On the n-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group

By restricting to a special class of smooth functions, the local action of the symmetry group is globalized. This special class of functions is constructed using parabolic induction

Global representations of the Heat and Schr\"odinger equation with singular potential

We study the $n$-dimensional Schr\"odinger equation with singular potential $V_\lambda(x)=\lambda |x|^{-2}$. Its solution space is studied as a global representation of $\widetilde{SL(2,\R)}\times O(n)$. A special subspace of solutions for which the action globalizes is constructed via nonstandard induction outside the semisimple category. The space of $K$-finite vectors is calculated, obtaining conditions for $\lambda$ so that this space is non-empty. The direct sum of solution spaces, over such admissible values of $\lambda$ is studied as a representation of the $2n+1$-dimensional Heisenberg group

Power Means of Matrices

In this talk we will study the different ways the power means of positive numbers can be extended to means of positive definite matrices. Then, we will analyze the properties these means satisfy. Among these properties, we will be interested in analytic properties such as monotonicity and convexity. Using these results, we will compare the power means with other interpolations between the Arithmetic-Geometric-Harmonic means

The twilight journey of Hendrik Petrus Berlage to the Dutch Indies: Mijn Indische Reis

[EN] In 1923, H.P. Berlage travelled to the Dutch East Indies. When he published his book about the journey, Mijn Indische Reis (Berlage 1931), he included only 36 of the 60 drawings – almost all originally in color but printed in black and white. The original drawings, preserved at the Nederlands Architectuurinstituut, the Dutch Institute of Architecture, were published in part by this institution under the title De indische reis van H.P. Berlage (Berlage & Molenaar 1993) in a box with 46 color reproductions on laid paper. The drawings of the trip included in this article correspond to this latter work. They are apparently very simple drawings, almost all produced with colored chalk, with a freedom and stroke fluidity that contrasts considerably with his “canonical” drawings which, despite their extraordinary quality, are conventional.[ES] En 1923 H. P. Berlage realizó un viaje a las Indias Orientales Neerlandesas. Cuando publica su libro sobre el viaje, Mijn Indische Reis (Berlage 1931), incluye solo 36 de los 60 dibujos realizados –casi todos a color–, pero impresos en blanco y negro. Los dibujos originales que se conservan en el Nederlands Architectuurinstituut, Instituto Holandés de Arquitectura, fueron publicados en parte por esta institución con el título De indische reis van H.P. Berlage (Berlage & Molenaar 1993) en un cofre con 46 reproducciones en color y en papel verjurado. Los dibujos del viaje recogidos en este artículo corresponden a esta última obra. Se trata de dibujos aparentemente muy sencillos, casi todos realizados con tizas de colores, con una libertad y soltura de trazo que contrastan considerablemente con sus dibujos “canónicos” que, a pesar de su extraordinaria calidad, no dejan de ser convencionales.Network of Heritage, Culture, Historical and Technical Services II. Project code: (ED-341D. R2016/023). Consellería de Educación y Ordenación universitaria. Xunta de Galicia. Library of the Architecture School of A Coruña.Franco Taboada, JA. (2018). El viaje crepuscular de Hendrik Petrus Berlage a las Indias holandesas: Mijn Indische Reis. EGA. Revista de Expresión Gráfica Arquitectónica. 23(34):88-105. https://doi.org/10.4995/ega.2018.11014SWORD881052334BERLAGE, H. P. (1931). Mijn Indische reis: ge-dachten over cultuur en kunst. Rotterdam, W.L. & J. Brusse.BELAGE, H. P. & MOLENAAR, J. (ca. 1993). De Indische reis van H. P. Berlage: collectie Nederlands Architectuurinstituut. Rotterdam, Nederlands ArchitectuurInstituut.BERLAGE, H. P. & WHYTE, I. B. (1996). Hendrik Petrus Berlage: thoughts on style, 1886-1909. Santa Monica, California, Getty Center for the History of Art and the Humanities.COHEN, J.-L. (1996). Mies van der Rohe. London, E & FN Spon.COWHERD, R. (2017). Identity Tectonics: Contested Modernities of Java and Bali, in Haughey, P. (Ed.), Across Space and Time. Architecture and the Politics of Modernity. New Jersey, Transaction Publishers, pp. 36-48. https://doi.org/10.4324/9781315083100-1NEUMEYER, F. (1991). The Artless word: Mies van de Rohe on the building art. Cambridge, The MIT Press.NOOTEBOOM, C. (1999). Nooit gebouwd Nederland. Blaricum, V+K Publishing

State space reparametrization for approximating nonlinear models in Bayesian state estimation

Recursive Bayesian state estimation is a powerful methodology which is useful for the integration of data about a process of interest while considering all the sources of uncertainty which are present in the observations and in modeling inaccuracies. However, in its general form it is intractable and approximations need to be made in order to use it in real life applications. The most widely used algorithm to perform recursive state estimation is the Kalman filter, which assumes that the probability distributions that it propagates are Gaussian and that the measurement and dynamical processes are linear. If these assumptions are satisfied, the Kalman filter is optimal. In most applications, however, this proves to be an oversimplification, due to which several techniques have arisen to handle model non-linearity and different types of distributions. In this thesis, a novel method for the estimation of distributions with nonlinear dynamical and measurement models is presented, which uses a reparametrization of the state space of the distributions in order to exploit the linear properties of the Kalman filter. This involves the mapping of the distribution into a different space, and a subsequent approximation as a Gaussian distribution. An analysis of the adequacy of this transformation is presented, which shows that it is a valid approach in a number of practically interesting filtering problems. The proposed approach is applied to the estimation of the state of Earth-orbiting objects, as it is a challenging estimation scenario which can benefit from the use of filter. Space situational awareness is increasingly important as near-Earth space becomes cluttered with satellites and debris. In this work, the sensors that are most commonly used to track objects in orbit, radars and telescopes, are modeled and a filter based on the previously discussed ideas is proposed. Finally, a multi-object estimation filter based on a recent estimation framework is presented which propagates high amounts of information while maintaining low computational complexity. This is important as there are many challenges to tracking large amounts of orbiting objects in a principled way using ground-based sensors, and naturally extends the single object filter described above to the multi-sensor, multi-object case