Signal and System Approximation from General Measurements

In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not directly used to generate the system output, but instead a sequence of numbers is used that is generated from the input signal by measurement functionals. We consider classical sampling which corresponds to a pointwise evaluation of the signal, as well as several more general measurement functionals. We show that a stable system approximation is not possible for pointwise sampling, because there exist signals and systems such that the approximation process diverges. This remains true even with oversampling. However, if more general measurement functionals are considered, a stable approximation is possible if oversampling is used. Further, we show that without oversampling we have divergence for a large class of practically relevant measurement procedures.Comment: This paper will be published as part of the book "New Perspectives on Approximation and Sampling Theory - Festschrift in honor of Paul Butzer's 85th birthday" in the Applied and Numerical Harmonic Analysis Series, Birkhauser (Springer-Verlag). Parts of this work have been presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing 2014 (ICASSP 2014

Reduced Hypoxia Risk in a Systemic Sclerosis Patient with Interstitial Lung Disease after Long-Term Pulmonary Rehabilitation

Pulmonary rehabilitation is effective for improving exercise capacity in patients with interstitial lung disease (ILD), and most programs last about 8 weeks. A 43-year-old male patient with systemic sclerosis and oxygen saturation (SpO2) declining because of severe ILD was hospitalized for treatment of chronic skin ulcers. During admission, he completed a 27-week walking exercise program with SpO2 monitoring. Consequently, continuous walking distance without severe hypoxia (SpO2 > 90%) increased from 60 m to 300 m after the program, although his six-minute walking distance remained the same. This suggests that walking exercise for several months may reduce the risk of hypoxia in patients with ILD, even though exercise capacity does not improve

Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence

We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1 dimensions [Phys. Rev. Lett. 104, 230601 (2010); Sci. Rep. 1, 34 (2011)]. Here we investigate both circular and flat interfaces and report their statistics in detail. First we demonstrate that their fluctuations show not only the KPZ scaling exponents but beyond: they asymptotically share even the precise forms of the distribution function and the spatial correlation function in common with solvable models of the KPZ class, demonstrating also an intimate relation to random matrix theory. We then determine other statistical properties for which no exact theoretical predictions were made, in particular the temporal correlation function and the persistence probabilities. Experimental results on finite-time effects and extreme-value statistics are also presented. Throughout the paper, emphasis is put on how the universal statistical properties depend on the global geometry of the interfaces, i.e., whether the interfaces are circular or flat. We thereby corroborate the powerful yet geometry-dependent universality of the KPZ class, which governs growing interfaces driven out of equilibrium.Comment: 31 pages, 21 figures, 1 table; references updated (v2,v3); Fig.19 updated & minor changes in text (v3); final version (v4); J. Stat. Phys. Online First (2012

Evaluation of effectiveness of 45S5 bioglass doped with niobium for repairing critical-sized bone defect in in vitro and in vivo models

Here, we investigated the biocompatibility of a bioactive sodium calcium silicate glass containing 2.6 mol% Nb2O5 (denoted BGPN2.6) and compare the results with the archetypal 45S5 bioglass. The glass bioactivity was tested using a range of in vitro and in vivo experiments to assess its suitability for bone regeneration applications. in vitro studies consisted of assessing the cytocompatibility of the BGPN2.6 glass with bone-marrow-derived mesenchymal stem cells (BM-MSCs). Systemic biocompatibility was verified by means of the quantification of biochemical markers and histopathology of liver, kidneys, and muscles. The glass genotoxicity was assessed using the micronucleus test. The regeneration of a calvarial defect was assessed using both qualitative and quantitative analysis of three-dimensional microcomputed tomography images. The BGPN2.6 glass was not cytotoxic to BM-MSCs. It is systemically biocompatible causing no signs of damage to high metabolic and excretory organs such as the liver and kidneys. No mutagenic potential was observed in the micronucleus test. MicroCT images showed that BGPN2.6 was able to nearly fully regenerate a critical-sized calvarial defect and was far superior to standard 45S5 Bioglass. Defects filled with BGPN2.6 glass showed over 90% coverage compare to just 66% for 45S5 Bioglass. For one animal the defect was completely filled in 8 weeks. These results clearly show that Nb-containing bioactive glasses are a safe and effective biomaterial for bone replacement

Measuring IgA anti-β2-glycoprotein I and IgG/IgA anti-domain I antibodies adds value to current serological assays for the antiphospholipid syndrome

Introduction Currently available clinical assays to detect antiphospholipid antibodies (aPL) test for IgG and IgM antibodies to cardiolipin (aCL) and beta(2)-glycoprotein I (a beta(2)GPI). It has been suggested that testing for IgA aPL and for antibodies to Domain I (DI), which carries the key antigenic epitopes of beta(2)GPI, could add value to these current tests. We performed an observational, multicenter cohort study to evaluate the utility of IgG, IgM and IgA assays to each of CL, beta(2)GPI and DI in APS. Methods Serum from 230 patients with APS (n = 111), SLE but not APS (n = 119), and 200 healthy controls were tested for IgG, IgM and IgA aCL, a beta(2)GPI and aDI activity. Patients with APS were further classified into thrombotic or obstetric APS. Logistic regression and receiver operator characteristic analyses were employed to compare results from the nine different assays. Results All assays displayed good specificity for APS; IgG aCL and IgG a beta(2)GPI assays however, had the highest sensitivity. Testing positive for IgA a beta(2)GPI resulted in a higher hazard ratio for APS compared to IgM a beta(2)GPI. Positive IgG, IgM or IgA aDI were all associated with APS, and in subjects positive for aCL and/or a beta(2)GPI, the presence of aDI raised the hazard ratio for APS by 3-5 fold. IgG aCL, a beta(2)GPI, aDI and IgA aDI were associated with thrombotic but not obstetric complications in patients with APS. Conclusion Measuring IgG aDI and IgA a beta(2)GPI and aDI may be useful in the management of patients with APS, particularly thrombotic APS

Canonical Graph Shapes

Abstract. Graphs are an intuitive model for states of a (software) system that include pointer structures — for instance, object-oriented programs. However, a naive encoding results in large individual states and large, or even unbounded, state spaces. As usual, some form of abstraction is necessary in order to arrive at a tractable model. In this paper we propose a decidable fragment of first-order graph logic that we call local shape logic (LSL) as a possible abstraction mechanism, inspired by previous work of Sagiv, Reps and Wilhelm. An LSL formula constrains the multiplicities of nodes and edges in state graphs; abstraction is achieved by reasoning not about individual, concrete state graphs but about their characteristic shape properties. We go on to define the concept of the canonical shape of a state graph, which is expressed in a monomorphic sub-fragment of LSL, for which we define a graphical representation. We show that the canonical shapes give rise to an automatic finite abstraction of the state space of a software system, and we give an upper bound to the size of this abstract state space