Related papers: Unique Factorization and Controllability of Tail-B…
It is shown that a trellis realization can be locally reduced if it is not state-trim, branch-trim, proper, observable, and controllable. These conditions are not sufficient for local irreducibility. Making use of notions that amount to…
This paper investigates tail-biting trellis realizations for linear block codes. Intrinsic trellis properties are used to characterize irreducibility on given intervals of the time axis. It proves beneficial to always consider the trellis…
This paper investigates properties of realizations of linear or group codes on general graphs that lead to local reducibility. Trimness and properness are dual properties of constraint codes. A linear or group realization with a constraint…
This paper is concerned with the local reducibility properties of linear realizations of codes on finite graphs. Trimness and properness are dual properties of constraint codes. A linear realization is locally reducible if any constraint…
This paper focuses on dualizing tail-biting trellises, particularly KV-trellises. These trellises are based on characteristic generators, as introduced by Koetter/Vardy (2003), and may be regarded as a natural generalization of minimal…
The correlators of two-dimensional rational conformal field theories that are obtained in the TFT construction of [FRSI,FRSII,FRSIV] are shown to be invariant under the action of the relative modular group and to obey bulk and boundary…
The validity of mode coupling theory (MCT) is restricted by an uncontrolled factorization approximation of density correlations. The factorization can be delayed and ultimately avoided, however, by explicitly including higher order…
A definition of atomic codeword for a group code is presented. Some properties of atomic codewords of group codes are investigated. Using these properties, it is shown that every minimal tail-biting trellis for a group code over a finite…
Control invariant sets are crucial for various methods that aim to design safe control policies for systems whose state constraints must be satisfied over an indefinite time horizon. In this article, we explore the connections among…
We characterize control of a qutrit implemented in the lowest three energy levels of a capacitively-shunted flux-biased superconducting circuit. Randomized benchmarking over the qutrit Clifford group yields an average fidelity of 98.89…
Optimal control for safety-critical systems is often dependent on the conservativeness of constraints. Control Barrier Functions (CBFs) serve as a medium to represent such constraints, but constructing a minimally conservative CBF is a…
An alternative formulation for the controllability problem of single input linear positive systems is presented. Driven by many industrial applications, this formulations focuses on the case where the region of interest is only a subset of…
We prove that the factorization of a saturated fusion system over a discrete $p$-toral group as a product of indecomposable subsystems is unique up to normal automorphisms of the fusion system and permutations of the factors. In particular,…
In order to obtain functional limit theorems for heavy tailed stationary processes arising from dynamical systems, one needs to understand the clustering patterns of the tail observations of the process. These patterns are well described by…
Behavior trees (BTs) are an optimally modular framework to assemble hierarchical hybrid control policies from a set of low-level control policies using a tree structure. Many robotic tasks are naturally decomposed into a hierarchy of…
Control Barrier Functions offer safety certificates by dictating controllers that enforce safety constraints. However, their response depends on the classK function that is used to restrict the rate of change of the value of the barrier…
In this paper, we show that under mild controllability assumptions a time-invariant Control Barrier Function (CBF) can be constructed based on predictions with a finite horizon. As a starting point, we require only a known subset of a…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category C with a distinguished object, a symmetric special…
In AdS/CFT, partition functions of decoupled CFTs living on separate asymptotic boundaries factorize. However, the presence of bulk wormholes connecting different boundaries tends to spoil the factorization of the bulk partition function,…