We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We start by providing a hybrid numeric-symbolic algorithm computing exact rational SOS decompositions for polynomials lying in the interior of the SOS cone. It computes an approximate SOS decomposition for ...

Acquisition of a system of systems can be an all new acquisition of multiple systems that are intended to operate together as a system-of-systems. Much more common in the DoD is acquisition of one or more new systems that are intended to interoperate with existing systems as a system of systems with new capabilities. In either case, successful acquisition of systems-of-systems (SoS) necessarily...

Small oxoacids of sulfur (SOS) are elusive molecules like sulfenic acid, HSOH, and sulfinic acid, HS(O)OH, generated during the oxidation of hydrogen sulfide, H2S, in aqueous solution. Unlike their alkyl homologs, there is a little data on their generation and speciation during H2S oxidation. These SOS may exhibit both nucleophilic and electrophilic reactivity, which we attribute to interconver...

The notion of sos-convexity has recently been proposed as a tractable sufficient condition for convexity of polynomials based on sum of squares decomposition. A multivariate polynomial p(x) = p(x1, . . . , xn) is said to be sos-convex if its Hessian H(x) can be factored as H(x) = M (x) M (x) with a possibly nonsquare polynomial matrix M(x). It turns out that one can reduce the problem of decidi...

The activation of the small guanosine triphosphatase Ras is critical for many biological events. It is therefore not surprising that the ubiquitously expressed Ras guanine nucleotide exchange factor (GEF) SOS (Son of Sevenless), which couples protein tyrosine kinases to Ras activation, is under tight autoinhibitory control. Several studies have revealed how multiple regulatory domains might aff...

An exact semidefinite linear programming (SDP) relaxation of a nonlinear semidefinite programming problem is a highly desirable feature because a semidefinite linear programming problem can efficiently be solved. This paper addresses the basic issue of which nonlinear semidefinite programming problems possess exact SDP relaxations under a constraint qualification. We do this by establishing exa...

Using estimated leaf unfolding data and two types of Normalized Difference Vegetation Index (NDVI and NDVI3g) data generated from the Advanced Very High Resolution Radiometer (AVHRR) in the deciduous broadleaf forest of northern China during 1986 to 2006, we analyzed spatial, temporal and spatiotemporal relationships and differences between ground-based growing season beginning (BGS) and NDVI (...

OBJECTIVE To develop and validate a self-reported outcomes measure for patients with sleep-disordered breathing-the Snore Outcomes Survey. DESIGN Item areas of the SOS were developed by an expert panel. Consecutive patients were enrolled into the study in a prospective manner. Patients received the SOS, the Epworth Sleepiness Scale, the Pittsburgh Sleep Quality Index, the Medical Outcomes Stu...

Quantitative ultrasound (QUS) measurement of tibial speed of sound (SOS) can be used to determine bone strength. Children conceived with assisted reproduction treatments (ART) are taller than naturally conceived (NC) children, so we hypothesized that these infants would have higher SOS levels than NC infants. Thirty-seven ART (ART group) and 51 NC neonates (NC group) were included in the study....

A Service-Oriented System of System (or SoS) considers system as a service and constructs a value-added SoS by outsourcing external systems through service composition. To cope with the dynamic and uncertain running environment and assure the overall Quality of Service (or QoS), online reliability prediction for SoS arises as a grand challenge in SoS research. Online reliability prediction is e...