Related papers: Acyclicity conditions on pasting diagrams
We study the Hard Core Model on the graphs ${\rm {\bf \scriptstyle G}}$ obtained from Archimedean tilings i.e. configurations in $\scriptstyle \{0,1\}^{{\rm {\bf G}}}$ with the nearest neighbor 1's forbidden. Our particular aim in choosing…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
We introduce a notion of harmonic chain for chain complexes over fields of positive characteristic. A list of conditions for when a Hodge decomposition theorem holds in this setting is given and we apply this theory to finite CW complexes.…
We study the driving of colloidal molecular crystals over periodic substrates such as those created with optical traps. The n-merization that occurs in the colloidal molecular crystal states produces a remarkably rich variety of distinct…
We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree…
The competing effect of a periodic pinning potential and random point disorder is studied for arrays of elastic lines or directed polymers. The groundstates are investigated by exact combinatorial optimization. In both two and three…
Models of complex networks are generally defined as graph stochastic processes in which edges and vertices are added or deleted over time to simulate the evolution of networks. Here, we define a unifying framework - probabilistic inductive…
We introduce a new class of identifiable DAG models where the conditional distribution of each node given its parents belongs to a family of generalized hypergeometric distributions (GHD). A family of generalized hypergeometric…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
Recent work on causal abstraction, in particular graphical approaches focusing on causal structure between clusters of variables, aims to summarize a high-dimensional causal structure in terms of a low-dimensional one. Existing methods for…
The equilibrium behavior of binary mixtures can be understood through the competition of energy scales, which classifies their corresponding phase diagrams into distinct topological regimes (Types I-IV). However, in many soft-matter…
Continuous wavelet transforms arising from the quasiregular representation of a semidirect product of a vector group with a matrix group -- the so-called dilation group -- have been studied by various authors. Recently the attention has…
Score-based approaches in the structure learning task are thriving because of their scalability. Continuous relaxation has been the key reason for this advancement. Despite achieving promising outcomes, most of these methods are still…
We consider a mixture of one neutral and two oppositely charged types of molecules confined to a surface. Using analytical techniques and molecular dynamics simulations, we construct the phase diagram of the system and exhibit the…
We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying…
Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present the first method for fitting these…
Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous…
Networks of interacting nodes connected by edges arise in almost every branch of scientific enquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical…