633 research outputs found
Vacuum Geometry and the Search for New Physics
We propose a new guiding principle for phenomenology: special geometry in the
vacuum space. New algorithmic methods which efficiently compute geometric
properties of the vacuum space of N=1 supersymmetric gauge theories are
described. We illustrate the technique on subsectors of the MSSM. The fragility
of geometric structure that we find in the moduli space motivates
phenomenologically realistic deformations of the superpotential, while arguing
against others. Special geometry in the vacuum may therefore signal the
presence of string physics underlying the low-energy effective theory.Comment: 8 pages, LaTeX; v2: revised title, minor changes in wording,
reference adde
Visual Representations: Defining Properties and Deep Approximations
Visual representations are defined in terms of minimal sufficient statistics
of visual data, for a class of tasks, that are also invariant to nuisance
variability. Minimal sufficiency guarantees that we can store a representation
in lieu of raw data with smallest complexity and no performance loss on the
task at hand. Invariance guarantees that the statistic is constant with respect
to uninformative transformations of the data. We derive analytical expressions
for such representations and show they are related to feature descriptors
commonly used in computer vision, as well as to convolutional neural networks.
This link highlights the assumptions and approximations tacitly assumed by
these methods and explains empirical practices such as clamping, pooling and
joint normalization.Comment: UCLA CSD TR140023, Nov. 12, 2014, revised April 13, 2015, November
13, 2015, February 28, 201
Purposive three-dimensional reconstruction by means of a controlled environment
Retrieving 3D data using imaging devices is a relevant task for many applications in medical imaging, surveillance, industrial quality control, and others. As soon as we gain procedural control over parameters of the imaging device, we encounter the necessity of well-defined reconstruction goals and we need methods to achieve them. Hence, we enter next-best-view planning. In this work, we present a formalization of the abstract view planning problem and deal with different planning aspects, whereat we focus on using an intensity camera without active illumination. As one aspect of view planning, employing a controlled environment also provides the planning and reconstruction methods with additional information. We incorporate the additional knowledge of camera parameters into the Kanade-Lucas-Tomasi method used for feature tracking. The resulting Guided KLT tracking method benefits from a constrained optimization space and yields improved accuracy while regarding the uncertainty of the additional input. Serving other planning tasks dealing with known objects, we propose a method for coarse registration of 3D surface triangulations. By the means of exact surface moments of surface triangulations we establish invariant surface descriptors based on moment invariants. These descriptors allow to tackle tasks of surface registration, classification, retrieval, and clustering, which are also relevant to view planning. In the main part of this work, we present a modular, online approach to view planning for 3D reconstruction. Based on the outcome of the Guided KLT tracking, we design a planning module for accuracy optimization with respect to an extended E-criterion. Further planning modules endow non-discrete surface estimation and visibility analysis. The modular nature of the proposed planning system allows to address a wide range of specific instances of view planning. The theoretical findings in this work are underlined by experiments evaluating the relevant terms
Symmetries and invariances in classical physics
Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Sections the meaning, application and interpretation of symmetry in classical physics. This is done both in general, and with attention to specific topics. The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such as Curie's principle), and reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted. Specific topics discussed include the historical path by which group theory entered classical physics, transformation theory in classical mechanics, the relativity principle in Einstein's Special Theory of Relativity, general covariance in his General Theory of Relativity, and Noether's theorems. In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic
Set-based state estimation and fault diagnosis using constrained zonotopes and applications
This doctoral thesis develops new methods for set-based state estimation and
active fault diagnosis (AFD) of (i) nonlinear discrete-time systems, (ii)
discrete-time nonlinear systems whose trajectories satisfy nonlinear equality
constraints (called invariants), (iii) linear descriptor systems, and (iv)
joint state and parameter estimation of nonlinear descriptor systems. Set-based
estimation aims to compute tight enclosures of the possible system states in
each time step subject to unknown-but-bounded uncertainties. To address this
issue, the present doctoral thesis proposes new methods for efficiently
propagating constrained zonotopes (CZs) through nonlinear mappings. Besides,
this thesis improves the standard prediction-update framework for systems with
invariants using new algorithms for refining CZs based on nonlinear
constraints. In addition, this thesis introduces a new approach for set-based
AFD of a class of nonlinear discrete-time systems. An affine parametrization of
the reachable sets is obtained for the design of an optimal input for set-based
AFD. In addition, this thesis presents new methods based on CZs for set-valued
state estimation and AFD of linear descriptor systems. Linear static
constraints on the state variables can be directly incorporated into CZs.
Moreover, this thesis proposes a new representation for unbounded sets based on
zonotopes, which allows to develop methods for state estimation and AFD also of
unstable linear descriptor systems, without the knowledge of an enclosure of
all the trajectories of the system. This thesis also develops a new method for
set-based joint state and parameter estimation of nonlinear descriptor systems
using CZs in a unified framework. Lastly, this manuscript applies the proposed
set-based state estimation and AFD methods using CZs to unmanned aerial
vehicles, water distribution networks, and a lithium-ion cell.Comment: My PhD Thesis from Federal University of Minas Gerais, Brazil. Most
of the research work has already been published in DOIs
10.1109/CDC.2018.8618678, 10.23919/ECC.2018.8550353,
10.1016/j.automatica.2019.108614, 10.1016/j.ifacol.2020.12.2484,
10.1016/j.ifacol.2021.08.308, 10.1016/j.automatica.2021.109638,
10.1109/TCST.2021.3130534, 10.1016/j.automatica.2022.11042
Information geometric methods for complexity
Research on the use of information geometry (IG) in modern physics has
witnessed significant advances recently. In this review article, we report on
the utilization of IG methods to define measures of complexity in both
classical and, whenever available, quantum physical settings. A paradigmatic
example of a dramatic change in complexity is given by phase transitions (PTs).
Hence we review both global and local aspects of PTs described in terms of the
scalar curvature of the parameter manifold and the components of the metric
tensor, respectively. We also report on the behavior of geodesic paths on the
parameter manifold used to gain insight into the dynamics of PTs. Going
further, we survey measures of complexity arising in the geometric framework.
In particular, we quantify complexity of networks in terms of the Riemannian
volume of the parameter space of a statistical manifold associated with a given
network. We are also concerned with complexity measures that account for the
interactions of a given number of parts of a system that cannot be described in
terms of a smaller number of parts of the system. Finally, we investigate
complexity measures of entropic motion on curved statistical manifolds that
arise from a probabilistic description of physical systems in the presence of
limited information. The Kullback-Leibler divergence, the distance to an
exponential family and volumes of curved parameter manifolds, are examples of
essential IG notions exploited in our discussion of complexity. We conclude by
discussing strengths, limits, and possible future applications of IG methods to
the physics of complexity.Comment: review article, 60 pages, no figure
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