Related papers: Maximum VC families

We study the Vapnik-Chervonenkis (VC) density of definable families in certain stable first-order theories. In particular we obtain uniform bounds on VC density of definable families in finite U-rank theories without the finite cover…

We give a sharp bound on the number of automorphisms of a stable curve of a given genus and describe all curves attaining this bound.

We study the following problem: given a class of logic programs C, determine the maximum number of stable models of a program from C. We establish the maximum for the class of all logic programs with at most n clauses, and for the class of…

In this paper we give characterizations of the super-stable theories, in terms of an external property called representation. In the sense of the representation property, the mentioned class of first-order theories can be regarded as "not…

Answering questions of Y. Rabinovich, we prove "stability" versions of upper bounds on maximal independent set counts in graphs under various restrictions. Roughly these say that being close to the maximum implies existence of a large…

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exist a convex…

For a NIP theory $T$, a sufficiently saturated model $\mathfrak{C}$ of $T$, and an invariant (over some small subset of $\mathfrak{C}$) global type $p$, we prove that there exists a finest relatively type-definable over a small set of…

We find the maximum number of maximal independent sets in two families of graphs: all graphs with $n$ vertices and at most $r$ cycles, and all such graphs that are also connected. In addition, we characterize the extremal graphs.

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

For a class of quasi-variational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve…

A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…

The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic…

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.

We characterize the ``best'' model geometries for the class of virtually free groups, and we show that there is a countable infinity of distinct ``best'' model geometries in an appropriate sense--these are the maximally symmetric trees. The…

In this paper we study structurally stable homoclinic classes. In a natural way, the structural stability for an individual homoclinic class is defined through the continuation of periodic points. Since the homoclinic classes is not…

Considering a family of upper frequently hypercyclic operators we care about the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for a family of operators to…

We study stable vector bundles over the modular curve X(p) corresponding to the principal congruence subgroup of the modular group of prime level p which are invariant with respect to its automorphism group.

We construct maximal green sequences of maximal length for any affine quiver of type $A$. We determine which sets of modules (equivalently $c$-vectors) can occur in such sequences and, among these, which are given by a linear stability…

A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…