Related papers: Discrete Knot Theory via Lattice-Filtered Move Gra…
In this work, we present a nonlinear dynamics perspective on generating and connecting gaits for energetically conservative models of legged systems. In particular, we show that the set of conservative gaits constitutes a connected space of…
Postulating a minimal discrete quantum of action $S=\hbar$ and a simple rule for the growth of an oriented graph, we construct a strict hierarchy of temporal layers $C N$ with discrete periods $\tau_N=N\hbar/E$. Each layer is specified by…
Recently, a class of solvable interaction round the face lattice models (IRF) were constructed for an arbitrary rational conformal field theory (RCFT) and an arbitrary field in it. The Boltzmann weights of the lattice models are related in…
The Number Field Sieve and its numerous variants is the best algorithm to compute discrete logarithms in medium and large characteristic finite fields. When the extension degree n is composite and the characteristic p is of medium size, the…
A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…
A subset of vertices of a graph is minimal if, within all subsets of the same size, its vertex boundary is minimal. We give a complete, geometric characterization of minimal sets for the planar integer lattice X. Our characterization…
The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
The main objective of this thesis is a classification project for integral lattices. Using Kneser's neighbour method we have developed the computer program tn to classify complete genera of integral lattices. Main results are detailed…
We present an alternative geometric representation for the eleven Archimedean lattices, in which each site and bond is uniquely labeled by an ordered pair of integers and characterized via a modular function. This structured labeling…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
The hard core model in statistical physics is a probability distribution on independent sets in a graph in which the weight of any independent set I is proportional to lambda^(|I|), where lambda > 0 is the vertex activity. We show that…
We consider supersymmetric conformal quantum field theories (SCFTs) with degrees of freedom labeled by lattice data. We will assume that in terms of the corresponding lattice the interactions are nearest neighbor and exactly marginal. For…
Inspired by complete graph theory, we demonstrate that a metallic claw "meta-atom" structure can carry a high number of nearly degenerate resonant modes. A photonic meta-crystal composing of a lattice of such meta-atoms exhibits a large…
Critical applications in areas such as medicine, robotics and autonomous systems require compact (i.e., memory efficient), uncertainty-aware neural networks suitable for edge and other resource-constrained deployments. We study compact…
We introduce several novel and computationally efficient methods for detecting "core--periphery structure" in networks. Core--periphery structure is a type of mesoscale structure that includes densely-connected core vertices and…
We consider the problem of molecular graph generation using deep models. While graphs are discrete, most existing methods use continuous latent variables, resulting in inaccurate modeling of discrete graph structures. In this work, we…
We give a detailed discussion of the recently developed Generalized Dynamical Mean-Field Theory (GDMFT) for a mixture of bosonic and fermionic particles. We show that this method is non-perturbative and exact in infinite dimensions and…
The abstract induced subgraph poset of a graph is the isomorphism class of the induced subgraph poset of the graph, suitably weighted by subgraph counting numbers. The abstract bond lattice and the abstract edge-subgraph poset are defined…
Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose…