243,666 research outputs found
Resolution-scale relativistic formulation of non-differentiable mechanics
This article motivates and presents the scale relativistic approach to
non-differentiability in mechanics and its relation to quantum mechanics. It
stems from the scale relativity proposal to extend the principle of relativity
to resolution-scale transformations, which leads to considering
non-differentiable dynamical paths. We first define a complex scale-covariant
time-differential operator and show that mechanics of non-differentiable paths
is implemented in the same way as classical mechanics but with the replacement
of the time derivative and velocity with the time-differential operator and
associated complex velocity. With this, the generalized form of Newton's
fundamental relation of dynamics is shown to take the form of a Langevin
equation in the case of stationary motion characterized by a null average
classical velocity. The numerical integration of the Langevin equation in the
case of a harmonic oscillator taken as an example reveals the same statistics
as the stationary solutions of the Schrodinger equation for the same problem.
This motivates the rest of the paper, which shows Schrodinger's equation to be
a reformulation of Newton's fundamental relation of dynamics as generalized to
non-differentiable geometries and leads to an alternative interpretation of the
other axioms of standard quantum mechanics in a coherent picture. This exercise
validates the scale relativistic approach and, at the same time, it allows to
envision macroscopic chaotic systems observed at resolution time-scales
exceeding their horizon of predictability as candidates in which to search for
quantum-like dynamics and structures.Comment: 30 pages, 4 figure
SLT-Resolution for the Well-Founded Semantics
Global SLS-resolution and SLG-resolution are two representative mechanisms
for top-down evaluation of the well-founded semantics of general logic
programs. Global SLS-resolution is linear for query evaluation but suffers from
infinite loops and redundant computations. In contrast, SLG-resolution resolves
infinite loops and redundant computations by means of tabling, but it is not
linear. The principal disadvantage of a non-linear approach is that it cannot
be implemented using a simple, efficient stack-based memory structure nor can
it be easily extended to handle some strictly sequential operators such as cuts
in Prolog.
In this paper, we present a linear tabling method, called SLT-resolution, for
top-down evaluation of the well-founded semantics. SLT-resolution is a
substantial extension of SLDNF-resolution with tabling. Its main features
include: (1) It resolves infinite loops and redundant computations while
preserving the linearity. (2) It is terminating, and sound and complete w.r.t.
the well-founded semantics for programs with the bounded-term-size property
with non-floundering queries. Its time complexity is comparable with
SLG-resolution and polynomial for function-free logic programs. (3) Because of
its linearity for query evaluation, SLT-resolution bridges the gap between the
well-founded semantics and standard Prolog implementation techniques. It can be
implemented by an extension to any existing Prolog abstract machines such as
WAM or ATOAM.Comment: Slight modificatio
The Scaling Behaviour of Stochastic Minimization Algorithms in a Perfect Funnel Landscape
We determined scaling laws for the numerical effort to find the optimal configurations of a simple model potential energy surface (PES) with a perfect funnel structure that reflects key characteristics of the protein interactions. Generalized Monte-Carlo methods(MCM, STUN) avoid an enumerative search of the PES and thus provide a natural resolution of the Levinthal paradox. We find that the computational effort grows with approximately the eighth power of the system size for MCM and STUN, while a genetic algorithm was found to scale exponentially. The scaling behaviour of a derived lattice model is also rationalized
Application of Generalized Partial Volume Estimation for Mutual Information based Registration of High Resolution SAR and Optical Imagery
Mutual information (MI) has proven its effectiveness for automated multimodal image registration for numerous remote sensing applications like image fusion. We analyze MI performance with respect to joint histogram bin size and the employed joint histogramming technique. The affect of generalized partial volume estimation (GPVE) utilizing B-spline kernels with different histogram bin sizes on MI performance has been thoroughly explored for registration of high resolution SAR (TerraSAR-X) and optical (IKONOS-2) satellite images. Our experiments highlight possibility of an inconsistent MI behavior with different joint histogram bin size which gets reduced with an increase in order of B-spline kernel employed in GPVE. In general, bin size reduction and/or increasing B-spline order have a smoothing affect on MI surfaces and even the lowest order B-spline with a suitable histogram bin size can achieve same pixel level accuracy as achieved by the higher order kernels more consistently
DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL
We present the latest major release version 6.0 of the quantified Boolean
formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of
the conflict-driven clause learning (CDCL) paradigm implemented in state of the
art propositional satisfiability (SAT) solvers. The Q-resolution calculus
(QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce
QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of
the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0
implements a variant of QCDCL which is based on a generalization of QRES. This
generalization is due to a set of additional axioms and leaves the original
Q-resolution rules unchanged. The generalization of QRES enables QCDCL to
potentially produce exponentially shorter proofs than the traditional variant.
We present an overview of the features implemented in DepQBF and report on
experimental results which demonstrate the effectiveness of generalized QRES in
QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS,
Springer, 201
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