Quadratic form theory over preordered von Neumann-regular rings

AbstractTo each pair, 〈R,T〉, consisting of a unitary commutative von Neumann-regular ring, R, where 2 is a unit and T is a preorder on R, we associate a reduced special group, GT(R), which faithfully reflects quadratic form theory, modulo T, over free R-modules and then show, using the representation of R as the ring of global sections of its affine scheme, together with results from [M. Dickmann, F. Miraglia, On quadratic forms whose total signature is zero mod 2n. Solution to a problem of M. Marshall, Invent. Math. 133 (1998) 243–278; M. Dickmann, F. Miraglia, Lam's Conjecture, Algebra Colloq. 10 (2003) 149–176; M. Dickmann, F. Miraglia, Algebraic K-theory of special groups, J. Pure Appl. Algebra 204 (2006) 195–234], that GT(R) satisfies a powerful K-theoretic property, the [SMC]-property. From this we conclude that quadratic form theory modulo T over free R-modules verifies Marshall's signature conjecture, Lam's conjecture, as well as a reduced version of Milnor's Witt ring conjecture

Orders and Relative Pythagorean Closures

Orders and Relative Pythagorean Closure

Long-range morphogen gradient formation by cell-to-cell signal propagation

Morphogen gradients are a central concept in developmental biology. Their formation often involves the secretion of morphogens from a local source, that spread by diffusion in the cell field, where molecules eventually get degraded. This implies limits to both the time and length scales over which morphogen gradients can form which are set by diffusion coefficients and degradationrates. Towards the goal of identifying plausible mechanisms capable of extending the gradient range, we here use theory to explore properties of a cell-to-cell signaling relay. Inspired by the millimeter-scale wnt-expression and signaling gradients in flatworms, we consider morphogen-mediated morphogen production in the cell field. We show that such a relay cangenerate stable morphogen and signaling gradients that are oriented by a local,morphogen-independent source of morphogen at a boundary. This gradient formation can be related to an effective diffusion and an effective degradation that result from morphogen production due to signaling relay. If the secretion of morphogen produced in response to the relay is polarized, it further gives rise to an effective drift. We find that signaling relay can generate long-range gradients in relevant times without relying on extreme choices of diffusion coefficients or degradation rates, thus exceeding the limits set by physiological diffusion coefficients and degradation rates. A signaling relay is hence an attractive principle to conceptualize long-range gradient formation by slowly diffusing morphogens that are relevant for patterning in adult contexts such as regeneration and tissue turn-over

Risk communication and generic preparedness: from agent-based to action-based planning - a conceptual framework

Responses to recent infectious disease outbreaks, such as to Influenza Pandemic 2009 and the on-going Ebola outbreak in West Africa, reveal the need for new and strengthened approaches to risk communication and governance. The article argues for a fundamental re-conceptualisation of current approaches to risk communication, preparedness planning and response. It calls for a reframing of the way we currently identify and respond to outbreaks around a set of core behaviour-based response patterns. This new model moves away from the current risk communication focus on a plethora of agent-specific threats to five generic response patterns that are based on socially relevant response activities such as 1) controlling vectors, 2) enhancing hygiene, 3) isolation of the sick, 4) protection of the well, and 5) systemic protection of people and their environments. Emphasis is placed on gaining relevant insights into the context specific needs of different communities related to these five patterns. Governance structures are then built and evaluated based on their capacity to collect, communicate, share and prepare the public to take appropriate action related to the five different patterns before, during and after an event. Reframing risk communication and preparedness approaches around a better understanding of the determinants of these general behavioural patterns in infectious control could strengthen infection control literacy, response competence and build resilience of both individuals and health systems to address future epidemics, pandemics and other public health threats

Reduction of heat sink common-mode currents in switching mode power supply circuits

In this paper, a new filter design for a heat sink is presented. The parasitic couplings between electric power devices and the heat sink are responsible for common-mode currents. The main focus is on the reduction of these currents to reduce the heat sink radiation. For this purpose a new filter design is proposed. In addition, experimental results are shown to validate the proposed filter

Spin relaxation in a two-electron quantum dot

We discuss the rate of relaxation of the total spin in the two-electron droplet in the vicinity of the magnetic field driven singlet-triplet transition. The total spin relaxation is attributed to spin-orbit and electron-phonon interactions. The relaxation process is found to depend on the spin of ground and excited states. This asymmetry is used to explain puzzles in recent high source-drain transport experiments.Comment: 9 pages in the PDF format, 1 figur