4,485 research outputs found
Control theoretically explainable application of autoencoder methods to fault detection in nonlinear dynamic systems
This paper is dedicated to control theoretically explainable application of
autoencoders to optimal fault detection in nonlinear dynamic systems.
Autoencoder-based learning is a standard method of machine learning technique
and widely applied for fault (anomaly) detection and classification. In the
context of representation learning, the so-called latent (hidden) variable
plays an important role towards an optimal fault detection. In ideal case, the
latent variable should be a minimal sufficient statistic. The existing
autoencoder-based fault detection schemes are mainly application-oriented, and
few efforts have been devoted to optimal autoencoder-based fault detection and
explainable applications. The main objective of our work is to establish a
framework for learning autoencoder-based optimal fault detection in nonlinear
dynamic systems. To this aim, a process model form for dynamic systems is
firstly introduced with the aid of control and system theory, which also leads
to a clear system interpretation of the latent variable. The major efforts are
devoted to the development of a control theoretical solution to the optimal
fault detection problem, in which an analog concept to minimal sufficient
statistic, the so-called lossless information compression, is introduced for
dynamic systems and fault detection specifications. In particular, the
existence conditions for such a latent variable are derived, based on which a
loss function and further a learning algorithm are developed. This learning
algorithm enables optimally training of autoencoders to achieve an optimal
fault detection in nonlinear dynamic systems. A case study on three-tank system
is given at the end of this paper to illustrate the capability of the proposed
autoencoder-based fault detection and to explain the essential role of the
latent variable in the proposed fault detection system
Foundations for a theory of emergent quantum mechanics and emergent classical gravity
Quantum systems are viewed as emergent systems from the fundamental degrees
of freedom. The laws and rules of quantum mechanics are understood as an
effective description, valid for the emergent systems and specially useful to
handle probabilistic predictions of observables. After introducing the
geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert
space theory, a Hilbert space structure is constructed from the Hilbert space
formulation of the underlying Hamilton-Randers model and associated with the
space of wave functions of quantum mechanical systems. We can prove the
emergence of the Born rule from ergodic considerations. A geometric mechanism
for a natural spontaneous collapse of the quantum states based on the
concentration of measure phenomena as it appears in metric geometry is
discussed.We show the existence of stable vacua states for the quantized matter
Hamiltonian. Another consequence of the concentration of measure is the
emergence of a weak equivalence principle for one of the dynamics of the
fundamental degrees of freedom. We suggest that the reduction of the quantum
state is driven by a gravitational type interaction.
Such interaction appears only in the dynamical domain when localization of
quantum observables happens, it must be a classical interaction. We discuss the
double slit experiment in the context of the framework proposed, the
interference phenomena associated with a quantum system in an external
gravitational potential, a mechanism explaining non-quantum locality and also
provide an argument in favour of an emergent interpretation of every
macroscopic time parameter. Entanglement is partially described in the context
of Hamilton-Randers theory and how naturally Bell's inequalities should be
violated.Comment: Extensive changes in chapter 1 and chapter 2; minor changes in other
chapters; several refereces added and others update; 192 pages including
index of contents and reference
Unveiling the Dynamics of the Universe
We explore the dynamics and evolution of the Universe at early and late
times, focusing on both dark energy and extended gravity models and their
astrophysical and cosmological consequences. Modified theories of gravity not
only provide an alternative explanation for the recent expansion history of the
universe, but they also offer a paradigm fundamentally distinct from the
simplest dark energy models of cosmic acceleration. In this review, we perform
a detailed theoretical and phenomenological analysis of different modified
gravity models and investigate their consistency. We also consider the
cosmological implications of well motivated physical models of the early
universe with a particular emphasis on inflation and topological defects.
Astrophysical and cosmological tests over a wide range of scales, from the
solar system to the observable horizon, severely restrict the allowed models of
the Universe. Here, we review several observational probes -- including
gravitational lensing, galaxy clusters, cosmic microwave background temperature
and polarization, supernova and baryon acoustic oscillations measurements --
and their relevance in constraining our cosmological description of the
Universe.Comment: 94 pages, 14 figures. Review paper accepted for publication in a
Special Issue of Symmetry. "Symmetry: Feature Papers 2016". V2: Matches
published version, now 79 pages (new format
Archipelagian Cosmology: Dynamics and Observables in a Universe with Discretized Matter Content
We consider a model of the Universe in which the matter content is in the
form of discrete islands, rather than a continuous fluid. In the appropriate
limits the resulting large-scale dynamics approach those of a
Friedmann-Robertson-Walker (FRW) universe. The optical properties of such a
space-time, however, do not. This illustrates the fact that the optical and
`average' dynamical properties of a relativistic universe are not equivalent,
and do not specify each other uniquely. We find the angular diameter distance,
luminosity distance and redshifts that would be measured by observers in these
space-times, using both analytic approximations and numerical simulations.
While different from their counterparts in FRW, the effects found do not look
like promising candidates to explain the observations usually attributed to the
existence of Dark Energy. This incongruity with standard FRW cosmology is not
due to the existence of any unexpectedly large structures or voids in the
Universe, but only to the fact that the matter content of the Universe is not a
continuous fluid.Comment: 49 pages, 15 figures. Corrections made to description of lattice
constructio
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State of the Art of Level Set Methods in Segmentation and Registration of Medical Imaging Modalities
Segmentation of medical images is an important step in various applications such as visualization, quantitative analysis and image-guided surgery. Numerous segmentation methods have been developed in the past two decades for extraction of organ contours on medical images. Low-level segmentation methods, such as pixel-based clustering, region growing, and filter-based edge detection, require additional pre-processing and post-processing as well as considerable amounts of expert intervention or information of the objects of interest. Furthermore the subsequent analysis of segmented objects is hampered by the primitive, pixel or voxel level representations from those region-based segmentation. Deformable models, on the other hand, provide an explicit representation of the boundary and the shape of the object. They combine several desirable features such as inherent connectivity and smoothness, which counteract noise and boundary irregularities, as well as the ability to incorporate knowledge about the object of interest. However, parametric deformable models have two main limitations. First, in situations where the initial model and desired object boundary differ greatly in size and shape, the model must be re-parameterized dynamically to faithfully recover the object boundary. The second limitation is that it has difficulty dealing with topological adaptation such as splitting or merging model parts, a useful property for recovering either multiple objects or objects with unknown topology. This difficulty is caused by the fact that a new parameterization must be constructed whenever topology change occurs, which requires sophisticated schemes. Level set deformable models, also referred to as geometric deformable models, provide an elegant solution to address the primary limitations of parametric deformable models. These methods have drawn a great deal of attention since their introduction in 1988. Advantages of the contour implicit formulation of the deformable model over parametric formulation include: (1) no parameterization of the contour, (2) topological flexibility, (3) good numerical stability, (4) straightforward extension of the 2D formulation to n-D. Recent reviews on the subject include papers from Suri. In this chapter we give a general overview of the level set segmentation methods with emphasize on new frameworks recently introduced in the context of medical imaging problems. We then introduce novel approaches that aim at combining segmentation and registration in a level set formulation. Finally we review a selective set of clinical works with detailed validation of the level set methods for several clinical applications
Continuous-variable optical quantum state tomography
This review covers latest developments in continuous-variable quantum-state
tomography of optical fields and photons, placing a special accent on its
practical aspects and applications in quantum information technology. Optical
homodyne tomography is reviewed as a method of reconstructing the state of
light in a given optical mode. A range of relevant practical topics are
discussed, such as state-reconstruction algorithms (with emphasis on the
maximum-likelihood technique), the technology of time-domain homodyne
detection, mode matching issues, and engineering of complex quantum states of
light. The paper also surveys quantum-state tomography for the transverse
spatial state (spatial mode) of the field in the special case of fields
containing precisely one photon.Comment: Finally, a revision! Comments to lvov(at)ucalgary.ca and
raymer(at)uoregon.edu are welcom
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