68,635 research outputs found
Curriculum Guidelines for Undergraduate Programs in Data Science
The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program
met for the purpose of composing guidelines for undergraduate programs in Data
Science. The group consisted of 25 undergraduate faculty from a variety of
institutions in the U.S., primarily from the disciplines of mathematics,
statistics and computer science. These guidelines are meant to provide some
structure for institutions planning for or revising a major in Data Science
Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond
There is a hidden intrigue in the title. CT is one of the most abstract
mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a
recent trend in software development, industrially supported by standards,
tools, and the status of a new "silver bullet". Surprisingly, categorical
patterns turn out to be directly applicable to mathematical modeling of
structures appearing in everyday MDE practice. Model merging, transformation,
synchronization, and other important model management scenarios can be seen as
executions of categorical specifications.
Moreover, the paper aims to elucidate a claim that relationships between CT
and MDE are more complex and richer than is normally assumed for "applied
mathematics". CT provides a toolbox of design patterns and structural
principles of real practical value for MDE. We will present examples of how an
elementary categorical arrangement of a model management scenario reveals
deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
The unexpected resurgence of Weyl geometry in late 20-th century physics
Weyl's original scale geometry of 1918 ("purely infinitesimal geometry") was
withdrawn by its author from physical theorizing in the early 1920s. It had a
comeback in the last third of the 20th century in different contexts: scalar
tensor theories of gravity, foundations of gravity, foundations of quantum
mechanics, elementary particle physics, and cosmology. It seems that Weyl
geometry continues to offer an open research potential for the foundations of
physics even after the turn to the new millennium.Comment: Completely rewritten conference paper 'Beyond Einstein', Mainz Sep
2008. Preprint ELHC (Epistemology of the LHC) 2017-02, 92 pages, 1 figur
Conservation of information and the foundations of quantum mechanics
We review a recent approach to the foundations of quantum mechanics inspired
by quantum information theory. The approach is based on a general framework,
which allows one to address a large class of physical theories which share
basic information-theoretic features. We first illustrate two very primitive
features, expressed by the axioms of causality and purity-preservation, which
are satisfied by both classical and quantum theory. We then discuss the axiom
of purification, which expresses a strong version of the Conservation of
Information and captures the core of a vast number of protocols in quantum
information. Purification is a highly non-classical feature and leads directly
to the emergence of entanglement at the purely conceptual level, without any
reference to the superposition principle. Supplemented by a few additional
requirements, satisfied by classical and quantum theory, it provides a complete
axiomatic characterization of quantum theory for finite dimensional systems.Comment: 11 pages, contribution to the Proceedings of the 3rd International
Conference on New Frontiers in Physics, July 28-August 6 2014, Orthodox
Academy of Crete, Kolymbari, Cret
Physics as Information Processing
I review some recent advances in foundational research at Pavia QUIT group.
The general idea is that there is only Quantum Theory without quantization
rules, and the whole Physics---including space-time and relativity--is emergent
from the quantum-information processing. And since Quantum Theory itself is
axiomatized solely on informational principles, the whole Physics must be
reformulated in information-theoretical terms: this is the "It from Bit of J.
A. Wheeler. The review is divided into four parts: a) the informational
axiomatization of Quantum Theory; b) how space-time and relativistic covariance
emerge from quantum computation; c) what is the information-theoretical meaning
of inertial mass and of , and how the quantum field emerges; d) an
observational consequence of the new quantum field theory: a mass-dependent
refraction index of vacuum. I will conclude with the research lines that will
follow in the immediate future.Comment: Work presented at the conference "Advances in Quantum Theory" held on
14-17 June 2010 at the Linnaeus University, Vaxjo, Swede
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