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We set up a framework for a model-independent analysis of the time variation of $e$, $\hbar$, and $c$ indiviually. It is shown that the time-evolution of each constant can be determined uniquely from the time evolution of the fine structure…
Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary…
Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their main result hinges on the stopping time property of the time changes, but…
This short note suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak and such that the traditional methods are not effective. The method requires…
We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…
This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over…
This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…
This survey presents recent Helly-type geometric theorems published since the appearance of the last comprehensive survey, more than ten years ago. We discuss how such theorems continue to be influential in computational geometry and in…
In this paper we propose the notion of dynamic deviation measure, as a dynamic time-consistent extension of the (static) notion of deviation measure. To achieve time-consistency we require that a dynamic deviation measures satisfies a…
Glassy systems are ubiquitous in nature, and are characterized by slow relaxations to equilibrium without a typical timescale, aging and memory effects. Understanding these is a long-standing problem in physics. We study the aging of the…
Although the notion of diagnostic problem has been extensively investigated in the context of static systems, in most practical applications the behavior of the modeled system is significantly variable during time. The goal of the paper is…
In this paper, we study a multivariate version of the generalized counting process (GCP) and discuss its various time-changed variants. The time is changed using random processes such as the stable subordinator, inverse stable subordinator,…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
This paper is devoted to the study of time-dependent hyperbolic systems and the derivation of dispersive estimates for their solutions. It is based on a diagonalisation of the full symbol within adapted symbol classes in order to extract…
(Draft 3) A generalized differential operator on the real line is defined by means of a limiting process. These generalized derivatives include, as a special case, the classical derivative and current studies of fractional differential…
We characterize various forms of positive dependence for a general class of time-inhomogeneous Markov processes called Feller evolution processes (FEPs) and for jump-FEPs. General FEPs can be studied through their time and state-space…
There is a lack of quantitative measures to evaluate the progression of topics through time in dynamic topic models (DTMs). Filling this gap, we propose a novel evaluation measure for DTMs that analyzes the changes in the quality of each…
A general input-output modelling technique for aperiodic-sampling linear systems has been developed. The procedure describes the dynamics of the system and includes the sequence of sampling periods among the variables to be handled. Some…
There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…
The covariance of two random variables measures the average joint deviations from their respective means. We generalise this well-known measure by replacing the means with other statistical functionals such as quantiles, expectiles, or…