Related papers: A new selection principle
Despite its omnipresence in robotics application, the nature of spatial knowledge and the mechanisms that underlie its emergence in autonomous agents are still poorly understood. Recent theoretical work suggests that the concept of space…
This study introduces a novel theoretical framework, the Stacked Autoencoder Evolution Hypothesis, which proposes that biological evolutionary systems operate through multi-layered self-encoding and decoding processes, analogous to stacked…
The continuity problem, i.e., the question whether effective maps between effectively given topological spaces are effectively continuous, is reconsidered. In earlier work it was shown that this is always the case, if the effective map also…
This is the first in a series of papers devoted to foundations of topological stacks. We begin developing a homotopy theory for topological stacks along the lines of classical homotopy theory of topological spaces. In this paper we go as…
We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…
Thermodynamic selection is an indirect competition between agents feeding on the same energy resource and obeying the laws of thermodynamics. We examine scenarios of this selection, where the agent is modeled as a heat-engine coupled to two…
Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system…
In this paper, we investigate what selection principles properties are possessed by small (with respect to the bounding and dominating numbers) unions of spaces with certain (star) selection principles.. Furthermore, we give several results…
One of the prime motivation for topology was Homotopy theory, which captures the general idea of a continuous transformation between two entities, which may be spaces or maps. In later decades, an algebraic formulation of topology was…
With the approaching TOPOSYM'16 (http://www.toposym.cz/programme.php), it is a pleasure to see selection principles gain increasing attention and becoming a standard part of topology and set theory. At least eight of the 28 speakers, and a…
We collect our recent results ([5] and [8]) and we get the equivalence of the three notions of the title under some conditions. We then use this equivalence in order to prove some consequences about Sasakian manifolds, complex almost…
We propose a novel method for selective classification (SC), a problem which allows a classifier to abstain from predicting some instances, thus trading off accuracy against coverage (the fraction of instances predicted). In contrast to…
Social networks are increasingly being used to conduct polls. We introduce a simple model of such social polling. We suppose agents vote sequentially, but the order in which agents choose to vote is not necessarily fixed. We also suppose…
The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the…
Recently, Acharjee et al. [S. Acharjee, M. \"Ozko\c{c} and F. Y. Issaka, Primal topological spaces, arXiv:2209.12676[math.GM]] introduced a new structure in topology named primal. Primal is the duel structure of grill. The main purpose of…
We summarize and deepen recent results on systems of orthogonal pure states on operator algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact spaces such as exposining points by…
The topological classification of all known non-magnetic crystalline compounds is now complete, revealing thousands of new candidate topological materials waiting to be explored in the lab.
We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and…
For a variety over certain topological rings $R$, like $\mathbb{Z}_p$ or $\mathbb{C}$, there is a well-studied way to topologize the $R$-points on the variety. In this paper, we generalize this definition to algebraic stacks. For an…
We use pointwise Kan extensions to generate new subcategories out of old ones. We investigate the properties of these newly produced categories and give sufficient conditions for their cartesian closedness to hold. Our methods are of…