Sufficient second-order conditions for bang-bang control problems

We provide sufficient optimality conditions for optimal control problems with bang-bang controls. Building on a structural assumption on the adjoint state, we additionally need a weak second-order condition. This second-order condition is formulated with functions from an extended critical cone, and it is equivalent to a formulation posed on measures supported on the set where the adjoint state vanishes. If our sufficient optimality condition is satisfied, we obtain a local quadratic growth condition in L1(Ω)The first author was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2014-57531-P. The second author was partially supported by the DFG under grant Wa 3626/1-1

Increase in degraded collagen type II in synovial fluid early in the rabbit meniscectomy model of osteoarthritis

SummaryObjectiveThe objective of this study was to determine whether collagen type II breakdown products in synovial fluid (SF), detected by an enzyme-linked immunoassay, represent a useful marker for early events in osteoarthritis (OA) in the rabbit medial meniscectomy model.DesignComplete medial meniscectomy was performed on the right knee joints of 32 rabbits. Balanced groups of rabbits were then sacrificed at 2, 4, 8, and 12 weeks post-surgery. An additional 8 unoperated and 11 sham-operated animals served as controls. SF lavages were performed on right and left knee joints of the same animals at sacrifice. The proteolytic epitope of type II collagen was monitored using an enzyme-linked immunoassay.ResultsMacroscopically visible surface fibrillation and focal erosions appeared as early as 2 weeks after meniscectomy in the femorotibial joint (P<0.01). OA developed gradually during the later observation period, and then predominantly on the medial tibial plateau and medial femur. Significant histological alterations in cartilage, including a loss of proteoglycans, surface irregularities, and clefts, were detected at 2 weeks after meniscectomy (P<0.01). Collagen type II epitope levels in SF lavage samples were elevated peaking at 2 weeks after meniscectomy (P<0.02). Levels decreased at later time points, but they were still raised at 12 weeks (P≤0.05). Highly significant correlations were found between the SF collagen type II epitope levels and the macroscopic and microscopic scoring results (Spearman rho correlation coefficient, macroscopy—collagen type II epitope r=0.222, P=0.025; microscopy—collagen type II epitope r=0.436, P≤0.01).ConclusionIn this rabbit model of medial meniscectomy, levels of type II collagen fragments in SF appear to provide a useful marker of the early degenerative changes

Probing microscopic origins of confined subdiffusion by first-passage observables

Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean square displacement (MSD). However, subdiffusive behavior can stem from different microscopic scenarios, which can not be identified solely by the MSD data. In this paper we present a theoretical framework which permits to calculate analytically first-passage observables (mean first-passage times, splitting probabilities and occupation times distributions) in disordered media in any dimensions. This analysis is applied to two representative microscopic models of subdiffusion: continuous-time random walks with heavy tailed waiting times, and diffusion on fractals. Our results show that first-passage observables provide tools to unambiguously discriminate between the two possible microscopic scenarios of subdiffusion. Moreover we suggest experiments based on first-passage observables which could help in determining the origin of subdiffusion in complex media such as living cells, and discuss the implications of anomalous transport to reaction kinetics in cells.Comment: 21 pages, 3 figures. Submitted versio

In vivo characterization of protein-protein interactions in the AP1 system with fluorescence correlation spectroscopy (FCS).

The aim of these studies is the quantitative investigation of protein-protein interactions in the AP1 system in vivo. First results of FCS measurements show an exchange in the nucleus of the proteins Fos-CFP and Jun-YFP in the stably mono-transfected HeLa-Cells. This is also shown by fitting the bleaching curves measured in the nucleus with an appropriate model. We obtained dissociation times between 10 and 20 seconds in the nucleus. In the autocorrelation function a free and an obstructed component of diffusion are shown. For further studies doubly transfected cells with both proteins, Fos-CFP and Jun-YFP, were prepared. These cells will now be characterized with FCCS to investigate the protein-protein interactions. In order to obtain the dissociation rates of the complex in the cell nucleus bleaching curves will be recorded on these cell lines. We also overexpressed and purified Jun-YFP and Fos-CFP for in vitro studies

Vibriophage VcA-3 as an epidemic strain marker for the U.S. Gulf Coast Vibrio cholerae O1 clone.

Toxigenic and nontoxigenic Vibrio cholerae O1, El Tor biotype strains, which are endemic to the U.S. Gulf Coast, can be lysogenic for bacteriophage VcA-3. To evaluate the presence of VcA-3 as an indicator of toxigenicity and as an epidemic strain marker, phage production and the presence of phage and cholera toxin genes were assayed in 98 strains of V. cholerae O1 (35 U.S. and 63 foreign strains). By using a HindIII chromosomal digest for Southern blot analysis, 39 of the study strains hybridized with the VcA-3 probe in 10 banding patterns. The 15 toxigenic and 6 of the 20 nontoxigenic U.S. isolates gave four VcA-3-related patterns. Among the foreign isolates, 12 of 12 toxigenic classical biotype strains, 1 of 43 toxigenic El Tor biotype strains, and 3 of 8 nontoxigenic atypical strains gave six patterns that were clearly distinct from that of VcA-3. Compared with Southern blot analysis, the phage production assay had a sensitivity of 1.0 and a specificity of 0.48, while the colony hybridization assay had a sensitivity of 1.0 and a specificity of 0.77 for identification of VcA-3. Neither assay reliably identified the toxigenic Gulf Coast clone. The presence of VcA-3, as defined by Southern blot analysis, always separated toxigenic U.S. from foreign isolates and often from nontoxigenic U.S. isolates of V. cholerae O1

Spectrum and Charge Ratio of Vertical Cosmic Ray Muons up to Momenta of 2.5 TeV/c

The ALEPH detector at LEP has been used to measure the momentum spectrum and charge ratio of vertical cosmic ray muons underground. The sea-level cosmic ray muon spectrum for momenta up to 2.5 TeV/c has been obtained by correcting for the overburden of 320 meter water equivalent (mwe). The results are compared with Monte Carlo models for air shower development in the atmosphere. From the analysis of the spectrum the total flux and the spectral index of the cosmic ray primaries is inferred. The charge ratio suggests a dominantly light composition of cosmic ray primaries with energies up to 10^15 eV

PT-symmetric models in curved manifolds

We consider the Laplace-Beltrami operator in tubular neighbourhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.Comment: 37 pages, PDFLaTeX with 11 figure

AltitudeOmics: The Integrative Physiology of Human Acclimatization to Hypobaric Hypoxia and Its Retention upon Reascent.

An understanding of human responses to hypoxia is important for the health of millions of people worldwide who visit, live, or work in the hypoxic environment encountered at high altitudes. In spite of dozens of studies over the last 100 years, the basic mechanisms controlling acclimatization to hypoxia remain largely unknown. The AltitudeOmics project aimed to bridge this gap. Our goals were 1) to describe a phenotype for successful acclimatization and assess its retention and 2) use these findings as a foundation for companion mechanistic studies. Our approach was to characterize acclimatization by measuring changes in arterial oxygenation and hemoglobin concentration [Hb], acute mountain sickness (AMS), cognitive function, and exercise performance in 21 subjects as they acclimatized to 5260 m over 16 days. We then focused on the retention of acclimatization by having subjects reascend to 5260 m after either 7 (n = 14) or 21 (n = 7) days at 1525 m. At 16 days at 5260 m we observed: 1) increases in arterial oxygenation and [Hb] (compared to acute hypoxia: PaO2 rose 9±4 mmHg to 45±4 while PaCO2 dropped a further 6±3 mmHg to 21±3, and [Hb] rose 1.8±0.7 g/dL to 16±2 g/dL; 2) no AMS; 3) improved cognitive function; and 4) improved exercise performance by 8±8% (all changes p&lt;0.01). Upon reascent, we observed retention of arterial oxygenation but not [Hb], protection from AMS, retention of exercise performance, less retention of cognitive function; and noted that some of these effects lasted for 21 days. Taken together, these findings reveal new information about retention of acclimatization, and can be used as a physiological foundation to explore the molecular mechanisms of acclimatization and its retention

Protein Diffusion in Mammalian Cell Cytoplasm

We introduce a new method for mesoscopic modeling of protein diffusion in an entire cell. This method is based on the construction of a three-dimensional digital model cell from confocal microscopy data. The model cell is segmented into the cytoplasm, nucleus, plasma membrane, and nuclear envelope, in which environment protein motion is modeled by fully numerical mesoscopic methods. Finer cellular structures that cannot be resolved with the imaging technique, which significantly affect protein motion, are accounted for in this method by assigning an effective, position-dependent porosity to the cell. This porosity can also be determined by confocal microscopy using the equilibrium distribution of a non-binding fluorescent protein. Distinction can now be made within this method between diffusion in the liquid phase of the cell (cytosol/nucleosol) and the cytoplasm/nucleoplasm. Here we applied the method to analyze fluorescence recovery after photobleach (FRAP) experiments in which the diffusion coefficient of a freely-diffusing model protein was determined for two different cell lines, and to explain the clear difference typically observed between conventional FRAP results and those of fluorescence correlation spectroscopy (FCS). A large difference was found in the FRAP experiments between diffusion in the cytoplasm/nucleoplasm and in the cytosol/nucleosol, for all of which the diffusion coefficients were determined. The cytosol results were found to be in very good agreement with those by FCS