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Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . | <fluency> Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transition . | Multi-potent stem or progenitor cells undergo a sequential series of binary fate decisions which ultimately generates the diversity of differentiated cell . Efforts to understand cell fate control have focused on simple gene regulatory circuits that predict the presence of multiple stable states, bifurcations and switch-like transitions . | fluency | 0.9993456 | 0903.4215 | 1 |
Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, directionality, and promiscuous expression. | <clarity> Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, directionality, and promiscuous expression. | Here, we construct a generic minimal model of the genetic regulatory network controlling cell fate determination, which exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, directionality, and promiscuous expression. | clarity | 0.99816626 | 0903.4215 | 1 |
Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, directionality, and promiscuous expression. | <fluency> Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, directionality, and promiscuous expression. | Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, directionality, branching, exclusivity, directionality, and promiscuous expression. | fluency | 0.715705 | 0903.4215 | 1 |
Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, directionality, and promiscuous expression. | <clarity> Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, directionality, and promiscuous expression. | Here, we construct a generic minimal model of the genetic regulatory network which naturally exhibits five elementary characteristics of cell differentiation: stability, branching, exclusivity, and promiscuous expression. | clarity | 0.99744993 | 0903.4215 | 1 |
We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | <fluency> We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | We argue that a modular architecture comprising repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | fluency | 0.99939513 | 0903.4215 | 1 |
We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | <coherence> We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | We argue that a modular architecture comprised of repeated network elements reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | coherence | 0.98771685 | 0903.4215 | 1 |
We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | <meaning-changed> We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by sequentially repressing selected modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | meaning-changed | 0.9958294 | 0903.4215 | 1 |
We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | <clarity> We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence restricting the dynamics to lower dimensional subspaces of the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | clarity | 0.9979 | 0903.4215 | 1 |
We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | <clarity> We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional phase spacethrough a simpler, lower dimensional subspace . | We argue that a modular architecture comprised of repeated network elements in principle reproduces these features of differentiation by repressing irrelevant modules and hence , channeling the dynamics in the high-dimensional state space . | clarity | 0.9934628 | 0903.4215 | 1 |
We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | <fluency> We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | We implement our model both with ordinary differential equations (ODEs) , to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | fluency | 0.9987507 | 0903.4215 | 1 |
We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | <fluency> We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation , and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | fluency | 0.9984509 | 0903.4215 | 1 |
We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | <fluency> We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) , to demonstrate the effect of noise on the system in simulations . | fluency | 0.9981019 | 0903.4215 | 1 |
We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | <clarity> We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system in simulations . | We implement our model both with ordinary differential equations (ODEs) to explore the role of bifurcations in producing the one-way character of differentiation and with stochastic differential equations (SDEs) to demonstrate the effect of noise on the system . | clarity | 0.99844617 | 0903.4215 | 1 |
We further argue that binary cell fate decisions are prevalent in cell differentiation due to general features of dynamical systems . | <clarity> We further argue that binary cell fate decisions are prevalent in cell differentiation due to general features of dynamical systems . | We further argue that binary cell fate decisions are prevalent in cell differentiation due to general features of the underlying dynamical system . | clarity | 0.9983809 | 0903.4215 | 1 |
This minimal model makes testable predictions about the structural basis for directional, discrete and diversifying cell phenotype development and thus , can guide the evaluation of real gene regulatory networks that govern differentiation. | <fluency> This minimal model makes testable predictions about the structural basis for directional, discrete and diversifying cell phenotype development and thus , can guide the evaluation of real gene regulatory networks that govern differentiation. | This minimal model makes testable predictions about the structural basis for directional, discrete and diversifying cell phenotype development and thus can guide the evaluation of real gene regulatory networks that govern differentiation. | fluency | 0.9993123 | 0903.4215 | 1 |
We obtain the Maximum Entropy distribution for an asset from call and digital option prices. | <fluency> We obtain the Maximum Entropy distribution for an asset from call and digital option prices. | We obtain the maximum entropy distribution for an asset from call and digital option prices. | fluency | 0.9992107 | 0903.4542 | 1 |
A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimize a formal derivation by Buchen and Kelly. | <fluency> A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimize a formal derivation by Buchen and Kelly. | A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimise a formal derivation by Buchen and Kelly. | fluency | 0.9989335 | 0903.4542 | 1 |
Finally, we present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options . | <coherence> Finally, we present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options . | We present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options . | coherence | 0.9665491 | 0903.4542 | 1 |
Finally, we present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options . | <meaning-changed> Finally, we present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options . | Finally, we present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options . Finally, we apply our approach to options on the S . | meaning-changed | 0.99947804 | 0903.4542 | 1 |
Finally, we present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options . | <meaning-changed> Finally, we present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options . | Finally, we present numerical results which show that our approach implies very realistic volatility surfaces even when calibrating only to at-the-money options P 500 index . | meaning-changed | 0.99938023 | 0903.4542 | 1 |
It is well-known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. | <fluency> It is well-known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. | It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. | fluency | 0.9993063 | 0903.4833 | 1 |
In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices. | <coherence> In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices. | In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices. | coherence | 0.9978806 | 0903.4833 | 1 |
In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices. | <fluency> In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices. | In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes , we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices. | fluency | 0.9993236 | 0903.4833 | 1 |
In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices. | <clarity> In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a time-homogeneous model for the stock price which reproduces the given option prices. | In the present paper we consider the inverse problem, i.e. given prices of perpetual American options for different strikes we show how to construct a time-homogeneous stock price model which reproduces the given option prices. | clarity | 0.91774905 | 0903.4833 | 1 |
Here we propose an objective scheme to quantify the precise amount of negative entropy, present in an extremely important biochemical pathway; namely, the TCA cycle. Our approach is based on the computational implementation of two-person non-cooperative finite zero-sum game between positive entropy and negative entropy . | <meaning-changed> Here we propose an objective scheme to quantify the precise amount of negative entropy, present in an extremely important biochemical pathway; namely, the TCA cycle. Our approach is based on the computational implementation of two-person non-cooperative finite zero-sum game between positive entropy and negative entropy . | Biological systems possess negative entropy. In them, one form of order produces another, URLanized form of order. We propose a formal scheme to calculate robustness of an entire biological system by quantifying the negative entropy present in it. Our Methodology is based upon a computational implementation of two-person non-cooperative finite zero-sum game between positive entropy and negative entropy . | meaning-changed | 0.958816 | 0903.4844 | 1 |
Our approach is based on the computational implementation of two-person non-cooperative finite zero-sum game between positive entropy and negative entropy . | <meaning-changed> Our approach is based on the computational implementation of two-person non-cooperative finite zero-sum game between positive entropy and negative entropy . | Our approach is based on the computational implementation of two-person non-cooperative finite zero-sum game between positive (physico-chemical) and negative (biological) entropy, present in the system(TCA cycle, for this work) . | meaning-changed | 0.9994987 | 0903.4844 | 1 |
Biochemical analogue of Nash equilibrium condition between these positive and negative entropy, could unambiguously provide a quantitative marker that describes the 'edge of life' for TCA cycle . Difference between concentration-profiles prevalent at the 'edge of life' and biologically observed TCA cycle, could quantitatively express the precise amount of negative entropy present in a typical biochemical network. We show here that it is not the existence of mere order, but the synchronization profile between ordered fluctuations, which accounts for biological robustness. An exhaustive sensitivity analysis could identify the concentrations, for which slightest perturbation can account for enormous increase in positive entropy. Since our algorithm is general, the same analysis can as well be performed on larger networks and (ideally) for an entire cell, if numerical data for concentration is available . | <clarity> Biochemical analogue of Nash equilibrium condition between these positive and negative entropy, could unambiguously provide a quantitative marker that describes the 'edge of life' for TCA cycle . Difference between concentration-profiles prevalent at the 'edge of life' and biologically observed TCA cycle, could quantitatively express the precise amount of negative entropy present in a typical biochemical network. We show here that it is not the existence of mere order, but the synchronization profile between ordered fluctuations, which accounts for biological robustness. An exhaustive sensitivity analysis could identify the concentrations, for which slightest perturbation can account for enormous increase in positive entropy. Since our algorithm is general, the same analysis can as well be performed on larger networks and (ideally) for an entire cell, if numerical data for concentration is available . | Biochemical analogue of Nash equilibrium , proposed here, could measure the robustness in TCA cycle in exact numeric terms, whereas the mixed strategy game between these entropies could quantitate the progression of stages of biological adaptation. Synchronization profile amongst macromolecular concentrations (even under environmental perturbations) is found to account for negative entropy and biological robustness. Emergence of synchronization profile was investigated with dynamically varying metabolite concentrations. Obtained results were verified with that from the deterministic simulation methods. Categorical plans to apply this algorithm in Cancer studies and anti-viral therapies are proposed alongside. From theoretical perspective, this work proposes a general, rigorous and alternative view of immunology . | clarity | 0.99444723 | 0903.4844 | 1 |
The mitotic spindle is an important intermediate structure in eucaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. | <fluency> The mitotic spindle is an important intermediate structure in eucaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. | The mitotic spindle is an important intermediate structure in eukaryotic cell division, in which each of a pair of duplicated chromosomes is attached through microtubules to centrosomal bodies located close to the two poles of the dividing cell. | fluency | 0.99936646 | 0904.0111 | 1 |
It is widely believed that the spindle starts forming by the `capture' of chromosome pairs, held together by kinetochores, by randomly searching microtubules. | <clarity> It is widely believed that the spindle starts forming by the `capture' of chromosome pairs, held together by kinetochores, by randomly searching microtubules. | Several mechanisms are at work towards the formation of the spindle, one of which is the `capture' of chromosome pairs, held together by kinetochores, by randomly searching microtubules. | clarity | 0.997837 | 0904.0111 | 1 |
We present a complete analytical formulation of this problem, in the case of a single fixed target and for arbitrary cell size. We derive a set of Green's functions for the microtubule dynamics and an associated set of first passage quantities. An implicit analytical expression for the probability distribution of the search time is then obtained , with appropriate boundary conditions at the outer cell membrane. We extract the conditions of optimized search from our formalism. Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it . | <meaning-changed> We present a complete analytical formulation of this problem, in the case of a single fixed target and for arbitrary cell size. We derive a set of Green's functions for the microtubule dynamics and an associated set of first passage quantities. An implicit analytical expression for the probability distribution of the search time is then obtained , with appropriate boundary conditions at the outer cell membrane. We extract the conditions of optimized search from our formalism. Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it . | Although the entire cell cycle can be up to 24 hours long, the mitotic phase typically takes only less than an hour. How does the cell keep the duration of mitosis within this limit? Previous theoretical studies have suggested that the chromosome search and capture is optimized by tuning the microtubule dynamic parameters to minimize the search time. In this paper, we examine this conjecture. We compute the mean search time for a single target by microtubules from a single nucleating site, using a systematic and rigorous theoretical approach, for arbitrary kinetic parameters. The result is extended to multiple targets and nucleating sites by physical arguments. Estimates of mitotic time scales are then obtained for different cells using experimental data. In yeast and mammalian cells, the observed changes in microtubule kinetics between interphase and mitosis are beneficial in reducing the search time. In{\it . | meaning-changed | 0.99758565 | 0904.0111 | 1 |
Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it . | <meaning-changed> Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it . | Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it Xenopus . | meaning-changed | 0.9993881 | 0904.0111 | 1 |
Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it . | <meaning-changed> Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it . | Our results are in qualitative and semi-quantitative agreement with known experimental results for different cell types{\it extracts, by contrast, the opposite effect is observed, in agreement with the current understanding that large cells use additional mechanisms to regulate the duration of the mitotic phase . | meaning-changed | 0.99939835 | 0904.0111 | 1 |
We provide a new approach to scenario generation for the purpose of risk management in the banking industry. | <meaning-changed> We provide a new approach to scenario generation for the purpose of risk management in the banking industry. | We provide a new dynamic approach to scenario generation for the purpose of risk management in the banking industry. | meaning-changed | 0.9993704 | 0904.0624 | 1 |
We provide a new approach to scenario generation for the purpose of risk management in the banking industry. | <fluency> We provide a new approach to scenario generation for the purpose of risk management in the banking industry. | We provide a new approach to scenario generation for the purposes of risk management in the banking industry. | fluency | 0.99614346 | 0904.0624 | 1 |
We connect ideas from standard techniques -- like historical and Monte Carlo simulation -- to a hybrid technique that shares the advantages of standard procedures but reduces several of their drawbacks. | <clarity> We connect ideas from standard techniques -- like historical and Monte Carlo simulation -- to a hybrid technique that shares the advantages of standard procedures but reduces several of their drawbacks. | We connect ideas from conventional techniques -- like historical and Monte Carlo simulation -- to a hybrid technique that shares the advantages of standard procedures but reduces several of their drawbacks. | clarity | 0.99794203 | 0904.0624 | 1 |
We connect ideas from standard techniques -- like historical and Monte Carlo simulation -- to a hybrid technique that shares the advantages of standard procedures but reduces several of their drawbacks. | <clarity> We connect ideas from standard techniques -- like historical and Monte Carlo simulation -- to a hybrid technique that shares the advantages of standard procedures but reduces several of their drawbacks. | We connect ideas from standard techniques -- like historical and Monte Carlo simulation -- and we come up with a hybrid method that shares the advantages of standard procedures but reduces several of their drawbacks. | clarity | 0.82606196 | 0904.0624 | 1 |
We connect ideas from standard techniques -- like historical and Monte Carlo simulation -- to a hybrid technique that shares the advantages of standard procedures but reduces several of their drawbacks. | <clarity> We connect ideas from standard techniques -- like historical and Monte Carlo simulation -- to a hybrid technique that shares the advantages of standard procedures but reduces several of their drawbacks. | We connect ideas from standard techniques -- like historical and Monte Carlo simulation -- to a hybrid technique that shares the advantages of standard procedures but eliminates several of their drawbacks. | clarity | 0.9988776 | 0904.0624 | 1 |
Instead of considering the static problem of constructing one or ten day ahead distributions , we embed the problem into a dynamic framework, where any time horizon can be consistently simulated. | <meaning-changed> Instead of considering the static problem of constructing one or ten day ahead distributions , we embed the problem into a dynamic framework, where any time horizon can be consistently simulated. | Instead of considering the static problem of constructing one or ten day ahead distributions for vectors of risk factors , we embed the problem into a dynamic framework, where any time horizon can be consistently simulated. | meaning-changed | 0.999355 | 0904.0624 | 1 |
Second , we use standard models from mathematical finance for each risk factor, bridging this way between the worlds of trading and risk management. | <coherence> Second , we use standard models from mathematical finance for each risk factor, bridging this way between the worlds of trading and risk management. | Additionally , we use standard models from mathematical finance for each risk factor, bridging this way between the worlds of trading and risk management. | coherence | 0.98565525 | 0904.0624 | 1 |
Second , we use standard models from mathematical finance for each risk factor, bridging this way between the worlds of trading and risk management. | <clarity> Second , we use standard models from mathematical finance for each risk factor, bridging this way between the worlds of trading and risk management. | Second , we use standard models from mathematical finance for each risk factor, whence bridging the worlds of trading and risk management. | clarity | 0.99900025 | 0904.0624 | 1 |
Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. | <fluency> Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. | Our approach is based on stochastic differential equations (SDEs) , like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. | fluency | 0.9992944 | 0904.0624 | 1 |
Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. | <fluency> Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. | Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation , governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. | fluency | 0.9993285 | 0904.0624 | 1 |
Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. | <clarity> Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical implementation of the respective SDEs. | Our approach is based on stochastic differential equations (SDEs) like the HJM-equation or the Black-Scholes equation governing the time evolution of risk factors, on an empirical calibration method to the market for the chosen SDEs, and on an Euler scheme (or high-order schemes) for the numerical evaluation of the respective SDEs. | clarity | 0.99879104 | 0904.0624 | 1 |
Furthermore we are able to easily incorporate "middle-size" and "large-size" events within our framework . Results of a concrete implementation are provided. | <meaning-changed> Furthermore we are able to easily incorporate "middle-size" and "large-size" events within our framework . Results of a concrete implementation are provided. | The empirical calibration procedure presented in this paper can be seen as the SDE-counterpart of the so called Filtered Historical Simulation method; the behavior of volatility stems in our case out of the assumptions on the underlying SDEs. Furthermore, we are able to easily incorporate "middle-size" and "large-size" events within our framework . Results of a concrete implementation are provided. | meaning-changed | 0.9993457 | 0904.0624 | 1 |
Furthermore we are able to easily incorporate "middle-size" and "large-size" events within our framework . Results of a concrete implementation are provided. The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager . | <clarity> Furthermore we are able to easily incorporate "middle-size" and "large-size" events within our framework . Results of a concrete implementation are provided. The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager . | Furthermore we are able to easily incorporate "middle-size" and "large-size" events within our framework always making a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager . | clarity | 0.9984334 | 0904.0624 | 1 |
The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager . | <meaning-changed> The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager . | The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary a-priori intuition of the risk manager . | meaning-changed | 0.5343371 | 0904.0624 | 1 |
The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager . | <meaning-changed> The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager . | The method also allows a precise distinction between the information obtained from the market and the one coming from the necessary intuition of the risk manager . Results of one concrete implementation are provided . | meaning-changed | 0.9995678 | 0904.0624 | 1 |
Under the frequent conditions of small molecule numbers, mass action theory becomes insufficient to describe the dynamics of such systems. | <clarity> Under the frequent conditions of small molecule numbers, mass action theory becomes insufficient to describe the dynamics of such systems. | Under conditions of small molecule numbers, mass action theory becomes insufficient to describe the dynamics of such systems. | clarity | 0.9985474 | 0904.0947 | 1 |
Under the frequent conditions of small molecule numbers, mass action theory becomes insufficient to describe the dynamics of such systems. | <meaning-changed> Under the frequent conditions of small molecule numbers, mass action theory becomes insufficient to describe the dynamics of such systems. | Under the frequent conditions of small molecule numbers, as is frequently the case in living cells, mass action theory becomes insufficient to describe the dynamics of such systems. | meaning-changed | 0.9994881 | 0904.0947 | 1 |
Under the frequent conditions of small molecule numbers, mass action theory becomes insufficient to describe the dynamics of such systems. | <clarity> Under the frequent conditions of small molecule numbers, mass action theory becomes insufficient to describe the dynamics of such systems. | Under the frequent conditions of small molecule numbers, mass action theory fails to describe the dynamics of such systems. | clarity | 0.99894196 | 0904.0947 | 1 |
Instead, the biochemical reactions must be treated as stochastic processes , producing intrinsic concentration fluctuations of the chemicals. | <clarity> Instead, the biochemical reactions must be treated as stochastic processes , producing intrinsic concentration fluctuations of the chemicals. | Instead, the biochemical reactions must be treated as stochastic processes that intrinsically generate concentration fluctuations of the chemicals. | clarity | 0.9536906 | 0904.0947 | 1 |
We investigate the stochastic reaction kinetics of covalent modification cycles (CMCs) by analytical modelling and numerically exact Monte-Carlo simulation of the temporaly fluctuating concentrationx(t). The statistical behaviour of this simple network module turns out to be so rich that CMCs can be viewed as versatile and tunable noise generators. | <coherence> We investigate the stochastic reaction kinetics of covalent modification cycles (CMCs) by analytical modelling and numerically exact Monte-Carlo simulation of the temporaly fluctuating concentrationx(t). The statistical behaviour of this simple network module turns out to be so rich that CMCs can be viewed as versatile and tunable noise generators. | We investigate the stochastic reaction kinetics of covalent modification cycles (CMCs) by analytical modelling and numerically exact Monte-Carlo simulation of the temporally fluctuating concentration. | coherence | 0.99794835 | 0904.0947 | 1 |
Depending on the parameter regime, we find for the probability density P(x) several qualitatively different classes of distribution functions, including powerlaw distributions with a fractional and tunable exponent. | <meaning-changed> Depending on the parameter regime, we find for the probability density P(x) several qualitatively different classes of distribution functions, including powerlaw distributions with a fractional and tunable exponent. | Depending on the parameter regime, we find for the probability density of the concentration qualitatively distinct classes of distribution functions, including powerlaw distributions with a fractional and tunable exponent. | meaning-changed | 0.8508131 | 0904.0947 | 1 |
These findings challenge the traditional view of biochemical control networks as deterministic computational systems . | <meaning-changed> These findings challenge the traditional view of biochemical control networks as deterministic computational systems . | These findings challenge the traditional view of biochemical control networks as deterministic computational systems and suggest that CMCs in cells can function as versatile and tunable noise generators . | meaning-changed | 0.99937445 | 0904.0947 | 1 |
We systematically investigate the community structure of the yeast protein interaction network . We employ methods that allow us to identify communities in the network at multiple resolutions as, a priori, there is no single scale of interest. | <meaning-changed> We systematically investigate the community structure of the yeast protein interaction network . We employ methods that allow us to identify communities in the network at multiple resolutions as, a priori, there is no single scale of interest. | Motivation: If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure might define protein modules with similar biological roles. We investigate the connection between biological modules and network communities in yeast and ask how the functional similarity of the network at multiple resolutions as, a priori, there is no single scale of interest. | meaning-changed | 0.9976439 | 0904.0989 | 1 |
We employ methods that allow us to identify communities in the network at multiple resolutions as, a priori, there is no single scale of interest. We use novel, stringent tests to find strong evidence for a link between topology and function. Crucially, our tests control for the fact that interacting partners are more similar than a randomly-chosen pair, which is essential for a fair test of functional similarity. We find that many biologically homogeneous communities , that are robust over many resolutions, are surprisingly large. We thus not only identify complexes from the interaction data but also larger collections of strongly-interacting proteins . Communities that contain interactions from tandem affinity purification and co-immunoprecipitation data are far more likely to be biologically homogeneous than those from yeast-two-hybrid and split-ubiquitin data. | <clarity> We employ methods that allow us to identify communities in the network at multiple resolutions as, a priori, there is no single scale of interest. We use novel, stringent tests to find strong evidence for a link between topology and function. Crucially, our tests control for the fact that interacting partners are more similar than a randomly-chosen pair, which is essential for a fair test of functional similarity. We find that many biologically homogeneous communities , that are robust over many resolutions, are surprisingly large. We thus not only identify complexes from the interaction data but also larger collections of strongly-interacting proteins . Communities that contain interactions from tandem affinity purification and co-immunoprecipitation data are far more likely to be biologically homogeneous than those from yeast-two-hybrid and split-ubiquitin data. | We employ methods that allow us to identify communities in the communities that we find depends on the scales at which we probe the network. Results: We find many proteins lie in functionally homogeneous communities (a maximum of 2777 out of 4028 proteins) which suggests that network structure does indeed help identify sets of proteins with similar functions. The homogeneity of the communities depends on the scale selected. We use a novel test and two independent characterizations of protein function to determine the functional homogeneity of communities. We exploit the connection between network structure and split-ubiquitin data. | clarity | 0.6335734 | 0904.0989 | 1 |
We thus not only identify complexes from the interaction data but also larger collections of strongly-interacting proteins . Communities that contain interactions from tandem affinity purification and co-immunoprecipitation data are far more likely to be biologically homogeneous than those from yeast-two-hybrid and split-ubiquitin data. We find that high clustering coefficient is a very good indicator of biological homogeneity in small communities. For larger communities, we find that link density is also important. Our results significantly improve the understanding of the modular structure of the protein interaction network- and how that modularity is reflected in biological homogeneity and experimental type. Our results suggest a method to select groups of functionally similar proteins even when no annotation is yet known, thereby yielding a valuable diagnostic tool to predict groups that act concertedly within the cell . | <clarity> We thus not only identify complexes from the interaction data but also larger collections of strongly-interacting proteins . Communities that contain interactions from tandem affinity purification and co-immunoprecipitation data are far more likely to be biologically homogeneous than those from yeast-two-hybrid and split-ubiquitin data. We find that high clustering coefficient is a very good indicator of biological homogeneity in small communities. For larger communities, we find that link density is also important. Our results significantly improve the understanding of the modular structure of the protein interaction network- and how that modularity is reflected in biological homogeneity and experimental type. Our results suggest a method to select groups of functionally similar proteins even when no annotation is yet known, thereby yielding a valuable diagnostic tool to predict groups that act concertedly within the cell . | We thus not only identify complexes from the interaction data but also larger collections of strongly-interacting proteins . Communities that contain interactions from tandem affinity purification and co-immunoprecipitation data are far more likely to be biologically homogeneous than those from yeast-two-hybrid and biological function to select groups of functionally similar proteins even when no annotation is yet known, thereby yielding a valuable diagnostic tool to predict groups that act concertedly within the cell . | clarity | 0.9931554 | 0904.0989 | 1 |
Our results suggest a method to select groups of functionally similar proteins even when no annotation is yet known, thereby yielding a valuable diagnostic tool to predict groups that act concertedly within the cell . | <meaning-changed> Our results suggest a method to select groups of functionally similar proteins even when no annotation is yet known, thereby yielding a valuable diagnostic tool to predict groups that act concertedly within the cell . | Our results suggest a method to select groups of proteins which are likely to participate in similar biological functions. We show that high mean clustering coefficient and low mean node betweenness centrality can be used to predict functionally homogeneous communities. Availability: All the data sets and the community detection algorithm are available online . | meaning-changed | 0.9970952 | 0904.0989 | 1 |
Motivation : If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure might define protein modules with similar biological roles. | <coherence> Motivation : If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure might define protein modules with similar biological roles. | Background : If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure might define protein modules with similar biological roles. | coherence | 0.81337255 | 0904.0989 | 2 |
Motivation : If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure might define protein modules with similar biological roles. | <clarity> Motivation : If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure might define protein modules with similar biological roles. | Motivation : If biology is modular then clusters, or communities, of proteins derived using only protein interaction network structure might define protein modules with similar biological roles. | clarity | 0.9943509 | 0904.0989 | 2 |
Motivation : If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure might define protein modules with similar biological roles. | <clarity> Motivation : If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure might define protein modules with similar biological roles. | Motivation : If biology is modular then clusters, or communities, of proteins derived using only protein-protein interaction network structure should define protein modules with similar biological roles. | clarity | 0.9318427 | 0904.0989 | 2 |
We investigate the connection between biological modules and network communities in yeast and ask how the functional similarity of the communities that we find depends on the scales at which we probe the network. | <fluency> We investigate the connection between biological modules and network communities in yeast and ask how the functional similarity of the communities that we find depends on the scales at which we probe the network. | We investigate the link between biological modules and network communities in yeast and ask how the functional similarity of the communities that we find depends on the scales at which we probe the network. | fluency | 0.9979487 | 0904.0989 | 2 |
We investigate the connection between biological modules and network communities in yeast and ask how the functional similarity of the communities that we find depends on the scales at which we probe the network. | <clarity> We investigate the connection between biological modules and network communities in yeast and ask how the functional similarity of the communities that we find depends on the scales at which we probe the network. | We investigate the connection between biological modules and network communities in yeast and its relationship to the scale at which we probe the network. | clarity | 0.9985399 | 0904.0989 | 2 |
Results: We find many proteins lie in functionally homogeneous communities (a maximum of 2777 out of 4028 proteins) which suggests that network structure does indeed help identify sets of proteins with similar functions. The homogeneity of the communities depends on the scale selected . | <clarity> Results: We find many proteins lie in functionally homogeneous communities (a maximum of 2777 out of 4028 proteins) which suggests that network structure does indeed help identify sets of proteins with similar functions. The homogeneity of the communities depends on the scale selected . | Results: Our results demonstrate that the functional homogeneity of communities depends on the scale selected . | clarity | 0.9976673 | 0904.0989 | 2 |
The homogeneity of the communities depends on the scale selected . We use a novel test and two independent characterizations of protein function to determine the functional homogeneity of communities. | <meaning-changed> The homogeneity of the communities depends on the scale selected . We use a novel test and two independent characterizations of protein function to determine the functional homogeneity of communities. | The homogeneity of the communities depends on the scale selected , and that almost all proteins lie in a functionally homogeneous community at some scale. We judge functional homogeneity using a novel test and two independent characterizations of protein function to determine the functional homogeneity of communities. | meaning-changed | 0.9993344 | 0904.0989 | 2 |
We use a novel test and two independent characterizations of protein function to determine the functional homogeneity of communities. | <meaning-changed> We use a novel test and two independent characterizations of protein function to determine the functional homogeneity of communities. | We use a novel test and three independent characterizations of protein function to determine the functional homogeneity of communities. | meaning-changed | 0.9959753 | 0904.0989 | 2 |
We use a novel test and two independent characterizations of protein function to determine the functional homogeneity of communities. We exploit the connection between network structure and biological function to select groups of proteins which are likely to participate in similar biological functions . | <clarity> We use a novel test and two independent characterizations of protein function to determine the functional homogeneity of communities. We exploit the connection between network structure and biological function to select groups of proteins which are likely to participate in similar biological functions . | We use a novel test and two independent characterizations of protein function , and find a high degree of overlap between these measures . | clarity | 0.9966685 | 0904.0989 | 2 |
We show that high mean clustering coefficient and low mean node betweenness centrality can be used to predict functionally homogeneouscommunities. | <fluency> We show that high mean clustering coefficient and low mean node betweenness centrality can be used to predict functionally homogeneouscommunities. | We show that a high mean clustering coefficient and low mean node betweenness centrality can be used to predict functionally homogeneouscommunities. | fluency | 0.99917245 | 0904.0989 | 2 |
We show that high mean clustering coefficient and low mean node betweenness centrality can be used to predict functionally homogeneouscommunities. | <clarity> We show that high mean clustering coefficient and low mean node betweenness centrality can be used to predict functionally homogeneouscommunities. | We show that high mean clustering coefficient of a community can be used to predict functionally homogeneouscommunities. | clarity | 0.99527574 | 0904.0989 | 2 |
We show that high mean clustering coefficient and low mean node betweenness centrality can be used to predict functionally homogeneouscommunities. Availability: All the data sets and the community detection algorithm are available online . | <meaning-changed> We show that high mean clustering coefficient and low mean node betweenness centrality can be used to predict functionally homogeneouscommunities. Availability: All the data sets and the community detection algorithm are available online . | We show that high mean clustering coefficient and low mean node betweenness centrality can be used to identify those that are functionally homogeneous. By tracing the community membership of a protein through multiple scales we demonstrate how our approach could be useful to biologists focusing on a particular protein. Conclusions: We show that there is no one scale of interest in the community structure of the yeast protein interaction network, but we can identify the range of resolution parameters that yield the most functionally coherent communities, and predict which communities are most likely to be functionally homogeneous . | meaning-changed | 0.99903214 | 0904.0989 | 2 |
We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . | <fluency> We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . | We apply a quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . | fluency | 0.99905175 | 0904.1078 | 1 |
We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . | <fluency> We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . | We apply the quadratic hedging scheme developed by Foellmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . | fluency | 0.9988907 | 0904.1078 | 1 |
We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . The main contributions of this work consist of showing that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure is only available in the presence of bounded innovations. | <coherence> We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process . The main contributions of this work consist of showing that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure is only available in the presence of bounded innovations. | We apply the quadratic hedging scheme developed by F\"ollmer , Schweizer, and Sondermann to European contingent products whose underlying asset is modeled using a GARCH process and show that local risk-minimizing strategies with respect to the physical measure do exist, even though an associated minimal martingale measure is only available in the presence of bounded innovations. | coherence | 0.5276208 | 0904.1078 | 1 |
More importantly, since those local risk-minimizing strategies are convoluted and difficult to evaluate, we introduce Girsanov-like risk-neutral measures for the log-prices that yield more tractable and useful results. | <clarity> More importantly, since those local risk-minimizing strategies are convoluted and difficult to evaluate, we introduce Girsanov-like risk-neutral measures for the log-prices that yield more tractable and useful results. | More importantly, since those local risk-minimizing strategies are in general convoluted and difficult to evaluate, we introduce Girsanov-like risk-neutral measures for the log-prices that yield more tractable and useful results. | clarity | 0.9859928 | 0904.1078 | 1 |
Regarding this subject, we focus on GARCH time series models with Gaussian and multinomial innovations and we provide specific conditions under which those martingale measures are appropriate in the context of quadratic hedging. | <clarity> Regarding this subject, we focus on GARCH time series models with Gaussian and multinomial innovations and we provide specific conditions under which those martingale measures are appropriate in the context of quadratic hedging. | Regarding this subject, we focus on GARCH time series models with Gaussian innovations and we provide specific conditions under which those martingale measures are appropriate in the context of quadratic hedging. | clarity | 0.99870014 | 0904.1078 | 1 |
Regarding this subject, we focus on GARCH time series models with Gaussian and multinomial innovations and we provide specific conditions under which those martingale measures are appropriate in the context of quadratic hedging. | <meaning-changed> Regarding this subject, we focus on GARCH time series models with Gaussian and multinomial innovations and we provide specific conditions under which those martingale measures are appropriate in the context of quadratic hedging. | Regarding this subject, we focus on GARCH time series models with Gaussian and multinomial innovations and we provide specific sufficient conditions that have to do with the finiteness of the kurtosis, under which those martingale measures are appropriate in the context of quadratic hedging. | meaning-changed | 0.9994343 | 0904.1078 | 1 |
In the Gaussian case, those conditions have to do with the finiteness of the kurtosis and , for multinomial innovations, an inequality between the trend terms of the prices and of the volatility equations needs to be satisfied . | <meaning-changed> In the Gaussian case, those conditions have to do with the finiteness of the kurtosis and , for multinomial innovations, an inequality between the trend terms of the prices and of the volatility equations needs to be satisfied . | When this equivalent martingale measure is adapted to the kurtosis and , for multinomial innovations, an inequality between the trend terms of the prices and of the volatility equations needs to be satisfied . | meaning-changed | 0.9977168 | 0904.1078 | 1 |
In the Gaussian case, those conditions have to do with the finiteness of the kurtosis and , for multinomial innovations, an inequality between the trend terms of the prices and of the volatility equations needs to be satisfied . | <meaning-changed> In the Gaussian case, those conditions have to do with the finiteness of the kurtosis and , for multinomial innovations, an inequality between the trend terms of the prices and of the volatility equations needs to be satisfied . | In the Gaussian case, those conditions have to do with the finiteness of the price representation we are able to recover out of it the classical pricing formulas of Duan and Heston-Nandi, as well as hedging schemes that improve the performance of those proposed in the literature . | meaning-changed | 0.99955744 | 0904.1078 | 1 |
We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare them with a previously proposed ensemble of networks generated by mimicking the transcriptional regulation process within the cell. | <meaning-changed> We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare them with a previously proposed ensemble of networks generated by mimicking the transcriptional regulation process within the cell. | We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare it with two unbiased ensembles: one obtained by reshuffling the edges and the other generated by mimicking the transcriptional regulation process within the cell. | meaning-changed | 0.99890375 | 0904.1515 | 1 |
We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare them with a previously proposed ensemble of networks generated by mimicking the transcriptional regulation process within the cell. | <clarity> We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare them with a previously proposed ensemble of networks generated by mimicking the transcriptional regulation process within the cell. | We investigate the structural and dynamical properties of the transcriptional regulatory network of the yeast {\it Saccharomyces cerevisiae} and compare them with a previously proposed ensemble of networks generated by mimicking the transcriptional regulation mechanism within the cell. | clarity | 0.9984433 | 0904.1515 | 1 |
Even though the model ensemble successfully reproduces the degree distributions , degree-degree correlations and the k-core structure observed in Yeast , we find subtle differences in the structure that are reflected in the dynamics of regulatory-like processes . | <meaning-changed> Even though the model ensemble successfully reproduces the degree distributions , degree-degree correlations and the k-core structure observed in Yeast , we find subtle differences in the structure that are reflected in the dynamics of regulatory-like processes . | Both ensembles reproduce the degree distributions (the first -by construction- exactly and the second approximately) , degree-degree correlations and the k-core structure observed in Yeast , we find subtle differences in the structure that are reflected in the dynamics of regulatory-like processes . | meaning-changed | 0.7677051 | 0904.1515 | 1 |
Even though the model ensemble successfully reproduces the degree distributions , degree-degree correlations and the k-core structure observed in Yeast , we find subtle differences in the structure that are reflected in the dynamics of regulatory-like processes . | <meaning-changed> Even though the model ensemble successfully reproduces the degree distributions , degree-degree correlations and the k-core structure observed in Yeast , we find subtle differences in the structure that are reflected in the dynamics of regulatory-like processes . | Even though the model ensemble successfully reproduces the degree distributions , degree-degree correlations and the k-core structure observed in Yeast . An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a URLanization which is achieved by subtle modifications in the network's degree distributions . | meaning-changed | 0.9994702 | 0904.1515 | 1 |
We use a Boolean model for the regulation dynamics and comment on the impact of various Boolean function classes that have been suggested to better represent in vivo regulatory interactions. | <clarity> We use a Boolean model for the regulation dynamics and comment on the impact of various Boolean function classes that have been suggested to better represent in vivo regulatory interactions. | We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions. | clarity | 0.99776614 | 0904.1515 | 1 |
In addition to an exceptionally large dynamical core network and an excess of self-intercting genes, we find that , even when these differences are eliminated, the Yeastaccommodates more dynamical attractors than best matching model networks which typically come with a single dominant attractor. | <clarity> In addition to an exceptionally large dynamical core network and an excess of self-intercting genes, we find that , even when these differences are eliminated, the Yeastaccommodates more dynamical attractors than best matching model networks which typically come with a single dominant attractor. | We find that the Yeast's core network has a qualitatively different behaviour, accommodating on average multiple attractors unlike typical members of both reference ensembles which converge to a single dominant attractor. | clarity | 0.99807346 | 0904.1515 | 1 |
We further investigate the robustness of the networks under minor perturbations. | <coherence> We further investigate the robustness of the networks under minor perturbations. | Finally, we investigate the robustness of the networks under minor perturbations. | coherence | 0.84683937 | 0904.1515 | 1 |
We further investigate the robustness of the networks under minor perturbations. We find that , requiring all inputs of the Boolean functions to be nonredundant squeezes the stability of the system to a narrower band near the order-chaos boundary, while the network stability still depends strongly on the used function class. | <coherence> We further investigate the robustness of the networks under minor perturbations. We find that , requiring all inputs of the Boolean functions to be nonredundant squeezes the stability of the system to a narrower band near the order-chaos boundary, while the network stability still depends strongly on the used function class. | We further investigate the robustness of the networks and find that the stability depends strongly on the used function class. | coherence | 0.9897189 | 0904.1515 | 1 |
The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | <meaning-changed> The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | The robustness measure is squeezed into a narrower band around the order-chaos boundary when Boolean inputs are required to be nonredundant on each node. However, the difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | meaning-changed | 0.9995646 | 0904.1515 | 1 |
The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | <meaning-changed> The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | The difference between the reference models and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | meaning-changed | 0.9991703 | 0904.1515 | 1 |
The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | <clarity> The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | The difference between the model and the Yeast 's core is marginal, which is consistent with the type of statistically outlier motifs found in the core . | clarity | 0.99904233 | 0904.1515 | 1 |
The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | <meaning-changed> The difference between the model and the Yeast in terms of stability is marginal, which is consistent with the type of statistically outlier motifs found in the core . | The difference between the model and the Yeast in terms of stability is marginal, suggesting that the dynamically stable network elements are located mostly on the peripherals of the regulatory network. Consistently, the statistically significant three-node motifs in the dynamical core of Yeast turn out to be different from and less stable than those found in the full transcriptional regulatory network . | meaning-changed | 0.9991755 | 0904.1515 | 1 |
Biochemical processes typically involve huge numbers of individual steps, each with its own dynamical rate constants. | <meaning-changed> Biochemical processes typically involve huge numbers of individual steps, each with its own dynamical rate constants. | Biochemical processes typically involve huge numbers of individual reversible steps, each with its own dynamical rate constants. | meaning-changed | 0.9987803 | 0904.1587 | 1 |
For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules Hopfield, 1974 . In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) distributions. | <clarity> For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules Hopfield, 1974 . In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) distributions. | For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules . In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) distributions. | clarity | 0.8059231 | 0904.1587 | 1 |
For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules Hopfield, 1974 . In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) distributions. | <clarity> For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules Hopfield, 1974 . In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) distributions. | For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules Hopfield, 1974 . In this work, we study the transient properties of such systems and fully characterize their first passage (completion) distributions. | clarity | 0.9982389 | 0904.1587 | 1 |
For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules Hopfield, 1974 . In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) distributions. | <meaning-changed> For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules Hopfield, 1974 . In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) distributions. | For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules Hopfield, 1974 . In this work, we study the transient properties of such systems and fully characterize their first passage time (completion) time distributions. | meaning-changed | 0.95551145 | 0904.1587 | 1 |
In particular, we provide explicit expressions for the mean and the variance of the kinetic proofreading completion time . | <meaning-changed> In particular, we provide explicit expressions for the mean and the variance of the kinetic proofreading completion time . | In particular, we provide explicit expressions for the mean and the variance of the completion time for a kinetic proofreading process and computational analyses for more complicated biochemical systems . | meaning-changed | 0.9993162 | 0904.1587 | 1 |
In both regimes, the full system dynamical complexity is trivial compared to its apparent structural complexity. | <clarity> In both regimes, the full system dynamical complexity is trivial compared to its apparent structural complexity. | In both regimes, the dynamical complexity of the full system is trivial compared to its apparent structural complexity. | clarity | 0.5359121 | 0904.1587 | 1 |
Similar simplicity will arise in the dynamics of other complex biochemical processes. | <clarity> Similar simplicity will arise in the dynamics of other complex biochemical processes. | Similar simplicity is likely to arise in the dynamics of other complex biochemical processes. | clarity | 0.99797326 | 0904.1587 | 1 |
Similar simplicity will arise in the dynamics of other complex biochemical processes. | <meaning-changed> Similar simplicity will arise in the dynamics of other complex biochemical processes. | Similar simplicity will arise in the dynamics of many complex multi-step biochemical processes. | meaning-changed | 0.6555356 | 0904.1587 | 1 |
We consider an economy of n firms which may default directly or may be infected by another defaulting firm (a domino effect being also possible). | <fluency> We consider an economy of n firms which may default directly or may be infected by another defaulting firm (a domino effect being also possible). | We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). | fluency | 0.9987431 | 0904.1653 | 1 |
The spontaneous default without external influence and the infections are described by not necessary independent Bernoulli-type random variables. | <fluency> The spontaneous default without external influence and the infections are described by not necessary independent Bernoulli-type random variables. | The spontaneous default without external influence and the infections are described by not necessarily independent Bernoulli-type random variables. | fluency | 0.99940455 | 0904.1653 | 1 |