Stochastic Perturbations of Periodic Orbits with Sliding

Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a discontinuity surface of the vector field. In this paper we consider the addition of small noise to a general Filippov system and study the resulting stochastic dynamics near such a periodic orbit. Since a straight-forward asymptotic expansion in terms of the noise amplitude is not possible due to the presence of discontinuity surfaces, in order to quantitatively determine the basic statistical properties of the dynamics, we treat different parts of the periodic orbit separately. Dynamics distant from discontinuity surfaces is analyzed by the use of a series expansion of the transitional probability density function. Stochastically perturbed sliding motion is analyzed through stochastic averaging methods. The influence of noise on points at which the periodic orbit escapes a discontinuity surface is determined by zooming into the transition point. We combine the results to quantitatively determine the effect of noise on the oscillation time for a three-dimensional canonical model of relay control. For some parameter values of this model, small noise induces a significantly large reduction in the average oscillation time. By interpreting our results geometrically, we are able to identify four features of the relay control system that contribute to this phenomenon.Comment: 44 pages, 9 figures, submitted to: J Nonlin. Sc

Propositional Dynamic Logic for Message-Passing Systems

We examine a bidirectional propositional dynamic logic (PDL) for finite and infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of multi-modal logic we can express properties both in the entire future and in the past of an event. Path expressions strengthen the classical until operator of temporal logic. For every formula defining an MSC language, we construct a communicating finite-state machine (CFM) accepting the same language. The CFM obtained has size exponential in the size of the formula. This synthesis problem is solved in full generality, i.e., also for MSCs with unbounded channels. The model checking problem for CFMs and HMSCs turns out to be in PSPACE for existentially bounded MSCs. Finally, we show that, for PDL with intersection, the semantics of a formula cannot be captured by a CFM anymore

"Nearly" Generic Monitoring and Control Programs Maintain Beam Quality

We describe a tool chain that enables experimentation and study of real C++ applications. Our tool chain enables reverse engineering and program analysis by exploiting gcc, and thus accepts any C++ application that can be analysed by the C++ parser and front end of gcc. Our current test suite consists of large, open-source applications with diverse problem domains, including language processing and gaming. Our tool chain is designed using a GXL-based pipe-filter architecture; therefore, the individual applications and libraries that constitute our tool chain each provide a point of access. The preferred point of access is the g4api Application Programming Interface (API), which is located at the end of the chain. g4api provides access to information about the C++ program under study, including information about declarations, such as classes (including template instantiations); namespaces; functions; and variables, statements and some expressions. Access to the information is via either a pointer to the global namespace, or a list interface

Improvements of the Set Up and Procedures for Beam Energy Measurements at BESSY II

With a 7 T wiggler in operation all attempts to detect the resonant depolarization of the electron spins were unsuccessful at BESSY II. This was attributed to the severely reduced degree of spin polarization of the electrons moving in the alternating fields of the strong wiggler which on the other hand nearly doubles the radiation loss per turn. The key to a clear detection of the depolarization is the improvement of the sensitivity of the polarimeter, based on the spin dependent Touschek scattering cross section and the more effective and thus full depolarization of the beam. With these improvements the high precision beam energy determination can again be performed in parallel to the normal user operation and without any noticeable perturbations to the bea

Changes in Fungal Community Composition in Response to Elevated Atmospheric CO2 and Nitrogen Fertilization Varies with Soil Horizon

Increasing levels of atmospheric carbon dioxide (CO(2)) and rates of nitrogen (N)-deposition to forest ecosystems are predicted to alter the structure and function of soil fungal communities, but the spatially heterogeneous distribution of soil fungi has hampered investigations aimed at understanding such impacts. We hypothesized that soil physical and chemical properties and fungal community composition would be differentially impacted by elevated atmospheric CO(2) (eCO(2)) and N-fertilization in spatially separated field samples, in the forest floor, 0–2, 2–5, and 5–10 cm depth intervals in a loblolly pine Free-Air Carbon Dioxide Enrichment (FACE) experiment. In all soils, quantitative PCR-based estimates of fungal biomass were highest in the forest floor. Fungal richness, based on pyrosequencing of the fungal ribosomal large subunit gene, increased in response to N-fertilization in 0–2 cm and forest floor intervals. Composition shifted in forest floor, 0–2 and 2–5 cm intervals in response to N-fertilization, but the shift was most distinct in the 0–2 cm interval, in which the largest number of statistically significant changes in soil chemical parameters (i.e., phosphorus, organic matter, calcium, pH) was also observed. In the 0–2 cm interval, increased recovery of sequences from the Thelephoraceae, Tricholomataceae, Hypocreaceae, Clavicipitaceae, and Herpotrichiellaceae families and decreased recovery of sequences from the Amanitaceae correlated with N-fertilization. In this same depth interval, Amanitaceae, Tricholomataceae, and Herpotriciellaceae sequences were recovered less frequently from soils exposed to eCO(2) relative to ambient conditions. These results demonstrated that vertical stratification should be taken into consideration in future efforts to elucidate environmental impacts on fungal communities and their feedbacks on ecosystem processes

BIOCHEMICAL AND FUNCTIONAL CHARACTERIZATION OF A POTENTIAL 2’, 3’-CYCLIC-NUCLEOTIDE 3’-PHOSPHODIESTERASE (CNPASE) FOUND IN TUMORIGENIC FISH RETROVIRUSES

Tumorigenic retroviruses cause seasonal cancer in fish. Many of these retroviruses contain an interesting unknown gene of cellular origin. Computational programs predict that this gene encodes a CNPase (2’,3’-Cyclic-nucleotide 3’-phosphodiesterase). In mammals, the natural function of CNPase is unknown. The purpose of the experiment is to isolate and characterize the potential viral CNPase. Utilizing a vector from zebrafish endogenous retrovirus (ZFERV), the potential CNPase genetic sequence will be isolated and analyzed. Thereafter, the potential CNPase protein will be expressed and purified, and characterization will include enzymatic activity assays, inhibition activity studies, and NMR studies. Future studies involve functional characterization of the potential CNPase, including binding and transformation studies. Potential CNPase is predicted to function as an oncogene that promotes tumorigenesis in fish. Exploring this potential CNPase may aide in the treatment of affected fish as well as provide insight into the function of this enzyme in humans

Mean Field Effects for Counterpropagating Traveling Wave Solutions of Reaction-Diffusion Systems

In many problems, e.g., in combustion or solidification, one observes traveling waves that propagate with constant velocity and shape in the x direction, say, are independent of y and z and describe transitions between two equilibrium states, e.g., the burned and the unburned reactants. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves having additional structure, such as traveling waves in the y and z directions, which can themselves be subject to instabilities as parameters are further varied. To investigate this scenario we consider a system of reaction-diffusion equations with a traveling wave solution as a basic state. We determine solutions bifurcating from the basic state that describe counterpropagating traveling waves in directions orthogonal to the direction of propagation of the basic state and determine their stability. Specifically, we derive long wave modulation equations for the amplitudes of the counterpropagating traveling waves that are coupled to an equation for a mean field, generated by the translation of the basic state in the direction of its propagation. The modulation equations are then employed to determine stability boundaries to long wave perturbations for both unidirectional and counterpropagating traveling waves. The stability analysis is delicate because the results depend on the order in which transverse and longitudinal perturbation wavenumbers are taken to zero. For the unidirectional wave we demonstrate that it is sufficient to consider the cases of (i) purely transverse perturbations, (ii) purely longitudinal perturbations, and (iii) longitudinal perturbations with a small transverse component. These yield Eckhaus type, zigzag type, and skew type instabilities, respectively. The latter arise as a specific result of interaction with the mean field. We also consider the degenerate case of very small group velocity, as well as other degenerate cases, which yield several additional instability boundaries. The stability analysis is then extended to the case of counterpropagating traveling waves

Fuzzy K-NN applied to moulds detection

peer reviewedThe possibility to detect Aspergillus versicolor growing on different building materials by a metal oxide sensor array is studied. Results show that an accurate classification rate of 89 +/- 3% can be obtained combining an extended linear discriminant analysis plus a fuzzy k-NN classifier. The classification ability of the classifier is assessed within the dataset by crossvalidation and also in a second dataset collected 5 months later. There is a slight decrease in the classification performance for all the algorithms, being the most sensitive the most accurate one