F-term uplifting via consistent D-terms

The issue of fine-tuning necessary to achieve satisfactory degree of hierarchy between moduli masses, the gravitino mass and the scale of the cosmological constant has been revisited in the context of supergravities with consistent D-terms. We have studied (extended) racetrack models where supersymmetry breaking and moduli stabilisation cannot be separated from each other. We show that even in such cases the realistic hierarchy can be achieved on the expense of a single fine-tuning. The presence of two condensates changes the role of the constant term in the superpotential, W_0, and solutions with small vacuum energy and large gravitino mass can be found even for very small values of W_0. Models where D-terms are allowed to vanish at finite vevs of moduli fields - denoted `cancellable' D-terms - and the ones where D-terms may vanish only at infinite vevs of some moduli - denoted `non-cancellable' - differ markedly in their properties. It turns out that the tuning with respect to the Planck scale required in the case of cancellable D-terms is much weaker than in the case of non-cancellable ones. We have shown that, against intuition, a vanishing D-term can trigger F-term uplifting of the vacuum energy due to the stringent constraint it imposes on vacuum expectation values of charged fields. Finally we note that our models only rely on two dimensionful parameters: M_P and W_0.Comment: 10 pages, 2 figures, plain Latex, references adde

Realistic boundary conditions for stochastic simulations of reaction-diffusion processes

Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed and precise picture, and several stochastic simulation algorithms have been proposed in recent years. Such models typically give the same description of the reaction-diffusion processes far from the boundary of the simulated domain, but the behaviour close to a reactive boundary (e.g. a membrane with receptors) is unfortunately model-dependent. In this paper, we study four different approaches to stochastic modelling of reaction-diffusion problems and show the correct choice of the boundary condition for each model. The reactive boundary is treated as partially reflective, which means that some molecules hitting the boundary are adsorbed (e.g. bound to the receptor) and some molecules are reflected. The probability that the molecule is adsorbed rather than reflected depends on the reactivity of the boundary (e.g. on the rate constant of the adsorbing chemical reaction and on the number of available receptors), and on the stochastic model used. This dependence is derived for each model.Comment: 24 pages, submitted to Physical Biolog

High-frequency characterization of Permalloy nanosized strips using network analyzer ferromagnetic resonance

We report on the dynamic properties of Permalloy nanostrips at gagahertz frequencies. The thickness of the strips is 100 nm, strip width is 300 nm, strip spacing is 1 μm, and length is 0.3–100 μm; aspect ratios are 1:1, 1:2, 1:3, 1:5, 1:10, and 1:333. The dynamic behavior was studied by network analyzer ferromagnetic resonance (FMR) using Permalloy strips on a coplanar waveguide in flip-chip geometry. The FMR mode frequencies (fr) can be controlled by the aspect ratio as well as by the applied magnetic field (H). In longer strips (1:10 and 1:333), the excitation frequencies show a soft mode behavior (Heff = 990 Oe) when the field is along the hard axis. However, along the easy axis (along the strip length), fr increases with applied field. At a field of 3 kOe, fr values are almost independent of aspect ratio along the easy axis except for the 1:1 strip. Along the hard axis, the frequencies are strongly dependent upon the aspect ratio. We also observed that the frequency linewidths of the strips are dependent on the aspect rati

Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. In both cases, it is shown that the commonly used implementation of bimolecular reactions (i.e. the reactions of the form A + B -> C, or A + A -> C) might lead to incorrect results. Improvements of both SSAs are suggested which overcome the difficulties highlighted. In particular, a formula is presented for the smallest possible compartment size (lattice spacing) which can be correctly implemented in the first model. This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site).Comment: 33 pages, submitted to Physical Biolog

Unusual formation of the musculocutaneous and median nerves: a case report refined by intraneural dissection and literature review

This report presents a detailed anatomical investigation of an upper limb specimen showing an atypical formation of the musculocutaneous nerve (MCN) and median nerve (MN). The study was refined by intraneural dissection, which supplements earlier descriptions of similar anatomical variations and allows for revision of the accepted classification.The case described in this report was an incidental finding during routine dissection of a fixed isolated upper limb. Intraneural dissection revealed partial fusion between the MCN and aberrant bundles of the MN. Those aberrant bundles joined the main steam of the MN at the level at which the MCN branched off as an independent nerve. The procedure allowed the aberrant fibres of the MN to be differentiated from the MCN. The presence of separate bundles in a territory corresponding to the MCN was confirmed, although those bundles and the aberrant MN bundles were covered by a common epineurium. The aberrant MN bundles running within the MCN did not contribute to innervation of the forearm muscles. They rejoined the main nerve trunk in the arm.A comprehensive understanding of the diverse anatomical variations of the upper limb nerves could be crucial for the safety and success of surgical procedures, especially procedures for reconstructing the brachial plexus or its branches

From microscopic to macroscopic descriptions of cell\ud migration on growing domains

Cell migration and growth are essential components of the development of multicellular organisms. The role of various cues in directing cell migration is widespread, in particular, the role of signals in the environment in the control of cell motility and directional guidance. In many cases, especially in developmental biology, growth of the domain also plays a large role in the distribution of cells and, in some cases, cell or signal distribution may actually drive domain growth. There is a ubiquitous use of partial differential equations (PDEs) for modelling the time evolution of cellular density and environmental cues. In the last twenty years, a lot of attention has been devoted to connecting macroscopic PDEs with more detailed microscopic models of cellular motility, including models of directional sensing and signal transduction pathways. However, domain growth is largely omitted in the literature. In this paper, individual-based models describing cell movement and domain growth are studied, and correspondence with a macroscopic-level PDE describing the evolution of cell density is demonstrated. The individual-based models are formulated in terms of random walkers on a lattice. Domain growth provides an extra mathematical challenge by making the lattice size variable over time. A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs

Making Maps Of The Cosmic Microwave Background: The MAXIMA Example

This work describes Cosmic Microwave Background (CMB) data analysis algorithms and their implementations, developed to produce a pixelized map of the sky and a corresponding pixel-pixel noise correlation matrix from time ordered data for a CMB mapping experiment. We discuss in turn algorithms for estimating noise properties from the time ordered data, techniques for manipulating the time ordered data, and a number of variants of the maximum likelihood map-making procedure. We pay particular attention to issues pertinent to real CMB data, and present ways of incorporating them within the framework of maximum likelihood map-making. Making a map of the sky is shown to be not only an intermediate step rendering an image of the sky, but also an important diagnostic stage, when tests for and/or removal of systematic effects can efficiently be performed. The case under study is the MAXIMA data set. However, the methods discussed are expected to be applicable to the analysis of other current and forthcoming CMB experiments.Comment: Replaced to match the published version, only minor change

Distributed MAP in the SpinJa Model Checker

Spin in Java (SpinJa) is an explicit state model checker for the Promela modelling language also used by the SPIN model checker. Designed to be extensible and reusable, the implementation of SpinJa follows a layered approach in which each new layer extends the functionality of the previous one. While SpinJa has preliminary support for shared-memory model checking, it did not yet support distributed-memory model checking. This tool paper presents a distributed implementation of a maximal accepting predecessors (MAP) search algorithm on top of SpinJa.Comment: In Proceedings PDMC 2011, arXiv:1111.006