Generalized Urn Models of Evolutionary Processes

Generalized Polya urn models can describe the dynamics of finite populations of interacting genotypes. Three basic questions these models can address are: Under what conditions does a population exhibit growth? On the event of growth, at what rate does the population increase? What is the long-term behavior of the distribution of genotypes? To address these questions, we associate a mean limit ordinary differential equation (ODE) with the urn model. Previously, it has been shown that on the event of population growth, the limiting distribution of genotypes is a connected internally chain recurrent set for the mean limit ODE. To determine when growth and convergence occurs with positive probability, we prove two results. First, if the mean limit ODE has an ``attainable'' attractor at which growth is expected, then growth and convergence toward this attractor occurs with positive probability. Second, the population distribution almost surely does not converge to sets where growth is not expecte

Model evaluation for glycolytic oscillations in yeast biotransformations of xenobiotics

Anaerobic glycolysis in yeast perturbed by the reduction of xenobiotic ketones is studied numerically in two models which possess the same topology but different levels of complexity. By comparing both models' predictions for concentrations and fluxes as well as steady or oscillatory temporal behavior we answer the question what phenomena require what kind of minimum model abstraction. While mean concentrations and fluxes are predicted in agreement by both models we observe different domains of oscillatory behavior in parameter space. Generic properties of the glycolytic response to ketones are discussed

Stochastic Relational Presheaves and Dynamic Logic for Contextuality

Presheaf models provide a formulation of labelled transition systems that is useful for, among other things, modelling concurrent computation. This paper aims to extend such models further to represent stochastic dynamics such as shown in quantum systems. After reviewing what presheaf models represent and what certain operations on them mean in terms of notions such as internal and external choices, composition of systems, and so on, I will show how to extend those models and ideas by combining them with ideas from other category-theoretic approaches to relational models and to stochastic processes. It turns out that my extension yields a transitional formulation of sheaf-theoretic structures that Abramsky and Brandenburger proposed to characterize non-locality and contextuality. An alternative characterization of contextuality will then be given in terms of a dynamic modal logic of the models I put forward.Comment: In Proceedings QPL 2014, arXiv:1412.810

String Inflation After Planck 2013

We briefly summarize the impact of the recent Planck measurements for string inflationary models, and outline what might be expected to be learned in the near future from the expected improvement in sensitivity to the primordial tensor-to-scalar ratio. We comment on whether these models provide sufficient added value to compensate for their complexity, and ask how they fare in the face of the new constraints on non-gaussianity and dark radiation. We argue that as a group the predictions made before Planck agree well with what has been seen, and draw conclusions from this about what is likely to mean as sensitivity to primordial gravitational waves improves.Comment: LaTeX, 21 pages plus references; slight modification of the discussion of inflection point inflation, references added and typos correcte

A short note on the problematic concept of excess demand in asset pricing models with mean-variance optimization

Referring to asset pricing models where demand is proportional to excess returns and said to be derived from a mean-variance optimization problem, the note formulates what probably is common knowledge but hardly ever made an explicit subject of discussion. This is an insufficient distinction between the desired holding of the risky asset on the part of the speculative agents, which is the solution to the optimization problem and usually directly presented as excess demand, and the desired change in this holding, which is what should reasonably constitute the excess demand on the market. The note arrives at the conclusion that in models with a market maker the story of the maximization of expected wealth should be dropped

Filtering and Forecasting Spot Electricity Prices in the Increasingly Deregulated Australian Electricity Market

Modelling and forecasting the volatile spot pricing process for electricity presents a number of challenges. For increasingly deregulated electricity markets, like that in the Australian state of New South Wales, there is need to price a range of derivative securities used for hedging. Any derivative pricing model that hopes to capture the pricing dynamics within this market must be able to cope with the extreme volatility of the observed spot prices. By applying wavelet analysis, we examine both the price and demand series at different time locations and levels of resolution to reveal and differentiate what is signal and what is noise. Further, we cleanse the data of leakage from the high frequency, mean reverting price spikes into the more fundamental levels of frequency resolution. As it is from these levels that we base the reconstruction of our filtered series, we need to ensure they are least contaminated by noise. Using the filtered data, we explore time series models as possible candidates for explaining the pricing process and evaluate their forecasting ability. These models include one from the threshold autoregressive (AR) model. What we find is that models from the TAR class produce forecasts that best appear to capture the mean and variance components of the actual data.electricity; wavelets, time series models; forecasting

On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering

We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general class of stochastic filtering algorithms, including sequential Monte Carlo type models and mean eld particle interpretation models. We illustrate these results in the context of the Bernoulli and the Probability Hypothesis Density filter, yielding what seems to be the first results of this kind in this subject

Avalanche size distributions in mean field plastic yielding models

I discuss the size distribution ${\cal N}(S)$ of avalanches occurring at the yielding transition of mean field (i.e., Hebraud-Lequeux) models of amorphous solids. The size distribution follows a power law dependence of the form: ${\cal N}(S)\sim S^{-\tau}$. However (contrary to what is found in its depinning counterpart) the value of $\tau$ depends on details of the dynamic protocol used. For random triggering of avalanches I recover the $\tau=3/2$ exponent typical of mean field models, which in particular is valid for the depinning case. However, for the physically relevant case of external loading through a quasistatic increase of applied strain, a smaller exponent (close to 1) is obtained. This result is rationalized by mapping the problem to an effective random walk in the presence of a moving absorbing boundary