6,627 research outputs found
Profinite Galois descent in K(h)-local homotopy theory
We investigate the category of K(h)-local spectra through the action of the Morava stabiliser group. Using condensed mathematics, we give a model for the continuous action of this profinite group on the ∞-category of K(h)-local modules over Morava E-theory, and explain how this gives rise to descent spectral sequences computing the Picard and Brauer groups of K(h)-local spectra. In the second part, we focus on the computation of these spectral sequences at height one, showing that they recover the Hopkins-Mahowald-Sadofsky computation of the Picard group, and giving a complete computation of the Brauer group relative to p-completed complex K-theory
UMSL Bulletin 2023-2024
The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp
Multidisciplinary perspectives on Artificial Intelligence and the law
This open access book presents an interdisciplinary, multi-authored, edited collection of chapters on Artificial Intelligence (‘AI’) and the Law. AI technology has come to play a central role in the modern data economy. Through a combination of increased computing power, the growing availability of data and the advancement of algorithms, AI has now become an umbrella term for some of the most transformational technological breakthroughs of this age. The importance of AI stems from both the opportunities that it offers and the challenges that it entails. While AI applications hold the promise of economic growth and efficiency gains, they also create significant risks and uncertainty. The potential and perils of AI have thus come to dominate modern discussions of technology and ethics – and although AI was initially allowed to largely develop without guidelines or rules, few would deny that the law is set to play a fundamental role in shaping the future of AI. As the debate over AI is far from over, the need for rigorous analysis has never been greater. This book thus brings together contributors from different fields and backgrounds to explore how the law might provide answers to some of the most pressing questions raised by AI. An outcome of the Católica Research Centre for the Future of Law and its interdisciplinary working group on Law and Artificial Intelligence, it includes contributions by leading scholars in the fields of technology, ethics and the law.info:eu-repo/semantics/publishedVersio
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
One stone, two birds: A lightweight multidimensional learned index with cardinality support
Innovative learning based structures have recently been proposed to tackle
index and cardinality estimation tasks, specifically learned indexes and data
driven cardinality estimators. These structures exhibit excellent performance
in capturing data distribution, making them promising for integration into AI
driven database kernels. However, accurate estimation for corner case queries
requires a large number of network parameters, resulting in higher computing
resources on expensive GPUs and more storage overhead. Additionally, the
separate implementation for CE and learned index result in a redundancy waste
by storage of single table distribution twice. These present challenges for
designing AI driven database kernels. As in real database scenarios, a compact
kernel is necessary to process queries within a limited storage and time
budget. Directly integrating these two AI approaches would result in a heavy
and complex kernel due to a large number of network parameters and repeated
storage of data distribution parameters. Our proposed CardIndex structure
effectively killed two birds with one stone. It is a fast multidim learned
index that also serves as a lightweight cardinality estimator with parameters
scaled at the KB level. Due to its special structure and small parameter size,
it can obtain both CDF and PDF information for tuples with an incredibly low
latency of 1 to 10 microseconds. For tasks with low selectivity estimation, we
did not increase the model's parameters to obtain fine grained point density.
Instead, we fully utilized our structure's characteristics and proposed a
hybrid estimation algorithm in providing fast and exact results
Higher Geometric Structures on Manifolds and the Gauge Theory of Deligne Cohomology
We study smooth higher symmetry groups and moduli -stacks of generic
higher geometric structures on manifolds. Symmetries are automorphisms which
cover non-trivial diffeomorphisms of the base manifold. We construct the smooth
higher symmetry group of any geometric structure on and show that this
completely classifies, via a universal property, equivariant structures on the
higher geometry. We construct moduli stacks of higher geometric data as
-categorical quotients by the action of the higher symmetries, extract
information about the homotopy types of these moduli -stacks, and prove
a helpful sufficient criterion for when two such higher moduli stacks are
equivalent.
In the second part of the paper we study higher -connections.
First, we observe that higher connections come organised into higher groupoids,
which further carry affine actions by Baez-Crans-type higher vector spaces. We
compute a presentation of the higher gauge actions for -gerbes with
-connection, comment on the relation to higher-form symmetries, and present
a new String group model. We construct smooth moduli -stacks of higher
Maxwell and Einstein-Maxwell solutions, correcting previous such considerations
in the literature, and compute the homotopy groups of several moduli
-stacks of higher - connections. Finally, we show that a
discrepancy between two approaches to the differential geometry of NSNS
supergravity (via generalised and higher geometry, respectively) vanishes at
the level of moduli -stacks of NSNS supergravity solutions.Comment: 102 pages; comments welcom
An injectivity theorem on snc compact K\"ahler spaces: an application of the theory of harmonic integrals on log-canonical centers via adjoint ideal sheaves
Let be a log-canonical (lc) pair, in which is a compact K\"ahler
manifold and is a reduced snc divisor, and let be a holomorphic line
bundle on equipped with a smooth metric . Via the use
of the adjoint ideal sheaves (constructed from and ) and the
associated residue morphisms, sections of on
(as well as those of on ) can be related to
the -valued holomorphic top-forms on each lc center of by an
inductive use of a certain residue exact sequence derived from the adjoint
ideal sheaves. The theory of harmonic integrals is valid on each lc center
(which is compact K\"ahler), so this provides a pathway to apply the techniques
in harmonic theory to the possibly singular K\"ahler space . To illustrate
the use of such apparatus in problems concerning lc pairs, we prove a
Koll\'ar-type injectivity theorem for the cohomology on when is
semi-positive. This in turn also solves the conjecture by Fujino on the
injectivity theorem for the compact K\"ahler lc pair , providing an
alternative proof of a recent result by Cao and P\u{a}un.Comment: 30 page
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