49,033 research outputs found
(M-theory-)Killing spinors on symmetric spaces
We show how the theory of invariant principal bundle connections for
reductive homogeneous spaces can be applied to determine the holonomy of
generalised Killing spinor covariant derivatives of the form in a purely algebraic and algorithmic way, where is a left-invariant homomorphism. Specialising this
to the case of symmetric M-theory backgrounds (i.e. with a
symmetric space and an invariant closed 4-form), we derive several criteria
for such a background to preserve some supersymmetry and consequently find all
supersymmetric symmetric M-theory backgrounds.Comment: Updated abstract for clarity. Added missing geometries to section 6.
Main result stand
Computation of Galois groups of rational polynomials
Computational Galois theory, in particular the problem of computing the
Galois group of a given polynomial is a very old problem. Currently, the best
algorithmic solution is Stauduhar's method. Computationally, one of the key
challenges in the application of Stauduhar's method is to find, for a given
pair of groups H<G a G-relative H-invariant, that is a multivariate polynomial
F that is H-invariant, but not G-invariant. While generic, theoretical methods
are known to find such F, in general they yield impractical answers. We give a
general method for computing invariants of large degree which improves on
previous known methods, as well as various special invariants that are derived
from the structure of the groups. We then apply our new invariants to the task
of computing the Galois groups of polynomials over the rational numbers,
resulting in the first practical degree independent algorithm.Comment: Improved version and new titl
Scanner Invariant Representations for Diffusion MRI Harmonization
Purpose: In the present work we describe the correction of diffusion-weighted
MRI for site and scanner biases using a novel method based on invariant
representation.
Theory and Methods: Pooled imaging data from multiple sources are subject to
variation between the sources. Correcting for these biases has become very
important as imaging studies increase in size and multi-site cases become more
common. We propose learning an intermediate representation invariant to
site/protocol variables, a technique adapted from information theory-based
algorithmic fairness; by leveraging the data processing inequality, such a
representation can then be used to create an image reconstruction that is
uninformative of its original source, yet still faithful to underlying
structures. To implement this, we use a deep learning method based on
variational auto-encoders (VAE) to construct scanner invariant encodings of the
imaging data.
Results: To evaluate our method, we use training data from the 2018 MICCAI
Computational Diffusion MRI (CDMRI) Challenge Harmonization dataset. Our
proposed method shows improvements on independent test data relative to a
recently published baseline method on each subtask, mapping data from three
different scanning contexts to and from one separate target scanning context.
Conclusion: As imaging studies continue to grow, the use of pooled multi-site
imaging will similarly increase. Invariant representation presents a strong
candidate for the harmonization of these data
Emergence and algorithmic information dynamics of systems and observers
Previous work has shown that perturbation analysis in software space can
produce candidate computable generative models and uncover possible causal
properties from the finite description of an object or system quantifying the
algorithmic contribution of each of its elements relative to the whole. One of
the challenges for defining emergence is that one observer's prior knowledge
may cause a phenomenon to present itself to such observer as emergent while for
another as reducible. When attempting to quantify emergence, we demonstrate
that the methods of Algorithmic Information Dynamics can deal with the richness
of such observer-object dependencies both in theory and practice. By
formalising the act of observing as mutual algorithmic perturbation, the
emergence of algorithmic information is rendered invariant, minimal, and robust
in the face of information cost and distortion, while still observer-dependent.
We demonstrate that the unbounded increase of emergent algorithmic information
implies asymptotically observer-independent emergence, which eventually
overcomes any formal theory that an observer might devise to finitely
characterise a phenomenon. We discuss observer-dependent emergence and
asymptotically observer-independent emergence solving some previous suggestions
indicating a hard distinction between strong and weak emergence
A Local Deterministic Model of Quantum Spin Measurement
The conventional view, that Einstein was wrong to believe that quantum
physics is local and deterministic, is challenged. A parametrised model, Q, for
the state vector evolution of spin 1/2 particles during measurement is
developed. Q draws on recent work on so-called riddled basins in dynamical
systems theory, and is local, deterministic, nonlinear and time asymmetric.
Moreover the evolution of the state vector to one of two chaotic attractors
(taken to represent observed spin states) is effectively uncomputable.
Motivation for this model arises from Penrose's speculations about the nature
and role of quantum gravity. Although the evolution of Q's state vector is
uncomputable, the probability that the system will evolve to one of the two
attractors is computable. These probabilities correspond quantitatively to the
statistics of spin 1/2 particles. In an ensemble sense the evolution of the
state vector towards an attractor can be described by a diffusive random walk.
Bell's theorem and a version of the Bell-Kochen_specker quantum entanglement
paradox are discussed. It is shown that proving an inconsistency with locality
demands the existence of definite truth values to certain counterfactual
propositions. In Q these deterministic propositions are physically uncomputable
and no non-algorithmic solution is either known or suspected. Adapting the
mathematical formalist approach, the non-existence of definite truth values to
such counterfactual propositions is posited. No inconsistency with experiment
is found. Hence Q is not necessarily constrained by Bell's inequality.Comment: This paper has been accepted for publication in the Proceedings of
the Royal Society of London (Proc.Roy.Soc.A) I will mail the paper's figures
on request (write to [email protected]
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