Stefan Heil To compress text files, a neural predictor network P is used to approximate the conditional probability distribution of possible "next characters", given n previous characters. P's outputs are fed into standard coding algorithms that generate short codes for characters with high predicted probability and long codes for highly unpredictable characters. Tested on short German newspape...

We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions, we construct a smooth approximation of the global solution of the Stefan problem with undercooling, which, until the contact, gives the classical solution mentioned abo...

Kazuhiro Yamamoto,1,* Daniel Friedrich,1 Tobias Westphal,1 Stefan Goßler,1 Karsten Danzmann,1 Kentaro Somiya,2 Stefan L. Danilishin,3 and Roman Schnabel1 1Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) and Institut für Gravitationsphysik, Leibniz Universität Hannover, Callinstrasse 38, D-30167 Hannover, Germany 2Theoretical Astrophysics, California Institute of Technology...

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection fr...

We consider a new Stefan-type problem for the classical heat equation with latent and phase-change temperature depending of variable time. prove equivalence this Stefan class boundary value problems nonlinear canonical evolution involving source term two free boundaries. This is obtained by applying reduction to Burgers reciprocal-type transformations. Moreover, particular case, we obtain uniqu...