Related papers: Functional equations as an important analytic meth…
Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…
Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary nonlinear drift, and nonlinear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based…
Stochastic Einstein equations are considered when 3D space metric $\gamma_{ij}$ are stochastic functions. The probability density for the stochastic quantities is connected with the Perelman's entropy functional. As an example, the Friedman…
We discuss an approach to mathematically modelling systems made of objects that are coupled together, using generative models of the dependence relationships between states (or trajectories) of the things comprising such systems. This broad…
Auto Feature Engineering (AFE) plays a crucial role in developing practical machine learning pipelines by automating the transformation of raw data into meaningful features that enhance model performance. By generating features in a…
The output of a machine learning algorithm can usually be represented by one or more multivariate functions of its input variables. Knowing the global properties of such functions can help in understanding the system that produced the data…
Effectivity functions are the basic formalism for investigating the semantics game logic. We discuss algebraic properties of stochastic effectivity functions, in particular the relationship to stochastic relations, morphisms and congruences…
In two recent works \cite{BMM,BK}, it has been shown that the counting generating functions (CGF) for the 23 walks with small steps confined in a quadrant and associated with a finite group of birational transformations are holonomic, and…
Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies,…
Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…
Non-equilibrium stationary fluctuations may exhibit a special symmetry called fluctuation relations (FR). Here, we show that this property is always satisfied by the subtraction of two random and independent variables related by a…
It is shown that the solution maps of an abstract functional differential equations (FDEs) are $\alpha$-contractions in the phase space equipped with an equivalent norm under appropriate assumptions. This result can be applied to…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
One of the most challenging problems in enumerative combinatorics is to count Wilf classes, where you are given a pattern, or set of patterns, and you are asked to find a "formula", or at least an efficient algorithm, that inputs a positive…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
In this paper we investigate the normal and the large fluctuations of additive functionals associated with a stochastic process under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very…
Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of non-linear deterministic equations is assumed to characterize its dynamics and stationary properties. We…