3,099 research outputs found
Existence of Cascade Discrete-Continuous State Estimators for Systems on a Partial Order
In this paper, a cascade discrete-continuous state estimator on a partial order is proposed and its existence investigated. The continuous state estimation error is bounded by a monotonically nonincreasing function of the discrete state estimation error, with both the estimation errors converging to zero. This work shows that the lattice approach to estimation is general as the proposed estimator can be constructed for any observable and discrete state observable system. The main advantage of using the lattice approach for estimation becomes clear when the system has monotone properties that can be exploited in the estimator design. In such a case, the computational complexity of the estimator can be drastically reduced and tractability can be achieved. Some examples are proposed to illustrate these ideas
Modelling and Terrestrial Laser Scanning Methodology (2009–2018) on Debris Cones in Temperate High Mountains
Producción CientíficaDebris cones are a very common landform in temperate high mountains. They are the
most representative examples of the periglacial and nival processes. This work studies the dynamic
behavior of two debris cones (Cone A and Cone B) in the Picos de Europa, in the north of the
Iberian Peninsula. Their evolution was measured uninterruptedly throughout each August for
10 years (2009–2018) using the Terrestrial Laser Scanning (TLS) technique. The observations and
calculations of the two debris cones were treated independently, but both showed the same behavior.
Therefore, if these results are extrapolated to other debris cones in similar environments (temperate
high mountain), they should show behavior similar to that of the two debris cones analyzed. Material
falls onto the cones from the walls, and transfer of sediments follows linear trajectories according to
the maximum slope. In order to understand the linear evolution of the two debris cones, profiles were
created along the maximum slope lines of the Digital Elevation Model (DEM) of 2009, and these profile
lines were extrapolated to the remaining years of measurement. In order to determine volumetric
surface behavior in the DEMs, each year for the period 2009–2018 was compared. In addition,
the statistical predictive value for position (Z) in year 2018 was calculated for the same planimetric
position (X,Y) throughout the profiles of maximum slopes. To do so, the real field data from 2009–2017
were interpolated and used to form a sample of curves. These curves are interpreted as the realization
of a functional random variable that can be predicted using statistical techniques. The predictive
curve obtained was compared with the 2018 field data. The results of both coordinates (Z), the real
field data, and the statistical data are coherent within the margin of error of the data collection.Fondo Europeo de Desarrollo Regional - Agencia Estatal de Investigación (grant TIN2016-76843-C4-2-R)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grant CGL2015-68144-R
Abstracts of theses in mathematics
summary:Krejčíř, Pavel: The theory and applications of spatial statistics and stochastic geometry.
Vítek, Tomáš: Detection of changes in econometric models.
Hliněný, Petr: Contact representations of graphs.
Kliková, Alice: Finite volume -- finite element solution of compressible flow.
Hrach, Karel: Bayesian analysis of models with non-negative residuals.
Svatoš, Jan: M-estimators in the linear model for nonregular densities.
Ševčík, Petr: Extremal martingale measures in finance.
Hlávka, Zdeněk: Robust sequential estimation.
Holub, Štěpán: Equations in free monoids.
Klaschka Jan: Mathematical methods of state change assessment in medical research.
Unzeitigová, Vladimíra: Mathematical models of health insurance for commercial insurance companies -- embedded value of accident insurance.
Friesl, Michal: Bayesian estimation in exponent competing risks and related models with applications to insurance.
Fiala, Jiří: Locally injective homomorphisms.
Kaplický, Petr: Qualitative properties of solutions of systems of mechanics.
Ghoneim, Sobha: Selfdistributive rings and near-rings
Signal processing with Fourier analysis, novel algorithms and applications
Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github
- …