Related papers: Simplicial Complexes Obtained from Qualitative Pro…
Models can be simple for different reasons: because they yield a simple and computationally efficient interpretation of a generic dataset (e.g. in terms of pairwise dependences) - as in statistical learning - or because they capture the…
We develop a cohomological method to classify amalgams of groups. We generalize this to simplicial amalgams in any concrete category. We compute the non-commutative 1-cohomology for several examples of amalgams defined over small simplices.
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective plane over a finite field, and present…
We consider the construction of neural network architectures for data on simplicial complexes. In studying maps on the chain complex of a simplicial complex, we define three desirable properties of a simplicial neural network architecture:…
Strong placement games (SP-games) are a class of combinatorial games whose structure allows one to describe the game via simplicial complexes. A natural question is whether well-known invariants of combinatorial games, such as "game value",…
In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such…
We develop a theory of limits for sequences of dense abstract simplicial complexes, where a sequence is considered convergent if its homomorphism densities converge. The limiting objects are represented by stacks of measurable [0,1]-valued…
In our recent work we described conditions under which a multi-parameter random simplicial complex is connected and simply connected. We showed that the Betti numbers of multi-parameter random simplicial complexes in one specific dimension…
Can the apparent complexity we observe in the real world be generated from simple initial conditions via simple, deterministic rules?
In this work, we define cooperative games on simplicial complexes, generalizing the study of probabilistic values of Weber and quasi-probabilistic values of Bilbao, Driessen, Jim\'{e}nez Losada and Lebr\'{o}n. Applications to Multi-Touch…
For each strongly connected finite-dimensional (pure) simplicial complex we construct a finite group, the group of projectivities of the complex, which is a combinatorial but not a topological invariant. This group is studied for…
As an alternative to Kripke models, simplicial complexes are a versatile semantic primitive on which to interpret epistemic logic. Given a set of vertices, a simplicial complex is a downward closed set of subsets, called simplexes, of the…
The categoricity spectrum of a class of structures is the collection of cardinals in which the class has a single model up to isomorphism. Assuming that cardinal exponentiation is injective (a weakening of the generalized continuum…
The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected…
This paper investigates symmetric composite binary quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown quantum state. While asymptotic error exponents for this problem are…
We show how to construct a cubic partial cube from any simplicial arrangement of lines or pseudolines in the projective plane. As a consequence, we find nine new infinite families of cubic partial cubes as well as many sporadic examples.
A likelihood order is defined over linear subspaces of a finite dimensional Hilbert space. It is shown that such an order that satisfies some plausible axioms can be represented by a quantum probability in two cases: pure state and uniform…
Recently, much work has been carried out to study simplicial interpretations of modal logic. While notions of (distributed) knowledge have been well investigated in this context, it has been open how to model belief in simplicial models. We…
We consider the exact sampling of the first passage of a stable subordinator across a non-increasing regular barrier. First, the sampling is reduced to one from a bivariate distribution parameterized by the index $\alpha$ of the…