102,386 research outputs found
Holism, Physical Theories and Quantum Mechanics
Motivated by the question what it is that makes quantum mechanics a holistic
theory (if so), I try to define for general physical theories what we mean by
`holism'. For this purpose I propose an epistemological criterion to decide
whether or not a physical theory is holistic, namely: a physical theory is
holistic if and only if it is impossible in principle to infer the global
properties, as assigned in the theory, by local resources available to an
agent. I propose that these resources include at least all local operations and
classical communication. This approach is contrasted with the well-known
approaches to holism in terms of supervenience. The criterion for holism
proposed here involves a shift in emphasis from ontology to epistemology. I
apply this epistemological criterion to classical physics and Bohmian mechanics
as represented on a phase and configuration space respectively, and for quantum
mechanics (in the orthodox interpretation) using the formalism of general
quantum operations as completely positive trace non-increasing maps.
Furthermore, I provide an interesting example from which one can conclude that
quantum mechanics is holistic in the above mentioned sense, although, perhaps
surprisingly, no entanglement is needed.Comment: Published versio
Power of unentangled measurements on two antiparallel spins
We consider a pair of antiparallel spins polarized in a random direction to
encode quantum information. We wish to extract as much information as possible
on the polarization direction attainable by an unentangled measurement, i.e.,
by a measurement, whose outcomes are associated with product states. We develop
analytically the upper bound 0.7935 bits to the Shannon mutual information
obtainable by an unentangled measurement, which is definitely less than the
value 0.8664 bits attained by an entangled measurement. This proves our main
result, that not every ensemble of product states can be optimally
distinguished by an unentangled measurement, if the measure of
distinguishability is defined in the sense of Shannon. We also present results
from numerical calculations and discuss briefly the case of parallel spins.Comment: Latex file, 18 pages, 1 figure; published versio
Disentangling agglomeration and network externalities : a conceptual typology
Agglomeration and network externalities are fuzzy concepts. When different meanings are (un)intentionally juxtaposed in analyses of the agglomeration/network externalities-menagerie, researchers may reach inaccurate conclusions about how they interlock. Both externality types can be analytically combined, but only when one adopts a coherent approach to their conceptualization and operationalization, to which end we provide a combinatorial typology. We illustrate the typology by applying a state-of-the-art bipartite network projection detailing the presence of globalized producer services firms in cities in 2012. This leads to two one-mode graphs that can be validly interpreted as topological renderings of agglomeration and network externalities
Cosmological gravitomagnetism and Mach's principle
The spin axes of gyroscopes experimentally define local non-rotating frames.
But what physical cause governs the time-evolution of gyroscope axes? We
consider linear perturbations of Friedmann-Robertson-Walker cosmologies with
k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin
axes of gyroscopes relative to the directions of geodesics to quasars in the
asymptotic unperturbed FRW space? Using Cartan's formalism with local
orthonormal bases we cast the laws of linear cosmological gravitomagnetism into
a form showing the close correspondence with the laws of ordinary magnetism.
Our results, valid for any equation of state for cosmological matter, are: 1)
The dragging of a gyroscope axis by rotational perturbations of matter beyond
the Hubble-dot radius from the gyroscope is exponentially suppressed, where dot
is the derivative with respect to cosmic time. 2) If the perturbation of matter
is a homogeneous rotation inside some radius around a gyroscope, then exact
dragging of the gyroscope axis by the rotational perturbation is reached
exponentially fast as the rotation radius grows beyond the H-dot radius. 3) For
the most general linear cosmological perturbations the time-evolution of all
gyroscope spin axes exactly follow a weighted average of the energy currents of
cosmological matter. The weight function is the same as in Ampere's law except
that the inverse square law is replaced by the Yukawa force with the Hubble-dot
cutoff. Our results demonstrate (in first order perturbation theory for FRW
cosmologies with k = 0) the validity of Mach's hypothesis that axes of local
non-rotating frames precisely follow an average of the motion of cosmic matter.Comment: 18 pages, 1 figure. Comments and references adde
Ultrametric embedding: application to data fingerprinting and to fast data clustering
We begin with pervasive ultrametricity due to high dimensionality and/or
spatial sparsity. How extent or degree of ultrametricity can be quantified
leads us to the discussion of varied practical cases when ultrametricity can be
partially or locally present in data. We show how the ultrametricity can be
assessed in text or document collections, and in time series signals. An aspect
of importance here is that to draw benefit from this perspective the data may
need to be recoded. Such data recoding can also be powerful in proximity
searching, as we will show, where the data is embedded globally and not locally
in an ultrametric space.Comment: 14 pages, 1 figure. New content and modified title compared to the 19
May 2006 versio
Visual illusions: An interesting tool to investigate developmental dyslexia and autism spectrum disorder
A visual illusion refers to a percept that is different in some aspect from the physical stimulus. Illusions are a powerful non-invasive tool for understanding the neurobiology of vision, telling us, indirectly, how the brain processes visual stimuli. There are some neurodevelopmental disorders characterized by visual deficits. Surprisingly, just a few studies investigated illusory perception in clinical populations. Our aim is to review the literature supporting a possible role for visual illusions in helping us understand the visual deficits in developmental dyslexia and autism spectrum disorder. Future studies could develop new tools – based on visual illusions – to identify an early risk for neurodevelopmental disorders
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