Related papers: Plans on measures and AM-modulus
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…
We determine the Haar measure on the compact $p$-adic special orthogonal groups of rotations $\mathrm{SO}(d)_p$ in dimension $d=2,3$, by exploiting the machinery of inverse limits of measure spaces, for every prime $p>2$. We characterise…
This paper generalizes the results of [13] and then provides an interesting example. We construct a family of $W$-like maps $\{W_a\}$ with a turning fixed point having slope $s_1$ on one side and $-s_2$ on the other. Each $W_a$ has an…
Partial observability and uncertainty are common problems in sequential decision-making that particularly impede the use of formal models such as Markov decision processes (MDPs). However, in practice, agents may be able to employ costly…
Let $p$ be a prime. We discuss methods of solution of congruences modulo $p^n$ using $p$-adic numbers; these methods are similar to computations with real numbers (local methods). Examples of relations between local and global methods are…
This paper explores the modulus (discrete $p$-modulus) of the family of edge covers on a discrete graph. This modulus is closely related to that of the larger family of fractional edge covers; the modulus of the latter family is guaranteed…
The Tamari lattice and the associahedron provide methods of measuring associativity on a line. The real moduli space of marked curves captures the space of such associativity. We consider a natural generalization by considering the moduli…
F. Gehring and W. Ziemer proved that the p-modulus of the family of paths connecting two continua is dual to the p^*-modulus of the corresponding family of separating hypersurfaces. In this paper we show that a similar result holds in…
In this paper we study Probability Measures (PM) from a functional point of view: we show that PMs can be considered as functionals (generalized functions) that belong to some functional space endowed with an inner product. This approach…
Pump-probe microscopy is an emerging nonlinear imaging technique based on high repetition rate lasers and fast intensity modulation. Here we present new methods for pump-probe microscopy that keep the beam intensity constant and instead…
We consider a family of measures on a $q$-homogeneous tree that decrease exponentially with respect to the distance from the origin. Such measures are doubling with respect to the Gromov distance. We define atomic Hardy and BMO spaces for…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
Many applications require the collection of data on different variables or measurements over many system performance metrics. We term those broadly as measures or variables. Often data collection along each measure incurs a cost, thus it is…
Various methodological options exist on evaluating differences in both subgroups and the overall population. Most desirable is the simultaneous study of multiple endpoints in several populations. We investigate a newer method using multiple…
The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major…
Recently, two of the authors obtained estimates for the adjoint restriction operator to finite type curves with respect to general measures. Strikingly, it turns out that some of such estimates are sharp, especially when the measures are…
Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. This work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear…
Subject of this paper is ASN-Minimax (AM) double sampling plans by variables for a normally distributed quality characteristic with unknown standard deviation and two-sided specification limits. Based on the estimator p* of the fraction…
The notion of a (metric) modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by the author [V. V. Chistyakov, Metric modulars and their application, Dokl.…
Measurement incompatibility is one of the basic aspects of quantum theory. Here we study the structure of the set of compatible -- i.e. jointly measurable -- measurements. We are interested in whether or not there exist compatible…