We consider graph properties that can be checked from labels, i.e., bit sequences, of logarithmic length attached to vertices. We prove that there exists such a labeling for checking a first-order formula with free set variables in the graphs of ever
y class that is emph{nicely locally cwd-decomposable}. This notion generalizes that of a emph{nicely locally tree-decomposable} class. The graphs of such classes can be covered by graphs of bounded emph{clique-width} with limited overlaps. We also consider such labelings for emph{bounded} first-order formulas on graph classes of emph{bounded expansion}. Some of these results are extended to counting queries.
For many decades, statisticians have made attempts to prepare the Bayesian omelette without breaking the Bayesian eggs; that is, to obtain probabilistic likelihood-based inferences without relying on informative prior distributions. A recent example
is Murray Aitkins recent book, {em Statistical Inference}, which presents an approach to statistical hypothesis testing based on comparisons of posterior distributions of likelihoods under competing models. Aitkin develops and illustrates his method using some simple examples of inference from iid data and two-way tests of independence. We analyze in this note some consequences of the inferential paradigm adopted therein, discussing why the approach is incompatible with a Bayesian perspective and why we do not find it relevant for applied work.
The aim of this article is to prove a Thom-Sebastiani theorem for the asymptotics of the fiber-integrals. This means that we describe the asymptotics of the fiber-integrals of the function $f oplus g : (x,y) to f(x) + g(y)$ on $(mathbb{C}^ptimes mat
hbb{C}^q, (0,0))$ in term of the asymptotics of the fiber-integrals of the holomorphic germs $f : (mathbb{C}^p,0) to (mathbb{C},0)$ and $g : (mathbb{C}^q,0) to (mathbb{C},0)$. This reduces to compute the asymptotics of a convolution $Phi_*Psi$ from the asymptotics of $Phi$ and $Psi$ modulo smooth terms. To obtain a precise theorem, giving the non vanishing of expected singular terms in the asymptotic expansion of $foplus g$, we have to compute the constants coming from the convolution process. We show that they are given by rational fractions of Gamma factors. This enable us to show that these constants do not vanish.
We consider a Josephson junction where the weak-link is formed by a non-centrosymmetric ferromagnet. In such a junction, the superconducting current acts as a direct driving force on the magnetic moment. We show that the a.c. Josephson effect generat
es a magnetic precession providing then a feedback to the current. Magnetic dynamics result in several anomalies of current-phase relations (second harmonic, dissipative current) which are strongly enhanced near the ferromagnetic resonance frequency.
These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.
These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first author for her Ph.D.thesis.
The concept of (a,b)-module comes from the study the Gauss-Manin lattices of an isolated singularity of a germ of an holomorphic function. It is a very simple abstract algebraic structure, but very rich, whose prototype is the formal completion of th
e Brieskorn-module of an isolated singularity. The aim of this article is to prove a very basic theorem on regular (a,b)-modules showing that a given regular (a,b)-module is completely characterized by some finite order jet of its structure. Moreover a very simple bound for such a sufficient order is given in term of the rank and of two very simple invariants : the regularity order which count the number of times you need to apply $b^{-1}.a simeq partial_z.z$ in order to reach a simple pole (a,b)-module. The second invariant is the width which corresponds, in the simple pole case, to the maximal integral difference between to eigenvalues of $b^{-1}.a$ (the logarithm of the monodromy). In the computation of examples this theorem is quite helpfull because it tells you at which power of $b$ in the expansions you may stop without loosing any information.
In this article we show that all results proved for a large class of holomorphic germs $f : (mathbb{C}^{n+1}, 0) to (mathbb{C}, 0)$ with a 1-dimension singularity in [B.II] are valid for an arbitrary such germ.
