Related papers: On embedding of repetitive Meyer multiple sets int…

Let M be the generic poset, defined as the Fra\"iss\'e limit of the class of finite posets. We show that every countably infinite poset A can be embedded with coinfinite image into M so that each automorphism of the image of A extends…

We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any kind of structural failure must fail with a proper class of…

In this paper we explore the topological properties of self-replicating, 3-dimensional manifolds, which are modeled by idempotents in the (2+1)-cobordism category. We give a classification theorem for all such idempotents. Additionally, we…

Many, if not most, systems of interest in science are naturally described as nonlinear dynamical systems. Empirically, we commonly access these systems through time series measurements. Often such time series may consist of discrete random…

The celebrated Takens' embedding theorem concerns embedding an attractor of a dynamical system in a Euclidean space of appropriate dimension through a generic delay-observation map. The embedding also establishes a topological conjugacy. In…

Let X be an irreducible smooth complex projective curve of genus g at least 4. Let M(r,\Lambda) be the moduli space of stable vector bundles over X or rank r and fixed determinant \Lambda, of degree d. We give a new proof of the fact that…

Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.

Metric embedding is a powerful tool used extensively in mathematics and computer science. We devise a new method of using metric embeddings recursively, which turns out to be particularly effective in $\ell_p$ spaces, $p>2$, yielding…

Regression is one of the most commonly used statistical techniques. However, testing regression systems is a great challenge because of the absence of test oracle in general. In this paper, we show that Metamorphic Testing is an effective…

We define iterated monodromy groups of more general structures than partial self-covering. This generalization makes it possible to define a natural notion of a combinatorial model of an expanding dynamical system. We prove that a naturally…

In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…

Multi-model fitting has been extensively studied from the random sampling and clustering perspectives. Most assume that only a single type/class of model is present and their generalizations to fitting multiple types of models/structures…

There is growing evidence that independently trained AI systems come to represent the world in the same way. In other words, independently trained embeddings from text, vision, audio, and neural signals share an underlying geometry. We call…

Natural language definitions possess a recursive, self-explanatory semantic structure that can support representation learning methods able to preserve explicit conceptual relations and constraints in the latent space. This paper presents a…

We first introduce the class of quasi-algebraically stable meromorphic maps of $\P^k.$ This class is strictly larger than that of algebraically stable meromorphic self-maps of $\P^k.$ Then we prove that all maps in the new class enjoy a…

This paper concerns the characterisation of second order marginals for random sets in a discrete setting. Under the instance of unit covariances, this problem possesses a combinatorial symmetry, exploited jointly in the companion paper to…

We introduce a strategy to study irreducible representations of automorphism groups of finite modules over local rings. We prove that these automorphism groups fit in a hierarchy that facilitates a stratification of their irreducible…

This paper studies a meta-simplex concept and geometric embedding framework for multi-population replicator dynamics. Central results are two embedding theorems which constitute a formal reduction of multi-population replicator dynamics to…

We propose several ways of reusing subword embeddings and other weights in subword-aware neural language models. The proposed techniques do not benefit a competitive character-aware model, but some of them improve the performance of…

In this paper we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly oredered associative ring on some specially defined subgroup concides with the composition of an inner…