General existence and uniqueness of viscosity solutions for impulse control of jump-diffusions

General theorems for existence and uniqueness of viscosity solutions for Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVI) with integral term are established. Such nonlinear partial integro-differential equations (PIDE) arise in the study of combined impulse and stochastic control for jump-diffusion processes. The HJBQVI consists of an HJB part (for stochastic control) combined with a nonlocal impulse intervention term. Existence results are proved via stochastic means, whereas our uniqueness (comparison) results adapt techniques from viscosity solution theory. This paper is to our knowledge the first treating rigorously impulse control for jump-diffusion processes in a general viscosity solution framework; the jump part may have infinite activity. In the proofs, no prior continuity of the value function is assumed, quadratic costs are allowed, and elliptic and parabolic results are presented for solutions possibly unbounded at infinity

Nanosecond molecular relaxations in lipid bilayers studied by high energy resolution neutron scattering and in-situ diffraction

We report a high energy-resolution neutron backscattering study to investigate slow motions on nanosecond time scales in highly oriented solid supported phospholipid bilayers of the model system DMPC -d54 (deuterated 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine), hydrated with heavy water. Wave vector resolved quasi-elastic neutron scattering (QENS) is used to determine relaxation times $\tau$, which can be associated with different molecular components, i.e., the lipid acyl chains and the interstitial water molecules in the different phases of the model membrane system. The inelastic data are complemented both by energy resolved and energy integrated in-situ diffraction. From a combined analysis of the inelastic data in the energy and time domain, the respective character of the relaxation, i.e., the exponent of the exponential decay is also determined. From this analysis we quantify two relaxation processes. We associate the fast relaxation with translational diffusion of lipid and water molecules while the slow process likely stems from collective dynamics

Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity

The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]

Scale-Free topologies and Activatory-Inhibitory interactions

A simple model of activatory-inhibitory interactions controlling the activity of agents (substrates) through a "saturated response" dynamical rule in a scale-free network is thoroughly studied. After discussing the most remarkable dynamical features of the model, namely fragmentation and multistability, we present a characterization of the temporal (periodic and chaotic) fluctuations of the quasi-stasis asymptotic states of network activity. The double (both structural and dynamical) source of entangled complexity of the system temporal fluctuations, as an important partial aspect of the Correlation Structure-Function problem, is further discussed to the light of the numerical results, with a view on potential applications of these general results.Comment: Revtex style, 12 pages and 12 figures. Enlarged manuscript with major revision and new results incorporated. To appear in Chaos (2006

Motional Coherence in Fluid Phospholipid Membranes

URL:http://link.aps.org/doi/10.1103/PhysRevLett.101.248106 DOI:10.1103/PhysRevLett.101.248106We report a high energy-resolution neutron backscattering study, combined with in situ diffraction, to investigate slow molecular motions on nanosecond time scales in the fluid phase of phospholipid bilayers of 1,2-dimyristoyl-sn-glycero-3-phoshatidylcholine. A cooperative structural relaxation process was observed. From the in-plane scattering vector dependence of the relaxation rates in hydrogenated and deuterated samples, combined with results from a 0.1  μs long all-atom molecular dynamics simulation, it is concluded that correlated dynamics in lipid membranes occurs over several lipid distances, spanning a time interval from pico- to nanoseconds.We acknowledge financial support from the DFG through Project No. SA 772/8-2

Laboratory evidence of disseminated intravascular coagulation is associated with a fatal outcome in children with cerebral malaria despite an absence of clinically evident thrombosis or bleeding

Background A procoagulant state is implicated in cerebral malaria (CM ) pathogenesis, but whether disseminated intravascular coagulation (DIC ) is present or associated with a fatal outcome is unclear. Objectives To determine the frequency of overt DIC , according to ISTH criteria, in children with fatal and non‐fatal CM . Methods/patients Malawian children were recruited into a prospective cohort study in the following diagnostic groups: retinopathy‐positive CM (n = 140), retinopathy‐negative CM (n = 36), non‐malarial coma (n = 14), uncomplicated malaria (UM ), (n = 91), mild non‐malarial febrile illness (n = 85), and healthy controls (n = 36). Assays in the ISTH DIC criteria were performed, and three fibrin‐related markers, i.e. protein C, antithrombin, and soluble thrombomodulin, were measured. Results and conclusions Data enabling assignment of the presence or absence of ‘overt DIC ’ were available for 98 of 140 children with retinopathy‐positive CM . Overt DIC was present in 19 (19%), and was associated with a fatal outcome (odds ratio [OR] 3.068; 95% confidence interval [CI] 1.085–8.609; P = 0.035]. The levels of the three fibrin‐related markers and soluble thrombomodulin were higher in CM patients than in UM patients (all P < 0.001). The mean fibrin degradation product level was higher in fatal CM patients (71.3 μg mL−1 [95% CI 49.0–93.6]) than in non‐fatal CM patients (48.0 μg mL−1 [95% CI 37.7–58.2]; P = 0.032), but, in multivariate logistic regression, thrombomodulin was the only coagulation‐related marker that was independently associated with a fatal outcome (OR 1.084 for each ng mL−1 increase [95% CI 1.017–1.156]; P = 0.014). Despite these laboratory derangements, no child in the study had clinically evident bleeding or thrombosis. An overt DIC score and high thrombomodulin levels are associated with a fatal outcome in CM , but infrequently indicate a consumptive coagulopathy

Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

Coarse Bifurcation Diagrams via Microscopic Simulators: A State-Feedback Control-Based Approach

The arc-length continuation framework is used for the design of state feedback control laws that enable a microscopic simulator trace its own open-loop coarse bifurcation diagram. The steering of the system along solution branches is achieved through the manipulation of the bifurcation parameter, which becomes our actuator. The design approach is based on the assumption that the eigenvalues of the linearized system can be decomposed into two well separated clusters: one containing eigenvalues with large negative real parts and one containing (possibly unstable) eigenvalues close to the origin