Related papers: Universal Analog Computation: Fra\"iss\'e Limits o…
Neuromorphic computing is a relatively new discipline of computer science, where the principles of biological brain's computation and memory are used to create a new way of processing information, based on networks of spiking neurons. Those…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
A myriad of applications ranging from engineering and scientific simulations, image and signal processing as well as high-sensitive data retrieval demand high processing power reaching up to teraflops for their efficient execution. While a…
Axiomatic approach has demonstrated its power in mathematics. The main goal of this preprint is to show that axiomatic methods are also very efficient for computer science. It is possible to apply these methods to many problems in computer…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Termination properties of actual Prolog systems with constraints are fragile and difficult to analyse. The lack of the occurs-check, moded and overloaded arithmetical evaluation via is/2 and the occasional nontermination of finite domain…
Building on work of Ruelle and Putnam in the Smale space case, Thomsen defined the homoclinic and heteroclinic $C^\ast$-algebras for an expansive dynamical system. In this paper we define a class of expansive dynamical systems, called…
Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to $d$-level systems by conjugating an analog…
This article proposes a universal simulation platform for simulating systems undergoing duress. In other words, this paper introduces a total simulation package which includes a number of methods of simulating the flexibility of a given…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
The design and operation of systems are conventionally viewed as a sequential decision-making process that is informed by data from physical experiments and simulations. However, the integration of these high-dimensional and heterogeneous…
Simplification of fractional powers of positive rational numbers and of sums, products and powers of such numbers is taught in beginning algebra. Such numbers can often be expressed in many ways, as this article discusses in some detail.…
We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track…
Differentiable programming is the combination of classical neural networks modules with algorithmic ones in an end-to-end differentiable model. These new models, that use automatic differentiation to calculate gradients, have new learning…
All but a few digital computers used for scientific computations have supported floating-point and digital arithmetic of rather limited numerical precision. The underlying assumptions were that the systems being studied were basically…
If two control systems on manifolds of the same dimension are dynamic equivalent, we prove that either they are static equivalent --i.e. equivalent via a classical diffeomorphism-- or they are both ruled; for systems of different…
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…
A general scheme to perform universal quantum computation within decoherence-free subspaces (DFSs) of a system's Hilbert space is presented. This scheme leads to the first fault-tolerant realization of universal quantum computation on DFSs…
Data classification, the process of analyzing data and organizing it into categories, is a fundamental computing problem of natural and artificial information processing systems. Ideally, the performance of classifier models would be…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…