Exploiting the adaptation dynamics to predict the distribution of beneficial fitness effects

Adaptation of asexual populations is driven by beneficial mutations and therefore the dynamics of this process, besides other factors, depend on the distribution of beneficial fitness effects. It is known that on uncorrelated fitness landscapes, this distribution can only be of three types: truncated, exponential and power law. We performed extensive stochastic simulations to study the adaptation dynamics on rugged fitness landscapes, and identified two quantities that can be used to distinguish the underlying distribution of beneficial fitness effects. The first quantity studied here is the fitness difference between successive mutations that spread in the population, which is found to decrease in the case of truncated distributions, remain nearly a constant for exponentially decaying distributions and increase when the fitness distribution decays as a power law. The second quantity of interest, namely, the rate of change of fitness with time also shows quantitatively different behaviour for different beneficial fitness distributions. The patterns displayed by the two aforementioned quantities are found to hold for both low and high mutation rates. We discuss how these patterns can be exploited to determine the distribution of beneficial fitness effects in microbial experiments.Comment: Communicated to PLOS ON

A Flexible Class of Purchase Incidence Models

Purchase incidence models estimated on household scanner panel data typically assume the household's decision interval to be one week. However, it is well known in the econometrics literature that discrete-time models are highly sensitive to the assumed time interval of decision-making. In this study we investigate the consequences of endogenizing the household's decision interval, instead of restricting it to be one week. We characterize the household's random utility maximization problem, and therefore its purchase likelihood function, as a function of the household's decision interval. Such a flexible purchase incidence model is then used to explicitly estimate households' decision intervals in addition to their response to marketing activity and their baseline hazard functions. The proposed model of purchase incidence not only nests traditionally used choice models (such as the binary logit model) and hazard models (such as the discrete hazard model), but also allows for a gamut of more flexible parametric specifications. We estimate the proposed model across four category-level scanner panel datasets and find that the traditional assumption of restricting the household's decision interval to be one week may be too restrictive. We find that households are not only quite heterogeneous in their decision intervals but often have decision intervals longer than a week. From a managerial perspective, we show that estimated price elasticities are systematically understated if one does not allow for the effects of decision intervals. We demonstrate, using a fourth product category, that the results obtained from the category-level analyses generalize to the context of a full model of purchase incidence and brand choice.Decision intervals, Purchase incidence models, Choice models, Logit, Hazard ,

Machine learning-based prediction of a BOS reactor performance from operating parameters

A machine learning-based analysis was applied to process data obtained from a Basic Oxygen Steelmaking (BOS) pilot plant. The first purpose was to identify correlations between operating parameters and reactor performance, defined as rate of decarburization (dc/dt). Correlation analysis showed, as expected a strong positive correlation between the rate of decarburization (dc/dt) and total oxygen flow. On the other hand, the decarburization rate exhibited a negative correlation with lance height. Less obviously, the decarburization rate, also showed a positive correlation with temperature of the waste gas and CO2 content in the waste gas. The second purpose was to train the pilot-plant dataset and develop a neural network based regression to predict the decarburization rate. This was used to predict the decarburization rate in a BOS furnace in an actual manufacturing plant based on lance height and total oxygen flow. The performance was satisfactory with a coefficient of determination of 0.98, confirming that the trained model can adequately predict the variation in the decarburization rate (dc/dt) within BOS reactors. View Full-Tex

Phase lagging model of brain response to external stimuli - modeling of single action potential

In this paper we detail a phase lagging model of brain response to external stimuli. The model is derived using the basic laws of physics like conservation of energy law. This model eliminates the paradox of instantaneous propagation of the action potential in the brain. The solution of this model is then presented. The model is further applied in the case of a single neuron and is verified by simulating a single action potential. The results of this modeling are useful not only for the fundamental understanding of single action potential generation, but also they can be applied in case of neuronal interactions where the results can be verified against the real EEG signal.Comment: 19 page

Analytical approximations to the spectra of quark-antiquark potentials

A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of our results is verified by comparing them both with the literature on the subject and with the numerical results obtained with a Fortran code. As an application of the method that we propose, we consider the meson spectroscopy with various phenomenological potentials.Comment: 12 pages, 4 figures, 1 tabl