Related papers: Coding Polish spaces
We introduce a notion of equivariant coarse cohomology of the complement of a subspace in a metric space. We use this cohomology to define a notion of coarse cohomology of the configuration space of a metric space and develop tools to…
A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…
The large amount of cosmological data already available (and in the near future) makes necessary the development of efficient numerical codes. Many software products have been implemented to perform cosmological analyses considering one or…
In this paper we develop a technique of constructing uni- formly continuous maps between function spaces Cp(X) endowed with the pointwise topology. We prove that if a space X is compact metrizable and strongly countable-dimensional, then…
We design hypersequent calculus proof systems for the theories of Riesz spaces and modal Riesz spaces and prove the key theorems: soundness, completeness and cut elimination. These are then used to obtain completely syntactic proofs of some…
Let $\Gamma$ be a Polish space and let $K$ be a separable and pointwise compact set of real-valued functions on $\Gamma$. It is shown that if each function in $K$ has only countably many discontinuities then $C(K)$ may be equipped with a…
We provide sufficient conditions for uniqueness of an invariant probability measure of a Markov kernel in terms of (generalized) couplings. Our main theorem generalizes previous results which require the state space to be Polish. We provide…
We describe some Cartesian products of metric spaces and find conditions under which products of ultrametric spaces are ultrametric.
A Polish space is not always homeomorphic to a computably presented Polish space. In this article, we examine degrees of non-computability of presenting homeomorphic copies of compact Polish spaces. We show that there exists a…
We consider stability theory for Polish spaces and more generally for definable structures (say, with elements of a set of reals). We clarify by proving some equivalent conditions for $\aleph_0$-stability. We succeed to prove existence of…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
We associate to every action of a Polish group on a standard probability space a Polish group that we call the orbit full group. For discrete groups, we recover the well-known full groups of pmp equivalence relations equipped with the…
A space is functionally countable if every real-valued continuous function has countable image. A stronger property recently defined by Tkachuk is exponentially separability. We start by studying these properties in GO spaces, where we…
It is proved that two useful and apparently different metrics on the set of Borel probabilities on countable products of Polish spaces of bounded diameters are equal. This paves the way for advances in their computation.
Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and…
The interplay between process behaviour and spatial aspects of computation has become more and more relevant in Computer Science, especially in the field of collective adaptive systems, but also, more generally, when dealing with systems…
We consider the joint design of polar coding and higher-order modulation schemes for ever increased spectral efficiency. The close connection between the polar code construction and the multi-level coding approach is described in detail.…
Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on the world's largest computers are spent simulating problems…
Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch…
Parallel computing has turned out to be the enabling technology to solve complex physical systems. However, the transition from shared memory, vector computers to massively parallel, distributed memory systems and, recently, to hybrid…