Related papers: A Variant of Probabilistic Topology
We introduce an extension of the P\'olya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random…
The paper is focused on the problem of estimating the probability $p$ of individual contaminated sample, under group testing. The precision of the estimator is given by the probability of proportional closeness, a concept defined in the…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
We introduce categories of extended Gaussian maps and Gaussian relations which unify Gaussian probability distributions with relational nondeterminism in the form of linear relations. Both have crucial and well-understood applications in…
The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…
Each series $\sum_{n=1}^\infty a_n$ of real positive terms gives rise to a topology on $\mathbb{N} = \{1,2,3,...\}$ by declaring a proper subset $A\subseteq \mathbb{N}$ to be closed if $\sum_{n\in A} a_n < \infty$. We explore the…
We survey some of the major open problems involving selection principles, diagonalizations, and covering properties in topology and infinite combinatorics. Background details, definitions and motivations are also provided.
We play with a graph-theoretic analogue of the folklore infinite monkey theorem. We define a notion of graph likelihood as the probability that a given graph is constructed by a monkey in a number of time steps equal to the number of…
A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a…
Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which $P(\mathbb{N})$ is complete. The collection $D$ of sets with asymptotic density is closed in this pseudometric, and closed…
Composite likelihood has shown promise in settings where the number of parameters $p$ is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable.…
Let S be a topological property of sequences (such as, for example, "to contain a convergent subsequence" or "to have an accumulation point"). We introduce the following open-point game OP(X,S) on a topological space X. In the n'th move,…
This paper proposes a theory of encapsulation, establishing a relationship between encapsulation and information hiding through the concept of potential structural complexity (P.S.C.), the maximum possible number of source code dependencies…
We give a light introduction to selection principles in topology, a young subfield of infinite-combinatorial topology. Emphasis is put on the modern approach to the problems it deals with. Recent results are described, and open problems are…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
For a pair of spaces $X$ and $Y$ such that $Y \subseteq X$, we define the relative topological complexity of the pair $(X,Y)$ as a new variant of relative topological complexity. Intuitively, this corresponds to counting the smallest number…
Let S be a set of states of a physical system and p(s) the probability of the occurrence of an event when the system is in state s. A function p from S to [0,1] is called a numerical event or alternatively, an S-probability. If a set P of…
We give a characterization of countable discrete subspace $A$ of a topological space $X$ such that there exists a (linear) continuous mapping $\varphi:C_p^*(A)\to C_p(X)$ with $\varphi(y)|_A=y$ for every $y\in C_p^*(A)$. Using this…
We consider a random generalisation of the classical Fibonacci substitution. The substitution we consider is defined as the rule mapping $\mathtt{a}\mapsto \mathtt{baa}$ and $\mathtt{b} \mapsto \mathtt{ab}$ with probability $p$ and…
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.