Related papers: Posets with Interfaces as a Model for Concurrency
We use a phase-separated driven two-dimensional Ising lattice gas to study fluid interfaces exposed to shear flow parallel to the interface. The interface is stabilized by two parallel walls with opposing surface fields and a driving field…
In this paper, we show that there is a close relation between consistency in a constraint network and set intersection. A proof schema is provided as a generic way to obtain consistency properties from properties on set intersection. This…
Pose prediction is to predict future poses given a window of previous poses. In this paper, we propose a new problem that predicts poses using 3D joint coordinate sequences. Different from the traditional pose prediction based on Mocap…
Visualizing sets of elements and their relations is an important research area in information visualization. In this paper, we present MosaicSets: a novel approach to create Euler-like diagrams from non-spatial set systems such that each…
We study theoretically situations where competition arises between an interdiffusion process and a cross-linking chemical reaction at interfaces between pieces of the same polymer material. An example of such a situation is observable in…
World models have been recently proposed as sandbox environments in which AI agents can be trained and evaluated before deployment. While realistic world models often have high computational demands, this can often be alleviated by…
Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…
We introduce and study additive posets. We show that the top homology group (with coefficients in Z/2Z) of a finite dimensional CW-complex carries a structure of an additive poset invariant under subdivisions. Applications to CW-complexes…
Basic assumptions about comparison-based indexing are laid down and a general design space is derived from these. An index structure spanning this design space (the sprawl) is described, along with an associated family of partitioning…
Interleaving distances provide a fundamental tool for comparing persistence modules and have been widely used in topological data analysis. Their definitions are typically based on translation structures (shift operations) on the indexing…
Many categorical frameworks have been proposed to formalize the idea of gluing Petri nets with each other. Such frameworks model net gluings in terms of sharing of resources or synchronization of transitions. Interpretations given to these…
We investigate linear and additive codes in partially ordered Hamming-like spaces that satisfy the extension property, meaning that automorphisms of ideals extend to automorphisms of the poset. The codes are naturally described in terms of…
Previous methods solve feature matching and pose estimation using a two-stage process by first finding matches and then estimating the pose. As they ignore the geometric relationships between the two tasks, they focus on either improving…
We introduce the Generalized Turing Test (GTT), a formal framework for comparing the capabilities of arbitrary agents via indistinguishability. For agents A and B, we define the Turing comparator A $\geq$ B to hold if B, acting as a…
In this paper, we introduce a partial order on rings with involution, which is a generalization of the partial order on the set of projections in a Rickart *-ring. We prove that a *-ring with the natural partial order form a sectionally…
We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is…
We introduce Cayley posets as posets arising naturally from pairs $S<T$ of semigroups, much in the same way that Cayley graph arises from a (semi)group and a subset. We show that Cayley posets are a common generalization of several known…
A poset $P = (X,\prec)$ has an interval representation if each $x \in X$ can be assigned a real interval $I_x$ so that $x \prec y$ in $P$ if and only if $I_x$ lies completely to the left of $I_y$. Such orders are called \emph{interval…
A poset is representable if it can be embedded in a field of sets in such a way that existing finite meets and joins become intersections and unions respectively (we say finite meets and joins are preserved). More generally, for cardinals…
The category $\mathbf{Rel}$ is the category of sets (objects) and relations (morphisms). Equipped with the direct product of sets, $\mathbf{Rel}$ is a monoidal category. Moreover, $\mathbf{Rel}$ is a locally posetal 2-category, since every…