On the accuracy of solving confluent Prony systems

In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as frequency estimation and nonlinear Fourier inversion. Consequently, the question of stability of solution with respect to errors in the right-hand side becomes critical for the success of any particular application. We investigate the question of "maximal possible accuracy" of solving Prony-type systems, putting stress on the "local" behavior which approximates situations with low absolute measurement error. The accuracy estimates are formulated in very simple geometric terms, shedding some light on the structure of the problem. Numerical tests suggest that "global" solution techniques such as Prony's algorithm and ESPRIT method are suboptimal when compared to this theoretical "best local" behavior

Don't know, can't know: Embracing deeper uncertainties when analysing risks

This article is available open access through the publisher’s website at the link below. Copyright @ 2011 The Royal Society.Numerous types of uncertainty arise when using formal models in the analysis of risks. Uncertainty is best seen as a relation, allowing a clear separation of the object, source and ‘owner’ of the uncertainty, and we argue that all expressions of uncertainty are constructed from judgements based on possibly inadequate assumptions, and are therefore contingent. We consider a five-level structure for assessing and communicating uncertainties, distinguishing three within-model levels—event, parameter and model uncertainty—and two extra-model levels concerning acknowledged and unknown inadequacies in the modelling process, including possible disagreements about the framing of the problem. We consider the forms of expression of uncertainty within the five levels, providing numerous examples of the way in which inadequacies in understanding are handled, and examining criticisms of the attempts taken by the Intergovernmental Panel on Climate Change to separate the likelihood of events from the confidence in the science. Expressing our confidence in the adequacy of the modelling process requires an assessment of the quality of the underlying evidence, and we draw on a scale that is widely used within evidence-based medicine. We conclude that the contingent nature of risk-modelling needs to be explicitly acknowledged in advice given to policy-makers, and that unconditional expressions of uncertainty remain an aspiration

Evolution of constrained layer damping using a cellular automaton algorithm

Constrained layer damping (CLD) is a highly effective passive vibration control strategy if optimized adequately. Factors controlling CLD performance are well documented for the flexural modes of beams but not for more complicated mode shapes or structures. The current paper introduces an approach that is suitable for locating CLD on any type of structure. It follows the cellular automaton (CA) principle and relies on the use of finite element models to describe the vibration properties of the structure. The ability of the algorithm to reach the best solution is demonstrated by applying it to the bending and torsion modes of a plate. Configurations that give the most weight-efficient coverage for each type of mode are first obtained by adapting the existing 'optimum length' principle used for treated beams. Next, a CA algorithm is developed, which grows CLD patches one at a time on the surface of the plate according to a simple set of rules. The effectiveness of the algorithm is then assessed by comparing the generated configurations with the known optimum ones

ProNodal acts via FGFR3 to govern duration of Shh expression in the prechordal mesoderm

The secreted glycoprotein sonic hedgehog (Shh) is expressed in the prechordal mesoderm, where it plays a crucial role in induction and patterning of the ventral forebrain. Currently little is known about how Shh is regulated in prechordal tissue. Here we show that in the embryonic chick, Shh is expressed transiently in prechordal mesoderm, and is governed by unprocessed Nodal. Exposure of prechordal mesoderm microcultures to Nodal-conditioned medium, the Nodal inhibitor CerS, or to an ALK4/5/7 inhibitor reveals that Nodal is required to maintain both Shh and Gsc expression, but whereas Gsc is largely maintained through canonical signalling, Nodal signals through a non-canonical route to maintain Shh. Further, Shh expression can be maintained by a recombinant Nodal cleavage mutant, proNodal, but not by purified mature Nodal. A number of lines of evidence suggest that proNodal acts via FGFR3. ProNodal and FGFR3 co-immunoprecipitate and proNodal increases FGFR3 tyrosine phosphorylation. In microcultures, soluble FGFR3 abolishes Shh without affecting Gsc expression. Further, prechordal mesoderm cells in which Fgfr3 expression is reduced by Fgfr3 siRNA fail to bind to proNodal. Finally, targeted electroporation of Fgfr3 siRNA to prechordal mesoderm in vivo results in premature Shh downregulation without affecting Gsc. We report an inverse correlation between proNodal-FGFR3 signalling and pSmad1/5/8, and show that proNodal-FGFR3 signalling antagonises BMP-mediated pSmad1/5/8 signalling, which is poised to downregulate Shh. Our studies suggest that proNodal/FGFR3 signalling governs Shh duration by repressing canonical BMP signalling, and that local BMPs rapidly silence Shh once endogenous Nodal-FGFR3 signalling is downregulated

Pitfalls and artifacts using the D-SPECT dedicated cardiac camera

Myocardial perfusion imaging is a well-established and widely used imaging technique for the assessment of patients with known or suspected coronary artery disease. Pitfalls and artifacts associated with conventional gamma cameras are well known, and the ways to avoid and correct them have been described. In recent years solid-state detector dedicated cardiac cameras were introduced and have been shown to offer improved accuracy in addition to new imaging protocols and novel applications. The purpose of this manuscript is to familiarize the readers with the causes and effects of technical, patient-related, and operator-related pitfalls and artifacts associated with the D-SPECT dedicated cardiac camera with solid-state detectors. The manuscript offers guidance on how to avoid these factors, how to detect them, and how to correct better for them, providing high-quality diagnostic images

Class of solvable reaction-diffusion processes on Cayley tree

Considering the most general one-species reaction-diffusion processes on a Cayley tree, it has been shown that there exist two integrable models. In the first model, the reactions are the various creation processes, i.e. $\circ\circ\to\bullet\circ$, $\circ\circ\to\bullet\bullet$ and $\circ\bullet\to\bullet\bullet$, and in the second model, only the diffusion process $\bullet\circ\to\circ\bullet$ exists. For the first model, the probabilities $P_l(m;t)$, of finding $m$ particles on $l$-th shell of Cayley tree, have been found exactly, and for the second model, the functions $P_l(1;t)$ have been calculated. It has been shown that these are the only integrable models, if one restricts himself to $L+1$-shell probabilities $P(m_0,m_1,...,m_L;t)$s.Comment: 9 pages, to be appeared in Physica

The JAK/STAT3 Pathway Is a Common Inducer of Astrocyte Reactivity in Alzheimer's and Huntington's Diseases.

Astrocyte reactivity is a hallmark of neurodegenerative diseases (ND), but its effects on disease outcomes remain highly debated. Elucidation of the signaling cascades inducing reactivity in astrocytes during ND would help characterize the function of these cells and identify novel molecular targets to modulate disease progression. The Janus kinase/signal transducer and activator of transcription 3 (JAK/STAT3) pathway is associated with reactive astrocytes in models of acute injury, but it is unknown whether this pathway is directly responsible for astrocyte reactivity in progressive pathological conditions such as ND. In this study, we examined whether the JAK/STAT3 pathway promotes astrocyte reactivity in several animal models of ND. The JAK/STAT3 pathway was activated in reactive astrocytes in two transgenic mouse models of Alzheimer's disease and in a mouse and a nonhuman primate lentiviral vector-based model of Huntington's disease (HD). To determine whether this cascade was instrumental for astrocyte reactivity, we used a lentiviral vector that specifically targets astrocytes in vivo to overexpress the endogenous inhibitor of the JAK/STAT3 pathway [suppressor of cytokine signaling 3 (SOCS3)]. SOCS3 significantly inhibited this pathway in astrocytes, prevented astrocyte reactivity, and decreased microglial activation in models of both diseases. Inhibition of the JAK/STAT3 pathway within reactive astrocytes also increased the number of huntingtin aggregates, a neuropathological hallmark of HD, but did not influence neuronal death. Our data demonstrate that the JAK/STAT3 pathway is a common mediator of astrocyte reactivity that is highly conserved between disease states, species, and brain regions. This universal signaling cascade represents a potent target to study the role of reactive astrocytes in ND