SE-Sync: a certifiably correct algorithm for synchronization over the special Euclidean group

Many important geometric estimation problems naturally take the form of synchronization over the special Euclidean group: estimate the values of a set of unknown group elements (Formula presented.) given noisy measurements of a subset of their pairwise relative transforms (Formula presented.). Examples of this class include the foundational problems of pose-graph simultaneous localization and mapping (SLAM) (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing), among others. This inference problem is typically formulated as a non-convex maximum-likelihood estimation that is computationally hard to solve in general. Nevertheless, in this paper we present an algorithm that is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime. The crux of our approach is the development of a semidefinite relaxation of the maximum-likelihood estimation (MLE) whose minimizer provides an exact maximum-likelihood estimate so long as the magnitude of the noise corrupting the available measurements falls below a certain critical threshold; furthermore, whenever exactness obtains, it is possible to verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop a specialized optimization scheme for solving large-scale instances of this semidefinite relaxation by exploiting its low-rank, geometric, and graph-theoretic structure to reduce it to an equivalent optimization problem defined on a low-dimensional Riemannian manifold, and then design a Riemannian truncated-Newton trust-region method to solve this reduction efficiently. Finally, we combine this fast optimization approach with a simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety of simulated and real-world pose-graph SLAM datasets shows that SE-Sync is capable of recovering certifiably globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics and computer vision applications, and does so significantly faster than the Gauss–Newton-based approach that forms the basis of current state-of-the-art techniques

SE-Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group

Many important geometric estimation problems naturally take the form of synchronization over the special Euclidean group: estimate the values of a set of unknown poses given noisy measurements of a subset of their pairwise relative transforms. Examples of this class include the foundational problems of pose-graph simultaneous localization and mapping (SLAM) (in robotics), camera motion estimation (in computer vision), and sensor network localization (in distributed sensing), among others. This inference problem is typically formulated as a nonconvex maximum-likelihood estimation that is computationally hard to solve in general. Nevertheless, in this paper we present an algorithm that is able to efficiently recover certifiably globally optimal solutions of the special Euclidean synchronization problem in a non-adversarial noise regime. The crux of our approach is the development of a semidefinite relaxation of the maximum-likelihood estimation whose minimizer provides an exact MLE so long as the magnitude of the noise corrupting the available measurements falls below a certain critical threshold; furthermore, whenever exactness obtains, it is possible to verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop a specialized optimization scheme for solving large-scale instances of this semidefinite relaxation by exploiting its low-rank, geometric, and graph-theoretic structure to reduce it to an equivalent optimization problem defined on a low-dimensional Riemannian manifold, and then design a Riemannian truncated-Newton trust-region method to solve this reduction efficiently. Finally, we combine this fast optimization approach with a simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety of simulated and real-world pose-graph SLAM datasets shows that SE-Sync is capable of recovering certifiably globally optimal solutions when the available measurements are corrupted by noise up to an order of magnitude greater than that typically encountered in robotics and computer vision applications, and does so more than an order of magnitude faster than the Gauss-Newton-based approach that forms the basis of current state-of-the-art techniques

Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models

We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of the continuous spectrum and we analyze the effect of various type of perturbations on the spectral singularities. We provide algorithms to obtain convergent series expansions for the coordinates of the singularities.Comment: 20 page

Spin dependent point potentials in one and three dimensions

We consider a system realized with one spinless quantum particle and an array of $N$ spins 1/2 in dimension one and three. We characterize all the Hamiltonians obtained as point perturbations of an assigned free dynamics in terms of some ``generalized boundary conditions''. For every boundary condition we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin dependent point potentials that could be of interest as multi-component solvable models.Comment: 15 pages, some misprints corrected, one example added, some references modified or adde

Dissociative electron attachment to the H2O molecule. I. Complex-valued potential-energy surfaces for the 2B1, 2A1, and 2B2 metastable states of the water anion

We present the results of calculations defining global, three-dimensional representations of the complex-valued potential-energy surfaces of the doublet B1, doublet A1, and doublet B2 metastable states of the water anion that underlie the physical process of dissociative electron attachment to water. The real part of the resonance energies is obtained from configuration-interaction calculations performed in a restricted Hilbert space, while the imaginary part of the energies (the widths) is derived from complex Kohn scattering calculations. A diabatization is performed on the 2A1 and 2B2 surfaces, due to the presence of a conical intersection between them. We discuss the implications that the shapes of the constructed potential-energy surfaces will have upon the nuclear dynamics of dissociative electron attachment to H2O. This work originally appeared as Phys Rev A 75, 012710 (2007). Typesetting errors in the published version have been corrected here.Comment: Corrected version of PRA 75, 012710 (2007

Idiopathic Pulmonary Fibrosis (IPF) incidence and prevalence in Italy

Background: Studies of Idiopathic Pulmonary Fibrosis (IPF) epidemiology show regional variations of incidence and prevalence; no epidemiological studies have been carried out in Italy. Objective: To determine incidence and prevalence rates of IPF in the population of a large Italian region.Methods: in this cross-sectional study study data were collected on all patients of 18 years of age and older admitted as primary or secondary idiopathic fibrosing alveolitis (ICD9-CM 516.3) to Lazio hospitals, from 1/1/2005 to 31/12/2009, using regional hospital discharge, population and cause of death databases. Reporting accuracy was assessed on a random sample of hospital charts carrying the ICD9-CM 516.3, 516.8, 516.9 and 515 codes, by reviewing radiology and pathology findings to define cases as IPF “confident”, “possible” or “inconsistent”. Results: Annual prevalence and incidence of IPF were estimated at 25.6 per 100,000 and 7.5 per 100,000 using the ICD9-CM code 516.3 without chart audit while they were estimated at 31.6 per 100,000 and at 9,3 per 100,000 for the IPF “confident” definition after hospital chart audit. Conclusion: The data provide a first estimate of IPF incidence in Italy and indicate that incidence and prevalence in southern European regions may be similar to those observed in northern Europe and North America. (Sarcoidosis Vasc Diffuse Lung Dis 2014; 31: 191-197

Microstructural and Mechanical Properties of Al2O3 and Al2O3/TiB2 Ceramics Consolidated by Plasma Pressure Compaction

Alumina oxide ceramics were produced by plasma pressure compaction (P2C) sintering process. Two types of pure α-alumina (Al2O3) and a mixture of alumina and titanium diboride (TiB2) powders were used as starting materials. Microstructure and mechanical properties, namely hardness, elastic modulus, and fracture toughness, were analyzed and correlated to the type of the sintered powders and the adopted manufacturing route. The microstructural development and the chemical composition variation induced by the sintering process were assessed by using scanning electron microscopy and x-ray diffraction. Nano-indentation and Chevron notch beam techniques were adopted to estimate the mechanical properties of the sintered ceramics. The conducted analyses show the capability of P2C technique to produce sound alumina ceramics. Pure alumina bulks exhibit a good level of compaction and mechanical properties close to those achievable with conventional sintering processes, such as hot isostatic pressing or spark plasma sintering. No significant alterations in the chemical composition of the ceramics were observed. The addition of the titanium diboride in the alumina powders caused a moderate increase in the grain size lowering the hardness and Young’s modulus of the sintered alumina and, at the same time, increased its fracture toughness to the occurrence of toughening mechanisms, like crack bridging and crack deflection

Catalytic Access to Diastereometrically Pure Four‐ and Five‐Membered Silyl‐Heterocycles Using Transborylation

: Silyl-heterocycles offer a unique handle to expand and explore chemical space, reactivity, and functionality. The shortage of catalytic methods for the preparation of diverse and functionalized silyl-heterocycles however limits widespread exploration and exploitation. Herein the borane-catalyzed intramolecular 1,1-carboboration of silyl-alkynes has been developed for the synthesis of 2,3-dihydrosilolyl and silylcyclobut-2-enyl boronic esters. Successful, catalytic carboboration has been achieved on a variety of functionally diverse silyl-alkynes, using a borane catalyst and transborylation-enabled turnover. Mechanistic studies, including 13C-labelling, computational studies, and single-turnover experiments, suggest a reaction pathway proceeding by 1,2-hydroboration, 1,1-carboboration, and transborylation to release the alkenyl boronic ester product and regenerate the borane catalyst