Related papers: Cayley Trees and Bethe Lattices, a concise analysi…
We present numerical methods to solve the Generalized Hartree-Fock theory for fermionic systems in lattices, both in thermal equilibrium and out of equilibrium. Specifically, we show how to determine the covariance matrix corresponding to…
Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We…
We study those automatic sequences which are produced by an automaton whose underlying graph is the Cayley graph of a finite group. For $2$-automatic sequences, we find a characterization in terms of what we call homogeneity, and among…
Let \Gamma be a geometrically finite tree lattice. We prove a Khintchine-Sullivan type theorem for the Hausdorff measure of the points at infinity of the tree that are well approximated by the parabolic fixed points of G. Using Bruhat-Tits…
We reconsider some classical natural semantics of integers (namely iterators of functions, cardinals of sets, index of equivalence relations), in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including…
By using biclique partitions of digraphs, this paper gives reduction formulas for the number of oriented spanning trees, stationary distribution vector and Kemeny's constant of digraphs. As applications, we give a method for enumerating…
We present the Probabilistic Context Neighborhood model designed for two-dimensional lattices as a variation of a Markov Random Field assuming discrete values. In this model, the neighborhood structure has a fixed geometry but a variable…
We give an algebraic construction of the topological graph-tree configuration pairing of Sinha and Walter beginning with the classical presentation of Lie coalgebras via coefficients of words in the associative Lie polynomial. Our work…
Flat band physics is a central theme in modern condensed matter physics. By constructing a tight--binding single particle system that has vanishing momentum dispersion in one or more bands, and subsequently including more particles and…
We investigate subsets of the symmetric group with structure similar to that of a graph. The trees of these subsets correspond to minimal conjugate generating sets of the symmetric group. There are two main theorems in this paper. The first…
This work presents novel algorithms for learning Bayesian network structures with bounded treewidth. Both exact and approximate methods are developed. The exact method combines mixed-integer linear programming formulations for structure…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity…
In an attempt to prove the Graceful Tree Conjecture, we present two propagation of graphs. The first is to propagate graceful graphs, and the second is to propagate trees from a gracefully labeled tree. The motivation in propagating such…
The Binary Search Tree (BST) is average in computer science which supports a compact data structure in memory and oneself even conducts a row of quick algorithms, by which people often apply it in dynamical circumstance. Besides these…
Past approaches for statistical shape analysis of objects have focused mainly on objects within the same topological classes, e.g., scalar functions, Euclidean curves, or surfaces, etc. For objects that differ in more complex ways, the…
The role of consistent measures in the rigorous construction of nonabelian lattice theories is analized. General conditions that measures must fulfill to insure consistency, positivity and a mass gap are obtained. The impact of nongeneric…
Cayley's formula is a fundamental result in combinatorics that counts the number of labeled trees on n vertices. While existing proofs use approaches such as Prufer sequences and the Matrix-Tree Theorem, we give a combinatorial proof that…