Path-Complete p-Dominant Switching Linear Systems

The notion of path-complete $p$-dominance for switching linear systems (in short, path-dominance) is introduced as a way to generalize the notion of dominant/slow modes for LTI systems. Path-dominance is characterized by the contraction property of a set of quadratic cones in the state space. We show that path-dominant systems have a low-dimensional dominant behavior, and hence allow for a simplified analysis of their dynamics. An algorithm for deciding the path-dominance of a given system is presented

On path-complete Lyapunov functions: geometry and comparison

We study optimization-based criteria for the stability of switching systems, known as Path-Complete Lyapunov Functions, and ask the question “can we decide algorithmically when a criterion is less conservative than another'”. Our contribution is twofold. First, we show that a Path-Complete Lyapunov Function, which is a multiple Lyapunov function by nature, can always be expressed as a common Lyapunov function taking the form of a combination of minima and maxima of the elementary functions that compose it. Geometrically, our results provide for each Path-Complete criterion an implied invariant set. Second, we provide a linear programming criterion allowing to compare the conservativeness of two arbitrary given Path-Complete Lyapunov functions

Path-complete positivity of switching systems

The notion of path-complete positivity is introduced as a way to generalize the property of positivity from one LTI system to a family of switched LTI systems whose switching rule is constrained by a finite automaton. The generalization builds upon the analogy between stability and positivity, the former referring to the contraction of a norm, the latter referring to the contraction of a cone (or, equivalently, a projective norm). We motivate and investigate the potential of path-positivity and we propose an algorithm for the automatic verification of positivity.European Commission (670645

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

Human mandibular shape is associated with masticatory muscle force

Understanding how and to what extent forces applied to the mandible by the masticatory muscles influence its form, is of considerable importance from clinical, anthropological and evolutionary perspectives. This study investigates these questions. Head CT scans of 382 adults were utilized to measure masseter and temporalis muscle cross-sectional areas (CSA) as a surrogate for muscle force, and 17 mandibular anthropometric measurements. Sixty-two mandibles of young individuals (20-40 years) whose scans were without artefacts (e.g., due to tooth filling) were segmented and landmarked for geometric morphometric analysis. The association between shape and muscle CSA (controlled for size) was assessed using two-block partial least squares analysis. Correlations were computed between mandibular variables and muscle CSAs (all controlled for size). A significant association was found between mandibular shape and muscle CSAs, i.e. larger CSAs are associated with a wider more trapezoidal ramus, more massive coronoid, more rectangular body and a more curved basal arch. Linear measurements yielded low correlations with muscle CSAs. In conclusion, this study demonstrates an association between mandibular muscle force and mandibular shape, which is not as readily identified from linear measurements. Retrodiction of masticatory muscle force and so of mandibular loading is therefore best based on overall mandibular shape

Diffraction techniques and vibrational spectroscopy opportunities to characterise bones

From a histological point of view, bones that allow body mobility and protection of internal organs consist not only of different organic and inorganic tissues but include vascular and nervous elements as well. Moreover, due to its ability to host different ions and cations, its mineral part represents an important reservoir, playing a key role in the metabolic activity of the organism. From a structural point of view, bones can be considered as a composite material displaying a hierarchical structure at different scales. At the nanometre scale, an organic part, i.e. collagen fibrils and an inorganic part, i.e. calcium phosphate nanocrystals are intimately mixed to assure particular mechanical properties

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference

Prevention of acute kidney injury and protection of renal function in the intensive care unit

Acute renal failure on the intensive care unit is associated with significant mortality and morbidity. To determine recommendations for the prevention of acute kidney injury (AKI), focusing on the role of potential preventative maneuvers including volume expansion, diuretics, use of inotropes, vasopressors/vasodilators, hormonal interventions, nutrition, and extracorporeal techniques. A systematic search of the literature was performed for studies using these potential protective agents in adult patients at risk for acute renal failure/kidney injury between 1966 and 2009. The following clinical conditions were considered: major surgery, critical illness, sepsis, shock, and use of potentially nephrotoxic drugs and radiocontrast media. Where possible the following endpoints were extracted: creatinine clearance, glomerular filtration rate, increase in serum creatinine, urine output, and markers of tubular injury. Clinical endpoints included the need for renal replacement therapy, length of stay, and mortality. Studies are graded according to the international Grades of Recommendation, Assessment, Development, and Evaluation (GRADE) group system Several measures are recommended, though none carries grade 1A. We recommend prompt resuscitation of the circulation with special attention to providing adequate hydration whilst avoiding high-molecular-weight hydroxy-ethyl starch (HES) preparations, maintaining adequate blood pressure using vasopressors in vasodilatory shock. We suggest using vasopressors in vasodilatory hypotension, specific vasodilators under strict hemodynamic control, sodium bicarbonate for emergency procedures administering contrast media, and periprocedural hemofiltration in severe chronic renal insufficiency undergoing coronary intervention

Path-Complete p-Dominant Switching Linear Systems

The notion of path-complete $p$-dominance for switching linear systems (in short, path-dominance) is introduced as a way to generalize the notion of dominant/slow modes for LTI systems. Path-dominance is characterized by the contraction property of a set of quadratic cones in the state space. We show that path-dominant systems have a low-dimensional dominant behavior, and hence allow for a simplified analysis of their dynamics. An algorithm for deciding the path-dominance of a given system is presented

Path-complete positivity of switching systems

The notion of path-complete positivity is introduced as a way to generalize the property of positivity from one LTI system to a family of switched LTI systems whose switching rule is constrained by a finite automaton. The generalization builds upon the analogy between stability and positivity, the former referring to the contraction of a norm, the latter referring to the contraction of a cone (or, equivalently, a projective norm). We motivate and investigate the potential of path-positivity and we propose an algorithm for the automatic verification of positivity