1,676 research outputs found
Nowhere dense graph classes, stability, and the independence property
A class of graphs is nowhere dense if for every integer r there is a finite
upper bound on the size of cliques that occur as (topological) r-minors. We
observe that this tameness notion from algorithmic graph theory is essentially
the earlier stability theoretic notion of superflatness. For subgraph-closed
classes of graphs we prove equivalence to stability and to not having the
independence property.Comment: 9 page
Was heißt Fortschritt im Wissen? Gnoseotopische Überlegungen zur Aufklärung und ihren Folgen
This article focuses on the question of what “progress in knowledge” (Fortschritt im Wissen) since the Enlightenment could mean. The answer is rooted in a shift in perspective in our understanding of the Enlightenment, and in an awareness of the gnoseotope at the center of this perspectival shift. Given the fact that human knowledge has always been considered limited, the axiom called gnoseotope (from Greek gnōsis: cognition, knowledge and topos: place, area, field) can be defined as the area of relatively secure knowledge, which is subject to both quantitative (cumulative) and qualitative (paradigmatic) historical changes. Considering the further fact that human ignorance has been acknowledged since Antiquity and taken for granted for millennia of human history, the awareness of this ignorance becomes particularly problematic during the Enlightenment when irreducible yet systematically repressed elements of human ignorance were integrated into the epistemology of 18th-century rationalism. This article discusses the development in the shift from ignorance as a given to ignorance as a systematically reflected part of the conditions of human knowledge from a historical point of view through the examples of Christian Wolff, Alexander Gottlieb Baumgarten, and Johann Georg Sulzer. The argument does not focus on the ‘completion’ of the rationalist system of 18th-century philosophy, but rather on the subversive quality of the introduction of subrational elements into that system, resulting in the ultimate breakdown of the system and in the expansion of the horizon of the Enlightenment gnoseotope. In this sense, the Enlightenment can be seen as expanding from from an age (“Enlightenment” with an upper-case “E”) to a method (“enlightenment” with a lower-case “e”). The article concludes with recent debates (as initiated by Ulrich Beck, Rainer Specht, and contemporary natural scientists) about the effects that a gnoseotopical perspective has on globalization and ecological politics, and more broadly with reflections on the current need for core Enlightenment ideas in their full complexity
Teaching It In A Knowledge Economy Raising Tacit Productivity
The growth of interactions represents a broad shift in the nature of economic activity. Interactions are defined as the searching, coordinating, and monitoring that people and firms do when they exchange goods, services, or ideas, for many employees today, collaborative, complex problem solving is the essence of their work, these “tacit” activates -- involving the exchange of information, the making of judgments, and a need to draw on multifaceted forms of knowledge in exchanges with coworkers, customers, and suppliers – are increasingly a part of the standard model for companies in the developed world
An approach to popular medicine in Ubrique (1996-1997)
La necesidad de curar una enfermedad es
consustancial a la evolución de la especie
humana. En el proceso de desarrollo como
civilización, los mecanismos empleados para conseguir
este fin han ido parejos con el aumento de
conocimientos en diferentes ramas del saber.
Conforme iba avanzando la técnica, otros mecanismos
más antiguos quedaban relegados en segundo
término o, incluso, eran definitivamente dados de
lado en beneficio del saber emergente.
En Medicina, en cambio, la esencia de la enfermedad,
no bien conocida o asimilada por las personas
enfermas y sanas, ha permitido que técnicas,
remedios y formas de actuar que se podría creer
quedaron superadas por otra Medicina más tecnificada
hayan perdurado y sean incluso ampliamente
utilizadas en la actualidad.
El lugar escogido para la realización del trabajo
es Ubrique, donde se han entrevistado 43 personas
que han aportado información diversa tanto
sobre enfermedades o problemas de salud como
sobre los remedios más útiles.The need to cure illness is inherent to evolution
of human mankind. In its developmental
process as a civilization, the means for
this aim have accompanied the increasing knowledge
in all areas of wisdom. As technique improved,
ancient methods were forgotten or relegated
by the emergent knowledge.
Regarding Medicine, on the contrary, the
essence of illness having not been known or accepted
by healthy and sick has allowed techniques,
remedies and methods to live through modern
Medicine and be used nowadays.
The chosen setting for this work is Ubrique,
where 43 interviewed people have furnished us
with information on disorders or health problems
and useful remedies
The Attractor and the Quantum States
The dissipative dynamics anticipated in the proof of 't Hooft's existence
theorem -- "For any quantum system there exists at least one deterministic
model that reproduces all its dynamics after prequantization" -- is constructed
here explicitly. We propose a generalization of Liouville's classical phase
space equation, incorporating dissipation and diffusion, and demonstrate that
it describes the emergence of quantum states and their dynamics in the
Schroedinger picture. Asymptotically, there is a stable ground state and two
decoupled sets of degrees of freedom, which transform into each other under the
energy-parity symmetry of Kaplan and Sundrum. They recover the familiar Hilbert
space and its dual. Expectations of observables are shown to agree with the
Born rule, which is not imposed a priori. This attractor mechanism is
applicable in the presence of interactions, to few-body or field theories in
particular.Comment: 14 pages; based on invited talk at 4th Workshop ad memoriam of Carlo
Novero "Advances in Foundations of Quantum Mechanics and Quantum Information
with Atoms and Photons", Torino, May 2008; submitted to Int J Qu Inf
A path integral for classical dynamics, entanglement, and Jaynes-Cummings model at the quantum-classical divide
The Liouville equation differs from the von Neumann equation 'only' by a
characteristic superoperator. We demonstrate this for Hamiltonian dynamics, in
general, and for the Jaynes-Cummings model, in particular. -- Employing
superspace (instead of Hilbert space), we describe time evolution of density
matrices in terms of path integrals which are formally identical for quantum
and classical mechanics. They only differ by the interaction contributing to
the action. This allows to import tools developed for Feynman path integrals,
in order to deal with superoperators instead of quantum mechanical commutators
in real time evolution. Perturbation theory is derived. Besides applications in
classical statistical physics, the "classical path integral" and the parallel
study of classical and quantum evolution indicate new aspects of (dynamically
assisted) entanglement (generation). Our findings suggest to distinguish
'intra'- from 'inter-space' entanglement.Comment: 22 pages; based on invited talk at Quantum 2010 - Advances in
Foundations of Quantum mechanics and Quantum Information with Atoms and
Photons (Torino, May 2010). To appear in Int. J. Qu. Inf
Interpreting nowhere dense graph classes as a classical notion of model theory
A class of graphs is nowhere dense if for every integer r there is a finite upper bound on the size of complete graphs that occur as r-minors. We observe that this recent tameness notion from (algorithmic) graph theory is essentially the earlier stability theoretic notion of superflatness. For subgraph-closed classes of graphs we prove equivalence to stability and to not having the independence property. Expressed in terms of PAC learning, the concept classes definable in first-order logic in a subgraph-closed graph class have bounded sample complexity, if and only if the class is nowhere dense
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