A stochastic model of evolution

We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event then the type that is killed is the one with the smallest fitness. We show that there is a sharp phase transition when the birth probability is larger than the death probability. The set of species with fitness higher than a certain critical value approach an uniform distribution. On the other hand all the species with fitness less than the critical disappear after a finite (random) time.Comment: 6 pages, 1 figure, TeX, Added references, To appear in Markov Processes and Related Field

On a link between a species survival time in an evolution model and the Bessel distributions

We consider a stochastic model for species evolution. A new species is born at rate lambda and a species dies at rate mu. A random number, sampled from a given distribution F, is associated with each new species at the time of birth. Every time there is a death event, the species that is killed is the one with the smallest fitness. We consider the (random) survival time of a species with a given fitness f. We show that the survival time distribution depends crucially on whether ff_c where f_c is a critical fitness that is computed explicitly.Comment: 13 page

Mapping Topographic Structure in White Matter Pathways with Level Set Trees

Fiber tractography on diffusion imaging data offers rich potential for describing white matter pathways in the human brain, but characterizing the spatial organization in these large and complex data sets remains a challenge. We show that level set trees---which provide a concise representation of the hierarchical mode structure of probability density functions---offer a statistically-principled framework for visualizing and analyzing topography in fiber streamlines. Using diffusion spectrum imaging data collected on neurologically healthy controls (N=30), we mapped white matter pathways from the cortex into the striatum using a deterministic tractography algorithm that estimates fiber bundles as dimensionless streamlines. Level set trees were used for interactive exploration of patterns in the endpoint distributions of the mapped fiber tracks and an efficient segmentation of the tracks that has empirical accuracy comparable to standard nonparametric clustering methods. We show that level set trees can also be generalized to model pseudo-density functions in order to analyze a broader array of data types, including entire fiber streamlines. Finally, resampling methods show the reliability of the level set tree as a descriptive measure of topographic structure, illustrating its potential as a statistical descriptor in brain imaging analysis. These results highlight the broad applicability of level set trees for visualizing and analyzing high-dimensional data like fiber tractography output

Cellular Models for River Networks

A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed. The roles of boundary and initial conditions are carefully analyzed as well as the key effect of quenched disorder embedded in random pinning of the landscape surface. It is found that the above features strongly affect the scaling behavior of key morphological quantities. In particular, we conclude that randomly pinned regions (whose structural disorder bears much physical meaning mimicking uneven landscape-forming rainfall events, geological diversity or heterogeneity in surficial properties like vegetation, soil cover or type) play a key role for the robust emergence of aggregation patterns bearing much resemblance to real river networks.Comment: 7 pages, revtex style, 14 figure

Enterprise Eco-watching and Appraisal: Asset Modelling and Sustainability Assessment

AbstractAt the millennium turnover, the ecology globalisation shows the impeding threats of over-depletion/pollution: the sustainable growth requires supply-chain visibility, resource bookkeeping and renovation planning. The lifecycle starts when the idea of a product is born and lasts until complete disposal after realisation and operation. In the musts’ specification/analysis, the basic design (global plan, detailed design, assembly design, etc.) are followed by manufacturing, assembly, testing, diagnostics and operation, advertising, service, maintenance, etc.; then, disassembly and firing are scheduled, requiring reclamation and recovery, by re-cycling (material reprocessing) or re-using (part refurbishing). The present paper provides pilot clues for understanding the product-process agendas, using the TYPUS metrics and the KILT model, developed by the authors, in previous works

Driver Attention Assessment Using Physiological Measures from EEG, ECG, and EDA Signals †

In this paper, we consider the evaluation of the mental attention state of individuals driving in a simulated environment. We tested a pool of subjects while driving on a highway and trying to overcome various obstacles placed along the course in both manual and autonomous driving scenarios. Most systems described in the literature use cameras to evaluate features such as blink rate and gaze direction. In this study, we instead analyse the subjects' Electrodermal activity (EDA) Skin Potential Response (SPR), their Electrocardiogram (ECG), and their Electroencephalogram (EEG). From these signals we extract a number of physiological measures, including eye blink rate and beta frequency band power from EEG, heart rate from ECG, and SPR features, then investigate their capability to assess the mental state and engagement level of the test subjects. In particular, and as confirmed by statistical tests, the signals reveal that in the manual scenario the subjects experienced a more challenged mental state and paid higher attention to driving tasks compared to the autonomous scenario. A different experiment in which subjects drove in three different setups, i.e., a manual driving scenario and two autonomous driving scenarios characterized by different vehicle settings, confirmed that manual driving is more mentally demanding than autonomous driving. Therefore, we can conclude that the proposed approach is an appropriate way to monitor driver attention