achieve expected \ell_1 error \epsilon.
Edit intent: clarity
Original:  Second, the d^{\Theta( I /\epsilon)} samples required to accurately estimate the Markov model when observations are drawn from an alphabet of size d is necessary for any computationally tractable learning /prediction algorithm, assuming the hardness of strongly refuting a certain class of CSPs.
Revised:  Second, the d^{\Theta( I /\epsilon)} samples required to estimate the Markov model when observations are drawn from an alphabet of size d is necessary for any computationally tractable learning /prediction algorithm, assuming the hardness of strongly refuting a certain class of CSPs.
Edit intent: clarity
Original:  Second, the d^{\Theta( I /\epsilon)} samples required to accurately estimate the Markov model when observations are drawn from an alphabet of size d is necessary for any computationally tractable learning /prediction algorithm, assuming the hardness of strongly refuting a certain class of CSPs.
Revised:  Second, the d^{\Theta( I /\epsilon)} samples required to accurately estimate the Markov model for an observation alphabet of size d is necessary for any computationally tractable learning /prediction algorithm, assuming the hardness of strongly refuting a certain class of CSPs.
Edit intent: clarity
Original:  Second, the d^{\Theta( I /\epsilon)} samples required to accurately estimate the Markov model when observations are drawn from an alphabet of size d is necessary for any computationally tractable learning /prediction algorithm, assuming the hardness of strongly refuting a certain class of CSPs.
Revised:  Second, the d^{\Theta( I /\epsilon)} samples required to accurately estimate the Markov model when observations are drawn from an alphabet of size d is necessary for any computationally tractable learning algorithm, assuming the hardness of strongly refuting a certain class of CSPs.
Edit intent: clarity
Original:  In this paper, we present Self-composable Programming (Self), a way of programming for constructing reusable software patterns.
Revised:  Self-composable Programming (Self), a way of programming for constructing reusable software patterns.
Edit intent: coherence
Original: The network virtualization allows new on-demand management capabilities , in this work we demonstrate such a service, namely, on-demand efficient monitoring or anonymity.
Revised: The network virtualization allows new on-demand management capabilities . We demonstrate such a service, namely, on-demand efficient monitoring or anonymity.
Edit intent: clarity
Original:  To better understand random backpropagation, we first connect it to the notions of local learning and the learning channel .
Revised:  To better understand random backpropagation, we first connect it to the notions of local learning and learning channels .
Edit intent: fluency
Original:  Worse, current measurement practice often involves the exploitation of side-effects and unintended features of the network ;
Revised:  Worse, current measurement practice often involves the exploitation of side-effects and unintended features of the network ,
Edit intent: fluency
Original:  Here we propose a novel memory-centric, reconfigurable, general purpose computing platform to handle the exploding amount of data in a fast and energy-efficient manner.
Revised:  Here we propose a novel memory-centric, reconfigurable, general purpose computing platform to handle the explosive amount of data in a fast and energy-efficient manner.
Edit intent: fluency
Original:  The system can be tailored to achieve maximal energy efficiency based on the data flow by dynamically allocating the basic computing fabric to storage, arithmetic, and analog  including neuromorphic computing tasks.
Revised:  The system can be tailored to achieve maximal energy efficiency based on the data flow by dynamically allocating the basic computing fabric to storage, arithmetic, and analog computing including neuromorphic computing tasks.
Edit intent: fluency
Original: For decades, advances in electronics were directly related to the scaling of CMOS transistors according to Moore's law.
Revised: For decades, advances in electronics were directly driven by the scaling of CMOS transistors according to Moore's law.
Edit intent: clarity
Original:  However, both the CMOS scaling and the classical computer architecture are approaching fundamental and practical limits, and new computing architectures based on emerging devices, such as non-volatile memories e.g. resistive memory (RRAM) devices, are expected to sustain the exponential growth of computing capability.
Revised:  However, both the CMOS scaling and the classical computer architecture are approaching fundamental and practical limits, and new computing architectures based on emerging devices, such as resistive random-access memory (RRAM) devices, are expected to sustain the exponential growth of computing capability.
Edit intent: clarity
Original:  Here we propose a novel memory-centric, reconfigurable, general purpose computing platform to handle the explosive amount of data in a fast and energy-efficient manner.
Revised:  Here we propose a novel memory-centric, reconfigurable, general purpose computing platform that is capable of handling the explosive amount of data in a fast and energy-efficient manner.
Edit intent: clarity
Original:  The proposed computing architecture is based on a single physicalresistive memory-centric fabric that can be optimally reconfigured and utilized to perform different computing and data storage tasks in a massively parallel approach.
Revised:  The proposed computing architecture is based on a uniform, physical, resistive, memory-centric fabric that can be optimally reconfigured and utilized to perform different computing and data storage tasks in a massively parallel approach.
Edit intent: clarity
Original:  The system can be tailored to achieve maximal energy efficiency based on the data flow by dynamically allocating the basic computing fabric to storage, arithmetic, and analog computing including neuromorphic computing tasks.
Revised:  The system can be tailored to achieve maximal energy efficiency based on the data flow by dynamically allocating the basic computing fabric for storage, arithmetic, and analog computing including neuromorphic computing tasks.
Edit intent: fluency
Original:  namely parallel TSP and parallel colored TSP . For a given graph where each vertex has a unique token on it, the TSP requires to find a shortest way to modify a token placement into another by swapping tokens on adjacent vertices.
Revised:  namely parallel TSP and parallel colored TSP . For a given graph where each vertex has a unique token on it, those problems require to find a shortest way to modify a token placement into another by swapping tokens on adjacent vertices.
Edit intent: clarity
Original:  We also analyze a derandomized version of this test, where (for example) the polynomials P_1,\ldots,P_k can be the same random polynomial P.
Revised:  We also analyze a derandomized version of this test, where (for example) the polynomials P_1,\ldots,P_k can be the same random polynomial P.
Edit intent: fluency
Original: We consider the following multiplication-based tests to check if a given function f: F_q^n\to F_q is the evaluation of a degree-d polynomial over F_q for q prime  . * Test_{e,k}: Pick P_1,\ldots,P_k independent random degree-e polynomials and accept iff the function fP_1\cdots P_k is the evaluation of a degree-(d+ek) polynomial .
Revised: We consider the following multiplication-based tests to check if a given function f: F_q^n\to F_q is the evaluation of a degree-d polynomial over F_q for q prime ) . * Test_{e,k}: Pick P_1,\ldots,P_k independent random degree-e polynomials and accept iff the function fP_1\cdots P_k is the evaluation of a degree-(d+ek) polynomial .
Edit intent: fluency
Original:  We also analyze a derandomized version of this test, where (for example) the polynomials P_1, \ldots \dots ,P_k can be the same random polynomial P.
Revised:  We also analyze a derandomized version of this test, where (for example) the polynomials P_1, \dots ,P_k can be the same random polynomial P.
Edit intent: fluency
Original:  Creating a giant component is hence easier in a population where vertices tend to connect to their own type.
Edit intent: coherence
Original:  For the Erd \"{os-R\'{e}nyi } graph and the configuration model, the focus is on the component structure.
Revised:  For the Erd \H{os-R\'{e}nyi } graph and the configuration model, the focus is on the component structure.
Edit intent: clarity
Original:  We propose a multi-scale statistical model for those smartphone touches.
Edit intent: coherence
Original:  At short-time scale, the model is governed by refractory effects, while at longer time scales, the touching rate is governed by the priority difference between smartphone tasks and other tasks.
Revised:  At short-time scale, the model is governed by refractory effects, while at longer time scales, the inter-touch intervals are governed by the priority difference between smartphone tasks and other tasks.
Edit intent: clarity
Original:  In contrast, little do we know about the events that occur at the shorter time-scales and how they relate to the scale-invariant pattern.
Revised:  In contrast, at shorter time-scales and how they relate to the scale-invariant pattern.
Edit intent: clarity
Original:  To capture these intervals, we propose a priority-based generative model for smartphone touching events.
Revised:  To capture these intervals, we extend a priority-based generative model for smartphone touching events.
Edit intent: clarity
Original:  To capture these intervals, we propose a priority-based generative model for smartphone touching events.
Revised:  To capture these intervals, we propose a priority-based generative model to smartphone touching events.
Edit intent: fluency
Original:  The flexibility of the model allows to capture inter-individual variations at short and long time scales while its tractability enables very efficient model fitting.
Revised:  The flexibility of the model allows to capture inter-individual variations at short and long time scales while its tractability enables efficient model fitting.
Edit intent: clarity
Original:  We show that each individuals has a specific power-low exponent which is tightly related to the effective refractory time constant suggesting that the fine motor control properties (which influence short intervals) are related to the higher cognitive processes (which affect longer intervals) .
Revised:  According to our model, each individual has a specific power-low exponent which is tightly related to the effective refractory time constant suggesting that the fine motor control properties (which influence short intervals) are related to the higher cognitive processes (which affect longer intervals) .
Edit intent: clarity
Original:  We show that each individuals has a specific power-low exponent which is tightly related to the effective refractory time constant suggesting that the fine motor control properties (which influence short intervals) are related to the higher cognitive processes (which affect longer intervals) .
Revised:  We show that each individuals has a specific power-low exponent which is tightly related to the effective refractory time constant suggesting that motor processes which influence the fast actions are related to the higher cognitive processes (which affect longer intervals) .
Edit intent: clarity
Original:  We show that each individuals has a specific power-low exponent which is tightly related to the effective refractory time constant suggesting that the fine motor control properties (which influence short intervals) are related to the higher cognitive processes (which affect longer intervals) .
Revised:  We show that each individuals has a specific power-low exponent which is tightly related to the effective refractory time constant suggesting that the fine motor control properties (which influence short intervals) are related to the higher cognitive processes governing the longer inter-event intervals .
Edit intent: clarity
Original: We extend the notion of A-discriminant  , and Kapranov's parametrization of A-discriminant varieties, to complex exponents.
Revised: We extend the definition of A-discriminant , and Kapranov's parametrization of A-discriminant varieties, to complex exponents.
Edit intent: clarity
Original: We extend the notion of A-discriminant  , and Kapranov's parametrization of A-discriminant varieties, to complex exponents.
Revised: We extend the notion of A-discriminant varieties , and Kapranov's parametrization of A-discriminant varieties, to complex exponents.
Edit intent: fluency
Original:  As an application, we focus on the special case where A is a set of n +3 points in \mathbb{R n-variate exponential sum with spectrum \mathcal{A number of possible isotopy types for the real zero set of g is O(n^2).
Revised:  As an application, we study the special case where A is a set of n +3 points in \mathbb{R n-variate exponential sum with spectrum \mathcal{A number of possible isotopy types for the real zero set of g is O(n^2).
Edit intent: clarity
Original: A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in healthy and disease.
Revised: A novel approach rooted on the notion of consensus clustering, a strategy developed for community detection in complex networks, is proposed to cope with the heterogeneity that characterizes connectivity matrices in health and disease.
Edit intent: fluency
Original:  (i) define, for each node, of a distance matrix for the set of subjects  (ii)
Revised:  (i) define, for each node, a distance matrix for the set of subjects (ii)
Edit intent: clarity
Original:  cluster the distance matrix for each node , (iii) build the consensus network from the corresponding partitions and (iv) extract groups of subjects by finding the communities of the consensus network thus obtained  . Applications on a toy model and two real data sets, show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.
Revised:  cluster the distance matrix for each node ; (iii) build the consensus network from the corresponding partitions and (iv) extract groups of subjects by finding the communities of the consensus network thus obtained . Applications on a toy model and two real data sets, show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.
Edit intent: fluency
Original:  cluster the distance matrix for each node , (iii) build the consensus network from the corresponding partitions and (iv) extract groups of subjects by finding the communities of the consensus network thus obtained  . Applications on a toy model and two real data sets, show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.
Revised:  cluster the distance matrix for each node , (iii) build the consensus network from the corresponding partitions ; (iv) extract groups of subjects by finding the communities of the consensus network thus obtained . Applications on a toy model and two real data sets, show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.
Edit intent: coherence
Original:  cluster the distance matrix for each node , (iii) build the consensus network from the corresponding partitions and (iv) extract groups of subjects by finding the communities of the consensus network thus obtained  . Applications on a toy model and two real data sets, show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.
Revised:  cluster the distance matrix for each node , (iii) build the consensus network from the corresponding partitions and (iv) extract groups of subjects by finding the communities of the consensus network thus obtained . Differently from the previous implementations of consensus clustering, we thus propose to use the consensus strategy to combine the information arising from the connectivity patterns of each node. The proposed approach may be seen either as an exploratory technique or as an unsupervised pre-training step to help the subsequent construction of a supervised classifier . Applications on a toy model and two real data sets, show the effectiveness of the proposed methodology, which represents heterogeneity of a set of subjects in terms of a weighted network, the consensus matrix.
Edit intent: coherence
Original:  We solved analytically this equation by means of the Green function method and show that three parameters are sufficient to describe the movement: a characteristic time, the steady-state solution and a control parameter.
Revised:  We have solved this equation analytically by means of the Green function method and show that three parameters are sufficient to describe the movement: a characteristic time, the steady-state solution and a control parameter.
Edit intent: fluency
Original:  We solved analytically this equation by means of the Green function method and show that three parameters are sufficient to describe the movement: a characteristic time, the steady-state solution and a control parameter.
Revised:  We solved analytically this equation by means of the Green function method and shown that three parameters are sufficient to describe the movement: a characteristic time, the steady-state solution and a control parameter.
Edit intent: fluency
Original:  We solved analytically this equation by means of the Green function method and show that three parameters are sufficient to describe the movement: a characteristic time, the steady-state solution and a control parameter.
Revised:  We solved analytically this equation by means of the Green function method and show that three parameters are sufficient to describe the movement: the characteristic time, the steady-state solution and a control parameter.
Edit intent: fluency
Original:  We solved analytically this equation by means of the Green function method and show that three parameters are sufficient to describe the movement: a characteristic time, the steady-state solution and a control parameter.
Revised:  We solved analytically this equation by means of the Green function method and show that three parameters are sufficient to describe the movement: a characteristic time, the steady-state solution and the control parameter.
Edit intent: fluency
Original:  We show that , in the tumble motion , the deflection is a non-stationary stochastic processes during times where the tumble occurs.
Revised:  We show that in the tumble motion , the deflection is a non-stationary stochastic processes during times where the tumble occurs.
Edit intent: fluency
Original:  We show that , in the tumble motion , the deflection is a non-stationary stochastic processes during times where the tumble occurs.
Revised:  We show that , in the tumble motion the deflection is a non-stationary stochastic processes during times where the tumble occurs.
Edit intent: fluency
Original:  We show that , in the tumble motion , the deflection is a non-stationary stochastic processes during times where the tumble occurs.
Revised:  We show that , in the tumble motion , the deflection is a non-stationary stochastic process during times at which the tumbling occurs.
Edit intent: clarity
Original:  We show that the deflection during the run is an Ornstein-Uhlenbeck process, which for typical run times is stationary.
Revised:  We show that the deflection during the run is an OrnsteinUhlenbeck process, which for typical run times is stationary.
Edit intent: fluency
Original:  We conclude that, along the run, the rotational boosts do not exist or are neglectable and that only the rotational diffusion remains.
Revised:  We conclude that, along the run, the rotational boosts do not exist and that only the rotational diffusion remains.
Edit intent: clarity
Original:  Thus we have a single model to explain the turns of the bacterium during the run or tumble movements, through a control parameter that can be tuned through a critical value that can explain the transition between the two turn behaviours.
Revised:  Thus we have a single model to explain the turns of through a critical value that can explain the transition between the two turn behaviours.
Edit intent: clarity
Original:  This model is  also able to explain very satisfactory all available statistical experimental data, such as PDFs and average values of turning angles and times, of both run and tumble motions.
Revised:  This model is also able to explain in a very satisfactory way all available statistical experimental data, such as PDFs and average values of turning angles and times, of both run and tumble motions.
Edit intent: clarity