On volumes of hyperideal tetrahedra with constrained edge lengths

Hyperideal tetrahedra are the fundamental building blocks of hyperbolic 3-manifolds with geodesic boundary. The study of their geometric properties (in particular, of their volume) has applications also in other areas of low-dimensional topology, like the computation of quantum invariants of 3-manifolds and the use of variational methods in the study of circle packings on surfaces. The Schl\"afli formula neatly describes the behaviour of the volume of hyperideal tetrahedra with respect to dihedral angles, while the dependence of volume on edge lengths is worse understood. In this paper we prove that, for every $\ell<\ell_0$, where $\ell_0$ is an explicit constant, regular hyperideal tetrahedra of edge length $\ell$ maximize the volume among hyperideal tetrahedra whose edge lengths are all not smaller than $\ell$. This result provides a fundamental step in the computation of the ideal simplicial volume of an infinite family of hyperbolic 3-manifolds with geodesic boundary.Comment: 20 pages, 2 figures, Some minor changes, To appear in Periodica Mathematica Hungaric

Innovation and Global Sustainable Development: What Role for Development Banking?

This chapter explores the potential role of development banks in fostering innovation within the context of sustainable development, considering their explicit mandates and collaborations with governments. Development banks are argued to play a pivotal role in supporting innovation by providing substantial financial resources to projects that address the complex challenges outlined in the Sustainable Development Goals (SDGs) while ensuring the preservation of natural resources for future generations. A critical review of economic literature examines the characteristics of development banks that enable them to fulfill their social mandate, including their expertise and ability to mobilize private finance. Collaboration with governments and risk mitigation for private investors are highlighted as means to facilitate the achievement of the SDGs. However, challenges associated with public intervention and state-owned enterprises, such as political opportunism and crowding-out of private sector investment, are acknowledged. By reviewing the literature, describing recent developments, and presenting empirical evidence, this research provides valuable insights for policymakers, scholars, and practitioners to critically evaluate the potential and effectiveness of development banks in promoting innovation

Ideal simplicial volume of manifolds with boundary

We define the ideal simplicial volume for compact manifolds with boundary. Roughly speaking, the ideal simplicial volume of a manifold $M$ measures the minimal size of possibly ideal triangulations of $M$ "with real coefficients", thus providing a variation of the ordinary simplicial volume defined by Gromov in 1982, the main difference being that ideal simplices are now allowed to appear in representatives of the fundamental class. We show that the ideal simplicial volume is bounded above by the ordinary simplicial volume, and that it vanishes if and only if the ordinary simplicial volume does. We show that, for manifolds with amenable boundary, the ideal simplicial volume coincides with the classical one, whereas for hyperbolic manifolds with geodesic boundary it can be strictly smaller. We compute the ideal simplicial volume of an infinite family of hyperbolic $3$-manifolds with geodesic boundary, for which the exact value of the classical simplicial volume is not known, and we exhibit examples where the ideal simplicial volume provides shaper bounds on mapping degrees than the classical simplicial volume.Comment: 40 pages, 2 figures, some minor changes, to appear in International Mathematics Research Notices (IMRN

Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning

Innovation and Global Sustainable Development: What Role for Development Banking?

This chapter explores the potential role of development banks in fostering innovation within the context of sustainable development, considering their explicit mandates and collaborations with governments. Development banks are argued to play a pivotal role in supporting innovation by providing substantial financial resources to projects that address the complex challenges outlined in the Sustainable Development Goals (SDGs) while ensuring the preservation of natural resources for future generations. A critical review of economic literature examines the characteristics of development banks that enable them to fulfill their social mandate, including their expertise and ability to mobilize private finance. Collaboration with governments and risk mitigation for private investors are highlighted as means to facilitate the achievement of the SDGs. However, challenges associated with public intervention and state-owned enterprises, such as political opportunism and crowding-out of private sector investment, are acknowledged. By reviewing the literature, describing recent developments, and presenting empirical evidence, this research provides valuable insights for policymakers, scholars, and practitioners to critically evaluate the potential and effectiveness of development banks in promoting innovation

Robot Impedance Control and Passivity Analysis with Inner Torque and Velocity Feedback Loops

Impedance control is a well-established technique to control interaction forces in robotics. However, real implementations of impedance control with an inner loop may suffer from several limitations. Although common practice in designing nested control systems is to maximize the bandwidth of the inner loop to improve tracking performance, it may not be the most suitable approach when a certain range of impedance parameters has to be rendered. In particular, it turns out that the viable range of stable stiffness and damping values can be strongly affected by the bandwidth of the inner control loops (e.g. a torque loop) as well as by the filtering and sampling frequency. This paper provides an extensive analysis on how these aspects influence the stability region of impedance parameters as well as the passivity of the system. This will be supported by both simulations and experimental data. Moreover, a methodology for designing joint impedance controllers based on an inner torque loop and a positive velocity feedback loop will be presented. The goal of the velocity feedback is to increase (given the constraints to preserve stability) the bandwidth of the torque loop without the need of a complex controller.Comment: 14 pages in Control Theory and Technology (2016

Germanium Plasmonic Nanoantennas for Third-Harmonic Generation in the Mid Infrared

We explore the nonlinear optical properties of plasmonic semiconductor antennas resonant in the mid infrared. The nanostructures are fabricated on silicon substrates from heavily doped germanium films with a plasma frequency of 30 THz, equivalent to a wavelength of 10 μm. Illumination with ultrashort pulses at 10.8 μm produces coherent emission at 3.6 μm via third-harmonic generation