Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems

AbstractDefinitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated

Computing singularities of perturbation series

Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the perturbed Hamiltonian on a vector, and does not rely on the terms in the perturbation series. Some illustrative model problems are studied, including a Helium-like model with $\delta$-function interactions for which M{\o}ller--Plesset perturbation theory is considered and the radius of convergence found.Comment: 11 figures, submitte

Hypoxia counteracts taxol-induced apoptosis in MDA-MB-231 breast cancer cells:Role of autophagy and JNK activation

Cancer cell resistance against chemotherapy is still a heavy burden to improve anticancer treatments. Autophagy activation and the development of hypoxic regions within the tumors are known to promote cancer cell resistance. Therefore, we sought to evaluate the role of autophagy and hypoxia on the taxol-induced apoptosis in MDA-MB-231 breast cancer cells. The results showed that taxol induced apoptosis after 16 h of incubation, and that hypoxia protected MDA-MB-231 cells from taxol-induced apoptosis. In parallel, taxol induced autophagy activation already after 2 h of incubation both under normoxia and hypoxia. Autophagy activation after taxol exposure was shown to be a protective mechanism against taxol-induced cell death both under normoxia and hypoxia. However, at longer incubation time, the autophagic process reached a saturation point under normoxia leading to cell death, whereas under hypoxia, autophagy flow still correctly took place allowing the cells to survive. Autophagy induction is induced after taxol exposure via mechanistic target of rapamycin (mTOR) inhibition, which is more important in cells exposed to hypoxia. Taxol also induced c-Jun N-terminal kinase (JNK) activation and phosphorylation of its substrates B-cell CLL/lymphoma 2 (Bcl(2)) and BCL2-like 1 (Bcl(XL)) under normoxia and hypoxia very early after taxol exposure. Bcl(2) and Bcl(XL) phosphorylation was decreased more importantly under hypoxia after long incubation time. The role of JNK in autophagy and apoptosis induction was studied using siRNAs. The results showed that JNK activation promotes resistance against taxol-induced apoptosis under normoxia and hypoxia without being involved in induction of autophagy. In conclusion, the resistance against taxol-induced cell death observed under hypoxia can be explained by a more effective autophagic flow activated via the classical mTOR pathway and by a mechanism involving JNK, which could be dependent on Bcl(2) and Bcl(XL) phosphorylation but independent of JNK-induced autophagy activation

Theoretical Considerations on the Effect of Ion Formation Conditions on the Transmission Through a Laser Microprobe Mass Analyzer

A theoretical study on the ion transmission through the laser microprobe mass analyzer LAMMA 500 was made using ray-tracing computer programs. The calculations reveal that the ion transmission is strongly affected by the initial conditions of ion formation. Chromatic and spherical aberrations give rise to considerable discrimination in the univoltage lens. A correlation is attempted between measured and theoretical transmission curves. For the latter a physically plausible plasma model was initially assumed to generate the input parameters, i.e., locus of ion formation and angular and energy distributions of the ions (atomic and cluster ions). The model needs correction for aberration and space-charge effects : comparison of experimental and calculated ion transmission curves suggests, indeed, a more important contribution of particles with high energy and emitted under large angles, than initially assumed

An Empirical Evaluation of the Performance of Real-Time Illumination Approaches: Realistic Scenes in Augmented Reality

Augmented, Virtual, and Mixed Reality (AR/VR/MR) systems have been developed in general, with many of these applications having accomplished significant results, rendering a virtual object in the appropriate illumination model of the real environment is still under investigation. The entertainment industry has presented an astounding outcome in several media form, albeit the rendering process has mostly been done offline. The physical scene contains the illumination information which can be sampled and then used to render the virtual objects in real-time for realistic scene. In this paper, we evaluate the accuracy of our previous and current developed systems that provide real-time dynamic illumination for coherent interactive augmented reality based on the virtual object’s appearance in association with the real world and related criteria. The system achieves that through three simultaneous aspects. (1) The first is to estimate the incident light angle in the real environment using a live-feed 360∘ camera instrumented on an AR device. (2) The second is to simulate the reflected light using two routes: (a) global cube map construction and (b) local sampling. (3) The third is to define the shading properties for the virtual object to depict the correct lighting assets and suitable shadowing imitation. Finally, the performance efficiency is examined in both routes of the system to reduce the general cost. Also, The results are evaluated through shadow observation and user study

Stability and Stabilization of Systems with Time Delay: Limitations and Opportunities

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, in heredity, and in competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilisation of dynamical systems subjected to time-delays. It presents a wide and self-contained panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis

Structured pseudospectra and random eigenvalues problems in vibrating systems

This paper introduces the concept of pseudospectra as a generalized tool for uncertainty quantification and propagation in structural dynamics. Different types of pseudospectra of matrices and matrix polynomials are explained. Particular emphasis is given to structured pseudospectra for matrix polynomials, which offer a deterministic way of dealing with uncertainties for structural dynamic systems. The pseudospectra analysis is compared with the results from Monte Carlo simulations of uncertain discrete systems. Two illustrative example problems, one with probabilistic uncertainty with various types of statistical distributions and the other with interval type of uncertainty, are studied in detail. Excellent agreement is found between the pseudospectra results and Monte Carlo simulation results