74 research outputs found
Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators
We consider networks of delay-coupled Stuart-Landau oscillators. In these
systems, the coupling phase has been found to be a crucial control parameter.
By proper choice of this parameter one can switch between different synchronous
oscillatory states of the network. Applying the speed-gradient method, we
derive an adaptive algorithm for an automatic adjustment of the coupling phase
such that a desired state can be selected from an otherwise multistable regime.
We propose goal functions based on both the difference of the oscillators and a
generalized order parameter and demonstrate that the speed-gradient method
allows one to find appropriate coupling phases with which different states of
synchronization, e.g., in-phase oscillation, splay or various cluster states,
can be selected.Comment: 8 pages, 7 figure
Timing jitter of passively mode-locked semiconductor lasers subject to optical feedback; a semi-analytic approach
We propose a semi-analytical method of calculating the timing fluctuations in
mode-locked semiconductor lasers and apply it to study the effect of delayed
coherent optical feedback on pulse timing jitter in these lasers. The proposed
method greatly reduces computation times and therefore allows for the
investigation of the dependence of timing fluctuations over greater parameter
domains. We show that resonant feedback leads to a reduction in the timing
jitter and that a frequency-pulling region forms about the main resonances,
within which a timing jitter reduction is observed. The width of these
frequency-pulling regions increases linearly with short feedback delay times.
We derive an analytic expression for the timing jitter, which predicts a
monotonous decrease in the timing jitter for resonant feedback of increasing
delay lengths, when timing jitter effects are fully separated from amplitude
jitter effects. For long feedback cavities the decrease in timing jitter scales
approximately as with the increase of the feedback delay time
Efficient fault tolerance for selected scientific computing algorithms on heterogeneous and approximate computer architectures
Scientific computing and simulation technology play an essential role to solve central challenges in science and engineering. The high computational power of heterogeneous computer architectures allows to accelerate applications in these domains, which are often dominated by compute-intensive mathematical tasks. Scientific, economic and political decision processes increasingly rely on such applications and therefore induce a strong demand to compute correct and trustworthy results. However, the continued semiconductor technology scaling increasingly imposes serious threats to the reliability and efficiency of upcoming devices. Different reliability threats can cause crashes or erroneous results without indication. Software-based fault tolerance techniques can protect algorithmic tasks by adding appropriate operations to detect and correct errors at runtime. Major challenges are induced by the runtime overhead of such operations and by rounding errors in floating-point arithmetic that can cause false positives. The end of Dennard scaling induces central challenges to further increase the compute efficiency between semiconductor technology generations. Approximate computing exploits the inherent error resilience of different applications to achieve efficiency gains with respect to, for instance, power, energy, and execution times. However, scientific applications often induce strict accuracy requirements which require careful utilization of approximation techniques.
This thesis provides fault tolerance and approximate computing methods that enable the reliable and efficient execution of linear algebra operations and Conjugate Gradient solvers using heterogeneous and approximate computer architectures. The presented fault tolerance techniques detect and correct errors at runtime with low runtime overhead and high error coverage. At the same time, these fault tolerance techniques are exploited to enable the execution of the Conjugate Gradient solvers on approximate hardware by monitoring the underlying error resilience while adjusting the approximation error accordingly. Besides, parameter evaluation and estimation methods are presented that determine the computational efficiency of application executions on approximate hardware.
An extensive experimental evaluation shows the efficiency and efficacy of the presented methods with respect to the runtime overhead to detect and correct errors, the error coverage as well as the achieved energy reduction in executing the Conjugate Gradient solvers on approximate hardware
Complex partial synchronization patterns in networks of delay-coupled neurons
We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Controlling cluster synchronization by adapting the topology
We suggest an adaptive control scheme for the control of zero-lag and cluster
synchronization in delay-coupled networks. Based on the speed-gradient method,
our scheme adapts the topology of a network such that the target state is
realized. It is robust towards different initial condition as well as changes
in the coupling parameters. The emerging topology is characterized by a
delicate interplay of excitatory and inhibitory links leading to the
stabilization of the desired cluster state. As a crucial parameter determining
this interplay we identify the delay time. Furthermore, we show how to
construct networks such that they exhibit not only a given cluster state but
also with a given oscillation frequency. We apply our method to coupled
Stuart-Landau oscillators, a paradigmatic normal form that naturally arises in
an expansion of systems close to a Hopf bifurcation. The successful and robust
control of this generic model opens up possible applications in a wide range of
systems in physics, chemistry, technology, and life science
Nonuniform Self-Organized Dynamical States in Superconductors with Periodic Pinning
We consider magnetic flux moving in superconductors with periodic pinning
arrays. We show that sample heating by moving vortices produces negative
differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in
the voltage-current characteristic (VI curve). The uniform flux flow state is
unstable in the NDR region of the VI curve. Domain structures appear during the
NDR part of the VI curve of an N type, while a filamentary instability is
observed for the NDR of an S type. The simultaneous existence of the NDR of
both types gives rise to the appearance of striking self-organized (both
stationary and non-stationary) two-dimensional dynamical structures.Comment: 4 pages, 2 figure
Negative differential resistivity in superconductors with periodic arrays of pinning sites
We study theoretically the effects of heating on the magnetic flux moving in
superconductors with a periodic array of pinning sites (PAPS). The
voltage-current characteristic (VI-curve) of superconductors with a PAPS
includes a region with negative differential resistivity (NDR) of S-type (i.e.,
S-shaped VI-curve), while the heating of the superconductor by moving flux
lines produces NDR of N-type (i.e., with an N-shaped VI-curve). We analyze the
instability of the uniform flux flow corresponding to different parts of the
VI-curve with NDR. Especially, we focus on the appearance of the filamentary
instability that corresponds to an S-type NDR, which is extremely unusual for
superconductors. We argue that the simultaneous existence of NDR of both N- and
S-type gives rise to the appearance of self-organized two-dimensional dynamical
structures in the flux flow mode. We study the effect of the pinning site
positional disorder on the NDR and show that moderate disorder does not change
the predicted results, while strong disorder completely suppresses the S-type
NDR.Comment: 10 pages, 1 table, 7 figure
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Correction to: Relevance of biomarkers across different neurodegenerative diseases
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