On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

Scanning electron microscopy of Ancylostoma spp. dog infective larvae captured and destroyed by the nematophagous fungus Duddingtonia flagrans

The interaction between the nematode-trapping fungus Duddingtonia flagrans (isolate CG768) against Ancylostoma spp. dog infective larvae (L₃) was evaluated by means of scanning electron microscopy. Adhesive network trap formation was observed 6 h after the beginning of the interaction, and the capture of Ancylostoma spp. L₃ was observed 8 h after the inoculation these larvae on the cellulose membranes colonized by the fungus. Scanning electron micrographs were taken at 0, 12, 24, 36 and 48 h, where 0 is the time when Ancylostoma spp. L₃ was first captured by the fungus. Details of the capture structure formed by the fungus were described. Nematophagous Fungus Helper Bacteria (NHB) were found at interactions points between the D. flagrans and Ancylostoma spp. L₃. The cuticle penetration by the differentiated fungal hyphae with the exit of nematode internal contents was observed 36 h after the capture. Ancylostoma spp. L₃ were completely destroyed after 48 h of interaction with the fungus. The scanning electron microscopy technique was efficient on the study of this interaction, showing that the nematode-trapping fungus D. flagrans (isolate CG768) is a potential exterminator of Ancylostoma spp. L₃.     

Towards dynamic control of magnetic fields to focus magnetic carriers to targets deep inside the body

Magnetic drug delivery has the potential to target therapy to specific regions in the body, improving efficacy and reducing side effects for treatment of cancer, stroke, infection, and other diseases. Using stationary external magnets, which attract the magnetic drug carriers, this treatment is limited to shallow targets (<5 cm below skin depth using the strongest possible, still safe, practical magnetic fields). We consider dynamic magnetic actuation and present initial results that show it is possible to vary magnets one against the other to focus carriers between them on average. The many remaining tasks for deep targeting in-vivo are then briefly noted.     

Essential countability of treeable equivalence relations

We establish a dichotomy theorem characterizing the circumstances under which a treeable Borel equivalence relation E is essentially countable. Under additional topological assumptions on the treeing, we in fact show that E   is essentially countable if and only if there is no continuous embedding of _E1${\mathbb{E}}_1$ into E. Our techniques also yield the first classical proof of the analogous result for hypersmooth equivalence relations, and allow us to show that up to continuous Kakutani embeddability, there is a minimum Borel function which is not essentially countable-to-one.     

Existence of Néel Order in the S=1 Bilinear-Biquadratic Heisenberg Model via Random Loops

We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, and also in the presence of trapped geodesics. In the boundary case, we show injectivity of the attenuated ray transform on tensor fields with values in a Hermitian bundle (i.e., vector valued case). We also show that a connection and Higgs field on a Hermitian bundle are determined up to gauge by the knowledge of the parallel transport between boundary points along all possible geodesics. The main tools are an energy identity, the Pestov identity with a unitary connection, which is presented in a general form, and a precise analysis of the singularities of solutions of transport equations when there are trapped geodesics. In the case of closed manifolds, we obtain similar results modulo the obstruction given by twisted conformal Killing tensors, and we also study this obstruction.     

Modeling of thermal effects in antivascular ultrasound therapy

Antivascular ultrasound consisting of low-intensity sonication in the presence of circulating microbubbles of an ultrasound contrast agent has been demonstrated to disrupt blood flow in solid cancers. In this study a mathematical framework is described for the microbubble-induced heating that occurs during antivascular ultrasound. Biological tissues are modeled as a continuum of microbubble-filled vasculature, cells, and interstitial fluids with compressibility equal to the sum of the compressibility of each component. The mathematical simulations show that the absorption of ultrasound waves by viscous damping of the microbubble oscillations induced significant local heating of the tissue vasculature. The extent and the rate of temperature increase not only depends on the properties of the microbubbles and the sonication parameters but is also influenced markedly by the blood flow. Slow flow conditions lead to higher tissue temperatures due to a stronger interaction between microbubbles and ultrasound and reduced heat dissipation. Because tumors have slower blood flow than healthy tissue, the microbubble-induced ultrasound antivascular therapy is likely to affect cancerous tissue more extensively than healthy tissue, providing a way to selectively target the vasculature of cancers.     

A posteriori error analysis of round-off errors in the numerical solution of ordinary differential equations

We prove sharp, computable error estimates for the propagation of errors in the numerical solution of ordinary differential equations. The new estimates extend previous estimates of the influence of data errors and discretization errors with a new term accounting for the propagation of numerical round-off errors, showing that the accumulated round-off error is inversely proportional to the square root of the step size. As a consequence, the numeric precision eventually sets the limit for the pointwise computability of accurate solutions of any ODE. The theoretical results are supported by numerically computed solutions and error estimates for the Lorenz system and the van der Pol oscillator.     

Organic semiconductors for solution-processable field-effect transistors (OFETs)

The cost-effective production of flexible electronic components will profit considerably from the development of solution-processable, organic semiconductor materials. Particular attention is focused on soluble semiconductors for organic field-effect transistors (OFETs). The hitherto differentiation between "small molecules" and polymeric materials no longer plays a role, rather more the ability to process materials from solution to homogeneous semiconducting films with optimal electronic properties (high charge-carrier mobility, low threshold voltage, high on/off ratio) is pivotal. Key classes of materials for this purpose are soluble oligoacenes, soluble oligo- and polythiophenes and their respective copolymers, and oligo- and polytriarylamines. In this context, micro- or nanocrystalline materials have the general advantage of somewhat higher charge-carrier mobilities, which, however, could be offset in the case of amorphous, glassy materials by simpler and more reproducible processing.