567 research outputs found

    On the stability of periodic orbits in delay equations with large delay

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    We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is characterized by a set of curves, which we call asymptotic continuous spectrum, that is independent on the delay.Comment: postprint versio

    Optimum ground states for spin-32\frac{3}{2} chains

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    We present a set of {\em optimum ground states} for a large class of spin-32\frac{3}{2} chains. Such global ground states are simultaneously ground states of the local Hamiltonian, i.e. the nearest neighbour interaction in the present case. They are constructed in the form of a matrix product. We find three types of phases, namely a {\em weak antiferromagnet}, a {\em weak ferromagnet}, and a {\em dimerized antiferromagnet}. The main physical properties of these phases are calculated exactly by using a transfer matrix technique, in particular magnetization and two spin correlations. Depending on the model parameters, they show a surprisingly rich structure.Comment: LaTeX, 22 pages, 6 embedded Postscript figure

    DelayAndPeriodicity

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    Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic solutions. In particular, we show that delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times. As delay increases, the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions. We also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers. We show that the spectrum of multipliers can be splitted into two parts: pseudo-continuous and strongly unstable. The pseudo-continuous part of the spectrum mediates destabilization of periodic solutions.Comment: 24 pages, 9 figure

    Use of fuzzy edge single-photon emission computed tomography analysis in definite Alzheimer's disease - a retrospective study

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    <p>Abstract</p> <p>Background</p> <p>Definite Alzheimer's disease (AD) requires neuropathological confirmation. Single-photon emission computed tomography (SPECT) may enhance diagnostic accuracy, but due to restricted sensitivity and specificity, the role of SPECT is largely limited with regard to this purpose.</p> <p>Methods</p> <p>We propose a new method of SPECT data analysis. The method is based on a combination of parietal lobe selection (as regions-of-interest (ROI)), 3D fuzzy edge detection, and 3D watershed transformation. We applied the algorithm to three-dimensional SPECT images of human brains and compared the number of watershed regions inside the ROI between AD patients and controls. The Student's two-sample t-test was used for testing domain number equity in both groups.</p> <p>Results</p> <p>AD patients had a significantly reduced number of watershed regions compared to controls (<it>p </it>< 0.01). A sensitivity of 94.1% and specificity of 80% was obtained with a threshold value of 57.11 for the watershed domain number. The narrowing of the SPECT analysis to parietal regions leads to a substantial increase in both sensitivity and specificity.</p> <p>Conclusions</p> <p>Our non-invasive, relatively low-cost, and easy method can contribute to a more precise diagnosis of AD.</p
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