Related papers: Separations of Matroid Freeness Properties
We unify the study of quotients of matroids, polymatroids, valuated matroids and strong maps of submodular functions in the framework of Murota's discrete convex analysis. As a main result, we compile a list of ten equivalent…
The standard oracle model for matroid algorithms assumes that each independence query can be answered in constant time, regardless of the size of the queried set. While this abstraction has underpinned much of the theoretical progress in…
Given a small random sample of $n$-bit strings labeled by an unknown Boolean function, which properties of this function can be tested computationally efficiently? We show an equivalence between properties that are efficiently testable from…
When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…
From the configuration of a matroid (which records the size and rank of the cyclic flats and the containments among them, but not the sets), one can compute several much-studied matroid invariants, including the Tutte polynomial and a…
A $Q$-manifold $M$ is a supermanifold endowed with an odd vector field $Q$ squaring to zero. The Lie derivative $L_Q$ along $Q$ makes the algebra of smooth tensor fields on $M$ into a differential algebra. In this paper, we define and study…
We investigate the lattice of machine invariant classes. This is an infinite completely distributive lattice but it is not a Boolean lattice. We show the subword complexity and the growth function create machine invariant classes. So the…
It is currently known how to characterize functions that neural networks can learn with SGD for two extremal parameterizations: neural networks in the linear regime, and neural networks with no structural constraints. However, for the main…
Neural networks have been shown to frequently fail to learn critical safety and correctness properties purely from data, highlighting the need for training methods that directly integrate logical specifications. While adversarial training…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
We define an independence system associated with simple graphs. We prove that the independence system is a matroid for certain families of graphs, including trees, with bases as minimal resolving sets. Consequently, the greedy algorithm on…
We consider lattice Hamiltonians that arise from putting Haldane pseudopotentials into a second quantized or "guiding-center-only" form. These are fascinating examples for frustration free lattice Hamiltonians. This is so since even though…
In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus $\tau$ and its conjugate, $\bar\tau$. We point out that certain combinations of…
This lecture is devoted to review some of the main properties of multisymplectic geometry. In particular, after reminding the standard definition of multisymplectic manifold, we introduce its characteristic submanifolds, the canonical…
A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the…
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…
Metamorphic testing (MT) is a general approach for the testing of a specific kind of software systems -- so-called ``non-testable'', where the ``classical'' testing approaches are difficult to apply. MT is an effective approach for…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
Verification of temporal logic properties plays a crucial role in proving the desired behaviors of hybrid systems. In this paper, we propose an interval method for verifying the properties described by a bounded linear temporal logic. We…
A matroid base polytope is a polytope in which each vertex has 0,1 coordinates and each edge is parallel to a difference of two coordinate vectors. Matroid base polytopes are described combinatorially by integral submodular functions on a…