Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming

We study the global asymptotic stability in probability of the zero solution of linear stochastic differential equations with constant coefficients. We develop a sum-of-squares program that verifies whether a parameterized candidate Lyapunov function is in fact a global Lyapunov function for such a system. Our class of candidate Lyapunov functions are naturally adapted to the problem. We consider functions of the form V(x) = ||x||pQ := (xt>Qx) p/2, where the parameters are the positive definite matrix Q and the number p > 0. We give several examples of our proposed method and show how it improves previous results

Conference Title (Transport Research Arena– Europe 2012)

Conference of European Road Directors, CEDR, initiated work on studying the effects of climate change on roads. The work belongs to Strategic Plan 2 (2009-2013), Thematic Domain Operation and is organised as twin tasks dealing with adaptation on one hand (task 16) and mitigation of climate change on the other hand (task 17). This paper describes the work within task group 16 on adaptation to climate change, from the initiation of the work to the publishing of the report to CEDR, October 2011. The mandate of the adaptation group can be summarised as follows: Show the consequences of climate change for infrastructures, and propose actions towards adapting the road network and management procedures to climate change. The work started by performing two surveys in road administrations in the participating countries: a survey of risks related to climate change, and a survey of ongoing adaptation work. The report to CEDR consists of a summary of the results of the surveys, and is followed by a more detailed examination of the effects of climate change on the road network. Suggestions for adaptation work are offered and criteria for prioritising possible actions are proposed. A thematic collection of examples demonstrating adaptation work in the participating countries is integrated in the report. Some of the examples refer to R&D programmes. Others describe current practice in one country that may be useful and relevant for application in another country. The report also suggests topics for future research, including opportunities for trans-European joint research programmes.Norwegian Public Road Administration (NPRA

Vinterdrift i endret klima

Rapporten inngår i en serie rapporter fra FoU-prosjektet “Klima og transport”, etatsprosjekt 2007-2010.Rapporten inngår i en serie rapporter fra FoU-prosjektet “Klima og transport”, etatsprosjekt 2007-2010. Hensikten med prosjektet er å forbedre rutiner og regelverk for planlegging, prosjektering, bygging, drift og vedlikehold av vegnettet som svar på endrede klimaforhold. Rapporten tilhører delprosjekt 6 – ”Konsekvenser for vinterdrift”, og inneholder en oversikt over de mest sannsynlige konsekvensene som klimaendringene kan ha for vinterdriften i tillegg til å gi råd om klimatilpasning og datainnsamling. De viktigste konklusjonene er at tilpasning bør først og fremst være i form av økt fleksibilitet og beredskap til å møte ekstreme værsituasjoner. Organisering av vinterdriften antas å kunne utvikles gradvis med hensyn til endret klima i og med at tidsskalaen for klimaendringene er lang sammenlignet med investeringer under vinterdriften.Statens vegvesen Vegdirektorate

Facilitated pronociceptive pain mechanisms in radiating back pain compared with localized back pain

Facilitated pain mechanisms and impaired pain inhibition are often found in chronic pain patients. This study compared clinical pain profiles, pain sensitivity, as well as pronociceptive and antinociceptive mechanisms in patients with localized low back pain (n = 18), localized neck pain (n = 17), low back and radiating leg pain (n = 18), or neck and radiating arm pain (n = 17). It was hypothesized that patients with radiating pain had facilitated pain mechanisms and impaired pain inhibition compared with localized pain patients. Cuff algometry was performed on the nonpainful lower leg to assess pressure pain threshold, tolerance, temporal summation of pain (increase in pain scores to 10 repeated stimulations at pressure pain tolerance intensity), and conditioning pain modulation (increase in pressure pain threshold during pain conditioning on the contralateral leg). Heat detection and heat pain threshold at the nonpainful hand were also assessed. Clinical pain intensity, psychological distress, and disability were assessed with questionnaires. Temporal summation of pain was increased in patients with radiating back pain compared with localized back pain (P &lt;.03). Patients with radiating arm pain or localized low back pain demonstrated hyperalgesia to heat and pressure in nonpainful body areas (P &lt;.05), as well as well as a facilitated clinical pain profile compared with patients with localized neck pain (P =.03). Patients with radiating pain patterns demonstrated facilitated temporal summation suggesting differences in the underlying pain mechanisms between patients with localized back pain and radiating pain. Perspective These findings have clinical implications because the underlying mechanisms in different back pain conditions may require different treatment strategies.</p

Computation of the stochastic basin of attraction by rigorous construction of a Lyapunov function

The y-basin of attraction of the zero solution of a nonlinear stochastic differential equation can be determined through a pair of a local and a non-local Lyapunov function. In this paper, we construct a non-local Lyapunov function by solving a second-order PDE using meshless collocation. We provide a-posteriori error estimates which guarantee that the constructed function is indeed a non-local Lyapunov function. Combining this method with the computation of a local Lyapunov function for the linearisation around an equilibrium of the stochastic differential equation in question, a problem which is much more manageable than computing a Lyapunov function in a large area containing the equilibrium, we provide a rigorous estimate of the stochastic y-basin of attraction of the equilibrium