Sard's approximation processes and oblique projections

Three problems arising in approximation theory are studied. These problems have already been studied by Arthur Sard. The main goal of this paper is to use geometrical compatibility theory to extend Sard's results and get characterizations of the sets of solutions.Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Giribet, Juan Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin

Aerial multi-camera robotic jib crane

A formulation based on a team of unmanned aerial vehicles operating as a fully articulated multi-camera jib crane is proposed for the application of aerial cinematography. An optimization-based controller commands the formation to follow an artistic trajectory defined by the director of photography, while actively avoiding collisions and cameras' mutual visibility. The proposed scheme, based on the cluster-space formulation, presents an intuitive way of maneuvering the virtual camera fixture while automatically adjusting the motions by imposing artistic and safety constraints, facilitating the operator task.Fil: Moreno, Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; ArgentinaFil: Presenza, Juan Francisco. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; ArgentinaFil: Mas, Ignacio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto Tecnológico de Buenos Aires; ArgentinaFil: Giribet, Juan Ignacio. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin

Trajectory following with a MAV under Rotor Fault Conditions

Lately, a novel multirotor aerial vehicle capable of handling single rotor failures was presented. When a rotor fails, physically reconfiguring one of the remaining rotors of a hexarotor allows to compensate for maneuverability limitations. In this work, experimental results show the performance of the vehicle in a trajectory-following task in both nominal and fault conditions.Fil: Pose, Claudio Daniel. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Presenza, Juan Francisco. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Mas, Ignacio Agustin. Instituto Tecnológico de Buenos Aires. Departamento de Física - Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Giribet, Juan Ignacio. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentin

Shorted operators and minus order

Let H be a Hilbert space, L(H) the algebra of bounded linear operators on H and W ∈ L(H) a positive operator. Given a closed subspace S of H, we characterize the shorted operator W/S of W to S as the maximum and as the infimum of certain sets, for the minus order − ≤. Also, given A ∈ L(H) with closed range, we study the following operator approximation problem considering the minus order: min− ≤ {(AX − I) ∗W(AX − I) : X ∈ L(H), subject to N(A ∗W) ⊆ N(X)}. We show that, under certain conditions, the shorted operator of W/R(A) is the minimum of this problem and we characterize the set of solutions.Fil: Contino, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Giribet, Juan Ignacio. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentin

Trajectory Following with a MAV under Rotor Fault Conditions

Lately, a novel multirotor aerial vehicle capable of handling single rotor failures was presented. When a rotor fails, physically reconfiguring one of the remaining rotors of an hexarotor allows to compensate for maneuverability limitations. In this work, experimental results show the per- formance of the vehicle in a trajectory-following task in both nominal and fault conditions.Fil: Pose, Claudio Daniel. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; ArgentinaFil: Francisco Presenza. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; ArgentinaFil: Mas, Ignacio Agustin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Instituto Tecnológico de Buenos Aires; ArgentinaFil: Giribet, Juan Ignacio. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Electronica; Argentina. Instituto Tecnológico de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina11th International Micro Air Vehicle Competition and ConferenceMadridEspañaUniversidad Politécnica de MadridConsejo Superior de Investigaciones Científica

On a class of non-Hermitian matrices with positive definite Schur complements

Given a positive definite matrix $A\in \mathbb{C}^{n\times n}$ and a Hermitian matrix $D\in \mathbb{C}^{m\times m}$, we characterize under which conditions there exists a strictly contractive matrix $K\in \mathbb{C}^{n\times m}$ such that the non-Hermitian block-matrix $$\left[ \begin{array}{cc} A & -AK \\ K^*A & D \end{array} \right]$$ has a positive definite Schur complement with respect to its submatrix~$A$. Additionally, we show that~$K$ can be chosen such that diagonalizability of the block-matrix is guaranteed and we compute its spectrum. Moreover, we show a connection to the recently developed frame theory for Krein spaces.Comment: 15 pages, this is a corrected and enhanced version of the originally submitted manuscrip

Estimación de temperatura en servidores mediante herramientas de Deep Learning

En este trabajo se propone el estudio de estimación de temperatura sobre un servidor, con el objetivo de poder predecir el funcionamiento del mismo bajo condiciones ambientales controladas. Para esto se propone la utilización de herramientas de Deep Learning como por ejemplo, MLP (Multi Layer Perceptron) y LSTM (Long Short-Term Memory). La utilización de éstas persigue el objetivo de poder compararlas y sacar conclusiones sobre su funcionamiento en el ámbito de un datacenter, donde se encuentra el servidor bajo estudio.Workshop: WASI – Agentes y Sistemas InteligentesRed de Universidades con Carreras en Informátic

Shorting selfadjoint operators in Hilbert spaces

Given a closed subspace S of a Hilbert space H and a (bounded) selfadjoint operator B acting on H, a min-max representation of the shorted operator (or Schur complement) of B to S is obtained under compatibility hypotheses. Also, an extension of Pekarev's formula is given.Facultad de Ciencias Exacta

Abstract splines in Krein spaces

We present generalizations to Krein spaces of the abstract interpolation and smoothing problems proposed by Atteia in Hilbert spaces: given a Krein space K and Hilbert spaces H and E (bounded) surjective operators T:H→K and VH→E, ρ>0 and a fixed z0∈E, we study the existence of solutions of the problems argmin{[Tx,Tx]K: Vx=z0} and argmin{[Tx,Tx]K+ρ{norm of matrix}Vx-z0{norm of matrix}E2x∈H}.Facultad de Ciencias Exacta

Indefinite least-squares problems and pseudo-regularity

Given two Krein spaces H and K, a (bounded) closed-range operator C:H→K and a vector y∈K, the indefinite least-squares problem consists in finding those vectors u∈H such that [Cu - y, Cu - y] = minx∈H[Cx - y, Cx - y]. The indefinite least-squares problem has been thoroughly studied before under the assumption that the range of C is a uniformly J-positive subspace of K. Along this article the range of C is only supposed to be a J-nonnegative pseudo-regular subspace of K. This work is devoted to present a description for the set of solutions of this abstract problem in terms of the family of J-normal projections onto the range of C.Facultad de Ciencias Exacta