Related papers: Interval-Dismantling for Lattices
Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more…
We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…
Semantic segmentation is a core ability required by autonomous agents, as being able to distinguish which parts of the scene belong to which object class is crucial for navigation and interaction with the environment. Approaches which use…
We derive discontinuity relations, also known as cutting rules, and explore the analytic properties of cosmological correlators, fundamental observables of the primordial universe. Our emphasis is on how these relations arise from unitarity…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
Four-dimensional twisted group lattices are used as models for space-time structure. Compared to other attempts at space-time deformation, they have two main advantages: They have a physical interpretation and there is no difficulty in…
This paper deals with lattices $(L,\Vert~\Vert)$ over polynomial rings, where $L$ is a finitely generated module over $k[t]$, the polynomial ring over the field $k$ in the indeterminate $t$, and $\Vert~\Vert$ is a discrete real-valued…
The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable…
We construct a lattice theory describing a system of interacting nonrelativistic spin s=1/2 fermions at nonzero chemical potential. The theory is applicable whenever the interparticle separation is large compared to the range of the…
The set of permutations on a finite set can be given a lattice structure (known as the weak Bruhat order). The lattice structure is generalized to the set of words on a fixed alphabet $\Sigma = \{ x, y, z, ... \}$, where each letter has a…
Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…
We introduce a pointfree theory of convergence on lattices and coframes. A convergence lattice is a lattice $L$ with a monotonic map $\lim_L$ from the lattice of filters on $L$ to $L$, meant to be an abstract version of the map sending…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden…
It is shown that, given a lattice H in a totally disconnected, locally compact group G, the contraction subgroups in G and the values of the scale function on G are determined by their restrictions to H. Group theoretic properties intrinsic…
We study Cayley configuration spaces of a class of 1 degree-of-freedom linkages (graphs with specified edge lengths), obtained by dropping an edge from a tree-decomposable graph. The class includes well-known mechanisms based on the…
DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elements defined in the literature easily available in a standard…
Labeled transition systems can be a great way to visualize the complex behavior of parallel and communicating systems. However, if, during a particular timeframe, no synchronization or communication between processes occurs, then multiple…
We consider convection-diffusion problems in time-dependent domains and present a space-time finite element method based on quadrature in time which is simple to implement and avoids remeshing procedures as the domain is moving. The…