158,625 research outputs found
Some Varieties of Superparadox. The implications of dynamic contradiction, the characteristic form of breakdown of breakdown of sense to which self-reference is prone
The Problem of the Paradoxes came to the fore in philosophy and mathematics with the discovery of Russell's Paradox in 1901. It is the "forgotten" intellectual-scientific problem of the Twentieth Century, because for more than sixty years a pretence was maintained, by a consensus of logicians, that the problem had been "solved"
Specious rules: an efficient and effective unifying method for removing misleading and uninformative patterns in association rule mining
We present theoretical analysis and a suite of tests and procedures for
addressing a broad class of redundant and misleading association rules we call
\emph{specious rules}. Specious dependencies, also known as \emph{spurious},
\emph{apparent}, or \emph{illusory associations}, refer to a well-known
phenomenon where marginal dependencies are merely products of interactions with
other variables and disappear when conditioned on those variables.
The most extreme example is Yule-Simpson's paradox where two variables
present positive dependence in the marginal contingency table but negative in
all partial tables defined by different levels of a confounding factor. It is
accepted wisdom that in data of any nontrivial dimensionality it is infeasible
to control for all of the exponentially many possible confounds of this nature.
In this paper, we consider the problem of specious dependencies in the context
of statistical association rule mining. We define specious rules and show they
offer a unifying framework which covers many types of previously proposed
redundant or misleading association rules. After theoretical analysis, we
introduce practical algorithms for detecting and pruning out specious
association rules efficiently under many key goodness measures, including
mutual information and exact hypergeometric probabilities. We demonstrate that
the procedure greatly reduces the number of associations discovered, providing
an elegant and effective solution to the problem of association mining
discovering large numbers of misleading and redundant rules.Comment: Note: This is a corrected version of the paper published in SDM'17.
In the equation on page 4, the range of the sum has been correcte
Quantum Information Paradox: Real or Fictitious?
One of the outstanding puzzles of theoretical physics is whether quantum
information indeed gets lost in the case of Black Hole (BH) evaporation or
accretion. Let us recall that Quantum Mechanics (QM) demands an upper limit on
the acceleration of a test particle. On the other hand, it is pointed out here
that, if a Schwarzschild BH would exist, the acceleration of the test particle
would blow up at the event horizon in violation of QM. Thus the concept of an
exact BH is in contradiction of QM and quantum gravity (QG). It is also
reminded that the mass of a BH actually appears as an INTEGRATION CONSTANT of
Einstein equations. And it has been shown that the value of this integration
constant is actually zero. Thus even classically, there cannot be finite mass
BHs though zero mass BH is allowed. It has been further shown that during
continued gravitational collapse, radiation emanating from the contracting
object gets trapped within it by the runaway gravitational field. As a
consequence, the contracting body attains a quasi-static state where outward
trapped radiation pressure gets balanced by inward gravitational pull and the
ideal classical BH state is never formed in a finite proper time. In other
words, continued gravitational collapse results in an "Eternally Collapsing
Object" which is a ball of hot plasma and which is asymptotically approaching
the true BH state with M=0 after radiating away its entire mass energy. And if
we include QM, this contraction must halt at a radius suggested by highest QM
acceleration. In any case no EH is ever formed and in reality, there is no
quantum information paradox.Comment: 8 pages in Pramana Style, 6 in Revtex styl
Resolution of the Klein Paradox
We present a resolution of the Klein paradox within the framework of
one-particle relativistic quantum mechanics. Not only reflection becomes total
but the vacuum remains neutral as well. This is accomplished by replacing the
pair production process with virtual negative energy "incidence" within the
barrier in a similar manner to what is done with image charges in electrostatic
and virtual sources in optics.Comment: 9 pages, 8 figure
The physical basis for Parrondo's games
Several authors have implied that the original inspiration for Parrondo's
games was a physical system called a ``flashing Brownian ratchet''. The
relationship seems to be intuitively clear but, surprisingly, has not yet been
established with rigor. In this paper, we apply standard finite-difference
methods of numerical analysis to the Fokker-Planck equation. We derive a set of
finite difference equations and show that they have the same form as Parrondo's
games. Parrondo's games, are in effect, a particular way of sampling a
Fokker-Planck equation. Physical Brownian ratchets have been constructed and
have worked. It is hoped that the finite element method presented here will be
useful in the simulation and design of flashing Brownian ratchets.Comment: 10 pages and 2 figure
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