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Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
Recently it has been shown that the property of forward-flatness for discrete-time systems, which is a generalization of static feedback linearizability and a special case of a more general concept of flatness, can be checked by two…
This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained…
On the basis of an analysis of previous research, we present a generalized approach for measuring the difference of plans with an exemplary application to machine scheduling. Our work is motivated by the need for such measures, which are…
Statistical estimation of the prediction uncertainty of physical models is typically hindered by the inadequacy of these models due to various approximations they are built upon. The prediction errors due to model inadequacy can be handled…
The goal of this article is to survey various results concerning stochastic completeness of graphs. In particular, we present a variety of formulations of stochastic completeness and discuss how a discrepancy between uniqueness class and…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we…
We prove that each complete flat cone metric on a surface, perhaps with boundary and punctures, can be triangulated with finitely many types of triangles. We derive Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove…
In this paper, equilibrium and stability equations of functionally graded material (FGM) plate under thermal environment are formulated based on isogeometric analysis (IGA) in combination with higher-order shear deformation theory (HSDT).…
There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured.…
The purpose of this paper is to study metrics suitable for assessing uncertainty of power spectra when these are based on finite second-order statistics. The family of power spectra which is consistent with a given range of values for the…
Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated…
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.…
Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we…
Geometric programming (GP) is a well-known optimization tool for dealing with a wide range of nonlinear optimization and engineering problems. In general, it is assumed that the parameters of a GP problem are deterministic and accurate.…
We study the shape of inflated surfaces introduced in \cite{B1} and \cite{P1}. More precisely, we analyze profiles of surfaces obtained by inflating a convex polyhedron, or more generally an almost everywhere flat surface, with a symmetry…
A method of modifying the roughness of soda-lime glass spheres is presented, with the purpose of tuning inter-particle friction. The effect of chemical etching on the surface topography and the bulk frictional properties of grains is…