Related papers: Linear Combinations of Unordered Data Vectors
Venn-Abers predictors are probabilistic predictors that enjoy appealing properties of validity, but their major limitation is that they are applicable only to the case of binary classification, with a recent extension to bounded regression.…
Quantum measurements can be interpreted as a generalisation of probability vectors, in which non-negative real numbers are replaced by positive semi-definite operators. We extrapolate this analogy to define a generalisation of doubly…
We address the observability problem for ensembles that are described by probability distributions. The problem is to reconstruct a probability distribution of the initial state from the time-evolution of the probability distribution of the…
The reachability problem for vector addition systems is a central problem of net theory. This problem is known to be decidable but the complexity is still unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds complexity…
We generalize the notion of Davenport constants to a `higher degree' and obtain various lower and upper bounds, which are sometimes exact as is the case for certain finite commutative rings of prime power cardinality. Two simple examples…
Motivated by an influential result of Bourgain and Tzafriri, we consider continuous matrix functions $A:\mathbb{R}\to M_{n\times n}$ and lower $\ell_2$-norm bounds associated with their restriction to certain subspaces. We prove that for…
In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation,…
Reversible computation is an unconventional form of computing that extends the standard forward-only mode of computation with the ability to execute a sequence of operations in reverse at any point during computation. As such, in this…
A group is irreducibly represented if it has a faithful irreducible unitary representation. For countable groups, a criterion for irreducible representability is given, which generalises a result obtained for finite groups by W. Gasch\"utz…
We study fundamental clustering problems for incomplete data. Specifically, given a set of incomplete d-dimensional vectors (representing rows of a matrix), the goal is to complete the missing vector entries in a way that admits a…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…
The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic. In this setting, called reverse mathematics, one investigates which theorems provably imply which others in a…
For a finite subset $I$ of positive integers, the descent polynomial $\mathcal{D}(I;n)$ counts the number of permutations in $S_n$ that have descent set $I$. We generalize descent polynomials by considering permutations with a specific…
Bayesian inverse problem on an infinite dimensional separable Hilbert space with the whole state observed is well posed when the prior state distribution is a Gaussian probability measure and the data error covariance is a cylindric…
Given $n$ positive integers $a_1,a_2,\dots,a_n$, and a positive integer right hand side $\beta$, we consider the feasibility version of the subset sum problem which is the problem of determining whether a subset of $a_1,a_2,\dots,a_n$ adds…
We investigate the inverse scale space flow as a decomposition method for decomposing data into generalised singular vectors. We show that the inverse scale space flow, based on convex and absolutely one-homogeneous regularisation…
Admissible vectors for unitary representations of locally compact groups are the basis for group-frame and covariant coherent state expansions. Main tools in the study of admissible vectors have been Plancherel and central integral…
A renormalizable rigid supersymmetry for the four dimensional antisymmetric tensor field model in a curved space-time background is constructed. A closed algebra between the BRS and the supersymmetry operators is only realizable if the…
We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite number of pieces whose graphs are solutions of a linear…
This paper is an attempt to find out which properties of a finite group G can be expressed in terms of commutators of elements of coprime orders. A criterion of solubility of G in terms of such commutators is obtained. We also conjecture…