Related papers: On system rollback and totalised fields
One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.
In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems…
The circumcentered-reflection method (CRM) has been recently proposed as a methodology for accelerating several algorithms for solving the Convex Feasibility Problem (CFP), equivalent to finding a common fixed-point of the orthogonal…
Considered are operators that leave the set of non-invertible (in the sense of Ehrenpreis) distributions stable. They simultaneously generalise the operation of convolution by a distribution with compact support and the operation of…
An approach to build Probabilistic Arithmetic in which initial values of all correlated random variables are known, but with varying degrees of accuracy. As a result of the proposed Probabilistic Arithmetic operations, variable values,…
We consider Turing machines as actions over configurations in $\Sigma^{\mathbb{Z}^d}$ which only change them locally around a marked position that can move and carry a particular state. In this setting we study the monoid of Turing machines…
In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of "integral action" for proportional(-derivative)-controlled systems whose…
The fundamental dynamics of quantum particles is neutral with respect to the arrow of time. And yet, our experiments are not: we observe quantum systems evolving from the past to the future, but not the other way round. A fundamental…
We demonstrate the existence of an open set of data which exhibits \textit{reversal} and \textit{recirculation} for the stationary Prandtl equations (data is taken in an appropriately defined product space due to the simultaneous forward…
The property of linear discrete-time time-invariant system operators mapping inputs with at most $k-1$ sign changes to outputs with at most $k-1$ sign changes is investigated. We show that this property is tractable via the notion of…
This paper presents a decentralized algorithm for a team of agents to track time-varying fixed points that are the solutions to time-varying convex optimization problems. The algorithm is first-order, and it allows for total asynchrony in…
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…
We generalise clones, which are sets of functions $f:A^n \rightarrow A$, to sets of mappings $f:A^n \rightarrow A^m$. We formalise this and develop language that we can use to speak about it. We then look at bijective mappings, which have…
The dynamics of an open quantum system can be described by a quantum operation, a linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions,…
We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these functions, the classical definition would lead to divergent…
The field of molecular programming allows for the programming of the structure and behavior of matter at the molecular level, even to the point of encoding arbitrary computation. However, current approaches tend to be wasteful in terms of…
Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving…