In the early nineteenth century, a series of articles by Laplace and Poisson discussed the importance of ‘directness’ in mathematical methodology. In this thesis, we argue that their conception of a ‘direct’ proof is similar to the more widely contemplated notion of a ‘pure’ proof. More rigorous definitions of mathematical purity were proposed in recent publications by Arana and Detlefsen, as well as by Kahle and Pulcini: we compare Laplace and Poisson’s writings with these modern definitions of purity and show how the modern definitions fail to grasp some more nuanced aspects.

We propose a new parametric model for the modelling and estimation of event distributions for individuals in different firms. The analysis uses panel data and takes into account individual and firm effects in a non-linear model. Non-observable factors are treated as random effects. In our application, the distribution of accidents is affected by observable and non-observable factors from vehicles, drivers and fleets of vehicles. Observable and unobservable factors are significant to explain road accidents, which mean that insurance pricing should take into account all these factors. A fixed effects model is also estimated to test the consistency of the random effects model.

Many studies on the adoption of precision technologies have generally used logit models to explain the adoption behavior of individuals. This study investigates factors affecting the intensity of precision agriculture technologies adopted by cotton farmers. Particular attention is given to the role of spatial yield variability on the number of precision farming technologies adopted, using a count data estimation procedure and farm-level data. Results indicate that farmers with more within-field yield variability adopted a higher number of precision agriculture technologies. Younger and better educated producers and the number of precision agriculture technologies used were significantly correlated. Finally, farmers using computers for management decisions also adopted a higher number of precision agriculture technologies.

Ratemaking is one of the most important tasks of non-life actuaries. Usually, the ratemaking process is done in two steps. In the first step, a priori ratemaking, an a priori premium is computed based on the characteristics of the insureds. In the second step, called the a posteriori ratemaking, the past claims experience of each insured is considered to the a priori premium and set the final net premium. In practice, for automobile insurance, this correction is usually done with bonus-malus systems, or variations on them, which offer many advantages. In recent years, insurers have accumulated longitudinal information on their policyholders, and actuaries can now use many years of informations for a single insured. For this kind of data, called panel or longitudinal data, we propose an alternative to the two-step ratemaking approach and argue this old approach should no longer be used. As opposed to a posteriori models of cross-section data, the models proposed in this paper generate premiums based on empirical results rather than inductive probability. We propose a new way to deal with bonus-malus systems when panel data are available. Using car insurance data, a numerical illustration using at-fault and non-at-fault claims of a Canadian insurance company is included to support this discussion. Even if we apply the model for car insurance, as long as another line of business uses past claim experience to set the premiums, we maintain that a similar approach to the model proposed should be used.

Compartmentalization is a general principle in biological systems which is observable on all size scales, ranging from organelles inside of cells, cells in histology, and up to the level of groups, herds, swarms, meta-populations, and populations. Compartmental models are often used to model such phenomena, but such models can be both highly nonlinear and difficult to work with.

Fortunately, there are many significant biological systems that are amenable to linear compartmental models which are often more mathematically accessible. Moreover, the biology and mathematics is often so intertwined in such models that one can be used to better understand the other. Indeed, as we demonstrate in this paper, linear compartmental models of migratory dynamics can be used as an exciting and interactive means of introducing sophisticated mathematics, and conversely, the associated mathematics can be used to demonstrate important biological properties not only of seasonal migrations but also of compartmental models in general.

We have found this approach to be of great value in introducing derivatives, integrals, and the fundamental theorem of calculus. Additionally, these models are appropriate as applications in a differential equations course, and they can also be used to illustrate important ideas in probability and statistics, such as the Poisson distribution.

A simple upper bound for the variance of the frequency estimates in a multivariate tariff using class criteria is deduced. This upper bound is based exclusively on univariate statistics and can, therefore, be calculated before a GLM analysis is carried out. It can be used to estimate the number of claims that will be needed for a tariff calculation depending on the number of tariff criteria and the number of levels of each criterion.

The article is a revised version of a paper presented at the XXXIst ASTIN Colloquium in Porto Cervo.

We study the contribution made by three or four points to certain areas associated with a typical polygon in a Voronoi tessellation of a planar Poisson process. We obtain some new results about moments and distributions and give simple proofs of some known results. We also use Robbins' formula to obtain the first three moments of the area of a typical polygon and hence the variance of the area of the polygon covering the origin.

By using an adaptation of the radial generation method, we give an integral formula for the proportion of triangles in a Poisson-Voronoi tessellation, which gives a value of 0.0112354 to 7 decimal places. We also obtain the first four moments of some characteristics of triangles.

Animal remains were present in stomach contents of 6 of 13 fish species collected at 10 sites in freshwater streams on Moorea,French Polynesia. The eel Anguilla marmorata contained both freshwater and marine prey, and the eel Anguilla obscuracontained larvae of the pollution-tolerant rat-tailed maggots (Insecta : Diptera : Syrphidae). Fish stomachs contained prey notpreviously collected in these streams. There is clear habitat partitioning between the two most common stream fish. The spottedflagtail, Eleotris fusca, feeds benthically and stomachs contains large numbers of neritid and thiarid snails. The sleeper, Kuhliamarginata, feeds primarily on surface drift, with ants being the most common prey item. The freshwater fish of Moorea havefew parasites relative to those found in Hawaiian Island stream fishes.

Après avoir décrit succinctement les quatre grandes étapes de l'ovogenèse - stade protoplasmique, vitellogenèse endogène, vitellogenèse exogène et maturation finale -, cette courte revue compare la dynamique de croissance ovocytaire et ovarienne chez les poissons à pontes unique, multiples et continues. Elle présente ensuite, pour les différents modes de reproduction, l'essentiel des connaissances actuelles sur la régulation, par les stéroïdes sexuels, des différentes étapes du cycle reproducteur.

A biotelemetry experiment was designed to determine whether the selection of a residence area by adult barbel Barbus barbus (Cyprinidae) was dependent on the availability of physical habitat features, on the presence of fish shoals and/or on the presence of specific partners. The experiment took place in 3.0 km stretch of the River Ourthe (Belgium), where the latter features had been characterised by habitat and electric fishing surveys (1 190 fish ≥ 15  cm, at 265 locations). Six barbel (34.8–49.5 cm) belonging to a single shoal of 34 fish were tagged with 40 MHz radio transmitters, transplanted in pairs at different distances (−1 km, −30 m, +1 km) from the capture site and tracked from 3 September to 7 October 1990.

Fish showed variable mobility patterns and home range sizes (200–2 400 m). They selected 17 residence areas of which the cumulative frequency of occupation ranged from 0.1 to 79.5 day × fish. The comparison between the residence areas selected, habitat suitability and the location of fish shoals in the study area indicate that the presence of a shoal of at least 10 resident fish within a suitable habitat (normalised suitability index ≥ 1.0) is necessary but not sufficient to guarantee its long term selection and occupation. Homing movements of transplanted fish were directed towards the activity area rather than to the residence area itself. The fish that did not home, selected residence areas in a part of the river with a higher availability of potential feeding areas. These elements are discussed within the context of habitat utilisation and foraging strategies by a gregarious species. It is suggested that resident fish of the same species may ease the exploitation of a non familiar environment by a naive fish, and that this may positively trade off the benefit provided by home site fidelity, depending on the availability of food resources.

Surgery procedures were used to implant telemetry transmitters into the body cavity of adult (574–1 033 g) tilapias Oreochromis aureus in aquaculture tanks (4 m2, 1.5 m3, 26.5 ± 0.5 °C, ≥ 5.0 mg O2 l−1) and their effect on fish survival, growth and behaviour was evaluated. Only one out of 35 implanted fish died. With one exception, all fish consistently retained their transmitter until the end of the study (up to 30 months). Healing was faster when the incision was sutured with polyamide monofilament (5–14 days) than with other suture materials, due to tunnelling with atraumatic needles for catgut or fouling of braided silk. In all 10 fish sacrificed after 30 and 50 days, the transmitter had become encapsulated by connective tissue. No infection or damage to the viscera was observed.

The activity of four tilapias (903–1 033 g) equipped with motion sensitive transmitters was telemetered during the recovery from anaesthesia and surgical procedures. All four fish maintained a normal diurnal activity rhythm pattern throughout the study but had low levels of activity during the first 12–24 h. Based on the evolution of their resting posture after surgery, it is suggested that tilapias need 3 to 4 days to completely compensate the negative buoyancy resulting from anaesthesia and tagging.

We present a method of deriving the limiting distributions of the number of occurrences of success (S) runs of length k for all types of runs under the Markovian structure with stationary transition probabilities. In particular, we consider the following four bestknown types. 1. A string of S of exact length k preceded and followed by an F, except the first run which may not be preceded by an F, or the last run which may not be followed by an F. 2. A string of S of length k or more. 3. A string of S of exact length k, where recounting starts immediately after a run occurs. 4. A string of S of exact length k, allowing overlapping runs. It is shown that the limits are convolutions of two or more distributions with one of them being either Poisson or compound Poisson, depending on the type of runs in question. The completely stationary Markov case and the i.i.d. case are also treated.

Pike-perch Stizostedion lucioperca larvae fasted or given two diets (artificial feed, zooplankton) were studied by transmission electron microscopy and using specific cytological dyes. The objective of this work was to assess the changes in the yolk sac, liver and anterior intestine following the mouth opening stage (95 °C.d, day 5 - 5.8 mm) from endo- to exotrophy periods. The yolk sac included a syncytial envelope closely bound to the proteinaceous vitellus and the oil globule. Its development was similar to that observed in trout (Oncorhynchus mykiss and Salmo fario trutta )and sea-bream (Sparus aurata,) but without vitellus fragmentation into platelets. Vitellus resorption was never achieved in dying larvae. From the end of the endotrophic phase onwards, the amount of hepatic glycogen decreased. Carbohydrate disappeared at the beginning of the exotrophic phase then increased after 220 °C.d (day 10 - 6.0 mm), mainly in zooplankton-fed larvae. Lipids from enterocytes, sinusoids and general blood Stream showed a similar development. They were abundant at 95 °C.d, progressively disappeared up to 260 °C.d (day 12 - 6.3 mm), and increased again from 350 °C.d (day 16 - 6.7 mm) onwards if larvae were fed zooplankton. Dietary lipids did not seem to immediately replace yolk lipids despite absorption in the gut. Various hypotheses are proposed to explain the physiological abnormalities of this critical larval stage. Although zooplankton appeared to have better nutritional qualities than the artificial feed, these two foods proved to be quite unsatisfactory as they induced liver cell changes typical of food deficiency, generally observed in starving larvae.