Approximating the Real Structured Stability Radius with Frobenius Norm Bounded Perturbations

We propose a fast method to approximate the real stability radius of a linear dynamical system with output feedback, where the perturbations are restricted to be real valued and bounded with respect to the Frobenius norm. Our work builds on a number of scalable algorithms that have been proposed in recent years, ranging from methods that approximate the complex or real pseudospectral abscissa and radius of large sparse matrices (and generalizations of these methods for pseudospectra to spectral value sets) to algorithms for approximating the complex stability radius (the reciprocal of the $H_\infty$ norm). Although our algorithm is guaranteed to find only upper bounds to the real stability radius, it seems quite effective in practice. As far as we know, this is the first algorithm that addresses the Frobenius-norm version of this problem. Because the cost mainly consists of computing the eigenvalue with maximal real part for continuous-time systems (or modulus for discrete-time systems) of a sequence of matrices, our algorithm remains very efficient for large-scale systems provided that the system matrices are sparse

Hoffa’s fat pad thickness: a measurement method with sagittal MRI sequences

Background: Hoffa’s fat pad is a structure located within the fibrous joint capsule of the knee joint, but outside the synovial cavity. It plays an important biomechanical and metabolic role in knee joint, reducing the impact of forces generated by loading and producing cytokines. Changes in its size can induce modifications in the knee homeostasis. However, a great variability exists regarding its measurements. This work aims to evaluate the reliability of a measurement method of Hoffa’s fat pad dimensions through MRI. Methods: 3T sagittal IW 2D TSE fat-suppressed MRI sequences, taken from the OAI (Osteoarthritis initiative) database, of 191 male and female patients, aged between 40 and 80 years, were analysed; a manual measurement of the thickness of Hoffa’s fat pad of each subject was then performed by two different readers. The interobserver reliability and intraobserver reliability of the measurements were described by coefficient of variation (CV), Pearson correlation and Bland–Altman plots. Results: All statistical analyses have shown that not significant intra- or interobservers differences were evident (intraobserver CV % for the first observer was 2.17% for the right knee and 2.24% for the left knee, while for the second observer 2.31% for the right knee and 2.24% for the left knee; linear correlation was for the first observer r = 0.96 for the right knee and r = 0.96 for the left knee, while for the second observer r = 0.97 for the right knee and r = 0.96 for the left knee; in addition, the interobserver CV % was 1.25% for the right knee and 1.21% for the left knee and a high interobserver linear correlation was found: r = 0.97 for the right knee and r = 0.96 for the left knee). All results suggest that this manual measurement method of Hoffa’s fat pad thickness can be performed with satisfactory intra- and interobserver reliability. Conclusions: Hoffa’s fat pad thickness can be measured, using sagittal MRI images, with this manual method that represents, for his high reliability, an effective means for the study of this anatomical structure

A prototype for water content measurement in partially saturated soils

The paper presents the technological set-up and calibration of a system based on impedance spectroscopy for measuring water content in partially saturated soils. The technique adopted is relatively recent in geotechnical practice; it is used herein to characterize the electrical response of a soil specimen among two conducting electrodes upon application of an alternate voltage and the measurement of the current intensity resulting across the specimen, for frequency values in the range [500 Hz - 50 kHz]. The complex impedance of the soil specimen is due to both resistance, i.e. opposition to current, and reactance, i.e. tendency of the system to yield and retrieve energy, and it depends on the specimen water content. An on-purpose experimental plan has been conceived and is presented herein, aimed at building a calibration function for deriving the water content in pyroclastic soils from the impedance measurements. Preliminary results reveal an adequate level of repeatability of the measurements and suggest the existence of a monotonic correlation between the impedance modulus and the gravimetric water content

Ultrasound imaging, a stethoscope for body composition assessment

Bone and muscle are two deeply interconnected organs and a strong relationship between them exists in their development and maintenance. The peak of both bone and muscle mass is achieved in early adulthood, followed by a progressive decline after the age of 40. The increase in life expectancy in developed countries resulted in an increase of degenerative diseases affecting the musculoskeletal system. Osteoporosis and sarcopenia represent a major cause of morbidity and mortality in the elderly population and are associated with a significant increase in healthcare costs. Several imaging techniques are currently available for the non-invasive investigation of bone and muscle mass and quality. Conventional radiology, dual energy X-ray absorptiometry (DXA), computed tomography (CT), magnetic resonance imaging (MRI) and ultrasound often play a complementary role in the study of osteoporosis and sarcopenia, depicting different aspects of the same pathology. This paper presents the different imaging modalities currently used for the investigation of bone and muscle mass and quality in osteoporosis and sarcopenia with special emphasis on the clinical applications and limitations of each technique and with the intent to provide interesting insights into recent advances in the field of conventional imaging, novel high-resolution techniques and fracture risk

CNGS: Effects of possible alignment errors

Simulations of the CNGS neutrino beam from CERN to the Gran Sasso Laboratory (LNGS)assume that the proton beam and all secondary beam elements are perfectly aligned on an axis between the two laboratories. This study examines the effects on the neutrino flux at Gran Sasso of deviations from the axis of the primary proton beam and misalignment of secondary beam elements. It also examines how such deviation or misalignment can be detected at monitors placed along the secondary beam line at CERN and at Gran Sasso. Calculations are based on the CNGS neutrino beam, optimized for nu_mu ->nu_tau appearance experiments as described in the Addendum to the Conceptual Technical Design Report of CNGS. It is shown that the number of neutrino charged current events predicted at Gran Sasso is insensitive to all but the most extreme misalignments

Finite Element Simulation of Dense Wire Packings

A finite element program is presented to simulate the process of packing and coiling elastic wires in two- and three-dimensional confining cavities. The wire is represented by third order beam elements and embedded into a corotational formulation to capture the geometric nonlinearity resulting from large rotations and deformations. The hyperbolic equations of motion are integrated in time using two different integration methods from the Newmark family: an implicit iterative Newton-Raphson line search solver, and an explicit predictor-corrector scheme, both with adaptive time stepping. These two approaches reveal fundamentally different suitability for the problem of strongly self-interacting bodies found in densely packed cavities. Generalizing the spherical confinement symmetry investigated in recent studies, the packing of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic limit. Evidence is given that packings in oblate spheroids and scalene ellipsoids are energetically preferred to spheres.Comment: 17 pages, 7 figures, 1 tabl

Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

Analysis of size and shape differences between ancient and present-day Italian crania using metrics and geometric morphometrics based on multislice computed tomography

The Museum of Human Anatomy in Naples houses a collection of ancient Graeco-Roman crania. The aim of this study was to use multislice computed tomography (MSCT) to evaluate and objectively quantify potential differences in cranial dimensions and shapes between ancient Graeco-Roman crania (n = 36) and modern-day southern Italian crania (n = 35) and then to characterize the cranial changes occurring over more than 2000 years, known as secular change. The authors used traditional metric criteria and morphometric geometry to compare shape differences between the sets of crania. Statistically significant differences in size between the ancient and modern crania included shorter facial length, narrower external palate, smaller minimum cranial breadth, shorter right and left mastoid processes, and wider maximum occipital and nasal breadth. The shape changes from the ancient to modern crania included a global coronal enlargement of the face and cranial diameters, with more anterior projection of the face at the anterior nasal spine, but also posterior projection at the glabella and the nasion. It is not possible to determine whether these differences result exclusively from secular changes in the cranium or from other factors, including a mix of secular change and other unknown factors. To the best of our knowledge, this is the first MSCT-based study to compare ancient Graeco-Roman and modern-day southern Italian crania and to characterize shape and size differences

Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure