Asymptotic symmetries of difference equations on a lattice

It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In this note we extend the approach to asymptotic symmetries for the analysis of PDEs, to the case of difference equations

The Antarctic dry valley lakes: Relevance to Mars

The similarity of the early environments of Mars and Earth, and the biological evolution which occurred on early Earth, motivates exobiologists to seriously consider the possiblity of an early Martian biota. Environments are being identified which could contain Martian life and areas which may presently contain evidence of this former life. Sediments which were thought to be deposited in large ice-covered lakes are present on Mars. Such localities were identified within some of the canyons of the Valles Marineris and more recently in the ancient terrain in the Southern Hemisphere. Perennially ice-covered Antarctic lakes are being studied in order to develop quantitative models that relate environmental factors to the nature of the biological community and sediment forming processes. These models will be applied to the Martian paleolakes to establish the scientific rationale for the exobiological study of ancient Martian sediments

Mars rover sample return: An exobiology science scenario

A mission designed to collect and return samples from Mars will provide information regarding its composition, history, and evolution. At the same time, a sample return mission generates a technical challenge. Sophisticated, semi-autonomous, robotic spacecraft systems must be developed in order to carry out complex operations at the surface of a very distant planet. An interdisciplinary effort was conducted to consider how much a Mars mission can be realistically structured to maximize the planetary science return. The focus was to concentrate on a particular set of scientific objectives (exobiology), to determine the instrumentation and analyses required to search for biological signatures, and to evaluate what analyses and decision making can be effectively performed by the rover in order to minimize the overhead of constant communication between Mars and the Earth. Investigations were also begun in the area of machine vision to determine whether layered sedimentary structures can be recognized autonomously, and preliminary results are encouraging

Time‐invariant portfolio strategies in structured products with guaranteed minimum equity exposure

We introduce a new exotic option to be used within structured products to address a key disadvantage of standard time-invariant portfolio protection: the well-known cash-lock risk. Our approach suggests enriching the framework by including a threshold in the allocation mechanism so that a guaranteed minimum equity exposure (GMEE) is ensured at any point in time. To be able to offer such a solution still with hard capital protection, we apply an option-based structure with a dynamic allocation logic as underlying. We provide an in-depth analysis of the prices of such new exotic options, assuming a Heston–Vasicek-type financial market model, and compare our results with other options used within structured products. Our approach represents an interesting alternative for investors aiming at downsizing protection via time-invariant portfolio protection strategies, meanwhile being also afraid to experience a cash-lock event triggered by market turmoils

Superfast front propagation in reactive systems with anomalous diffusion

We study a reaction diffusion system where we consider a non-gaussian process instead of a standard diffusion. If the process increments follow a probability distribution with tails approaching to zero faster than a power law, the usual qualitative behaviours of the standard reaction diffusion system, i.e., exponential tails for the reacting field and a constant front speed, are recovered. On the contrary if the process has power law tails, also the reacting field shows power law tail and the front speed increases exponentially with time. The comparison with other reaction-transport systems which exhibit anomalous diffusion shows that, not only the presence of anomalous diffusion, but also the detailed mechanism, is relevant for the front propagation.Comment: 4 pages and 4 figure

Viking and Mars Rover exobiology

Other than Earth, Mars is the planet generating the greatest interest among those researching and contemplating the origin and distribution of life throughout the universe. The similarity of the early environments of Earth and Mars, and the biological evolution on early Earth provides the motivation to seriously consider the possibility of a primordial Martian biosphere. In 1975 the Viking project launched two unmanned spacecraft to Mars with the intent of finding evidence of the existence of present or past life on this planet. Three Viking Biology experiments were employed: the Labeled Release experiment, the Gas Exchange Experiment, and the Pyrolytic Release experiment. Each of these three experiments tested for microbial existence and utilization of a substrate by examining the gases evolved from specific chemical reactions. Although the results of these experiments were inconclusive, they inferred that there are no traces of extant life on Mars. However, the experiments did not specifically look for indication of extinct life. Therefore, most of the exobiologic strategies and experiments suggested for the Mars Rover Sample Return Mission involve searching for signature of extinct life. The most significant biological signatures and chemical traces to detect include: isotopic and chemical signatures of metabolic activity, anomalous concentrations of certain metals, trace and microfossils, organically preserved materials, carbonates, nitrates, and evaporites

Mars Rover Sample Return: A sample collection and analysis strategy for exobiology

For reasons defined elsewhere it is reasonable to search for biological signatures, both chemical and morphological, of extinct life on Mars. Life on Earth requries the presence of liquid water, therefore, it is important to explore sites on Mars where standing bodies of water may have once existed. Outcrops of layered deposits within the Valles Marineris appear to be ancient lake beds. Because the outcrops are well exposed, relatively shallow core samples would be very informative. The most important biological signature to detect would be organics, microfossils, or larger stromato-like structures, although the presence of cherts, carbonates, clays, and shales would be significant. In spite of the limitations of current robotics and pattern recognition, and the limitations of rover power, computation, Earth communication bandwidth, and time delays, a partial scenario was developed to implement such a scientific investigation. The rover instrumentation and the procedures and decisions and IR spectrometer are described in detail. Preliminary results from a collaborative effort are described, which indicate the rover will be able to autonomously detect stratification, and hence will ease the interpretation burden and lead to greater scientific productivity during the rover's lifetime

The influence of fractional diffusion in Fisher-KPP equations

We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the stan- dard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable L\'evy process, the front position is exponential in time. Our results provide a mathe- matically rigorous justification of numerous heuristics about this model

Crossbreeding to improve local chicken breeds: predicting growth performance of the crosses using the Gompertz model and estimated heterosis

The present study aims to validate the Gompertz model to predict the growth performance of chicken crosses according to growth curve parameters of the parental lines and the estimated heterosis for each curve parameter. A total of 252 one-day-old chicks of both sexes belonging to 6 genotypes, including Ross 308, Sasso (SA), Bionda Piemontese (BP), and Robusta Maculata (RM), and the crosses between these local breeds and SA (BP x SA and RM x SA) were randomly allocated in 18 pens (3 pens/genotype) in mixed-sex groups (14 animals/pen; 7 females and 7 males). The individual body weight (BW) of all birds was recorded once a week from hatching until slaughtering (81 d for Ross 308; 112 d for SA, 140 d for the other genotypes). We drew up our final dataset with 240 birds (40 birds/ genotype; 20 females and 20 males). The growth curve of each genotype was described using the Gompertz model, and the heterosis for each growth curve parameter was calculated as the difference between F-1 crosses and the average of parental breeds. The predicted growth curve parameters were evaluated by cross-validation. The Gompertz model accurately estimated the growth curves of all the genotypes (R-2 > 0.90). Heterosis was significant for almost all growth curve parameters in both crosses (P < 0.05). Heterosis ranged from -13.0 to +11.5%, depending on parameters, but varied slightly between the crossbreeds (BP x SA and RM x SA). The predicted values of adult BW, weight at the inflection point, and maximum growth rate were overestimated for BP x SA and under-estimated for RM x SA, with a mean error between observed and predicted values <12.71% for all the curve parameters. In conclusion, the growth performance of chicken crosses between local breeds and commercial strains can be accurately predicted with Gompertz parameters of the parental lines adjusting for heterosis