In various frameworks, to assess the joint distribution of a kdimensional random vector X = (X1, . . . , Xk), one selects some putative conditional distributions Q1, . . . , Qk. Each Qi is regarded as a possible (or putative) conditional distribution for Xi given (X1, . . . , Xi−1, Xi+1, . . . , Xk). The Qi are compatible if there is a joint distribution P for X with conditionals Q1, . . . , Qk...

We prove that there exists an integer p0 such that X split (p)(Q) is made of cusps and CM-points for any prime p > p0. Equivalently, for any non-CM elliptic curve E over Q and any prime p > p0 the image of Gal(¯ Q/Q) by the representation induced by the Galois action on the p-division points of E is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an ol...

Lattices that can be represented in a kagomé-like form are shown to satisfy a universal percolation criticality condition, expressed as a relation between P3 , the probability that all three vertices in the triangle connect, and P0 , the probability that none connect. A linear approximation for P3(P0) is derived and appears to provide a rigorous upper bound for critical thresholds. A numericall...

Kano et al. proved that if P0, P1, . . . , Pk−1 are pairwise disjoint collections of points in general position, then there exist spanning trees T0, T1, . . . , Tk−1, of P0, P1, . . . , Pk−1, respectively, such that the edges of T0 ∪ T1 ∪ · · · ∪ Tk−1 intersect in at most (k − 1)n − k(k − 1)/2 points. In this paper we show that this result is asymptotically tight within a factor of 3/2. To prov...

For a graph G, let pi (G), i = 0, ...,3 be the probability that three distinct random vertices span exactly i edges. We call (p0(G), ..., p3(G)) the 3-local profile of G. We investigate the set S3 ⊂ R4 of all vectors (p0, ..., p3) that are arbitrarily close to the 3-local profiles of arbitrarily large graphs. We give a full description of the projection of S3 to the (p0, p3) plane. The upper en...

P0, the major protein of peripheral nerve myelin, mediates membrane adhesion in the spiral wraps of the myelin sheath. We have determined the crystal structure of the extracellular domain from P0 (P0ex) at 1.9 A resolution. P0ex is folded like a typical immunoglobulin variable-like domain; five residues at the C-terminus are disordered, suggesting a flexible linkage to the membrane. The require...

Quiescent Schwann cells in the distal segment of the permanently transected nerve produced basal levels of the major myelin glycoprotein, P0, in the absence of myelin assembly. Low levels of P0 could be detected at 35 days after transection by autoradiographic analysis of radioiodinated lectin binding after protein separation by high-resolution sodium dodecyl sulfate pore gradient electrophores...

This paper shows the equivalence between Murota’s L-convex functions and Favati and Tardella’s submodular integrally convex functions: For a submodular integrally convex function g(p1, . . . , pn), the function g̃ defined by g̃(p0, p1, . . . , pn) = g(p1 − p0, . . . , pn − p0) is an L-convex function, and vice versa. This fact implies, in combination with known results for L-convex functions, tha...