On the Floquet Theory of Delay Differential Equations

We present an analytical approach to deal with nonlinear delay differential equations close to instabilities of time periodic reference states. To this end we start with approximately determining such reference states by extending the Poincar'e Lindstedt and the Shohat expansions which were originally developed for ordinary differential equations. Then we systematically elaborate a linear stability analysis around a time periodic reference state. This allows to approximately calculate the Floquet eigenvalues and their corresponding eigensolutions by using matrix valued continued fractions

Invasive pulmonary aspergillosis in chronic obstructive pulmonary disease: an emerging fungal pathogen

ABSTRACTAcute invasive pulmonary aspergillosis occurs predominantly in immunocompromised hosts, with increasing numbers of cases of invasive aspergillosis among patients with chronic obstructive pulmonary disease (COPD) being reported. Among 13 cases of invasive aspergillosis diagnosed in COPD patients admitted to the intensive care unit with acute respiratory distress, the only risk factor for invasive fungal infection was corticosteroid treatment. Invasive aspergillosis should be suspected in COPD patients receiving steroid treatment who have extensive pulmonary infiltrates. Survival depends on rapid diagnosis and early appropriate treatment. A decrease or interruption of steroid treatment should be considered as part of the overall therapeutic strategy

Geometric Friction Directs Cell Migration

In the absence of environmental cues, a migrating cell performs an isotropic random motion. Recently, the breaking of this isotropy has been observed when cells move in the presence of asymmetric adhesive patterns. However, up to now the mechanisms at work to direct cell migration in such environments remain unknown. Here, we show that a nonadhesive surface with asymmetric microgeometry consisting of dense arrays of tilted micropillars can direct cell motion. Our analysis reveals that most features of cell trajectories, including the bias, can be reproduced by a simple model of active Brownian particle in a ratchet potential, which we suggest originates from a generic elastic interaction of the cell body with the environment. The observed guiding effect, independent of adhesion, is therefore robust and could be used to direct cell migration both in vitro and in vivo

Mitotic Rounding Alters Cell Geometry to Ensure Efficient Bipolar Spindle Formation

Accurate animal cell division requires precise coordination of changes in the structure of the microtubule-based spindle and the actin-based cell cortex. Here, we use a series of perturbation experiments to dissect the relative roles of actin, cortical mechanics, and cell shape in spindle formation. We find that, whereas the actin cortex is largely dispensable for rounding and timely mitotic progression in isolated cells, it is needed to drive rounding to enable unperturbed spindle morphogenesis under conditions of confinement. Using different methods to limit mitotic cell height, we show that a failure to round up causes defects in spindle assembly, pole splitting, and a delay in mitotic progression. These defects can be rescued by increasing microtubule lengths and therefore appear to be a direct consequence of the limited reach of mitotic centrosome-nucleated microtubules. These findings help to explain why most animal cells round up as they enter mitosis

Confinement and Low Adhesion Induce Fast Amoeboid Migration of Slow Mesenchymal Cells

The mesenchymal-amoeboid transition (MAT) was proposed as a mechanism for cancer cells to adapt their migration mode to their environment. While the molecular pathways involved in this transition are well documented, the role of the microenvironment in the MAT is still poorly understood. Here, we investigated how confinement and adhesion affect this transition. We report that, in the absence of focal adhesions and under conditions of confinement, mesenchymal cells can spontaneously switch to a fast amoeboid migration phenotype. We identified two main types of fast migration-one involving a local protrusion and a second involving a myosin-II-dependent mechanical instability of the cell cortex that leads to a global cortical flow. Interestingly, transformed cells are more prone to adopt this fast migration mode. Finally, we propose a generic model that explains migration transitions and predicts a phase diagram of migration phenotypes based on three main control parameters: confinement, adhesion, and contractility

Generalized Totalizer Encoding for Pseudo-Boolean Constraints

Pseudo-Boolean constraints, also known as 0-1 Integer Linear Constraints, are used to model many real-world problems. A common approach to solve these constraints is to encode them into a SAT formula. The runtime of the SAT solver on such formula is sensitive to the manner in which the given pseudo-Boolean constraints are encoded. In this paper, we propose generalized Totalizer encoding (GTE), which is an arc-consistency preserving extension of the Totalizer encoding to pseudo-Boolean constraints. Unlike some other encodings, the number of auxiliary variables required for GTE does not depend on the magnitudes of the coefficients. Instead, it depends on the number of distinct combinations of these coefficients. We show the superiority of GTE with respect to other encodings when large pseudo-Boolean constraints have low number of distinct coefficients. Our experimental results also show that GTE remains competitive even when the pseudo-Boolean constraints do not have this characteristic.Comment: 10 pages, 2 figures, 2 tables. To be published in 21st International Conference on Principles and Practice of Constraint Programming 201

Quorum-sensing activity and related virulence factor expression in clinically pathogenic isolates of Pseudomonas aeruginosa

AbstractRespiratory isolates of Pseudomonas aeruginosa were collected from 58 critically-ill patients with ventilator-associated pneumonia. Expression of elastase and pyocyanin was assessed semi-quantitatively, while quorum-sensing activity was assessed by quantifying the levels of the autoinducers N-3-oxododecanoyl-L-homoserine lactone (C12-HSL) and N-butanoyl-L-homoserine lactone (C4-HSL). Correlations were sought between quorum-sensing activity and the expression of these two virulence factors, and all results were compared to those obtained with the laboratory reference strains PA103, a strain defective in quorum-sensing, and PAO1, a functional quorum-sensing strain. More than two-thirds of clinically pathogenic isolates had increased levels of elastase and/or pyocyanin, and high quorum-sensing activity, as assessed by autoinducer levels. However, a strong correlation between quorum-sensing activity and virulence factor production was revealed only for elastase and not for pyocyanin (C12-HSL/elastase, r = 0.7, p 2 × 10−9; C4-HSL/elastase, r = 0.7, p 2 × 10−9). These data suggest that the pathogenicity of P. aeruginosa isolates from critically-ill patients with ventilator-associated pneumonia is caused, at least in part, by an increase in elastase production regulated by quorum-sensing, while increased pyocyanin production in these isolates may be regulated predominantly by mechanisms other than quorum-sensing