In fish, the relative amount of tissues of different densities changes significantly over short periods throughout the year, depending on the availability of food, nutrition and their developmental status, such as sexual maturation. If a land-living animal accumulates fat it influences not only its general state of health, but also markedly increases its energy expenditure for locomotion owing ...

We propose statistical tests to discriminate between the finite and infinite activity of jumps in a semimartingale discretely observed at high frequency. The two statistics allow for a symmetric treatment of the problem: we can either take the null hypothesis to be finite activity, or infinite activity. When implemented on high-frequency stock returns, both tests point toward the presence of in...

In our book [3], Laurie Snell and I tell how a method from the classical theory of electricity called Rayleigh’s short-cut method can be used to determine whether or not a person walking around at random on the vertices of a given infinite graph is certain to return to the starting point. In this paper, I will present an application of Rayleigh’s method to the classical type problem for Riemann...

Based on transformation optics‎, ‎we propose an illusion device that can make‎ ‎objects look much smaller and different than they actually are‎. ‎In particular‎, ‎the device has a capability to hide a large object (like an elephant) into a‎ ‎small one (like a matchbox)‎. ‎Compared to previous proposals for illusion‎ ‎devices‎, ‎there is no requirement for negative refractive index or for spee...

When  ≥ 2 these processes are finite-valued, but not necessarily so when   2. In this case we have to be careful: if  = inf( : () =∞) and 0 = inf( :  0() = ∞) then both processes () and  0() are null at 0 and finite-valued on [0 ) and [0 0) respectively, the first continuous and the second one càdlàg with jumps not bigger than 1, and they are infinite on (∞) and (0∞). H...

There is no longer any reasonable doubt that adjuvant chemotherapy prolongs survival for premenopausal women with early breast cancer. Indeed, in more than 100 years of research into breast cancer management it is the first form of treatment convincingly shown to have survival benefit. Yet important questions linger over its real clinical value. These include the balance of benefit against morb...