5,048 research outputs found
More generalizations of pseudocompactness
We introduce a covering notion depending on two cardinals, which we call
--compactness, and which encompasses both
pseudocompactness and many other generalizations of pseudocompactness. For
Tychonoff spaces, pseudocompactness turns out to be equivalent to --compactness. We provide several characterizations of
--compactness, and we discuss its connection
with -pseudocompactness, for an ultrafilter. We analyze the behaviour of
the above notions with respect to products. Finally, we show that our results
hold in a more general framework, in which compactness properties are defined
relative to an arbitrary family of subsets of some topological space .Comment: 22 page
Relative Riemann-Zariski spaces
In this paper we study relative Riemann-Zariski spaces attached to a morphism
of schemes and generalizing the classical Riemann-Zariski space of a field. We
prove that similarly to the classical RZ spaces, the relative ones can be
described either as projective limits of schemes in the category of locally
ringed spaces or as certain spaces of valuations. We apply these spaces to
prove the following two new results: a strong version of stable modification
theorem for relative curves; a decomposition theorem which asserts that any
separated morphism between quasi-compact and quasi-separated schemes factors as
a composition of an affine morphism and a proper morphism. (In particular, we
obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat
Tensor network and (-adic) AdS/CFT
We use the tensor network living on the Bruhat-Tits tree to give a concrete
realization of the recently proposed -adic AdS/CFT correspondence (a
holographic duality based on the -adic number field ). Instead
of assuming the -adic AdS/CFT correspondence, we show how important features
of AdS/CFT such as the bulk operator reconstruction and the holographic
computation of boundary correlators are automatically implemented in this
tensor network.Comment: 59 pages, 18 figures; v3: improved presentation, added figures and
reference
LearnFCA: A Fuzzy FCA and Probability Based Approach for Learning and Classification
Formal concept analysis(FCA) is a mathematical theory based on lattice and order theory used for data analysis and knowledge representation. Over the past several years, many of its extensions have been proposed and applied in several domains including data mining, machine learning, knowledge management, semantic web, software development, chemistry ,biology, medicine, data analytics, biology and ontology engineering.
This thesis reviews the state-of-the-art of theory of Formal Concept Analysis(FCA) and its various extensions that have been developed and well-studied in the past several years. We discuss their historical roots, reproduce the original definitions and derivations with illustrative examples. Further, we provide a literature review of it’s applications and various approaches adopted by researchers in the areas of dataanalysis, knowledge management with emphasis to data-learning and classification problems.
We propose LearnFCA, a novel approach based on FuzzyFCA and probability theory for learning and classification problems. LearnFCA uses an enhanced version of FuzzyLattice which has been developed to store class labels and probability vectors and has the capability to be used for classifying instances with encoded and unlabelled features. We evaluate LearnFCA on encodings from three datasets - mnist, omniglot and cancer images with interesting results and varying degrees of success.
Adviser: Dr Jitender Deogu
Anti-unification and Generalization: A Survey
Anti-unification (AU), also known as generalization, is a fundamental
operation used for inductive inference and is the dual operation to
unification, an operation at the foundation of theorem proving. Interest in AU
from the AI and related communities is growing, but without a systematic study
of the concept, nor surveys of existing work, investigations7 often resort to
developing application-specific methods that may be covered by existing
approaches. We provide the first survey of AU research and its applications,
together with a general framework for categorizing existing and future
developments.Comment: Accepted at IJCAI 2023 - Survey Trac
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