A note on structured pseudospectra of block matrices

In this note we consider the question of equivalence of pseudospectra and structured pseudospectra of block matrices. The structures we study are all so called double structures; that is, the blocks of the given matrix are of the same structure as the block matrix. The approach is based on that of non-block matrices, which are also briefly studied, and the use of distance to singularity. We also list some open problems and conjectures

Eluate derived by extracorporal antibody-based immunoadsorption elevates the cytosolic Ca2+ concentration in podocytes via B-2 kinin receptors

Background/Aim: Patients with idiopathic focal segmental glomerulosclerosis (FSGS) often develop a recurrence of the disease after kidney transplantation. In a number of FSGS patients, plasmapheresis and immunoadsorption procedures have been shown to transiently reduce proteinuria and are thought to do this by eliminating a circulating factor. Direct cellular effects of eluates from immunoadsorption procedures on podocytes, the primary target of injury in FSGS, have not yet been reported. Methods: Eluates were derived from antibody-based immunoadsorption of a patient suffering from primary FSGS, a patient with systemic lupus erythematosus, and a healthy volunteer. The cytosolic free Ca2+ concentration ({[}Ca2+](i)) of differentiated podocytes was measured by single-cell fura-2 microfluorescence measurements. Free and total immunoreactive kinin levels were measured by radioimmunoassay. Results: FSGS eluates increased the {[}Ca2+](i) levels concentration dependently (EC50 0.14 mg/ml; n = 3-19). 1 mg/ml eluate increased the {[}Ca2+](i) values reversibly from 82 +/- 12 to 1,462 +/- 370 nmol/l, and then they returned back to 100 16 nmol/l (n = 19). The eluate-induced increase of {[}Ca2+](i) consisted of an initial Ca2+ peak followed by a Ca2+ plateau which depended on the extracellular Ca2+ concentration. The eluate-induced increase of {[}Ca2+](i) was inhibited by the specific B-2 kinin receptor antagonist Hoe 140 in a concentration-dependent manner (IC50 2.47 nmol/l). In addition, prior repetitive application of bradykinin desensitized the effect of eluate on {[}Ca2+](i). A colonic epithelial cell line not reacting to bradykinin did not respond to eluate either (n = 6). Similar to FSGS eluates, the eluate preparations of both the systemic lupus patient and the healthy volunteer led to a biphasic, concentration-dependent {[}Ca2+](i) increase in poclocytes which again was inhibited by Hoe 140. Free kinins were detected in all eluate preparations. Conclusion: The procedure of antibody-based immunoadsorption leads to kinin in the eluate which elevates the {[}Ca2+](i) level of podocytes via B-2 kinin receptors. Copyright (C) 2002 S. Karger AG, Basel

Synopsis of an engineering solution for a painful problem Phantom Limb Pain

This paper is synopsis of a recently proposed solution for treating patients who suffer from Phantom Limb Pain (PLP). The underpinning approach of this research and development project is based on an extension of “mirror box” therapy which has had some promising results in pain reduction. An outline of an immersive individually tailored environment giving the patient a virtually realised limb presence, as a means to pain reduction is provided. The virtual 3D holographic environment is meant to produce immersive, engaging and creative environments and tasks to encourage and maintain patients’ interest, an important aspect in two of the more challenging populations under consideration (over-60s and war veterans). The system is hoped to reduce PLP by more than 3 points on an 11 point Visual Analog Scale (VAS), when a score less than 3 could be attributed to distraction alone

Lagrangian Reachabililty

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201

Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known to only provide approximated results, is omnipresent in this activity. In order to validate the behaviors of numerical simulations using abstract interpretation-based static analysis, we present, theoretically and with experiments, a new partially relational abstract domain dedicated to floating-point variables. It comes from interval expansion of non-linear functions using slopes and it is able to mimic all the behaviors of the floating-point arithmetic. Hence it is adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems

Sharper and Simpler Nonlinear Interpolants for Program Verification

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool's effectiveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples

Copy number variation in a hospital-based cohort of children with epilepsy

Objective: To evaluate the diagnostic yield of microarray analysis in a hospital-based cohort of children with seizures and to identify novel candidate genes and susceptibility loci for epilepsy. Methods: Of all children who presented with their first seizure in the University Medical Center Groningen (January 2000 through May 2013) (n = 1,368), we included 226 (17%) children who underwent microarray analysis before June 2014. All 226 children had a definite diagnosis of epilepsy. All their copy number variants (CNVs) on chromosomes 1-22 and X that contain protein-coding genes and have a prevalence of <1% in healthy controls were evaluated for their pathogenicity. Results: Children selected for microarray analysis more often had developmental problems (82% vs. 25%, p < 0.001), facial dysmorphisms (49% vs. 8%, p < 0.001), or behavioral problems (41% vs. 13%, p < 0.001) than children who were not selected. We found known clinically relevant CNVs for epilepsy in 24 of the 226 children (11%). Seventeen of these 24 children had been diagnosed with symptomatic focal epilepsy not otherwise specified (71%) and five with West syndrome (21%). Of these 24 children, many had developmental problems (100%), behavioral problems (54%) or facial dysmorphisms (46%). We further identified five novel CNVs comprising four potential candidate genes for epilepsy:MYT1L, UNC5D, SCN4B,andNRXN3. Significance: The 11% yield in our hospital-based cohort underscores the importance of microarray analysis in diagnostic evaluation of children with epilepsy

Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite). We state a characterization in the form of equivalent conditions, and also propose some computationally cheap sufficient\,/\,necessary conditions. Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques

Synopsis of an engineering solution for a painful problem: Phantom limb pain

This paper is synopsis of a recently proposed solution for treating patients who suffer from Phantom Limb Pain (PLP). The underpinning approach of this research and development project is based on an extension of "mirror box" therapy which has had some promising results in pain reduction. An outline of an immersive individually tailored environment giving the patient a virtually realised limb presence, as a means to pain reduction is provided. The virtual 3D holographic environment is meant to produce immersive, engaging and creative environments and tasks to encourage and maintain patients' interest, an important aspect in two of the more challenging populations under consideration (over-60s and war veterans). The system is hoped to reduce PLP by more than 3 points on an 11 point Visual Analog Scale (VAS), when a score less than 3 could be attributed to distraction alone. Copyright © 2014 SCITEPRESS - Science and Technology Publications. All rights reserved.Published versio

Observation of the WW-Annihilation Decay Ds+→ωπ+D^{+}_{s} \rightarrow \omega \pi^{+} and Evidence for Ds+→ωK+D^{+}_{s} \rightarrow \omega K^{+}

We report on the observation of the $W$-annihilation decay $D^{+}_{s} \rightarrow \omega \pi^{+}$ and the evidence for $D_{s}^{+} \rightarrow \omega K^{+}$ with a data sample corresponding to an integrated luminosity of 3.19 fb$^{-1}$ collected with the BESIII detector at the center-of-mass energy $\sqrt{s} = 4.178$ GeV. We obtain the branching fractions $\mathcal{B}(D^{+}_{s} \rightarrow \omega \pi^{+}) = (1.77\pm0.32_{{\rm stat.}}\pm0.11_{{\rm sys.}}) \times 10^{-3}$ and $\mathcal{B}(D^{+}_{s} \rightarrow \omega K^{+}) = (0.87\pm0.24_{{\rm stat.}}\pm0.07_{{\rm sys.}}) \times 10^{-3}$, respectively