Related papers: All maps equivalent to a given map, completely pos…
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a…
Two notions for linear maps (operational convex combinations and operational exetreme points) are introduced. The set S of ucp maps on the n times n matrix algebra is the operational convex combinations of the identity map. An operational…
The dynamics of linear positive systems map the positive orthant to itself. In other words, it maps a set of vectors with zero sign variations to itself. This raises the following question: what linear systems map the set of vectors with…
Grid maps, especially occupancy grid maps, are ubiquitous in many mobile robot applications. To simplify the process of learning the map, grid maps subdivide the world into a grid of cells whose occupancies are independently estimated using…
It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
Given a base $b$, a "digit map" is a map $f: \mathbb{Z}^{\ge 0} \to \mathbb{Z}^{\ge 0}$ of the form $f(\sum_{i=0}^n a_ib^i) = \sum_{i=0}^n f_*(a_i)$, $0 \le a_i \le b-1$ for each $i$, where $f_* : \{0,1,\dots, b-1\} \to \mathbb{Z}^{\ge 0}$…
Mapping is essential in robotics and autonomous systems because it provides the spatial foundation for path planning. Efficient mapping enables planning algorithms to generate reliable paths while ensuring safety and adapting in real time…
In this paper we consider the cone of all positive, bounded operators acting on an infinite dimensional, complex Hilbert space, and examine bijective maps that preserve absolute continuity in both directions. It turns out that these maps…
Mapping is a time-consuming process for deploying robotic systems to new environments. The handling of maps is also risk-adverse when not managed effectively. We propose here, a standardised approach to handling such maps in a manner which…
Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(\Delta)=\{\Delta_\l\}$ passing through the operator $\Delta$ such that…
While object diagrams (ODs) are widely used as a means to document object-oriented systems, they are expressively weak, as they are limited to describe specific possible snapshots of the system at hand. In this paper we introduce modal…
Symbolic dynamics is a coarse-grained description of dynamics. By taking into account the ``geometry'' of the dynamics, it can be cast into a powerful tool for practitioners in nonlinear science. Detailed symbolic dynamics can be developed…
OpenStreetMap (OSM) is a community-based, freely available, editable map service that was created as an alternative to authoritative ones. Given that it is edited mainly by volunteers with different mapping skills, the completeness and…
An assignment map is a mathematical operator that describes initial system-environment states for open quantum systems. We reexamine the notion of assignments, introduced by Pechukas, and show the conditions assignments can account for…
Self-Organizing Maps (SOM) are popular unsupervised artificial neural network used to reduce dimensions and visualize data. Visual interpretation from Self-Organizing Maps (SOM) has been limited due to grid approach of data representation,…
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and…
This article is to give an infinite dimensional analogue of a result of Choi and Effros. We say that an (not necessarily unital) operator system $T$ is \emph{dualizable} if one can find an equivalent dual matrix norm on the dual space $T^*$…
Cycle consistency has long been exploited as a powerful prior for jointly optimizing maps within a collection of shapes. In this paper, we investigate its utility in the approaches of Deep Functional Maps, which are considered…
We present positive maps and matrix inequalities for variables from the positive cone. These inequalities contain partial transpose and reshuffling operations, and can be understood as positive multilinear maps that are in one-to-one…