Controllability of quasi-linear Hamiltonian NLS equations

We prove internal controllability in arbitrary time, for small data, for quasi-linear Hamiltonian NLS equations on the circle. We use a procedure of reduction to constant coefficients up to order zero and HUM method to prove the controllability of the linearized problem. Then we apply a Nash–Moser–Hörmander implicit function theorem as a black box.     

Complex varieties and higher integrability of Dir-minimizing Q-valued functions

We provide new elementary proofs of the following two results: every complex variety is locally the graph of a Dir-minimizing function, first proved by Almgren (Almgren’s big regularity paper, volume 1 of World Scientific Monograph Series in Mathematics, 2000); the gradients of Dir-minimizing functions, in principle square-summable, are p-integrable for some p > 2, proved by De Lellis and Spadaro (Higher integrability and approximation of minimal currents, 2009). In the planar case, we prove that our integrability exponents are optimal.     

Development of an Accurate Mass Retention Time Database for Untargeted Metabolomic Analysis and Its Application to Plasma and Urine Pediatric Samples

Liquid-chromatography coupled to high resolution mass spectrometry (LC-HRMS) is currently the method of choice for untargeted metabolomic analysis. The availability of established protocols to achieve a high confidence identification of metabolites is crucial. The aim of this work is to describe the workflow that we have applied to build an Accurate Mass Retention Time (AMRT) database using a commercial metabolite library of standards. LC-HRMS analysis was carried out using a Vanquish Horizon UHPLC system coupled to a Q-Exactive Plus Hybrid Quadrupole-Orbitrap Mass Spectrometer (Thermo Fisher Scientific, Milan, Italy). The fragmentation spectra, obtained with 12 collision energies, were acquired for each metabolite, in both polarities, through flow injection analysis. Several chromatographic conditions were tested to obtain a protocol that yielded stable retention times. The adopted chromatographic protocol included a gradient separation using a reversed phase (Waters Acquity BEH C18) and a HILIC (Waters Acquity BEH Amide) column. An AMRT database of 518 compounds was obtained and tested on real plasma and urine samples analyzed in data-dependent acquisition mode. Our AMRT library allowed a level 1 identification, according to the Metabolomics Standards Initiative, of 132 and 124 metabolites in human pediatric plasma and urine samples, respectively. This library represents a starting point for future metabolomic studies in pediatric settings.     

The degenerate two well problem for piecewise affine maps

The two well problem consists in finding maps u which satisfy some boundary conditions and whose gradient Du assumes values in the two wells ${\mathbb{S}_{A}, \mathbb{S}_{B}}$ . Here ${\mathbb{S}_{A}}$ (similarly ${\mathbb{S}_{B}}$ ) is the well generated by a 2 × 2 matrix A, i.e., ${\mathbb{S}_{A}}$ is the set of matrices of the form RA, where R is a rotation. We study specifically the case when at least one of the two matrices A, B is singular and we characterize piecewise affine maps u satisfying almost everywhere the differential inclusion ${Du(x) \in \mathbb{S}_{A} \cup \mathbb{S}_{B}}$ . In particular we describe the lamination and angle properties, which turn out to be different from those of the nonsingular case described in detail in [15]. We also show that the two well problem can be solved in some cases involving singular matrices, in strict contrast to the nonsingular (and not orthogonal) case.     

Fourier Self-Deconvolution Analysis of β-Sheet Contents in the Amide I Region of Hemoglobin Aqueous Solutions under Exposure to 900 MHz Microwaves and Bioprotective Effectiveness of Sugar and Salt Solutions

Spectroscopic Fourier self-deconvolution analysis was used to investigate β-sheet features in the secondary structure of hemoglobin under mobile phone microwaves at 900 MHz. To this end, four samples of hemoglobin in bidistilled water, sucrose, trehalose, and sodium chloride aqueous solutions were exposed for up to 4 hr to 900 MHz microwaves at an average H-field intensity of 42 mA/m. Quantitative spectral analyses highlighted significant increases in β-sheet contents in the Amide I region of hemoglobin samples in bidistilled water solution, but no appreciable change was observed in hemoglobin samples in sucrose, trehalose, and sodium chloride solutions. These results led us to conclude that mobile phone microwaves can denaturate hemoglobin in bidistilled water solution whereas sucrose, trehalose, and sodium chloride solutions produce a protective effect against microwaves, preserving the protein from unfolding.     

Astrophysical Black Holes as Natural Laboratories for Fundamental Physics and Strong-Field Gravity

Astrophysical tests of general relativity belong to two categories: 1) “internal”, i.e. consistency tests within the theory (for example, tests that astrophysical black holes are indeed described by the Kerr solution and its perturbations), or 2) “external”, i.e. tests of the many proposed extensions of the theory. I review some ways in which astrophysical black holes can be used as natural laboratories for both “internal” and “external” tests of general relativity. The examples provided here (ringdown tests of the black hole “no-hair” theorem, bosonic superradiant instabilities in rotating black holes and gravitational-wave tests of massive scalar-tensor theories) are shamelessly biased towards recent research by myself and my collaborators. Hopefully this colloquial introduction aimed mainly at astrophysicists will convince skeptics (if there are any) that space-based detectors will be crucial to study fundamental physics through gravitational-wave observations.     

The Beneficial Role of Random Strategies in Social and Financial Systems

In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics.     

Global sensitivity measures from given data

Simulation models support managers in the solution of complex problems. International agencies recommend uncertainty and global sensitivity methods as best practice in the audit, validation and application of scientific codes. However, numerical complexity, especially in the presence of a high number of factors, induces analysts to employ less informative but numerically cheaper methods. This work introduces a design for estimating global sensitivity indices from given data (including simulation input–output data), at the minimum computational cost. We address the problem starting with a statistic based on the L¹-norm. A formal definition of the estimators is provided and corresponding consistency theorems are proved. The determination of confidence intervals through a bias-reducing bootstrap estimator is investigated. The strategy is applied in the identification of the key drivers of uncertainty for the complex computer code developed at the National Aeronautics and Space Administration (NASA) assessing the risk of lunar space missions. We also introduce a symmetry result that enables the estimation of global sensitivity measures to datasets produced outside a conventional input–output functional framework.