Related papers: Time Scales and Mathematica
Two time scale stochastic approximation is analyzed when the iterates on either or both time scales do not necessarily converge.
Intrinsic time is an example of an event-based conception of time, used to analyze financial time series. Here, for the first time, we reveal the connection between intrinsic time and physical time. In detail, we present an analytic…
Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of…
We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…
Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript…
Clocks are a central part of many computing paradigms, and are mainly used to synchronise the delicate operation of switching, necessary to drive modern computational processes. Unfortunately, this synchronisation process is reaching a…
The relation between the notion of crystalline symmetry and characteristic time intervals when this symmetry could be observed is analyzed. Several time scales are shown to exist for a system of interacting particles. It is only when the…
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
A temporal graph is a data structure, consisting of nodes and edges in which the edges are associated with time labels. To analyze the temporal graph, the first step is to find a proper graph dataset/benchmark. While many temporal graph…
Recent progress in quantum gravity and string theory has raised interest among scientists to whether or not nature behaves discretely at the Planck scale. There are two attitudes twoards this discretenes i.e. top-down and bottom-up…
Time has always played a crucial role in cosmology. I review some of the aspects of the present cosmological model which are more directly related to time, such as: the definition of a cosmic time; the existence of typical timescales and…
To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many…
$\lambda$-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
The increasing relevance of areas such as real-time and embedded systems, pervasive computing, hybrid systems control, and biological and social systems modeling is bringing a growing attention to the temporal aspects of computing, not only…
We derive the Helmholtz theorem for Hamiltonian systems defined on time scales in the context of nonshifted calculus of variations which encompass the discrete and continuous case. Precisely, we give a theorem characterizing first order…
In the paper we consider an interesting possibility of a time as a stochastic process in quantum mechanics.In order to do it we reconsider time as a mechanical quantity in classical mechanics and afterwards we quantize it. We consider…
We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular…
Lifelong learning occurs on timescales ranging from minutes to decades. People can lose themselves in a new skill, practicing for hours until exhausted. And they can pursue mastery over days or decades, perhaps abandoning old skills…
We briefly review two concepts of time - the usual time associated with "being" and more recent ideas, answering to the description of "becoming". The approximation involved in the former is examined. Finally we argue that it is…