Application of the combined integral method to Stefan problems

In this paper we present a new, accurate form of the heat balance integral method, termed the Combined Integral Method (or CIM). The application of this method to Stefan problems is discussed. For simple test cases the results are compared with exact and asymptotic limits. In particular, it is shown that the CIM is more accurate than the second order, large Stefan number, perturbation solution for a wide range of Stefan numbers. In the initial examples it is shown that the CIM reduces the standard problem, consisting of a PDE defined over a domain specified by an ODE, to the solution of one or two algebraic equations. The latter examples, where the boundary temperature varies with time, reduce to a set of three first order ODEs.

Study and implementation of some quantitative trading models

Quantitative or algorithmic trading is the automatization of investments decisions obeying a fixed or dynamic sets of rules to determine trading orders. It has increasingly made its way up to 70% of the trading volume of one of the biggest financial markets such as the New York Stock Exchange (NYSE). However, there is not a signi cant amount of academic literature devoted to it due to the private nature of investment banks and hedge funds. This projects aims to review the literature and discuss the models available in a subject that publications are scarce and infrequently. We review the basic and fundamental mathematical concepts needed for modeling financial markets such as: stochastic processes, stochastic integration and basic models for prices and spreads dynamics necessary for building quantitative strategies. We also contrast these models with real market data with minutely sampling frequency from the Dow Jones Industrial Average (DJIA). Quantitative strategies try to exploit two types of behavior: trend following or mean reversion. The former is grouped in the so-called technical models and the later in the so-called pairs trading. Technical models have been discarded by financial theoreticians but we show that they can be properly cast into a well defined scientific predictor if the signal generated by them pass the test of being a Markov time. That is, we can tell if the signal has occurred or not by examining the information up to the current time; or more technically, if the event is F_t-measurable. On the other hand the concept of pairs trading or market neutral strategy is fairly simple. However it can be cast in a variety of mathematical models ranging from a method based on a simple euclidean distance, in a co-integration framework or involving stochastic differential equations such as the well-known Ornstein-Uhlenbeck mean reversal ODE and its variations. A model for forecasting any economic or financial magnitude could be properly defined with scientific rigor but it could also lack of any economical value and be considered useless from a practical point of view. This is why this project could not be complete without a backtesting of the mentioned strategies. Conducting a useful and realistic backtesting is by no means a trivial exercise since the \laws" that govern financial markets are constantly evolving in time. This is the reason because we make emphasis in the calibration process of the strategies' parameters to adapt the given market conditions. We find out that the parameters from technical models are more volatile than their counterpart form market neutral strategies and calibration must be done in a high-frequency sampling manner to constantly track the currently market situation. As a whole, the goal of this project is to provide an overview of a quantitative approach to investment reviewing basic strategies and illustrating them by means of a back-testing with real financial market data. The sources of the data used in this project are Bloomberg for intraday time series and Yahoo! for daily prices. All numeric computations and graphics used and shown in this project were implemented in MATLAB^R scratch from scratch as a part of this thesis. No other mathematical or statistical software was used.

Degradation of pheromone and plant volatile components by a same Odorant-Degrading Enzyme in the cotton leafworm, Spodoptera littoralis

Background: Odorant-Degrading Enzymes (ODEs) are supposed to be involved in the signal inactivation step within the olfactory sensilla of insects by quickly removing odorant molecules from the vicinity of the olfactory receptors. Only three ODEs have been both identified at the molecular level and functionally characterized: two were specialized in the degradation of pheromone compounds and the last one was shown to degrade a plant odorant. Methodology: Previous work has shown that the antennae of the cotton leafworm Spodoptera littoralis , a worldwide pest of agricultural crops, express numerous candidate ODEs. We focused on an esterase overexpressed in males antennae, namely SlCXE7. We studied its expression patterns and tested its catalytic properties towards three odorants, i.e. the two female sex pheromone components and a green leaf volatile emitted by host plants. Conclusion: SlCXE7 expression was concomitant during development with male responsiveness to odorants and during adult scotophase with the period of male most active sexual behaviour. Furthermore, SlCXE7 transcription could be induced by male exposure to the main pheromone component, suggesting a role of Pheromone-Degrading Enzyme. Interestingly, recombinant SlCXE7 was able to efficiently hydrolyze the pheromone compounds but also the plant volatile, with a higher affinity for the pheromone than for the plant compound. In male antennae, SlCXE7 expression was associated with both long and short sensilla, tuned to sex pheromones or plant odours, respectively. Our results thus suggested that a same ODE could have a dual function depending of it sensillar localisation. Within the pheromone-sensitive sensilla, SlCXE7 may play a role in pheromone signal termination and in reduction of odorant background noise, whereas it could be involved in plant odorant inactivation within the short sensilla.

Spectral analysis and limit behaviours in a spring-mass system

We consider a model for a damped spring-mass system that is a strongly damped wave equation with dynamic boundary conditions. In a previous paper we showed that for some values of the parameters of the model, the large time behaviour of the solutions is the same as for a classical spring-mass damper ODE. Here we use spectral analysis to show that for other values of the parameters, still of physical relevance and related to the effect of the spring inner viscosity, the limit behaviours are very different from that classical ODE

A carboxylesterase, Esterase-6, modulates sensory physiological and behavioural response dynamics to pheromone in Drosophila

Background: Insects respond to the spatial and temporal dynamics of a pheromone plume, which implies not only a strong response to"odor on", but also to"odor off". This requires mechanisms geared toward a fast signal termination. Several mechanisms may contribute to signal termination, among which odorant-degrading enzymes. These enzymes putatively play a role in signal dynamics by a rapid inactivation of odorants in the vicinity of the sensory receptors, although direct in vivo experimental evidences are lacking. Here we verified the role of an extracellular carboxylesterase, esterase-6 (Est-6), in the sensory physiological and behavioral dynamics of Drosophila melanogaster response to its pheromone, cis-vaccenyl acetate (cVA). Est-6 was previously linked to post-mating effects in the reproductive system of females. As Est-6 is also known to hydrolyze cVA in vitro and is expressed in the main olfactory organ, the antenna, we tested here its role in olfaction as a putative odorant-degrading enzyme. Results: We first confirm that Est-6 is highly expressed in olfactory sensilla, including cVA-sensitive sensilla, and we show that expression is likely associated with non-neuronal cells. Our electrophysiological approaches show that the dynamics of olfactory receptor neuron (ORN) responses is strongly influenced by Est-6, as in Est-6° null mutants (lacking the Est-6 gene) cVA-sensitive ORN showed increased firing rate and prolonged activity in response to cVA. Est-6° mutant males had a lower threshold of behavioral response to cVA, as revealed by the analysis of two cVAinduced behaviors. In particular, mutant males exhibited a strong decrease of male-male courtship, in association with a delay in courtship initiation. Conclusions: Our study presents evidence that Est-6 plays a role in the physiological and behavioral dynamics of sex pheromone response in Drosophila males and supports a role of Est-6 as an odorant-degrading enzyme (ODE) in male antennae. Our results also expand the role of Est-6 in Drosophila biology, from reproduction to olfaction, and highlight the role of ODEs in insect olfaction. Keywords: carboxylesterase, esterase 6, olfaction, pheromone, signal termination