We study the following generalization of the classical edge coloring problem: Given a weighted graph, find a partition of its edges into matchings (colors), each one of weight equal to the maximum weight of its edges, so that the total weight of the partition is minimized. We explore the frontier between polynomial and NP-hard variants of the problem as well as the approximability of the NP-har...

In this paper, (d + 1)-pencil lattices on simplicial partitions in Rd are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of this fact l...

We show how the smooth geometry of Calabi-Yau manifolds emerges from the thermodynamic limit of the statistical mechanical model of crystal melting defined in our previous paper. In particular, the thermodynamic partition function of molten crystals is shown to be equal to the classical limit of the partition function of the topological string theory by relating the Ronkin function of the chara...

The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite ...

the probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. here we illustrate that a wider context may be considered and show some structural restrictions on the group.

A partition function calculation for RNA secondary structure is presented that uses a current set of nearest neighbor parameters for conformational free energy at 37 degrees C, including coaxial stacking. For a diverse database of RNA sequences, base pairs in the predicted minimum free energy structure that are predicted by the partition function to have high base pairing probability have a sig...

The partition of nucleon spin between total angular momenta of quarks and gluons is described by the energy momentum tensor formfactors manifested also in the nucleon scattering by weak classical gravitational field. Natural generalization of equivalence principle is resulting in the identically zero ”Anomalous gravitomagnetic moment” being the straightforward analog of its electromagnetic coun...

We extend the classification of fermionic $\mathbb{Z}_2\times\mathbb{Z}_2$ heterotic string orbifolds to non--supersymmetric Pati--Salam (PS) models in two classes vacua, that we dub $\tilde S$--models and $S$--models. The first correspond compactifications a tachyonic ten--dimensional vacuum, whereas second tachyon--free $SO(16)\times SO(16)$ string. In both cases develop systematic method ext...

This letter addresses the optimum energy partition between the midamble and data fields, given the total energy per burst, in channel estimation for joint detected time-division code-division multiple-access systems. We show that, given the lengths of the data and midamble, in general, the optimal solution requires different amplitude levels. We also derive the burst structure leading to the op...