Weak bisimulations for the Giry monad

2010 ◽  
Vol 20 (5) ◽  
pp. 781-798
Author(s):  
ERNST-ERICH DOBERKAT
Keyword(s):  
Polish Spaces ◽  
Base Category ◽  
Giry Monad

We study the existence of bisimulations for Kleisli morphisms associated with the Giry monad of subprobabilities over Polish spaces. We first investigate these morphisms and show that the problem can be reduced to the existence of bisimulations for objects in the base category of stochastic relations using simulation equivalent congruences. This leads us to a criterion for two objects to be bisimilar.

scholarly journals Some Random Coupled Best Proximity Points for a Generalized ω-Cyclic Contraction in Polish Spaces

2017 ◽  
Vol 59 (1) ◽  
pp. 91-105 ◽  
Author(s):  
C. Kongban ◽  
P. Kumam
Keyword(s):  
Metric Spaces ◽  
Best Proximity Point ◽  
Cyclic Contraction ◽  
Polish Spaces ◽  
Best Proximity Points ◽  
Coupled Best Proximity Point

AbstractIn this paper, we will introduce the concepts of a random coupled best proximity point and then we prove the existence of random coupled best proximity points in separable metric spaces. Our results extend the previous work of Akbar et al.[1].

scholarly journals Graph directed Markov systems on Hilbert spaces

2009 ◽  
Vol 147 (2) ◽  
pp. 455-488 ◽  
Author(s):  
R. D. MAULDIN ◽  
T. SZAREK ◽  
M. URBAŃSKI
Keyword(s):  
Hausdorff Measure ◽  
Iterated Function System ◽  
Sufficient Conditions ◽  
Topological Pressure ◽  
Limit Set ◽  
Covering Theorem ◽  
Limit Sets ◽  
Markov Systems ◽  
Polish Spaces ◽  
Iterated Function

AbstractWe deal with contracting finite and countably infinite iterated function systems acting on Polish spaces, and we introduce conformal Graph Directed Markov Systems on Polish spaces. Sufficient conditions are provided for the closure of limit sets to be compact, connected, or locally connected. Conformal measures, topological pressure, and Bowen's formula (determining the Hausdorff dimension of limit sets in dynamical terms) are introduced and established. We show that, unlike the Euclidean case, the Hausdorff measure of the limit set of a finite iterated function system may vanish. Investigating this issue in greater detail, we introduce the concept of geometrically perfect measures and provide sufficient conditions for geometric perfectness. Geometrical perfectness guarantees the Hausdorff measure of the limit set to be positive. As a by–product of the mainstream of our investigations we prove a 4r–covering theorem for all metric spaces. It enables us to establish appropriate co–Frostman type theorems.

scholarly journals Closed categories generated by commutative monads

1971 ◽  
Vol 12 (4) ◽  
pp. 405-424 ◽  
Author(s):  
Anders Kock
Keyword(s):  
Adjoint Functors ◽  
Closed Category ◽  
Base Category

The notion of commutative monad was defined by the author in [4]. The content of the present paper may briefly be stated: The category of algebras for a commutative monad can in a canonical way be made into a closed category, the two adjoint functors connecting the category of algebras with the base category are in a canonical way closed functors, and the front- and end-adjunctions are closed transformations. (The terms ‘Closed Category’ etc. are from the paper [2] by Eilenberg and Kelly). In particular, the monad itself is a ‘closed monad’; this fact was also proved in [4].

scholarly journals Duality Theorem for a Minimax Vector Optimization Problem

2021 ◽  
Author(s):  
Jacob Atticus Armstrong Goodall
Keyword(s):  
Vector Optimization ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Optimal Transport ◽  
Probability Distributions ◽  
Vector Optimization Problem ◽  
Complexity Science ◽  
Polish Spaces ◽  
Leibler Divergence ◽  
Mathematical Optimisation

Abstract A duality theorem is stated and proved for a minimax vector optimization problem where the vectors are elements of the set of products of compact Polish spaces. A special case of this theorem is derived to show that two metrics on the space of probability distributions on countable products of Polish spaces are identical. The appendix includes a proof that, under the appropriate conditions, the function studied in the optimisation problem is indeed a metric. The optimisation problem is comparable to multi-commodity optimal transport where there is dependence between commodities. This paper builds on the work of R.S. MacKay who introduced the metrics in the context of complexity science in [4] and [5]. The metrics have the advantage of measuring distance uniformly over the whole network while other metrics on probability distributions fail to do so (e.g total variation, Kullback–Leibler divergence, see [5]). This opens up the potential of mathematical optimisation in the setting of complexity science.

scholarly journals Narratives Transcending Borders: Sabrina Janesch’s "Katzenberge" as a German Response to Polish Migration Literature

2020 ◽  
Vol 47 (2) ◽  
pp. 157-171
Author(s):  
Stephen Naumann
Keyword(s):  
World War Ii ◽  
Forced Migration ◽  
World War ◽  
Polish Spaces ◽  
Migration Literature ◽  
Polish Migration ◽  
Eastern Border ◽  
Border Narratives

The establishment of the Oder-Neisse border between Poland and Germany, as well as the westward shift of Poland’s eastern border resulted in migration for tens of millions in regions that had already been devastated by nearly a decade of forced evacuation, flight, war and genocide. In Poland, postwar authors such as Gdańsk’s own Stefan Chwin and Paweł Huelle have begun to establish a fascinating narrative connecting now-Polish spaces with what are at least in part non-Polish pasts. In Germany, meanwhile, coming to terms with a past that includes the Vertreibung, or forced migration, of millions of Germans during the mid-1940s has been limited at best, in no small part on account of its implication of Germans in the role of victim. In her 2010 debut novel Katzenberge, however, German author Sabrina Janesch employs a Polish migration story to connect with her German readers. Her narrator, like Janesch herself, is a young German who identifies with her Polish grandfather, whose death prompts her to trace the steps of his flight in 1945 from a Galician village to (then) German Silesia. This narrative, I argue, resonates with Janesch’s German audience because the expulsion experience is one with which they can identify. That it centers on Polish migration, however, not only avoids the context of guilt associated with German migration during World War II, but also creates an opportunity to better comprehend their Polish neighbors as well as the geographical spaces that connect them. Instead of allowing border narratives to be limited by the very border they attempt to define, engaging with multiple narratives of a given border provide enhanced meanings in local and national contexts and beyond. 

New Degree Spectra of Polish Spaces

2021 ◽  
Vol 62 (5) ◽  
pp. 882-894
Author(s):  
A. G. Melnikov
Keyword(s):  
Polish Spaces ◽  
Degree Spectra
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