Accurate control of hyperbolic trajectories in any dimension

The unsteady (nonautonomous) analog of a hyperbolic fixed point is a hyperbolic trajectory, whose importance is underscored by its attached stable and unstable manifolds, which have relevance in fluid flow barriers, chaotic basin boundaries, and the long-term behavior of the system. We develop a method for obtaining the unsteady control velocity which forces a hyperbolic trajectory to follow a user-prescribed variation with time. Our method is applicable in any dimension, and accuracy to any order is achievable.We demonstrate and validate our method by (1) controlling the fixed point at the origin of the Lorenz system, for example, obtaining a user-defined nonautonomous attractor, and (2) the saddle points in a droplet flow, using localized control which generates global transport.Sanjeeva Balasuriya, Kathrin Padberg-Gehl

Controlling the unsteady analogue of saddle stagnation points

It is well known that saddle stagnation points are crucial flow organizers in steady (autonomous) flows due to their accompanying stable and unstable manifolds. These have been extensively investigated experimentally, numerically, and theoretically in situations related to macroand micromixers in order to either restrict or enhance mixing. Saddle points are also important players in the dynamics of mechanical oscillators, in which such points and their associated invariant manifolds form boundaries of basins of attraction corresponding to qualitatively different types of behavior. The entity analogous to a saddle point in an unsteady (nonautonomous) flow is a timevarying hyperbolic trajectory with accompanying stable and unstable manifolds which move in time. Within the context of nearly steady flows, the unsteady velocity perturbation required to ensure that such a hyperbolic (saddle) trajectory follows a specified trajectory in space is derived and shown to be equivalent to that which can be obtained via a heuristic approach. An expression for the error in the hyperbolic trajectory's motion is also derived. This provides a new tool for the control of both fluid transport and mechanical oscillators. The method is applied to two examples-a four-roll mill and a Duffing oscillator-and the performance of the control strategy is shown to be excellent in both instances. © 2013 Society for Industrial and Applied Mathematics.Sanjeeva Balasuriya and Kathrin Padberg-Gehl

Phosphocholine-Modified Lipooligosaccharides of Haemophilus influenzae Inhibit ATP-Induced IL-1beta Release by Pulmonary Epithelial Cells

Phosphocholine-modified bacterial cell wall components are virulence factors enabling immune evasion and permanent colonization of the mammalian host, by mechanisms that are poorly understood. Recently, we demonstrated that free phosphocholine (PC) and PC-modified lipooligosaccharides (PC-LOS) from Haemophilus influenzae, an opportunistic pathogen of the upper and lower airways, function as unconventional nicotinic agonists and efficiently inhibit the ATP-induced release of monocytic IL-1beta. We hypothesize that H. influenzae PC-LOS exert similar effects on pulmonary epithelial cells and on the complex lung tissue. The human lung carcinoma-derived epithelial cell lines A549 and Calu-3 were primed with lipopolysaccharide from Escherichia coli followed by stimulation with ATP in the presence or absence of PC or PC-LOS or LOS devoid of PC. The involvement of nicotinic acetylcholine receptors was tested using specific antagonists. We demonstrate that PC and PC-LOS efficiently inhibit ATP-mediated IL-1beta release by A549 and Calu-3 cells via nicotinic acetylcholine receptors containing subunits alpha7, alpha9, and/or alpha10. Primed precision-cut lung slices behaved similarly. We conclude that H. influenzae hijacked an endogenous anti-inflammatory cholinergic control mechanism of the lung to evade innate immune responses of the host. These findings may pave the way towards a host-centered antibiotic treatment of chronic airway infections with H. influenzae

Application of semidefinite programming to maximize the spectral gap produced by node removal

The smallest positive eigenvalue of the Laplacian of a network is called the spectral gap and characterizes various dynamics on networks. We propose mathematical programming methods to maximize the spectral gap of a given network by removing a fixed number of nodes. We formulate relaxed versions of the original problem using semidefinite programming and apply them to example networks.Comment: 1 figure. Short paper presented in CompleNet, Berlin, March 13-15 (2013

Spectral early-warning signals for sudden changes in time-dependent flow patterns

Lagrangian coherent sets are known to crucially determine transport and mixing processes in non-autonomous flows. Prominent examples include vortices and jets in geophysical fluid flows. Coherent sets can be identified computationally by a probabilistic transfer-operator-based approach within a set-oriented numerical framework. Here, we study sudden changes in flow patterns that correspond to bifurcations of coherent sets. Significant changes in the spectral properties of a numerical transfer operator are heuristically related to critical events in the phase space of a time-dependent system. The transfer operator approach is applied to different example systems of increasing complexity. In particular, we study the 2002 splitting event of the Antarctic polar vortex

Isolated blunt abdominal aortic injury without concomitant abdominal injuries treated with endovascular stent grafting

Blunt injury of the abdominal aorta is a rare event, seen in only 0.07% to 0.17% of all blunt traumas. These injuries are frequently associated with other intra-abdominal injuries, with high rates of morbidity and mortality. We present a case of isolated blunt abdominal aortic trauma to the infrarenal aorta without concomitant abdominal or spinal injuries. The patient was treated with endovascular aortic stent grafting and is without complications 12 months after the procedure

Minimizing the stabbing number of matchings, trees, and triangulations

The (axis-parallel) stabbing number of a given set of line segments is the maximum number of segments that can be intersected by any one (axis-parallel) line. This paper deals with finding perfect matchings, spanning trees, or triangulations of minimum stabbing number for a given set of points. The complexity of these problems has been a long-standing open question; in fact, it is one of the original 30 outstanding open problems in computational geometry on the list by Demaine, Mitchell, and O'Rourke. The answer we provide is negative for a number of minimum stabbing problems by showing them NP-hard by means of a general proof technique. It implies non-trivial lower bounds on the approximability. On the positive side we propose a cut-based integer programming formulation for minimizing the stabbing number of matchings and spanning trees. We obtain lower bounds (in polynomial time) from the corresponding linear programming relaxations, and show that an optimal fractional solution always contains an edge of at least constant weight. This result constitutes a crucial step towards a constant-factor approximation via an iterated rounding scheme. In computational experiments we demonstrate that our approach allows for actually solving problems with up to several hundred points optimally or near-optimally.Comment: 25 pages, 12 figures, Latex. To appear in "Discrete and Computational Geometry". Previous version (extended abstract) appears in SODA 2004, pp. 430-43

How to read a next-generation sequencing report-what oncologists need to know.

Next-generation sequencing (NGS) of tumor cell-derived DNA/RNA to screen for targetable genomic alterations is now widely available and has become part of routine practice in oncology. NGS testing strategies depend on cancer type, disease stage and the impact of results on treatment selection. The European Society for Medical Oncology (ESMO) has recently published recommendations for the use of NGS in patients with advanced cancer. We complement the ESMO recommendations with a practical review of how oncologists should read and interpret NGS reports. A concise and straightforward NGS report contains details of the tumor sample, the technology used and highlights not only the most important and potentially actionable results, but also other pathogenic alterations detected. Variants of unknown significance should also be listed. Interpretation of NGS reports should be a joint effort between molecular pathologists, tumor biologists and clinicians. Rather than relying and acting on the information provided by the NGS report, oncologists need to obtain a basic level of understanding to read and interpret NGS results. Comprehensive annotated databases are available for clinicians to review the information detailed in the NGS report. Molecular tumor boards do not only stimulate debate and exchange, but may also help to interpret challenging reports and to ensure continuing medical education

Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators

The detection of regions in the ocean that are coherent over an extended period of time is a fundamental problem in many oceanic applications. For instance such regions are important for studying the transport of marine species and for the distribution of nutrients. In this study we demonstrate the efficacy of transfer operators in detecting and analysing such structures. We focus first on the detection of the Weddell and Ross Gyre for the four seasons spanning December 2003–November 2004 within the 3-D oceanic domain south of 30° S, and show distinct seasonal differences in both the three-dimensional structure and the persistence of the gyres. Further, we demonstrate a new technique based on the discretised transfer operators to calculate the mean residence time of water within parts of the gyres and determine pathways of water leaving and entering the gyres