Physics concepts have often been borrowed and independently developed by other fields of science. In this perspective a significant example is that of entropy in Information Theory. The aim of this paper is to provide a short and pedagogical introduction to the use of data compression techniques for the estimate of entropy and other relevant quantities in Information Theory and Algorithmic Info...

We model the surface brightness profiles of a sample of 119 Abell Brightest Cluster Galaxies (BCG), finding a generalised deVaucouleurs R law, where n is a free parameter, to be appropriate. Departures from the R law are shown to be a real feature of galaxy profiles, not due to observational errors or coupling of n with the other model parameters. BCG typically have values of n greater than 4. ...

In this note I would like to introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group G as a sheaf on some geometric object. This point of view necessarily leads to a conclusion that the standard approach to (continuous) representations of algebraic groups should be modified. Let us start with...

In this paper, using properties of Ramanujan sums and of the discrete Fourier transform of arithmetic functions, we give an explicit formula for the number of solutions of the linear congruence a1x1 + · · · + akxk ≡ b (mod n), with gcd(xi, n) = ti (1 ≤ i ≤ k), where a1, t1, . . . , ak, tk, b, n (n ≥ 1) are arbitrary integers. Some special cases of this problem have been already studied in many ...

By a theorem of Mclean, the deformation space of an associative sub-manifolds of an integrable G2 manifold (M, ϕ) at Y ⊂ M can be identified with the kernel of the Dirac operator D / : Ω 0 (ν) → Ω 0 (ν) on the normal bundle ν of Y. We generalize this to non-integrable case, and also show that the deformation space becomes smooth after perturbing it by natural parameters, which corresponds to mo...

A patient developed bacteremia with CDC group M-6, a Moraxella-like bacterium, after a complicated heart catheterization. He was treated with tobramycin and ampicillin. The aortic valve was later replaced and did not show any signs of infection. The slow growth of M-6 can delay diagnosis and give misleading antibiotic susceptibility results. Penicillin is not always active against this organism.