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0705.0053 | 1 | We show that the mutual fund theorems of Merton (1971) extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain four such theorems by considering a financial market both with and without a riskless asset and by considering both constant and random consumption. | We show that the mutual fund theorems of Merton (1971) extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain two such theorems by considering a financial market both with and without a riskless asset for random consumption. The striking result is that we obtain two-fund theorems despite the additional source of randomness from consumption. | [
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0705.1606 | 1 | The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of two-dimensional swimming bodies employing a variety of propulsion mechanisms -- motivated by biological and microrobotic designs -- is investigated, including the use of moving limbs, changing body shapes and fluid jets. The efficiencies of the mechanisms and the nature of the induced, time-dependent flow fields are found to differ widely among swimmers . | The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of two-dimensional swimming bodies employing a variety of propulsion mechanisms -- motivated by biological and microrobotic designs -- is investigated, including the use of moving limbs, changing body shapes and fluid jets. The swimming efficiency and the nature of the induced, time-dependent flow fields are found to differ widely among body designs and propulsion mechanisms . | [
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0705.1949 | 1 | 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 optimisation with transaction cost. We allow for correlations in risky assets and obtain optimal trading methods for general utility functions. Our analytical results are supported by numerical simulations in the context of the Long Term Growth Model . | [
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0706.0482 | 1 | We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. 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 . | We perform a stability analysis for the utility maximization problem in a general semimartingale model where both liquid and illiquid assets (random endowments) are present. Small misspecifications of preferences (as modeled via expected utility), as well as views of the world or the market model (as modeled via subjective probabilities) are considered. 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 preferences and probabilistic views . | [
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0706.2383 | 1 | 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 | [
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0706.2383 | 2 | the paper is withdrawn for the moment | The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of phosphorylations 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. | [
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0706.2383 | 3 | The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of phosphorylations 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 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 . | The utilization of multiple phosphorylation sites in regulating a biological response is ubiquitous in cell signaling. If each site contributes an additional, equivalent binding site, then one consequence of an increase in the number of phosphorylations 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 , is 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 are predicted . 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 . | [
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0707.0026 | 1 | A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions , whose imply that the distribution of probabilities in the systems are close . It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities . Additionally, the proof of the set of PSN with its morphisms form the category PSN, having the category of sequential dynamical systems SDS, as a full subcategory is given. Several examples of morphisms, subsystems and simulations are given. | A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions . It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities if the morphism is either an epimorphism or a monomorphism . Additionally, the proof of the set of PSN with its morphisms form the category PSN, having the category of sequential dynamical systems SDS, as a full subcategory is given. Several examples of morphisms, subsystems and simulations are given. | [
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0707.2076 | 1 | We propose a biologically motivated quantity, twinness, to evaluate local similarity between nodes in a network. 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 graph animal algorithm is used to estimate twinness for each pair of nodes (for subgraph sizes n=4 to n=12) in four different protein interaction networks (PINs). These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs - each obtained using state-of-the-art high throughput methods. In almost all cases, the average twinness of node pairs is vastly higher than expected from a null model obtained by switching links. 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 . 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. Indeed, we find that these paralogues are over-represented as twins compared to pairs chosen at random. These results indicate that twinness can detect ancestral relationships from currently available PIN data. | We propose a biologically motivated quantity, twinness, to evaluate local similarity between nodes in a network. 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 graph animal algorithm is used to estimate twinness for each pair of nodes (for subgraph sizes n=4 to n=12) in four different protein interaction networks (PINs). These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs -- each obtained using state-of-the-art high throughput methods. In almost all cases, the average twinness of node pairs is vastly higher than expected from a null model obtained by switching links. 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 . 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. Indeed, we find that these paralogous proteins are over-represented as twins compared to pairs chosen at random. These results indicate that twinness can detect ancestral relationships from currently available PIN data. | [
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0707.3621 | 1 | We calculate analytically the critical connectivity K_c of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. 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 . Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced . Further, damage propagation in RTN with in-degree distributions that exhibit a scale-free tail k_{in^{\gamma} is studied; we find that a decrease of \gamma can lead to a transition from supercritical (chaotic) to subcritical (ordered) dynamics} . Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. 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 . | We calculate analytically the critical connectivity K_c of Random Threshold Networks (RTN) for homogeneous and inhomogeneous thresholds, and confirm the results by numerical simulations. We find a super-linear increase of K_c with the (average) absolute threshold |h|, which approaches K_c(|h|) \sim with \alpha \approx } h^2/( 2 \ln{|h| 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^2 . Interestingly, we find that inhomogeneous distribution of thresholds leads to increased propagation of perturbations for sparsely connected networks, while for densely connected networks damage is reduced ^{\gamma} is studied; we find that a decrease of \gamma can lead to a transition from supercritical (chaotic) to subcritical (ordered) dynamics} ; the cross-over point yields a novel, characteristic connectivity K_d, that has no counterpart in Boolean networks . Last, local correlations between node thresholds and in-degree are introduced. Here, numerical simulations show that even weak (anti-)correlations can lead to a transition from ordered to chaotic dynamics, and vice versa. It is shown that the naive mean-field assumption typical for the annealed approximation leads to false predictions in this case, since correlations between thresholds and out-degree that emerge as a side-effect strongly modify damage propagation behavior . | [
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0708.0046 | 1 | The Markowitz mean-variance optimizing framework has served as the basis for modern portfolio theory for more than 50 years. 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 . This penalty stabilizes the optimization problem, encourages sparse portfolios, and facilitates treatment of transaction costs in a transparent way . 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 . 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 . | We consider the problem of portfolio selection within the classical Markowitz mean-variance optimizing framework , which has served as the basis for modern portfolio theory for more than 50 years. 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 ) . This penalty stabilizes the optimization problem, automatically encourages sparse portfolios, and facilitates an effective treatment of transaction costs . We implement our methodology using as our securities two sets of portfolios constructed by Fama and French: the 48 industry portfolios and 100 portfolios formed on size and book-to-market . 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 . | [
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0708.0370 | 1 | Biochemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated using the Gillespie Algorithm or the Next Reaction Method , which are exact simulation methods . 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 . 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. | Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the Gillespie Algorithm or the Next Reaction Method . 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 independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified Next Reaction Method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems with delays. | [
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0708.0377 | 1 | By explicitly representing well-stirred chemical reaction systems with independent, unit Poisson processes we develop a new adaptive tau-leaping procedure. 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. 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. 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 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. The procedure developed is novel in that accuracy is guaranteed by performing post-leap checks. 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. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values . | [
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0708.0377 | 2 | 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. The procedure developed is novel in that accuracy is guaranteed by performing post-leap checks. 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. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values . | 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. The procedure developed is novel in that accuracy is guaranteed by performing postleap checks. 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 biased by the rejections of leaps. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values | [
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0708.0544 | 1 | Continuous time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. 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. | Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. 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 more exotic market conditions. | [
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0708.0703 | 1 | 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. Here we investigated the response of a stochastic Hodgkin-Huxley neuron model to transient input pulses. We found that the response (firing or no firing), as well as the response time, is dependent on the state of the neuron at the moment when input pulse is applied. The state-dependent properties of the response is studied with phase plane analysis method. Using a simple pulse detectionscenario, we demonstrated channel noise enable the neuron to detect subthreshold signals. A simple neuronal network which can marvelously enhance the pulses detecting ability was also proposed. 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 . | Neurons 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. In this paper, we studied the response of a stochastic Hodgkin-Huxley neuron to transient input subthreshold pulses. It was found that the average response time decreases but variance increases as the amplitude of channel noise increases. In the case of single pulse detection, we show that channel noise enables one neuron to detect the subthreshold signals and an optimal membrane area (or channel noise intensity) exists for a single neuron to achieve optimal performance. However, the detection ability of a single neuron is limited by large errors. Here, we test a simple neuronal network that can enhance the pulse detecting abilities of neurons and find dozens of neurons can perfectly detect subthreshold pulses. The phenomenon 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 networks can be optimized for the number of neurons comprising the network . | [
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0708.2244 | 1 | 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. For unbiased update rules, there is no phase transition for RTNs of nonzero connectivity. 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 . | %DIFDELCMD < ]%%% %DIFDELCMD < ]%%% This paper has been withdrawn . | [
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0708.2707 | 1 | Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated 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. Furthermore, we found that while long-term learning promotes cooperation, innovation makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and innovation , when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. Learning and innovation help to preserve cooperation during network URLanization , and may be key mechanisms promoting the evolution of URLanizing, complex systems. | Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying the reinforcement learning strategy adoption rule, Q-learning on a variety of random, regular, small-word, scale-free and modular network models in repeated, multi-agent Prisoners Dilemma and Hawk-Dove games. Furthermore, we found that using the above model systems other long-term learning strategy adoption rules also promote cooperation, while introducing a low level of noise (as a model of innovation) to the strategy adoption rules makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and random elements in the strategy adoption rules , when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. These results suggest that a balanced duo of learning and innovation may help to preserve cooperation during the URLanization of real-world networks , and may play a prominent role in the evolution of URLanizing, complex systems. | [
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0708.2953 | 1 | The numbers of each sort of molecule present in an equilibrium chemical reaction mixture are Poisson distributed . We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain a nearly complete answer. In particular, we show that networks with certain topological features must have a Poisson distribution, whatever the reaction rates. Such driven systems also obey an analog of the fluctuation-dissipation theorem and can equilibrate when in contact with each other . Our results may be relevant to biological systems and to the larger question of how equilibrium ideas might extend to nonequilibrium systems. | In an equilibrium chemical reaction mixture , the number of molecules present obeys a Poisson distribution . We ask when the same is true of the steady state of a nonequilibrium reaction network and obtain an essentially complete answer. In particular, we show that networks with certain topological features must have a Poisson distribution, whatever the reaction rates. Such driven systems also obey an analog of the fluctuation-dissipation theorem . Our results may be relevant to biological systems and to the larger question of how equilibrium concepts might apply to nonequilibrium systems. | [
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0709.0561 | 1 | Using our recent contribution, the " partitioned leaping algorithm" [L. A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], we investigate the effects of stochasticity in two model biochemical reaction networks. By considering situations both where "leaping" proves beneficial and where it does not, we gain valuable insight that can aid in and advance the use of leaping methods in computational biology. In particular, we identify reaction subnetworks with small populations and large rate constants as a major bottleneck for leaping. 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 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 . 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 . | " Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the " partitioned leaping algorithm" (PLA) [L. A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. %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 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 . 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 . | [
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0709.0561 | 2 | "Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the "partitioned leaping algorithm" (PLA) [L.A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. 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 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. 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 . | "Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the "partitioned leaping algorithm" (PLA) [L.A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently-introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to be generally representative of real biological systems . We demonstrate how the PLA allows us to quantify subtle effects of stochasticity in these systems 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 bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them. 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 . | [
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0709.3291 | 1 | 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 . | [
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0709.3606 | 1 | 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 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 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 calculate the probability distribution of the metastable state of the plasmids and show on this example that the 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. | [
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0709.3675 | 1 | 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). A DP diffuses or walks along a MT to reach one of the tips of the MT andthen begins depolymerizing the MT itself . 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. 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 . | 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 . We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. 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. Our findings suggest that such motor proteins have a central role in ensuring precise control of MT lengths . | [
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0709.3675 | 2 | 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. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. 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 . Our findings suggest that such motor proteins have a central role in ensuring precise control of MT lengths . | In many intracellular processes, the length distribution of microtubules is controlled by depolymerizing motor proteins . Experiments have shown that, following non-specific 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. We develop a quantitative model to study the depolymerizing action of such a generic motor protein, and its possible effects on the length distribution of microtubules. 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 with a single peak. However, for highly processive motors and large motor densities, this distribution effectively becomes an exponential decay . Our findings suggest that such motor proteins may be selectively used by the cell to ensure precise control of MT lengths . The model is also used to analyze experimental observations of motor-induced depolymerization . | [
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0710.0892 | 1 | 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. The essence of the method is to extend the transitivity of indirect regulations ( i.e. A regulates B and B regulates C implies A regulates C) to longer cascades and effectively take care of the signs of the regulations. This algorithm is tailored for large and heavily interconnected networks, which are of growing importance due to the accruement of data from high-throughput experiments. 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 develop a matrix-based approach to predict and verify indirect interactions in gene and protein regulatory networks. It is based on the approximate transitivity of indirect regulations ( e.g. A regulates B and B regulates C often implies that A regulates C) and optimally takes into account the length of a cascade and signs of intermediate interactions. Our method is at its most powerful when applied to large and densely interconnected networks. It successfully predicts both the yet unknown indirect regulations, as well as the sign (activation or repression) of already known ones. The reliability of sign predictions was calibrated using the gold-standard sets of positive and negative interactions. We fine-tuned the parameters of our algorithm by maximizing the area under the Receiver Operating Characteristic (ROC) curve. We then applied the optimized algorithm to large literature-derived networks of all direct and indirect regulatory interactions in several URLanisms ( Homo sapiens, Saccharomyces cerevisiae, Arabidopsis thaliana and Drosophila melanogaster ) . | [
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0710.3959 | 1 | The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. 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. 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. 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. The characteristics of this copula in the bivariate case are described . We explain simulation and calibration procedures and provide examples . | The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. 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. 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. In this paper we propose the use of a grouped t copula , where each group consists of one risk factor only, so that a priori grouping is not required. The copula characteristics in the bivariate case are studied . We explain simulation and calibration procedures , including a simulation study on finite sample properties of the maximum likelihood estimators and Kendall's tau approximation. This new copula can be significantly different from the standard t copula in terms of risk measures such as tail dependence, value at risk and expected shortfall. Keywords: grouped t copula, tail dependence, risk management . | [
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0710.4127 | 1 | Stimulated by the long term goal of identifying gene targets for corn crop improvement, we perturbed a simple plant cell system by the addition of abscisic acid, a well-characterized plant hormone, and measured the gene expression with transcriptional microarrays for 150 minutes, every 10 minutes after treatment. Parameters of biochemistry-based models were inferred for 25 downstream (regulated) genes of interest using a thoroughly studied approximation of the posterior distribution, accounting for model uncertainty through Bayesian model averaging. The four causal gene interactions thereby identified as probable under a first-order difference model present testable hypotheses for future experimentation that could conceivably build knowledge of the complex biological system. The small scale of this result compared to many of the reconstructed networks reported in recent literature reflects a cautious approach to systems biology, but without a priori skepticism. The number of putative genes represented on the microarrays used is on the order of the size of the genome; a modification of the methodology for cases in which the number of measured genes is a small fraction of the genome size is also provided. For purposes of inferring biological networks, the main advantage of microarray technology over low-throughput methods may be that the representation of a large enough portion of the genome enables computation of an informative upper bound of how much confidence one may reasonably place in causal relationships between genes on the basis of observed data. | Motivation: Measurements of gene expression over time enable the reconstruction of transcriptional networks. However, Bayesian networks and many other current reconstruction methods rely on assumptions that conflict with the differential equations that describe transcriptional kinetics. Practical approximations of kinetic models would enable inferring causal relationships between genes from expression data of microarray, tag-based and conventional platforms, but conclusions are sensitive to the assumptions made. Results: The representation of a sufficiently large portion of genome enables computation of an upper bound on how much confidence one may place in influences between genes on the basis of expression data. Information about which genes encode transcription factors is not necessary but may be incorporated if available. The methodology is generalized to cover cases in which expression measurements are missing for many of the genes that might control the transcription of the genes of interest. The assumption that the gene expression level is roughly proportional to the rate of translation led to better empirical performance than did either the assumption that the gene expression level is roughly proportional to the protein level or the Bayesian model average of both assumptions. Availability: URL points to R code implementing the methods (R Development Core Team 2004). Supplementary information: URL | [
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0711.0916 | 1 | We present a theoretical investigation of the folding of small proteins assisted by chaperones. We describe the proteins in the framework of an effective potential model which contains the Ramachandran angles as degrees of freedom {\it . The cage of chaperonins is modeled by an external confining potential which is also able to take into account hydrophobic and hydrophilic effects inside the cavity. Using the Wang-Landau algorithm Phys. Rev. Lett.%DIFDELCMD < {\bf %%% 86 , 2050 (2001) we determine the density of states g(E ) and analyze in detail the thermodynamical properties of the confined proteins for different sizes of the cage . We show how the confinement through the chaperon dramatically reduces the phase space available for the protein leading to a much faster folding process. Slightly hydrophobic cages seem to make the native structure more stable . However, not any confining potential helps folding . If the inner walls of the cage are strongly hydrophobic, a denaturation process is induced, in which the proteins partially unfold and stick to the walls . | We present a theoretical study of the folding of small proteins inside confining potentials. Proteins are described in the framework of an effective potential model which contains the Ramachandran angles as degrees of freedom and does not need any{\it a priori information about the native state. Hydrogen bonds, dipole-dipole- and hydrophobic interactions are taken explicitly into account. An interesting feature displayed by this potential is the presence of some intermediates between the unfolded and native states. We consider different types of confining potentials in order to study the structural properties of proteins folding inside cages with repulsive or attractive walls . Using the Wang-Landau algorithm %DIFDELCMD < {\bf %%% we determine the density of states (DOS ) and analyze in detail the thermodynamical properties of the confined proteins for different sizes of the cages . We show that confinement dramatically reduces the phase space available to the protein and that the presence of intermediate states can be controlled by varying the properties of the confining potential. Cages with strongly attractive walls lead to the disappearance of the intermediate states and to a two-state folding into a less stable configuration. However, cages with slightly attractive walls make the native structure more stable than in the case of pure repulsive potentials, and the folding process occurs through intermediate configurations. In order to test the metastable states we analyze the free energy landscapes as a function of the configurational energy and of the end-to-end distance as an order parameter . | [
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0711.2624 | 1 | In this paper we will develop an original approach, based in the use of renewal equations, for obtaining pricing expressions for financial instruments whose underlying asset can be solely described through a simple continuous-time random walk (CTRW). This enhances the potential use of CTRW techniques in finance. We solve these equations for different contract specifications in a particular but exemplifying case. We recover the celebrated results for the Wiener process under certain limits. | In this paper we will develop an original approach, based in the use of renewal equations, for obtaining pricing expressions for financial instruments whose underlying asset can be solely described through a simple continuous-time random walk (CTRW). This enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits. | [
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0711.2624 | 2 | In this paper we will develop an original approach, based in the use of renewal equations, for obtaining pricing expressions for financial instruments whose underlying asset can be solely described through a simple continuous-time random walk (CTRW) . This enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits. | In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits. | [
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0711.2799 | 1 | Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by simultaneous updating at discrete time steps. Of particular importance for biological applications are networks in which the indegree for each variable is bounded by a fixed constant, as was stressed by Kauffman in his original papers. An important question is which conditions on the network topology can rule out exponentially long periodic orbits in the system. In this paper, we consider systems with positive feedback interconnections among all variables , which in a continuous setting guarantees a very stable dynamics. We present a construction that shows that for an arbitrary constant 0<c<2 and sufficiently large n there exist n-dimensional Boolean networks with this property in which both the indegree and outdegree of each for each variable is bounded by two and which nevertheless contain periodic orbits of length at least c^n. In Part II of this paper we will prove an inverse result showing that any system with such a dynamic behavior must in a sense be similar to the example described. | Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by simultaneous updating at discrete time steps. Of particular importance for biological applications are networks in which the indegree for each variable is bounded by a fixed constant, as was stressed by Kauffman in his original papers. An important question is which conditions on the network topology can rule out exponentially long periodic orbits in the system. In this paper, we consider systems with positive feedback interconnections among all variables (known as cooperative systems) , which in a continuous setting guarantees a very stable dynamics. We show that for an arbitrary constant 0<c<2 and sufficiently large n there exist n-dimensional cooperative Boolean networks in which both the indegree and outdegree of each variable is bounded by two , and which nevertheless contain periodic orbits of length at least c^n. In Part II of this paper we will prove an inverse result showing that any system with such a dynamic behavior must in a sense be similar to the example described. | [
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0711.3812 | 1 | Experiments in recent years have vividly demonstrated that gene expression can Hobe highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. Only when the correlation time of the fluctuations is long compared to the cell cycle time, do they affect the population's growth rate. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. We also apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions. | Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions. | [
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0712.2771 | 1 | We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. With asset prices undergoing a multiplicative random process , we derive approximate analytical results for the optimal investment fractions under various constraints . We show that , when returns and volatilities of the assets are small and borrowing is forbidden , the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. When short positions are also forbidden, only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is explored in detail. | We investigate the use of Kelly's strategy in the construction of an optimal portfolio of assets. For lognormally distributed asset returns , we derive approximate analytical results for the optimal investment fractions in various settings . We show that when mean returns and volatilities of the assets are small and there is no risk-free asset , the Kelly-optimal portfolio lies on Markowitz Efficient Frontier. Since in the investigated case the Kelly approach forbids short positions and borrowing, often only a small fraction of the available assets is included in the Kelly-optimal portfolio. This phenomenon, that we call condensation, is explored in detail. | [
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0712.2773 | 1 | Database replication is difficult but indispensable. We report on our experiences building and deploying middleware-based replication systems both as commercial products and research systems. We identify gaps that still separate academic research from industrial practiceand thus thwart potential technology transfer from academia to the field. We structure our analysis along three axes -- performance, availability and management -- and outline unmet database replication challenges at several levels. We hope to both motivate and aid researchers in bridging these gaps between theory and practice . We sift through the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies resulting from developing and deploying real systems at many customer sites . We propose two agendas, one for academic research and one for industrial R&D, which we expect can bridge the gaps within 5-10 years . | The need for high availability and performance in data management systems has been fueling a long running interest in database replication from both academia and industry. However, academic groups often attack replication problems in isolation, overlooking the need for completeness in their solutions, while commercial teams take a holistic approach that often misses opportunities for fundamental innovation. This has created over time a gap between academic research and industrial practice. This paper aims to characterize the gap along three axes : performance, availability , and administration. We build on our own experience developing and deploying replication systems in commercial and academic settings, as well as on a large body of prior related work . We sift through representative examples from the last decade of open-source, academic, and commercial database replication systems and combine this material with case studies from real systems deployed at Fortune 500 customers . We propose two agendas, one for academic research and one for industrial R&D, which we believe can bridge the gap within 5-10 years . This way, we hope to both motivate and help researchers in making the theory and practice of middleware-based database replication more relevant to each other . | [
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0712.3485 | 1 | Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and jump Poisson process. We show that the accuracy of the formula depends on the smoothness of the payoff . Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency . As a consequence, the calibration of such model becomes very fast . | Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function . Our approach relies on an asymptotic expansion related to small diffusion and small jump frequency /size. Our formula has excellent accuracy (the error on implied Black-Scholes volatilities for call option is smaller than 2 bp for various strikes and maturities). Additionally, model calibration becomes very rapid . | [
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0712.4304 | 1 | Kinesins are biomolecular motors which move on cylindrical nano-tubes called microtubules . A normal microtubule consists of more than one protofilament on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a microtubule is, therefore, analogous to vehicular traffic on multi-lane highways where each protofilament is the analogue of a single lane. We extend a recent model of the traffic of single-headed kinesin KIF1A [{\it Phys. Rev. E {\bf 75}, 041905 (2007)}] by incorporating processes which correspond to shifting of the motor proteins from one protofilament to another. On the basis of analytical treatment of our model, we predict the effects of lane changing on the flux of the KIF1A motors . Our quantitative predictions can be tested, in principle, by carrying out {\it in-vitro} experiments with fluorescently labelled KIF1A molecules. | KIF1A kinesins are single-headed motor proteins which move on cylindrical nano-tubes called microtubules (MT) . A normal MT consists of 13 protofilaments on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a MT is, therefore, analogous to vehicular traffic on multi-lane highways where each protofilament is the analogue of a single lane. Does lane-changing increase or decrease the motor flux per lane? We address this fundamental question here by appropriately extending a recent model [{\it Phys. Rev. E {\bf 75}, 041905 (2007)}] . By carrying out analytical calculations and computer simulations of this extended model, we predict that the flux per lane can increase or decrease with the increasing rate of lane changing , depending on the concentrations of motors and the rate of hydrolysis of ATP, the ``fuel'' molecules. Our predictions can be tested, in principle, by carrying out {\it in-vitro} experiments with fluorescently labelled KIF1A molecules. | [
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0801.0718 | 1 | In \mbox{%DIFAUXCMD Gua the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we show that stickiness is invariant under composition with continuous functions. We also prove a time change result on stickiness. As an application we provide sufficient conditions for continuous semimartingales to be sticky (A counter example show that not all semi-martingales are sticky). As a result, our paper provides an extended class of stochastic processes that are consistent with the no arbitrage property in a market with friction . | In 2 the notion of stickiness for stochastic processes was introduced. It was also shown that stickiness implies absense of arbitrage in a market with proportional transaction costs. In this paper, we investigate the notion of stickiness further. In particular, we give examples of processes that are not semimartingales but are sticky . | [
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0801.1480 | 1 | In this paper, we propose a thermodynamic mechanism for the formation of transcriptional foci via the joint agglomeration of DNA-looping proteins and protein-binding domains on DNA: The competition between the gain in protein-DNA binding free energy and the entropy loss due to DNA looping is argued to result in an effective attraction between loops. A mean-field description can be solved analytically via a mapping to a restricted random-graph ensemble . It shows the emergence of protein clusters containing a finite fraction of all looping proteins. If the entropy loss due to a single DNA loop is high enough, this transition is found to be of first order. | In this paper, we propose a thermodynamic mechanism for the formation of transcriptional foci via the joint agglomeration of DNA-looping proteins and protein-binding domains on DNA: The competition between the gain in protein-DNA binding free energy and the entropy loss due to DNA looping is argued to result in an effective attraction between loops. A mean-field approximation can be described analytically via a mapping to a restricted random-graph ensemble having local degree constraints and global constraints on the number of connected components . It shows the emergence of protein clusters containing a finite fraction of all looping proteins. If the entropy loss due to a single DNA loop is high enough, this transition is found to be of first order. | [
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0801.4592 | 1 | It is well-known that power control can affect the wireless network capacity. However, recent works show conflicting results: network capacity may increase or decrease with higher transmission power under different scenarios. In this work, we want to explore this paradoxand provide fundamental understanding on power control . Specifically, we want to explore the following questions: (1)Theoretically, should we increase or decrease transmission power to maximize network capacity? (2) Theoretically, how much network capacity gain can we achieve when using power control? (3) Under realistic situations, how do power control, link scheduling and routing interact with each other? Under which scenarios can we expect a large capacity gain by using higher transmission power? To answer these questions, firstly, we prove that the optimal network capacity is a non-decreasing function of transmission power. Secondly, we prove that the optimal network capacity can be increased unlimitedly by higher transmission power in some network configurations. However, when nodes are distributed uniformly, the gain of optimal network capacity by higher transmission power is upper-bounded by a positive constant. Thirdly, we discuss why network capacity in practice may increase or decrease with higher transmission power under different scenarios using carrier sensing and the minimum hop-count routing. Extensive simulations are carried out to verify our analysis . This work provides a deeper understanding on how power control can affect network capacity. Besides the theoretical contributions, it offers some design intuitions to wireless network researchers . | Recent works show conflicting results: network capacity may increase or decrease with higher transmission power under different scenarios. In this work, we want to understand this paradox . Specifically, we address the following questions: (1)Theoretically, should we increase or decrease transmission power to maximize network capacity? (2) Theoretically, how much network capacity gain can we achieve by power control? (3) Under realistic situations, how do power control, link scheduling and routing interact with each other? Under which scenarios can we expect a large capacity gain by using higher transmission power? To answer these questions, firstly, we prove that the optimal network capacity is a non-decreasing function of transmission power. Secondly, we prove that the optimal network capacity can be increased unlimitedly by higher transmission power in some network configurations. However, when nodes are distributed uniformly, the gain of optimal network capacity by higher transmission power is upper-bounded by a positive constant. Thirdly, we discuss why network capacity in practice may increase or decrease with higher transmission power under different scenarios using carrier sensing and the minimum hop-count routing. Extensive simulations are carried out to verify our analysis . | [
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0802.1288 | 1 | In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage-free under proportional transaction costs in the same spirit of Guasoni et al (2006 , 2007) . In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fractional HJM dynamics. We give a fairly complete characterization of finite-dimensional invariant manifolds for HJM models with fractional Brownian motion by means of Nagumo-type conditions. As an application, we investigate consistency of Nelson-Siegel family with respect to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case such family does not go well with the fractional HJM dynamics with deterministic volatility. In fact, there is no nontrivial fractional interest rate model consistent with the Nelson-Siegel family. | In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage free under proportional transaction costs in the same spirit of Guasoni Math. Finance 16 (2006 ) 569-582 . In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fractional HJM dynamics. We give a fairly complete characterization of finite-dimensional invariant manifolds for HJM models with fractional Brownian motion by means of Nagumo-type conditions. As an application, we investigate consistency of Nelson-Siegel family with respect to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case such a family does not go well with the fractional HJM dynamics with deterministic volatility. In fact, there is no nontrivial fractional interest rate model consistent with the Nelson-Siegel family. | [
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0802.2004 | 1 | We show that a simple model reproduces very closely the evolution of the GDP in constant dollars of many countries during the times of recession and recovery. A theoretical analysis illustrates how an optimal dynamical policy reduces both recession duration and severity, and increases the value of GDP at all times. We propose a criterion to distinguish a posteriori a dynamical policy from a static one . | We show that a simple model reproduces very closely the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. A theoretical analysis illustrates how an optimal dynamical policy reduces both recession duration and severity, and increases the value of GDP at all times. We propose a criterion to distinguish a posteriori a dynamical policy from a static one . Finally, we predict that Ukraine will recover its current and constant dollar 1990 GDPs in 2009 and Moldova in 2015 in current dollars and 2009 in constant dollars . | [
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0802.2004 | 2 | We show that a simple model reproduces very closely the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. A theoretical analysis illustrates how an optimal dynamical policy reduces both recession duration and severity, and increases the value of GDP at all times. We propose a criterion to distinguish a posteriori a dynamical policy from a static one. Finally, we predict that Ukraine will recover its current and constant dollar 1990 GDPs in 2009 and Moldova in 2015 in current dollars and 2009 in constant dollars . | We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. We then argue that it can be used to detect shocks and discuss its predictive power. Finally, a two-sector theoretical model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy . | [
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0802.2004 | 3 | We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during the times of recession and recovery. We then argue that it can be used to detect shocks and discuss its predictive power. Finally, a two-sector theoretical model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy. | We show that a simple and intuitive three-parameter equation fits remarkably well the evolution of the gross domestic product (GDP) in current and constant dollars of many countries during times of recession and recovery. We then argue that this equation is the response function of the economy to isolated shocks, hence that it can be used to detect large and small shocks, including those which do not lead to a recession; we also discuss its predictive power. Finally, a two-sector toy model of recession and recovery illustrates how the severity and length of recession depends on the dynamics of transfer rate between the growing and failing parts of the economy. | [
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0802.2172 | 1 | In that paper, we solve dynamically a partial hedging problem for an American contingent claim: assuming superhedging is not feasible, we explain in this context the notion of efficient hedging by introducing a risk minimization criterion: we consider here the problem of minimizing the conditional expected loss for a given convex and non decreasing loss function. To solve this problem, we provide a connection between the dynamic convex risk functional introduced and the solutionof a quadratic RBSDE (Reflected Backward Stochastic Differential Equations): this is achieved by studying the properties of specific non linear expectations . | In that paper, we provide a new characterization of the solutions of specific reflected backward stochastic differential equations (or RBSDEs) whose driver g is convex and has quadratic growth in its second variable: this is done by introducing the extended notion of g-Snell enveloppe. Then, in a second step, we relate this representation to a specific class of dynamic monetary concave functionals already introduced in a discrete time setting. This connection implies that the solution, characterized by means of non linear expectations , has again the time consistency property . | [
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0802.2512 | 1 | Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbor. In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient. Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of nodes with one or no neighbors to estimate the contribution of these cases to the mean clustering value. Furthermore, we provide a formula for estimating a clustering coefficient that excludes these undefined cases. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied . | Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbor. In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient. Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of leafs and isolated nodes to estimate the contribution of these cases to the mean clustering value. Furthermore, we provide a formula for estimating a clustering coefficient that excludes these undefined cases. This novel definition leads to values which are up to 140\% higher than the traditional values for the observed networks indicating that neighborhood connectivity is normally underestimated. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied . Values for the clustering coefficient vary with the ratio of isolated and leaf nodes which is critical for comparing networks. We suggest including ratio and definition in publications to enable comparisons across different studies . | [
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0802.2512 | 2 | Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbor . In such cases, local clustering has traditionally been set to zero and the node was included in the global clustering coefficient. Such a procedure leads to under-estimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of leafs and isolated nodes to estimate the contribution of these cases to the mean clustering value. Furthermore, we provide a formula for estimating a clustering coefficient that excludes these undefined cases . This novel definition leads to values which are up to 140\% higher than the traditional values for the observed networks indicating that neighborhood connectivity is normally underestimated. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied. Values for the clustering coefficient vary with the ratio of isolated and leaf nodes which is critical for comparing networks. We suggest including ratio and definition in publications to enable comparisons across different studies . | Many networks exhibit the small-world property of the neighborhood connectivity being higher than in comparable random networks. However, the standard measure of local neighborhood clustering is typically not defined if a node has one or no neighbors . In such cases, local clustering has traditionally been set to zero and this value influenced the global clustering coefficient. Such a procedure leads to underestimation of the neighborhood clustering in sparse networks. We propose to include \theta as the proportion of leafs and isolated nodes to estimate the contribution of these cases and provide a formula for estimating a clustering coefficient excluding these cases from the Watts and Strogatz (1998 Nature 393 440-2) definition of the clustering coefficient. Excluding leafs and isolated nodes leads to values which are up to 140\% higher than the traditional values for the observed networks indicating that neighborhood connectivity is normally underestimated. We find that the definition of the clustering coefficient has a major effect when comparing different networks. For metabolic networks of URLanisms, relations changed for 58\% of the comparisons when a different definition was applied. We also show that the definition influences small-world features and that the classification can change from non-small-world to small-world network. We discuss the use of an alternative measure, disconnectedness D, which is less influenced by leafs and isolated nodes . | [
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0802.3679 | 1 | In Black-Scholes delta-hedging method generalization, a "mirror-diffusion" inverse stochastic process is introduced with condition determined by the underlying price variance and payoff function. The process reduces an expected option value at maturity under equivalent martingale measure back to the current time. The normalized ksi-returns , correspondent to the kernel function in the found general solution and not dependent explicitly on time, were used for verification of the one-parameter model inherent efficiency, i.e. self-calibration using only historical volatility data. The model minimizes implied volatility bias (for 2004-2007 S& P100 index options) and theoretically yields skews correspondent to practical term structure for interest rate derivatives. It allows increasing the number of stock price distribution parameters. | The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic volatility data; it maintains the constant expected value at maturity of the hedged instantaneously self-financing portfolio. The payoff variance dependent on random stock price at maturity obtained under an equivalent martingale measure is taken as a condition for introduced "mirror-time" derivative diffusion discount process. Introduced ksi-return distribution , correspondent to the found general solution of backward drift-diffusion equation and normalized by theoretical diffusion coefficient, does not contain so-called "long tails" and unbiased for considered 2004-2007 S& P 100 index data. The model theoretically yields skews correspondent to practical term structure for interest rate derivatives. The method allows increasing the number of asset price probability distribution parameters. | [
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0802.4411 | 1 | We present a positivity preserving numerical scheme for the pathwise solution of nonlinear stochastic differential equations driven by a multi-dimensional Wiener process and governed by non-commutative linear and non-Lipschitz vector fields. This strong order one scheme uses: (i) Strang exponential splitting, an approximation that decomposes the stochastic flow separately into the drift flow, and the pure diffusion flow governed by the diffusion vector fields; (ii) an implicit Euler method to approximate the drift flow; and (iii) an implicit Milstein method to approximate the pure diffusion flow. The separate approximations for the drift and pure diffusion flows preserve positivity. Therefore the Strang exponential splitting approximation does also. We demonstrate the efficacy of our method by applying it to the Heston model and a variance curve model , and compare it against well-established positivity preserving schemes . | For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition density with fractional degrees of freedom. We prove that we can sample from this density by simulating Poisson distributed sums of powers of generalized Gaussian random variables. Further we prove that Marsaglia's polar method extends to the generalized Gaussian distribution, providing an exact and efficient method for generalized Gaussian sampling. We apply our methods to a variance curve model and the Heston model . | [
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0802.4411 | 2 | For nonlinear stochastic differential systems, we develop strong fully implicit positivity preserving numerical methods in the case that the zero boundary is non-attracting. These methods are implicit in the diffusion vector fields. They thus apply to a restricted class, namely those with sublinear form. This however, still includes most Langevin derived processes typical of volatility models in finance and molecular simulation in physics. When the zero boundary is attracting and attainable, we specialize to a prototypical model, namely the mean-reverting Cox--Ingersoll--Ross process. We thus consider the non-central chi-squared transition density with fractional degrees of freedom. We prove that we can sample from this density by simulating Poisson distributed sums of powers of generalized Gaussian random variables. Further we prove that Marsaglia's polar method extends to the generalized Gaussian distribution, providing an exact and efficient method for generalized Gaussian sampling. We apply our methods to a variance curve model and the Heston model . | In the Heston stochastic volatility model, the transition probability of the variance process can be represented by a non-central chi-square density. We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. We prove a new representation for this density based on sums of powers of generalized Gaussian random variables. Further we prove Marsaglia's polar method extends to this distribution, providing an exact method for generalized Gaussian sampling. The advantages are that for the mean-reverting square-root process in the Heston model and Cox-Ingersoll-Ross model, we can generate samples from the true transition density simply, efficiently and robustly . | [
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0802.4411 | 3 | In the Heston stochastic volatility model, the transition probability of the variance process can be represented by a non-central chi-square density. We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. We prove a new representation for this density based on sums of powers of generalized Gaussian random variables. Further we prove Marsaglia's polar method extends to this distribution, providing an exact method for generalized Gaussian sampling . The advantages are that for the mean-reverting square-root process in the Heston model and Cox-Ingersoll-Ross model, we can generate samples from the true transition density simply, efficiently and robustly . | The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random variables. Second we prove Marsaglia's polar method extends to this distribution, providing a simple, exact, robust and efficient acceptance-rejection method for generalized Gaussian sampling and thus central chi-square sampling. Third we derive a simple, high-accuracy, robust and efficient direct inversion method for generalized Gaussian sampling based on the Beasley-Springer-Moro method. Indeed the accuracy of the approximation to the inverse cumulative distribution function is to the tenth decimal place. We then apply our methods to non-central chi-square variance sampling in the Heston model . We focus on the case when the number of degrees of freedom is small and the zero boundary is attracting and attainable, typical in foreign exchange markets. Using the additivity property of the chi-square distribution, our methods apply in all parameter regimes . | [
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0803.0483 | 1 | Translocation of a single stranded DNA through genetically engineered \alpha-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from the neutral wild type \alpha-hemolysin channel. We assume that the wall charges compensate the fraction x of the bare charge q_{b} of the DNA piece residing in the channel. Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece grows with x and at q_{b x= 1. (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls. | Translocation of a single stranded DNA through genetically engineered \alpha-hemolysin channels with positively charged walls is studied. It is predicted that transport properties of such channels are dramatically different from neutral wild type \alpha-hemolysin channel. We assume that the wall charges compensate the fraction x of the bare charge q_{b} of the DNA piece residing in the channel. Our prediction are as follows (i) At small concentration of salt the blocked ion current decreases with x. (ii) The effective charge q of DNA piece , which is very small at x = 0 (neutral channel) grows with x and at x= 1 reaches q_{b (iii) The rate of DNA capture by the channel exponentially grows with x. Our theory is also applicable to translocation of a double stranded DNA in narrow solid state nanopores with positively charged walls. | [
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0803.1364 | 1 | In the Kelly game (Kelly, 1956 ), a gambler is allowed to invest a part of the wealth in each turn. With a certain probability this investment is doubled, and otherwise it is lost. Motivated by the complexity of real investments, we propose several modifications of this game to investigate the influence of diversification and limited information on investment performance. Analytical and numerical results obtained from these toy games are well related to their real-life counterparts . | Financial markets, with their vast range of different investment opportunities, can be seen as a system of many different simultaneous games with diverse and often unknown levels of risk and reward. We introduce generalizations to the classic Kelly investment game Kelly ( 1956 ) that incorporates these features, and use them to investigate the influence of diversification and limited information on Kelly-optimal portfolios. In particular we present approximate formulas for optimizing diversified portfolios and exact results for optimal investment in unknown games where the only available information is past outcomes . | [
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0803.1558 | 1 | We introduce some new quantitative measures of fluctuations in the process of synthesis of proteins from a single messenger RNA (mRNA) template. We calculate the statistical distributions of these fluctuating quantities and extract the strength of the corresponding translational noise. For these calculations{\bf we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions in ribosome traffic on the same mRNA track. By comparing our results for a specific gene of the%DIFDELCMD < {\it %%% Escherichia coli bacteria with those for the corresponding homogeneous mRNA template, we demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise . We also suggest {\it in-vitro} laboratory experimentsfor testing our theoretical predictions . | Proteins are polymerized by cyclic machines called ribosome which use their messenger RNA (mRNA) track also as the corresponding template and the process is called translation. We explore, in depth and detail, the stochastic nature of the translation. We compute various distributions associated with the translation process; one of them, namely dwell time distribution, has been measured in recent single ribosome experiments (Wen et al. Nature{\bf 452 , 598 (2008)). The form of this distribution predicted by our theory is consistent with that extracted from the experimental data. For our quantitative calculations, we use a model that captures both the mechano-chemistry of each individual ribosome as well as their steric interactions %DIFDELCMD < {\it %%% . We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. In principle, our new predictions can be tested by carrying out {\it in-vitro} experiments . | [
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0803.1890 | 1 | A financial market model where agents can only trade using realistic buy-and-hold strategies is considered. Minimal assumptions are made on the nature of the asset-price process - in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the No-Unbounded-Profit-with-Bounded-Risk (NUPBR) condition, we establish that asset-prices have be semimartingales, as well as a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than equivalent martingale measures. Further, the utility maximization problem is considered and it is shown that using only buy-and-hold strategies, optimal utilities and wealth processes resulting from continuous trading can be approximated arbitrarily well . | A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the asset-price process - in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition, we establish that asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures . | [
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0803.1890 | 2 | A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the asset-price process - in particular, the semimartingale property is not assumed. Via a natural assumption of limited opportunities for unlimited resulting wealth from trading, coined the "No Unbounded Profit with Bounded Risk" condition , we establish that asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves supermartingale deflators rather than Equivalent Martingale Measures. | A financial market model where agents trade using realistic combinations of buy-and-hold strategies is considered. Minimal assumptions are made on the discounted asset-price process - in particular, the semimartingale property is not assumed. Via a natural market viability assumption , namely, absence of arbitrages of the first kind, we establish that discounted asset-prices have to be semimartingales. In a slightly more specialized case, we extend the previous result in a weakened version of the Fundamental Theorem of Asset Pricing that involves strictly positive supermartingale deflators rather than Equivalent Martingale Measures. | [
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0804.0682 | 1 | We address the problem of proteasomal protein translocation . Proteasomes are important for all aspects of the cellular metabolism but the mechanism of protein transport remains unknown. We introduce a new stochastic model of the proteasomal transport. We account for the protein translocation and the topology of the positioning of cleavage centers of a proteasome from first principles. We show by test examples and by a comparison with experimental data that our model allows reconstruction of the translocation rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups. Finally we design an experimental set-up for a synthetic polypeptide with a periodic sequence of amino acids which enables more reliable determination of translocation rates . | We address the problem of proteasomal protein translocation and introduce a new stochastic model of the proteasomal digestion (cleavage) of proteins. In this model we account for the protein translocation and the positioning of cleavage sites of a proteasome from first principles. We show by test examples and by processing experimental data that our model allows reconstruction of the translocation and cleavage rates from mass spectroscopy data on digestion patterns and can be used to investigate the properties of transport in different experimental set-ups. Detailed investigation with this model will enable theoretical quantitative prediction of the proteasomal activity . | [
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0804.1034 | 1 | DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between alternative phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in Escherichia coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behaviour: the distribution of times in the on state shows a peak and successive flip times are correlated . This model should provide a framework for understanding how DNA inversion switch architecture determines switch flipping statistics, with relevance to the role of such switches in microbial population dynamics . | DNA inversion is an important mechanism by which bacteria and bacteriophage switch reversibly between phenotypic states. In such switches, the orientation of a short DNA element is flipped by a site-specific recombinase enzyme. We propose a simple model for a DNA inversion switch in which recombinase production is dependent on the switch state (orientational control). Our model is inspired by the fim switch in Escherichia coli. We present an exact analytical solution of the chemical master equation for the model switch, as well as stochastic simulations. Orientational control causes the switch to deviate from Poissonian behaviour: the distribution of times in the on state shows a peak and successive flip times are correlated . | [
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0804.1227 | 1 | {\it Transcription} is the process whereby RNA molecules are polymerized by molecular machines, called RNA polymerase (RNAP), using the corresponding DNA as the template. Recent {\it in-vivo} experiments with single cells have established that transcription takes place in ``bursts'' or ``pulses'' . In this letter we present a model that captures not only the mechano-chemistry of individual RNAPs and their steric interactions but also the switching of the gene between the ON and OFF states. This model accounts for the statistical properties of the transcriptional bursts. It also shows how the quantitative features of the distributions of these bursts can be tuned by controlling the appropriate steps of operation of the RNAP machines. | {\it Transcription} is the process whereby RNA molecules are polymerized by molecular machines, called RNA polymerase (RNAP), using the corresponding DNA as the template. Recent {\it in-vivo} experiments with single cells have established that transcription takes place in "bursts" or "pulses" . In this letter we present a model that captures not only the mechano-chemistry of individual RNAPs and their steric interactions but also the switching of the gene between the ON and OFF states. This model accounts for the statistical properties of the transcriptional bursts. It also shows how the quantitative features of the distributions of these bursts can be tuned by controlling the appropriate steps of operation of the RNAP machines. | [
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0804.1720 | 1 | Charge transport modification exhibiting an increase of conductance activated by an external green light in Bacteriorhodopsin is correlated to its conformational change. A theoretical model based on a map of the protein structure into a resistor network is implemented to account for a sequential tunneling mechanism of charge transfer through neighbouring amino-acids . The model is validated by comparison with current-voltage experiments and provides for the potential barriers involved in the charge transfer an average height of 69 meV over an interacting radius of 6 \aa . The predictability of the model is also tested on bovine rhodopsin, the prototype of the G protein coupled receptor (GPCR) family also sensitive to the light, with results exhibiting the opposite behaviour of a decrease of conductance in the presence of light. | When moving from native to light activated bacteriorhodopsin, modification of charge transport consisting of an increase of conductance is correlated to the protein conformational change. A theoretical model based on a map of the protein tertiary structure into a resistor network is implemented to account for a sequential tunneling mechanism of charge transfer through neighbouring amino acids . The model is validated by comparison with current-voltage experiments . The predictability of the model is further tested on bovine rhodopsin, a G-protein coupled receptor (GPCR) also sensitive to light. In this case, results show an opposite behaviour with a decrease of conductance in the presence of light. | [
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0804.2912 | 1 | The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes supermartingales , when deflated by it . The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices, the stable behavior of the numeraire portfolio is established when each of the aforementioned market parameters is changed in an infinitesimal way. | The numeraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes , when deflated by it , supermartingales . The numeraire portfolio depends on market characteristics, which include: (a) the information flow available to acting agents, given by a filtration; (b) the statistical evolution of the asset prices and, more generally, the states of nature, given by a probability measure; and (c) possible restrictions that acting agents might be facing on available investment strategies, modeled by a constraints set. In a financial market with continuous-path asset prices, we establish the stable behavior of the numeraire portfolio when each of the aforementioned market parameters is changed in an infinitesimal way. | [
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0804.3939 | 1 | Recent works on the emergence of homochirality introduce the concept of recycling, rather than the traditional open-flow system described by Frank. This approach has been criticized by Blackmond et al. They claimed that such systems are thermodynamically impossible, except in the cases where non-microreversible reactions are introduced, like in photochemical reactions, or under the influence of physical actions (e.g. by crystal crushing). This point of view reveals misunderstandings about this model of a recycled system, overlooks the possibility of energy exchanges that could take place in prebiotic systems, and leads the authors to unawarely remove the activation reaction and energy source from their `` non-equilibrium '' models. It is especially important to understand what are the concepts behind the notion of recycled systems, and of activation reactions. These points are fundamental to comprehending how chemical systems -- and especially prebiotic chemical systems -- can be maintained in non-equilibrium steady states, and how free energy can be used and exchanged between systems. The proposed approach aims at the decomposition of the problem, avoiding to embrace the whole system at the same time. | The question of the onset of the homochirality on prebiotic Earth still remains a fundamental question in the quest for the origin of life. Recent works in this field introduce the concept of recycling, rather than the traditional open-flow system described by Frank. This approach has been criticized by Blackmond et al. They claimed that such systems are thermodynamically impossible, except in the cases where non-microreversible reactions are introduced, like in photochemical reactions, or under the influence of physical actions (e.g. by crystal crushing). This point of view reveals misunderstandings about this model of a recycled system, overlooks the possibility of energy exchanges that could take place in prebiotic systems, and leads the authors to unawarely remove the activation reaction and energy source from their " non-equilibrium " models. It is especially important to understand what are the concepts behind the notion of recycled systems, and of activation reactions. These points are fundamental to comprehending how chemical systems -- and especially prebiotic chemical systems -- can be maintained in non-equilibrium steady states, and how free energy can be used and exchanged between systems. The proposed approach aims at the decomposition of the problem, avoiding to embrace the whole system at the same time. | [
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0804.4039 | 1 | In this work we model multicore platforms as chip multiprocessors made up from two different types cores; each type of cores has different computation capabilities. In this simple asymmetric multicore model we study the problem of executing parallel programs that are represented as DAGs or chains of tasks . We assume 2 (essential) speeds in our proposed platform. We relax this assumption and consider many speedsin our energy considerations. This problem has been considered previously in the field of parallel computing and scheduling theory for the general case where multiprocessor platforms have K distinct speeds. Our model is a bridge between the assumptions in these fields and recent advances in multicore processors technology . We provide a refined analysis of a recent scheduling method. Based on this analysis, we specialize the scheduling policy and provide an algorithm of (3 o(1)) expected approximation factor. Note that this improves the previous best factor (6 for two speeds) . | In this work we study the problem of scheduling tasks with dependencies in multiprocessor architectures where processors have different speeds. We present the preemptive algorithm "Save-Energy" that given a schedule of tasks it post processes it to improve the energy efficiency without any deterioration of the makespan. In terms of time efficiency, we show that preemptive scheduling in an asymmetric system can achieve the same or better optimal makespan than in a symmetric system. Motivited by real multiprocessor systems, we investigate architectures that exhibit limited asymmetry: there are two essentially different speeds . Interestingly, this special case has not been studied in the field of parallel computing and scheduling theory ; only the general case was studied where processors have K essentially different speeds. We present the non-preemptive algorithm ``Remnants'' that achieves almost optimal makespan . We provide a refined analysis of a recent scheduling method. Based on this analysis, we specialize the scheduling policy and provide an algorithm of (3 + o(1)) expected approximation factor. Note that this improves the previous best factor (6 for two speeds) . We believe that our work will convince researchers to revisit this well studied scheduling problem for these simple, yet realistic, asymmetric multiprocessor architectures . | [
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"before": "executing parallel programs that are represented as DAGs or chains of tasks",
"after": "scheduling tasks with dependencies in multiprocessor architectures where processors have different speeds. We present the preemptive algorithm \"Save-Energy\" that given a schedule of tasks it post processes it to improve the energy efficiency without any deterioration of the makespan. In terms of time efficiency, we show that preemptive scheduling in an asymmetric system can achieve the same or better optimal makespan than in a symmetric system. Motivited by real multiprocessor systems, we investigate architectures that exhibit limited asymmetry: there are two essentially different speeds",
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"before": "We assume 2 (essential) speeds in our proposed platform. We relax this assumption and consider many speedsin our energy considerations. This problem has been considered previously",
"after": "Interestingly, this special case has not been studied",
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{
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"before": "where multiprocessor platforms have K distinct speeds. Our model is a bridge between the assumptions in these fields and recent advances in multicore processors technology",
"after": "was studied where processors have K essentially different speeds. We present the non-preemptive algorithm ``Remnants'' that achieves almost optimal makespan",
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{
"type": "A",
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"after": ". We believe that our work will convince researchers to revisit this well studied scheduling problem for these simple, yet realistic, asymmetric multiprocessor architectures",
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End of preview. Expand
in Dataset Viewer.
Paper: Understanding Iterative Revision from Human-Written Text
Authors: Wanyu Du, Vipul Raheja, Dhruv Kumar, Zae Myung Kim, Melissa Lopez, Dongyeop Kang
Github repo: https://github.com/vipulraheja/IteraTeR
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