Related papers: Change of Variable for Multi-dimensional Integral
Variational inference is a general approach for approximating complex density functions, such as those arising in latent variable models, popular in machine learning. It has been applied to approximate the maximum likelihood estimator and…
Limit theorems for a random number of independent random variables are frequently called transfer theorems. Investigations into this direction for sums of random variables with independent random sample size have been originated by…
For single components fluids, vanishing isothermal compressibility implies that the mass density is constant, but the same conclusion is unknown for multicomponent fluids. Here the volume remains affected by changes of the composition. In…
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we…
Warfield proved that every injective module has the exchange property. This was generalized by Fuchs who showed that quasi-injective modules satisfy the exchange property. We extend this further and prove that a module invariant under…
In this note we prove a selection of commutativity theorems for various classes of semigroups. For instance, if in a separative or completely regular semigroup $S$ we have $x^p y^p = y^p x^p$ and $x^q y^q = y^q x^q$ for all $x,y\in S$ where…
We prove a uniqueness theorem for an entire function, which shares certain values with its higher order derivatives.
The famous Jacobian Conjecture asks if a morphism $f:K[x,y]\to K[x,y]$ with invertible Jacobian, is invertible ($K$ is a characteristic zero field). A known result says that if $K[f(x),f(y)] \subseteq K[x,y]$ is an integral extension, then…
We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…
Let $\mathbb{F}$ be a non-archimedean local field of positive characteristic different from 2. We consider distributions on $\mathrm{GL}(n+1,\mathbb{F})$ which are invariant under the adjoint action of $\mathrm{GL}(n,\mathbb{F})$. We prove…
We introduce the notion of a multidimensional hybrid preference domain on a (finite) set of alternatives that is a Cartesian product of finitely many components. We demonstrate that in a model of public goods provision, multidimensional…
We introduce a novel characterization of phase transitions based on hypothesis testing. In our formulation, a phase transition is defined as the breakdown of statistical indistinguishability under vanishing parameter perturbations in the…
The analysis of observable phenomena (for instance, in biology or physics) allows the detection of dynamical behaviors and, conversely, starting from a desired behavior allows the design of objects exhibiting that behavior in engineering.…
A module is called automorphism-invariant if it is invariant under any automorphism of its injective hull. Dickson and Fuller have shown that if $R$ is a finite-dimensional algebra over a field $\mathbb F$ with more than two elements then…
This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…
In this paper we develop a general theory of modules which are invariant under automorphisms of their covers and envelopes. When applied to specific cases like injective envelopes, pure-injective envelopes, cotorsion envelopes, projective…
This paper suggests a new interpretation of the Dempster-Shafer theory in terms of probabilistic interpretation of plausibility. A new rule of combination of independent evidence is shown and its preservation of interpretation is…
Given two relations containing multiple measurements - possibly with uncertainties - our objective is to find which sets of attributes from the first have a corresponding set on the second, using exclusively a sample of the data. This…
In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…
We define the notions of unilateral metric derivatives and ``metric derived numbers'' in analogy with Dini derivatives (also referred to as ``derived numbers'') and establish their basic properties. We also prove that the set of points…