Related papers: Metric Linear Orders and O-Minimality

We give a notion of Scott rank for separable metric structures based on the definability of the (metric closures of) automorphism orbits in continuous infinitary logic. This is a continuous analogue of work of Montalb\'an for countable…

In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be…

Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.

We consider distributed model-checking of Monadic Second-Order logic (MSO) on graphs which constitute the topology of communication networks. The graph is thus both the structure being checked and the system on which the distributed…

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the…

In this paper, we study relative metric regularity of set-valued mappings with emphasis on directional metric regularity. We establish characterizations of relative metric regularity without assuming the completeness of the image spaces, by…

Linearizability has become the key correctness criterion for concurrent data structures, ensuring that histories of the concurrent object under consideration are consistent, where consistency is judged with respect to a sequential history…

In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…

For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…

Let $\mathcal{R}=(R,\oplus,\leq,0)$ be an algebraic structure, where $\oplus$ is a commutative binary operation with identity $0$, and $\leq$ is a translation-invariant total order with least element $0$. Given a distinguished subset…

Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…

We investigate a property that extends the Danos-Regnier correctness criterion for linear logic proof-structures. The property applies to the correctness graphs of a proof-structure: it states that any such graph is acyclic and the number…

Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…

The DL-Lite description logics allow for modeling domain knowledge on top of databases and for efficient reasoning. We focus on metric temporal extensions of DL-Lite_bool and its fragments, and study the complexity of satisfiability. In…

Without imposing restrictions on a weighted graph's arc lengths, symmetry structures cannot be expected. But, they exist. To find them, the graphs are decomposed into a component that dictates all closed path properties (e.g., shortest and…

For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such…

In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel…

We study the Monadic Second Order (MSO) Hierarchy over infinite pictures, that is tilings. We give a characterization of existential MSO in terms of tilings and projections of tilings. Conversely, we characterise logic fragments…

We give necessary and sufficient geometric conditions for a theory definable in an o-minimal structure to interpret a real closed field. The proof goes through an analysis of thorn-minimal types in super-rosy dependent theories of finite…