timonziegenbein/iterater-with-prefixes · Datasets at Hugging Face

clarity

Make the sentence simple

Make the sentence simple: The efficiencies of the mechanisms and the nature of the induced, time-dependent flow fields are found to differ widely among swimmers .

The swimming efficiency and the nature of the induced, time-dependent flow fields are found to differ widely among swimmers .

The efficiencies of the mechanisms and the nature of the induced, time-dependent flow fields are found to differ widely among swimmers .

clarity

Simplify this paragraph

Simplify this paragraph: The efficiencies of the mechanisms and the nature of the induced, time-dependent flow fields are found to differ widely among swimmers .

The efficiencies of the mechanisms and the nature of the induced, time-dependent flow fields are found to differ widely among body designs and propulsion mechanisms .

The efficiencies of the mechanisms and the nature of the induced, time-dependent flow fields are found to differ widely among swimmers .

clarity

Make this sentence better readable

Make this sentence better readable: We employ perturbation analysis technique to study trading strategies for multi-asset portfolio and obtain optimal trading methods for wealth maximization under arbitrary utility functions .

We employ perturbation analysis technique to study multi-asset portfolio and obtain optimal trading methods for wealth maximization under arbitrary utility functions .

We employ perturbation analysis technique to study trading strategies for multi-asset portfolio and obtain optimal trading methods for wealth maximization under arbitrary utility functions .

fluency

Fix the grammatical mistakes

Fix the grammatical mistakes: Simple sufficient conditions are given for the problem to be well-posed, in the sense that optimal wealths and marginal utility-based prices are continuous functionals of the inputs .

Simple sufficient conditions are given for the problem to be well-posed, in the sense the optimal wealth and the marginal utility-based prices are continuous functionals of the inputs .

Simple sufficient conditions are given for the problem to be well-posed, in the sense that optimal wealths and marginal utility-based prices are continuous functionals of the inputs .

coherence

Fix coherence in the sentence

Fix coherence in the sentence: The utilization of multiple post translational modifications (PTMs) in regulating a biological response is ubiquitous in cell signaling. If each PTM contributes an additional, equivalent binding site, then one consequence of an increase in the number of PTMs may be to increase the probability that, upon disassociation, a ligand immediately rebinds to its receptor. How such effects may influence cell signaling systems has been less studied. Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses. Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predicted and studied. Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity. It is our hope that these calculations motivate experiments that can further unravel the many functional consequences of multi-site phosphorylation.

the paper is withdrawn for the moment

The utilization of multiple post translational modifications (PTMs) in regulating a biological response is ubiquitous in cell signaling. If each PTM contributes an additional, equivalent binding site, then one consequence of an increase in the number of PTMs may be to increase the probability that, upon disassociation, a ligand immediately rebinds to its receptor. How such effects may influence cell signaling systems has been less studied. Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses. Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predicted and studied. Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity. It is our hope that these calculations motivate experiments that can further unravel the many functional consequences of multi-site phosphorylation.

fluency

Make the sentence grammatical

Make the sentence grammatical: Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses.

Here, a self-consistent integral equation formalism for ligand rebinding , in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses.

Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses.

fluency

Fix grammar errors in this sentence

Fix grammar errors in this sentence: Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses.

Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations , is employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses.

Here, a self-consistent integral equation formalism for ligand rebinding in conjunction with Monte Carlo simulations are employed to further investigate the effects of multiple, equivalent binding sites on shaping biological responses.

clarity

Make this simpler

Make this simpler: Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predictedand studied . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity.

Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects are predicted . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity.

Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predictedand studied . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity.

clarity

Rewrite this with simpler wording

Rewrite this with simpler wording: Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predictedand studied . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity. It is our hope that these calculations motivate experiments that can further unravel the many functional consequences of multi-site phosphorylation .

Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predictedand studied . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly . The model also predicts that ligand rebinding in itself appears insufficient to generative a highly cooperative biological response .

Multiple regimes that characterize qualitatively different physics due to the differential prevalence of rebinding effects and their relation to systems-level properties are predictedand studied . Calculations suggest that when ligand rebinding contributes significantly to the dose response, a purely allovalent model can influence the binding curves nonlinearly but other mechanistic ingredients are required to achieve high degrees of biochemical cooperativity. It is our hope that these calculations motivate experiments that can further unravel the many functional consequences of multi-site phosphorylation .

clarity

Make this sentence more readable

Make this sentence more readable: The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions , whose imply that the distribution of probabilities in the systems are close .

The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions .

The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions , whose imply that the distribution of probabilities in the systems are close .

fluency

Fix grammar errors

Fix grammar errors: The twinness of a pair of nodes is the number of connected, labelled subgraphs of size n in which the two nodes possess identical neighbours.

The twinness of a pair of nodes is the number of connected, labeled subgraphs of size n in which the two nodes possess identical neighbours.

The twinness of a pair of nodes is the number of connected, labelled subgraphs of size n in which the two nodes possess identical neighbours.

fluency

Fix grammatical mistakes in this sentence

Fix grammatical mistakes in this sentence: These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs - each obtained using state-of-the-art high throughput methods.

These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs -- each obtained using state-of-the-art high throughput methods.

These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs - each obtained using state-of-the-art high throughput methods.

fluency

Remove all grammatical errors from this text

Remove all grammatical errors from this text: For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. Coli from the eukaryote S. Cerevisiae .

For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. coli from the eukaryote S. Cerevisiae .

For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. Coli from the eukaryote S. Cerevisiae .

fluency

Improve the grammaticality

Improve the grammaticality: For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. Coli from the eukaryote S. Cerevisiae .

For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. Coli from the eukaryote S. cerevisiae .

For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. Coli from the eukaryote S. Cerevisiae .

fluency

Fix the grammatical mistakes

Fix the grammatical mistakes: Interaction similarity is expected due to gene duplication, and whole genome duplication paralogues in S. Cerevisiae have been reported to co-cluster into the same complexes.

Interaction similarity is expected due to gene duplication, and whole genome duplication paralogues in S. cerevisiae have been reported to co-cluster into the same complexes.

Interaction similarity is expected due to gene duplication, and whole genome duplication paralogues in S. Cerevisiae have been reported to co-cluster into the same complexes.

clarity

Change to clearer wording

Change to clearer wording: Indeed, we find that these paralogues are over-represented as twins compared to pairs chosen at random.

Indeed, we find that these paralogous proteins are over-represented as twins compared to pairs chosen at random.

Indeed, we find that these paralogues are over-represented as twins compared to pairs chosen at random.

fluency

Fix disfluencies in the sentence

Fix disfluencies in the sentence: We find a super-linear increase of K_c with the (average) absolute threshold |h|, which approaches K_c(|h|) \sim |h|^{\alpha with \alpha \approx } 2 for large |h|, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than |h|^{\alpha .

We find a super-linear increase of K_c with the (average) absolute threshold |h|, which approaches K_c(|h|) \sim with \alpha \approx } 2 for large |h|, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than |h|^{\alpha .

We find a super-linear increase of K_c with the (average) absolute threshold |h|, which approaches K_c(|h|) \sim |h|^{\alpha with \alpha \approx } 2 for large |h|, and show that this asymptotic scaling is universal for RTN with Poissonian distributed connectivity and threshold distributions with a variance that grows slower than |h|^{\alpha .

coherence

Make the text more consistent

Make the text more consistent: Interestingly, in this case the annealed approximation fails to predict the dynamical behavior for sparse connectivities , suggesting that even weak topological correlations can strongly limit its applicability for finite N .

, suggesting that even weak topological correlations can strongly limit its applicability for finite N .

Interestingly, in this case the annealed approximation fails to predict the dynamical behavior for sparse connectivities , suggesting that even weak topological correlations can strongly limit its applicability for finite N .

coherence

Improve the cohesiveness of the text

Improve the cohesiveness of the text: The Markowitz mean-variance optimizing framework has served as the basis for modern portfolio theory for more than 50 years.

The Markowitz mean-variance optimizing framework , which has served as the basis for modern portfolio theory for more than 50 years.

The Markowitz mean-variance optimizing framework has served as the basis for modern portfolio theory for more than 50 years.

clarity

Write a simpler version for the sentence

Write a simpler version for the sentence: However, efforts to translate this theoretical foundation into a viable portfolio construction algorithm have been plagued by technical difficulties stemming from the instability of the original optimization problemwith respect to the available data. In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of an \ell_1 penalty .

To stabilize the problem, we propose to add to the Markowitz objective function through the addition of an \ell_1 penalty .

However, efforts to translate this theoretical foundation into a viable portfolio construction algorithm have been plagued by technical difficulties stemming from the instability of the original optimization problemwith respect to the available data. In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of an \ell_1 penalty .

fluency

Grammar improvements

Grammar improvements: In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of an \ell_1 penalty .

In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of an \ell_1 penalty ) .

In this paper we address these issues of estimation error by regularizing the Markowitz objective function through the addition of an \ell_1 penalty .

clarity

Write a better readable version of the sentence

Write a better readable version of the sentence: This penalty stabilizes the optimization problem, encourages sparse portfolios, and facilitates treatment of transaction costs in a transparent way .

This penalty stabilizes the optimization problem, encourages sparse portfolios, and facilitates treatment of transaction costs .

This penalty stabilizes the optimization problem, encourages sparse portfolios, and facilitates treatment of transaction costs in a transparent way .

coherence

Fix coherence in the sentence

Fix coherence in the sentence: We implement this methodology using the Fama and French 48 industry portfolios as our securities . Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the na\"{i .

We implement our methodology using as our securities . Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the na\"{i .

We implement this methodology using the Fama and French 48 industry portfolios as our securities . Using only a modest amount of training data, we construct portfolios whose out-of-sample performance, as measured by Sharpe ratio, is consistently and significantly better than that of the na\"{i .

clarity

Simplify this sentence

Simplify this sentence: In addition to their excellent performance, these portfolios have only a small number of active positions, a highly desirable attribute for real life applications. We conclude by discussing a collection of portfolio construction problems which can be naturally translated into optimizations involving \ell_1 penalties and which can thus be tackled by algorithms similar to those discussed here .

In addition to their excellent performance, these portfolios have only a small number of active positions, a desirable feature for small investors, for whom the fixed overhead portion of the transaction cost is not negligible .

In addition to their excellent performance, these portfolios have only a small number of active positions, a highly desirable attribute for real life applications. We conclude by discussing a collection of portfolio construction problems which can be naturally translated into optimizations involving \ell_1 penalties and which can thus be tackled by algorithms similar to those discussed here .

clarity

Make this sentence better readable

Make this sentence better readable: To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .

To stabilize the problem, we propose to add to the objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .

To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .

clarity

Make the sentence clearer

Make the sentence clearer: To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .

To stabilize the problem, we propose to add to the Markowitz objective function a penalty proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .

To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .

coherence

Fix coherence in this sentence

Fix coherence in this sentence: To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .

To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights .

To stabilize the problem, we propose to add to the Markowitz objective function a penalty which is proportional to the sum of the absolute values of the portfolio weights (\ell_1 penalty) .

clarity

Make this sentence more readable

Make this sentence more readable: This penalty stabilizes the optimization problem, automatically encourages sparse portfolios , and facilitates an effective treatment of transaction costs.

This penalty regularizes (stabilizes) the optimization problem, automatically encourages sparse portfolios , and facilitates an effective treatment of transaction costs.

This penalty stabilizes the optimization problem, automatically encourages sparse portfolios , and facilitates an effective treatment of transaction costs.

clarity

Simplify the sentence

Simplify the sentence: This penalty stabilizes the optimization problem, automatically encourages sparse portfolios , and facilitates an effective treatment of transaction costs.

This penalty stabilizes the optimization problem, encourages sparse portfolios , and facilitates an effective treatment of transaction costs.

This penalty stabilizes the optimization problem, automatically encourages sparse portfolios , and facilitates an effective treatment of transaction costs.

clarity

Make this sentence better readable

Make this sentence better readable: This penalty stabilizes the optimization problem, automatically encourages sparse portfolios , and facilitates an effective treatment of transaction costs.

This penalty stabilizes the optimization problem, automatically encourages sparse portfolios (i.e. portfolios with only few active positions), and allows to account for transaction costs.

This penalty stabilizes the optimization problem, automatically encourages sparse portfolios , and facilitates an effective treatment of transaction costs.

clarity

Use clearer wording

Use clearer wording: Biochemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes.

Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes.

Biochemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes.

coherence

Make the text more cohesive, logically linked and consistent as a whole

Make the text more cohesive, logically linked and consistent as a whole: These systems are oftentimes simulated using the Gillespie Algorithm or the Next Reaction Method , which are exact simulation methods .

These systems are oftentimes simulated using the Gillespie Algorithm or the Next Reaction Method .

These systems are oftentimes simulated using the Gillespie Algorithm or the Next Reaction Method , which are exact simulation methods .

clarity

Simplify the sentence

Simplify the sentence: In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function.

In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of an independent, unit Poisson process with integrated propensity function.

In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function.

fluency

Fix grammatical errors in this sentence

Fix grammatical errors in this sentence: In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function.

In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of independent, unit Poisson process with integrated propensity function.

In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function.

clarity

Rewrite this with simpler wording

Rewrite this with simpler wording: In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function. We use this representation to develop a modified version of the Next Reaction Method .

In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified Next Reaction Method .

In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function. We use this representation to develop a modified version of the Next Reaction Method .

clarity

Write a readable version of the sentence

Write a readable version of the sentence: We use this representation to develop a modified version of the Next Reaction Method . We then demonstrate how this modified Next Reaction Method is the appropriate method to use to simulate systems in which the rate constants are functions of time (that is, systems that are time dependent Markov Processes). Finally, we extend our modified Next Reaction Method to systems with delays and compare its efficiency with those of the recent algorithms designed for systems with delays.

We use this representation to develop a modified version of the Next Reaction Method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with delays and compare its efficiency with those of the recent algorithms designed for systems with delays.

We use this representation to develop a modified version of the Next Reaction Method . We then demonstrate how this modified Next Reaction Method is the appropriate method to use to simulate systems in which the rate constants are functions of time (that is, systems that are time dependent Markov Processes). Finally, we extend our modified Next Reaction Method to systems with delays and compare its efficiency with those of the recent algorithms designed for systems with delays.

clarity

Make this simpler

Make this simpler: By explicitly representing well-stirred chemical reaction systems with independent, unit Poisson processes we develop a new adaptive tau-leaping procedure.

By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit Poisson processes we develop a new adaptive tau-leaping procedure.

By explicitly representing well-stirred chemical reaction systems with independent, unit Poisson processes we develop a new adaptive tau-leaping procedure.

clarity

Write a clearer version for the sentence

Write a clearer version for the sentence: By explicitly representing well-stirred chemical reaction systems with independent, unit Poisson processes we develop a new adaptive tau-leaping procedure.

By explicitly representing well-stirred chemical reaction systems with independent, unit rate Poisson processes we develop a new adaptive tau-leaping procedure.

By explicitly representing well-stirred chemical reaction systems with independent, unit Poisson processes we develop a new adaptive tau-leaping procedure.

clarity

Write a clearer version for the sentence

Write a clearer version for the sentence: The procedure developed is novel in that we enforce any leap condition via a post-leap check as opposed to performing a pre-leap tau selection.

The procedure developed is novel in that accuracy is guaranteed by performing post-leap check as opposed to performing a pre-leap tau selection.

The procedure developed is novel in that we enforce any leap condition via a post-leap check as opposed to performing a pre-leap tau selection.

fluency

Fix disfluencies in the sentence

Fix disfluencies in the sentence: Further, we perform the post-leap check in such a way that the statistics of the sample paths generated will not be skewed by the rejection of a leap.

Further, we perform the post-leap checks in such a way that the statistics of the sample paths generated will not be skewed by the rejection of a leap.

Further, we perform the post-leap check in such a way that the statistics of the sample paths generated will not be skewed by the rejection of a leap.

coherence

Fix coherence in this text

Fix coherence in this text: By performing a post-leap check to ensure accuracy, the method developed in this paper is guaranteed to never produce negative population values . The efficiency of the method developed here is demonstrated on a model of a decaying dimer .

By performing a post-leap check to ensure accuracy, the method developed in this paper is guaranteed to never produce negative population values .

By performing a post-leap check to ensure accuracy, the method developed in this paper is guaranteed to never produce negative population values . The efficiency of the method developed here is demonstrated on a model of a decaying dimer .

fluency

Fix grammar errors

Fix grammar errors: By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes we develop a new adaptive tau-leaping procedure.

By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes , we develop a new adaptive tau-leaping procedure.

By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes we develop a new adaptive tau-leaping procedure.

fluency

Fix grammar errors in this sentence

Fix grammar errors in this sentence: The procedure developed is novel in that accuracy is guaranteed by performing post-leap checks.

The procedure developed is novel in that accuracy is guaranteed by performing postleap checks.

The procedure developed is novel in that accuracy is guaranteed by performing post-leap checks.

fluency

Fix grammar

Fix grammar: Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the post-leap checks in such a way that the statistics of the sample paths generated will not be skewed by the rejections of leaps.

Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the postleap checks in such a way that the statistics of the sample paths generated will not be skewed by the rejections of leaps.

Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the post-leap checks in such a way that the statistics of the sample paths generated will not be skewed by the rejections of leaps.

clarity

Make the sentence simple

Make the sentence simple: Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the post-leap checks in such a way that the statistics of the sample paths generated will not be skewed by the rejections of leaps.

Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the post-leap checks in such a way that the statistics of the sample paths generated will not be biased by the rejections of leaps.

Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the post-leap checks in such a way that the statistics of the sample paths generated will not be skewed by the rejections of leaps.

fluency

Fix grammaticality in this sentence

Fix grammaticality in this sentence: Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values .

Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values

Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values .

fluency

Remove all grammatical errors from this text

Remove all grammatical errors from this text: Continuous time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution.

Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution.

Continuous time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution.

fluency

Improve the grammaticality of this text

Improve the grammaticality of this text: Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions.

Our approach leads to option prices that fulfil financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions.

Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions.

clarity

Simplify

Simplify: Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions.

Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for more exotic market conditions.

Our approach leads to option prices that fulfil the financial formulas when canonical assumptions on the dynamics governing the process are made, but it is still suitable for considering more exotic market conditions.

clarity

Make the sentence simpler

Make the sentence simpler: Neurons in brains are subject to various kinds of noises.

Neurons are subject to various kinds of noises.

Neurons in brains are subject to various kinds of noises.

coherence

Fix coherence of the sentence

Fix coherence of the sentence: Neurons in brains are subject to various kinds of noises. Beside of the synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal processing properties of the neuron.

Neurons in brains are subject to various kinds of noise. In addition to synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal processing properties of the neuron.

Neurons in brains are subject to various kinds of noises. Beside of the synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal processing properties of the neuron.

clarity

Write a simpler version for the sentence

Write a simpler version for the sentence: Here we investigated the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses.

In this paper, we studied the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses.

Here we investigated the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses.

clarity

Rewrite the sentence more clearly

Rewrite the sentence more clearly: Here we investigated the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses.

Here we investigated the response of a stochastic Hodgkin-Huxley neuron to transient input pulses.

Here we investigated the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses.

clarity

Make this sentence readable

Make this sentence readable: The phenomena of intrinsic stochastic resonance is found both in single neuron level and network level. In single neuron level, the detection ability of the neuron was optimized versus the ion channel patch size(i. e., channel noise intensity). Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in .

The phenomena of intrinsic stochastic resonance is also found both at the level of single neurons and at the level of networks. At the network level, the detection ability of the network was optimized versus the number of neurons involved in .

The phenomena of intrinsic stochastic resonance is found both in single neuron level and network level. In single neuron level, the detection ability of the neuron was optimized versus the ion channel patch size(i. e., channel noise intensity). Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in .

clarity

Make this easier to understand

Make this easier to understand: Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in .

Whereas in network level, the detection ability of networks can be optimized for the number of neurons involved in .

Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in .

clarity

Simplify

Simplify: Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in .

Whereas in network level, the detection ability of the network was optimized versus the number of neurons comprising the network .

Whereas in network level, the detection ability of the network was optimized versus the number of neurons involved in .

coherence

Make the text more logical

Make the text more logical: Random Threshold Networks (RTN) are widely used in modeling biological systems, such as neural and gene regulatory networks. RTNs with binary elements and random topology have been found to display a phase transition to an ordered phase at low connectivities Physica A 310, 245 (2002)%DIFDELCMD < ]%%% . Here we show that this phase transition is the result of a seemingly minor detail in the update rule, which acts like a biasing external field for a paramagnetic system.

Physica A 310, 245 (2002)%DIFDELCMD < ]%%% . Here we show that this phase transition is the result of a seemingly minor detail in the update rule, which acts like a biasing external field for a paramagnetic system.

Random Threshold Networks (RTN) are widely used in modeling biological systems, such as neural and gene regulatory networks. RTNs with binary elements and random topology have been found to display a phase transition to an ordered phase at low connectivities Physica A 310, 245 (2002)%DIFDELCMD < ]%%% . Here we show that this phase transition is the result of a seemingly minor detail in the update rule, which acts like a biasing external field for a paramagnetic system.

coherence

Fix coherence in the sentence

Fix coherence in the sentence: RTNs with binary elements and random topology have been found to display a phase transition to an ordered phase at low connectivities Physica A 310, 245 (2002)%DIFDELCMD < ]%%% . Here we show that this phase transition is the result of a seemingly minor detail in the update rule, which acts like a biasing external field for a paramagnetic system.

RTNs with binary elements and random topology have been found to display a phase transition to an ordered phase at low connectivities %DIFDELCMD < ]%%% . Here we show that this phase transition is the result of a seemingly minor detail in the update rule, which acts like a biasing external field for a paramagnetic system.

RTNs with binary elements and random topology have been found to display a phase transition to an ordered phase at low connectivities Physica A 310, 245 (2002)%DIFDELCMD < ]%%% . Here we show that this phase transition is the result of a seemingly minor detail in the update rule, which acts like a biasing external field for a paramagnetic system.

coherence

Fix coherence mistakes in this sentence

Fix coherence mistakes in this sentence: We also show that RTNs with constant number of inputs, K, which have been claimed to be ordered for K=1 Phys. Lett. A 129, 157 (1988)%DIFDELCMD < ]%%% , are actually critical .

We also show that RTNs with constant number of inputs, K, which have been claimed to be ordered for K=1 %DIFDELCMD < ]%%% , are actually critical .

We also show that RTNs with constant number of inputs, K, which have been claimed to be ordered for K=1 Phys. Lett. A 129, 157 (1988)%DIFDELCMD < ]%%% , are actually critical .

clarity

Write a readable version of the sentence

Write a readable version of the sentence: Here we show that cooperation remains rather stable by applying long-term learning + innovative strategy adoption rules on a variety of random, regular, small-word, scale-free and modular networks in repeated, multi-agent games.

Here we show that cooperation remains rather stable by applying long-term learning + innovative strategy adoption rules on a variety of random, regular, small-word, scale-free and modular network models in repeated, multi-agent games.

Here we show that cooperation remains rather stable by applying long-term learning + innovative strategy adoption rules on a variety of random, regular, small-word, scale-free and modular networks in repeated, multi-agent games.

clarity

Make this sentence better readable

Make this sentence better readable: Learning and innovation help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems.

These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems.

Learning and innovation help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems.

clarity

Make the sentence clear

Make the sentence clear: Learning and innovation help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems.

Learning and innovation help to preserve cooperation during the URLanization of real-world networks , and may be key mechanisms promoting the evolution of URLanizing, complex systems.

Learning and innovation help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems.

clarity

Make the sentence simpler

Make the sentence simpler: Learning and innovation help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems.

Learning and innovation help to preserve cooperation during network URLanization , and may play a prominent role in the evolution of URLanizing, complex systems.

Learning and innovation help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems.

clarity

Improve this sentence for readability

Improve this sentence for readability: The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed .

In an equilibrium chemical reaction mixture are Poisson distributed .

The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed .

clarity

Make the sentence simpler

Make the sentence simpler: The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed .

The numbers of each sort of molecule present in an equilibrium chemical reaction mixture , the number of molecules present obeys a Poisson distribution .

The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed .

clarity

Write a clearer version for the sentence

Write a clearer version for the sentence: Such driven systems also obey an analog of the fluctuation-dissipation theorem and can equilibrate when in contact with each other .

Such driven systems also obey an analog of the fluctuation-dissipation theorem .

Such driven systems also obey an analog of the fluctuation-dissipation theorem and can equilibrate when in contact with each other .

clarity

Rewrite this sentence for simplicity

Rewrite this sentence for simplicity: Our results may be relevant to biological systems and to the larger question of how equilibrium ideas might extend to nonequilibrium systems.

Our results may be relevant to biological systems and to the larger question of how equilibrium concepts might apply to nonequilibrium systems.

Our results may be relevant to biological systems and to the larger question of how equilibrium ideas might extend to nonequilibrium systems.

coherence

Fix coherence in this text

Fix coherence in this text: We also demonstrate the use of "model reduction" in conjunction with leaping to circumvent this problem and expose a current need in this area: a model-reduction hierarchy analogous to that on which the leaping methods are based D. T. Gillespie, J. Chem. Phys. 113, 297 (2000); 115, 1716 (2001)%DIFDELCMD < ]%%% . In situations where leaping is seen to perform well, we emphasize the significant advantages to using these methods over more traditional simulation approaches.

We also demonstrate the use of "model reduction" in conjunction with leaping to circumvent this problem and expose a current need in this area: a model-reduction hierarchy analogous to that on which the leaping methods are based %DIFDELCMD < ]%%% . In situations where leaping is seen to perform well, we emphasize the significant advantages to using these methods over more traditional simulation approaches.

We also demonstrate the use of "model reduction" in conjunction with leaping to circumvent this problem and expose a current need in this area: a model-reduction hierarchy analogous to that on which the leaping methods are based D. T. Gillespie, J. Chem. Phys. 113, 297 (2000); 115, 1716 (2001)%DIFDELCMD < ]%%% . In situations where leaping is seen to perform well, we emphasize the significant advantages to using these methods over more traditional simulation approaches.

clarity

Rewrite the sentence more clearly

Rewrite the sentence more clearly: 115, 1716 (2001)%DIFDELCMD < ]%%% . In situations where leaping is seen to perform well, we emphasize the significant advantages to using these methods over more traditional simulation approaches. We show how leaping allows for statistical investigations beyond the reach of "exact-stochastic" methods and demonstrate how one can uncover, via such investigations, subtle stochastic effects that would be ignored in deterministic treatments.

115, 1716 (2001)%DIFDELCMD < ]%%% The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to test the limits of the leaping approach. We demonstrate how the PLA allows us to quantify subtle effects of stochasticity that would be ignored in deterministic treatments.

115, 1716 (2001)%DIFDELCMD < ]%%% . In situations where leaping is seen to perform well, we emphasize the significant advantages to using these methods over more traditional simulation approaches. We show how leaping allows for statistical investigations beyond the reach of "exact-stochastic" methods and demonstrate how one can uncover, via such investigations, subtle stochastic effects that would be ignored in deterministic treatments.

clarity

Improve this sentence for readability

Improve this sentence for readability: We show how leaping allows for statistical investigations beyond the reach of "exact-stochastic" methods and demonstrate how one can uncover, via such investigations, subtle stochastic effects that would be ignored in deterministic treatments. We then show, using examples taken from the literature, that conditions identified here as lending well to leaping do, in fact, arise in natural biological systems. This leads us to discuss and demonstrate how the statistical information garnered from a leaping study can be used to infer mechanistic details of a biological process and motivate experiments .

We show how leaping allows for statistical investigations beyond the reach of "exact-stochastic" methods and demonstrate how one can uncover, via such investigations, subtle stochastic effects that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly-used "exact" stochastic methods. We also illustrate prime bottlenecks that can hinder the approach and discuss possible strategies for overcoming them .

We show how leaping allows for statistical investigations beyond the reach of "exact-stochastic" methods and demonstrate how one can uncover, via such investigations, subtle stochastic effects that would be ignored in deterministic treatments. We then show, using examples taken from the literature, that conditions identified here as lending well to leaping do, in fact, arise in natural biological systems. This leads us to discuss and demonstrate how the statistical information garnered from a leaping study can be used to infer mechanistic details of a biological process and motivate experiments .

clarity

Rewrite this sentence clearly

Rewrite this sentence clearly: Overall, we demonstrate to biologists the great potential that leaping methods hold for real-world biological research while highlighting to algorithmists areas still in need of improvement .

Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while also elucidating the obstacles that one can expect to encounter .

Overall, we demonstrate to biologists the great potential that leaping methods hold for real-world biological research while highlighting to algorithmists areas still in need of improvement .

clarity

Improve this sentence for readability

Improve this sentence for readability: We also illustrate prime bottlenecks that can hinder the approach and discuss possible strategies for overcoming them.

We also illustrate bottlenecks that can hinder the approach and discuss possible strategies for overcoming them.

We also illustrate prime bottlenecks that can hinder the approach and discuss possible strategies for overcoming them.

clarity

Make the sentence clear

Make the sentence clear: We also illustrate prime bottlenecks that can hinder the approach and discuss possible strategies for overcoming them.

We also illustrate prime bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them.

We also illustrate prime bottlenecks that can hinder the approach and discuss possible strategies for overcoming them.

clarity

Write a readable version of the sentence

Write a readable version of the sentence: Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while also elucidating the obstacles that one can expect to encounter .

Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while at the same time elucidating obstacles that are often encountered in practice .

Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while also elucidating the obstacles that one can expect to encounter .

coherence

Fix coherence in this text

Fix coherence in this text: The major objective of this paper is to introduce a novel method for the functional annotation of genes. Our method is based on a graph theoretical measure we call joint betweenness, which is an extension of the well known betweenness centrality measure, involving pairs of genes. We apply our method to the transcriptional regulatory network of yeast to, first, provide a large scale proof of concept of our method and, second, make predictions about the biological function of previously unknown genes .

This paper has been withdrawn .

The major objective of this paper is to introduce a novel method for the functional annotation of genes. Our method is based on a graph theoretical measure we call joint betweenness, which is an extension of the well known betweenness centrality measure, involving pairs of genes. We apply our method to the transcriptional regulatory network of yeast to, first, provide a large scale proof of concept of our method and, second, make predictions about the biological function of previously unknown genes .

clarity

Make this easier to understand

Make this easier to understand: We find that discrete noise of inhibiting (signal) molecules can greatly delay the extinction of a regulated component in a prototypical biochemical regulatory network.

We find that discrete noise of inhibiting (signal) molecules can greatly delay the extinction of plasmids in a plasmid replication system: a prototypical biochemical regulatory network.

We find that discrete noise of inhibiting (signal) molecules can greatly delay the extinction of a regulated component in a prototypical biochemical regulatory network.

clarity

Rewrite the sentence to be simpler

Rewrite the sentence to be simpler: We calculate analytically the probability distribution of the metastable state of the regulated component and show that deterministic reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is short compared to the mean extinction time.

We calculate the probability distribution of the metastable state of the regulated component and show that deterministic reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is short compared to the mean extinction time.

We calculate analytically the probability distribution of the metastable state of the regulated component and show that deterministic reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is short compared to the mean extinction time.

clarity

Rewrite this sentence for readability

Rewrite this sentence for readability: We calculate analytically the probability distribution of the metastable state of the regulated component and show that deterministic reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is short compared to the mean extinction time.

We calculate analytically the probability distribution of the metastable state of the regulated component and show that deterministic reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is much shorter than the mean extinction time.

We calculate analytically the probability distribution of the metastable state of the regulated component and show that deterministic reaction rate equations may fail in predicting the average number of regulated molecules even when this number is large, and the time is short compared to the mean extinction time.

clarity

Make this easier to understand

Make this easier to understand: Microtubules (MTs), nano-tubes which act as struts in the scaffolding of eucaryotic cells, also serve as tracks for intracellular molecular motor transport in eucaryotic cells. In many biological processes, the length distribution of the MTs is controlled by a class of motor proteins called depolymerases (DPs).

In many intracellular processes, the length distribution of the MTs is controlled by a class of motor proteins called depolymerases (DPs).

Microtubules (MTs), nano-tubes which act as struts in the scaffolding of eucaryotic cells, also serve as tracks for intracellular molecular motor transport in eucaryotic cells. In many biological processes, the length distribution of the MTs is controlled by a class of motor proteins called depolymerases (DPs).

clarity

Make this sentence readable

Make this sentence readable: In many biological processes, the length distribution of the MTs is controlled by a class of motor proteins called depolymerases (DPs).

In many biological processes, the length distribution of microtubules is controlled by a class of motor proteins called depolymerases (DPs).

In many biological processes, the length distribution of the MTs is controlled by a class of motor proteins called depolymerases (DPs).

clarity

Rewrite the sentence to be simpler

Rewrite the sentence to be simpler: A DP diffuses or walks along a MT to reach one of the tips of the MT andthen begins depolymerizing the MT itself .

A DP diffuses or walks along a MT to reach one of the tips of the surface of a microtubule, depolymerases are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there .

A DP diffuses or walks along a MT to reach one of the tips of the MT andthen begins depolymerizing the MT itself .

clarity

Rewrite this sentence in a simpler manner

Rewrite this sentence in a simpler manner: We develop a quantitative model that captures both these processes within a single theoretical framework. We show that the action of both diffusing and walking DPs leads to a length-dependent depolymerization of the MT; however, their effects on the length distribution are different.

We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution are different.

We develop a quantitative model that captures both these processes within a single theoretical framework. We show that the action of both diffusing and walking DPs leads to a length-dependent depolymerization of the MT; however, their effects on the length distribution are different.

clarity

Make this sentence better readable

Make this sentence better readable: Under experimental conditions, the diffusing DP produces a non-monotonic distribution of lengths as opposed to a nearly exponential distribution in the case of the walking DP. The former also shows a minimum in the r.m.s fluctuation to mean ratio of the length against the DP concentration, while the latter does not. Our findings imply that a diffusing DP, like MCAK, might be used by the cell for precise length control during cell division, while a walking DP, like Kip3p, would be more useful for fast depolymerization .

Under experimental conditions, the diffusing DP produces a non-monotonic provided the motor processivity is sufficiently small. Our findings suggest that such motor proteins have a central role in ensuring precise control of MT lengths .

Under experimental conditions, the diffusing DP produces a non-monotonic distribution of lengths as opposed to a nearly exponential distribution in the case of the walking DP. The former also shows a minimum in the r.m.s fluctuation to mean ratio of the length against the DP concentration, while the latter does not. Our findings imply that a diffusing DP, like MCAK, might be used by the cell for precise length control during cell division, while a walking DP, like Kip3p, would be more useful for fast depolymerization .

clarity

Rewrite the sentence more clearly

Rewrite the sentence more clearly: In many intracellular processes, the length distribution of microtubules is controlled by a class of motor proteins, called depolymerases . Experiments have shown that, following binding to the surface of a microtubule, depolymerases are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there.

In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins . Experiments have shown that, following binding to the surface of a microtubule, depolymerases are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there.

In many intracellular processes, the length distribution of microtubules is controlled by a class of motor proteins, called depolymerases . Experiments have shown that, following binding to the surface of a microtubule, depolymerases are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there.

clarity

Rewrite this sentence for simplicity

Rewrite this sentence for simplicity: In many intracellular processes, the length distribution of microtubules is controlled by a class of motor proteins, called depolymerases . Experiments have shown that, following binding to the surface of a microtubule, depolymerases are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there.

In many intracellular processes, the length distribution of microtubules is controlled by a class of motor proteins, called depolymerases . Experiments have shown that, following binding to the surface of a microtubule, depolymerizers are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there.

In many intracellular processes, the length distribution of microtubules is controlled by a class of motor proteins, called depolymerases . Experiments have shown that, following binding to the surface of a microtubule, depolymerases are transported to the microtubule tip(s) by diffusion or directed walk and, then, depolymerize the microtubule from the tip(s) after accumulating there.

clarity

Rewrite the sentence to be simpler

Rewrite the sentence to be simpler: We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the distribution is non-monotonic provided the motor processivity is sufficiently small .

We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the length distribution is, in general, non-monotonic provided the motor processivity is sufficiently small .

We show that, when the motor protein concentration in solution exceeds a critical value, a steady state is reached where the distribution is non-monotonic provided the motor processivity is sufficiently small .

clarity

Rewrite this sentence for simplicity

Rewrite this sentence for simplicity: Our findings suggest that such motor proteins have a central role in ensuring precise control of MT lengths .

Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths .

Our findings suggest that such motor proteins have a central role in ensuring precise control of MT lengths .

clarity

Use simpler wording

Use simpler wording: We develop a network-based algorithm to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network.

We develop a matrix-based approach to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network.

We develop a network-based algorithm to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network.

clarity

Rewrite this sentence in a simpler manner

Rewrite this sentence in a simpler manner: We develop a network-based algorithm to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network. Indirect regulations are important as they constitute the majority of experimental data. Our approach is based on the network topology and can be easily incorporated using a matrix formalism.

We develop a network-based algorithm to predict and verify indirect interactions in gene and protein regulatory networks. It is based on the network topology and can be easily incorporated using a matrix formalism.

We develop a network-based algorithm to predict and verify indirect regulatory interactions in a large-scale genetic regulatory network. Indirect regulations are important as they constitute the majority of experimental data. Our approach is based on the network topology and can be easily incorporated using a matrix formalism.

clarity

Make the sentence clear

Make the sentence clear: Our approach is based on the network topology and can be easily incorporated using a matrix formalism. The essence of the method is to extend the transitivity of indirect regulations ( i.e.

Our approach is based on the approximate transitivity of indirect regulations ( i.e.

Our approach is based on the network topology and can be easily incorporated using a matrix formalism. The essence of the method is to extend the transitivity of indirect regulations ( i.e.

coherence

Fix coherence in the text

Fix coherence in the text: The essence of the method is to extend the transitivity of indirect regulations ( i.e.

The essence of the method is to extend the transitivity of indirect regulations ( e.g.

The essence of the method is to extend the transitivity of indirect regulations ( i.e.

clarity

Change to simpler wording

Change to simpler wording: A regulates B and B regulates C implies A regulates C) to longer cascades and effectively take care of the signs of the regulations.

A regulates B and B regulates C often implies that A regulates C) to longer cascades and effectively take care of the signs of the regulations.

A regulates B and B regulates C implies A regulates C) to longer cascades and effectively take care of the signs of the regulations.

coherence

Fix coherence in the text

Fix coherence in the text: We apply the algorithm to the regulatory networks of Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster , resulting in novel predictions with calibrated reliability .

We apply the algorithm to the regulatory networks of Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster ) .

We apply the algorithm to the regulatory networks of Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster , resulting in novel predictions with calibrated reliability .

fluency

Fix the grammatical mistakes

Fix the grammatical mistakes: However the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case.

However , the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case.

However the use of a standard t copula is often criticized due to its restriction of having a single parameter for the degrees of freedom (dof) that may limit its capability to model the tail dependence structure in a multivariate case.

fluency

Fix grammar errors in this sentence

Fix grammar errors in this sentence: To overcome this problem, grouped t copula was proposed recently where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter.

To overcome this problem, grouped t copula was proposed recently , where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter.

To overcome this problem, grouped t copula was proposed recently where risks are grouped a priori in such a way that each group has a standard t copula with its specific dof parameter.

coherence

Improve the cohesiveness of the text

Improve the cohesiveness of the text: In this paper we propose the use of a new t copula, generalizing grouped t copula to have each group consisting of one risk only, so that a priori grouping is not required.

In this paper we propose the use of a grouped t copula to have each group consisting of one risk only, so that a priori grouping is not required.

In this paper we propose the use of a new t copula, generalizing grouped t copula to have each group consisting of one risk only, so that a priori grouping is not required.

clarity

Change to simpler wording

Change to simpler wording: In this paper we propose the use of a new t copula, generalizing grouped t copula to have each group consisting of one risk only, so that a priori grouping is not required.

In this paper we propose the use of a new t copula, generalizing grouped t copula , where each group consists of one risk only, so that a priori grouping is not required.

In this paper we propose the use of a new t copula, generalizing grouped t copula to have each group consisting of one risk only, so that a priori grouping is not required.

clarity

Make this sentence more readable

Make this sentence more readable: In this paper we propose the use of a new t copula, generalizing grouped t copula to have each group consisting of one risk only, so that a priori grouping is not required.

In this paper we propose the use of a new t copula, generalizing grouped t copula to have each group consisting of one risk factor only, so that a priori grouping is not required.

In this paper we propose the use of a new t copula, generalizing grouped t copula to have each group consisting of one risk only, so that a priori grouping is not required.

clarity

Rewrite this sentence in a simpler manner

Rewrite this sentence in a simpler manner: The characteristics of this copula in the bivariate case are described .

The copula characteristics in the bivariate case are described .

The characteristics of this copula in the bivariate case are described .

clarity

Make the sentence simpler

Make the sentence simpler: The characteristics of this copula in the bivariate case are described .

The characteristics of this copula in the bivariate case are studied .

The characteristics of this copula in the bivariate case are described .