Synchronization of coupled limit cycles

A unified approach for analyzing synchronization in coupled systems of autonomous differential equations is presented in this work. Through a careful analysis of the variational equation of the coupled system we establish a sufficient condition for synchronization in terms of the geometric properties of the local limit cycles and the coupling operator. This result applies to a large class of differential equation models in physics and biology. The stability analysis is complemented with a discussion of numerical simulations of a compartmental model of a neuron.Comment: Journal of Nonlinear Science, accepte

Physical properties of FeSe0.5_{0.5}Te0.5_{0.5} single crystals grown under different conditions

We report on structural, magnetic, conductivity, and thermodynamic studies of FeSe$_{0.5}$Te$_{0.5}$ single crystals grown by self-flux and Bridgman methods. The samples were prepared from starting materials of different purity at various temperatures and cooling rates. The lowest values of the susceptibility in the normal state, the highest transition temperature $T_c$ of 14.5 K, and the largest heat-capacity anomaly at $T_c$ were obtained for pure (oxygen-free) samples. The critical current density $j_c$ of $8 \times 10^4$ A/cm$^2$ (at 2 K) achieved in pure samples is attributed to intrinsic inhomogeneity due to disorder at the cation and anion sites. The impure samples show increased $j_c$ up to $2.3 \times 10^5$ A/cm$^2$ due to additional pinning centers of Fe$_3$O$_4$. The upper critical field $H_{c2}$ of $\sim 500$ kOe is estimated from the resistivity study in magnetic fields parallel to the \emph{c}-axis. The anisotropy of the upper critical field $\gamma_{H_{c2}} = H_{_{c2}}^{ab}/H_{_{c2}}^{c}$ reaches a value $\sim 6$ at $T\longrightarrow T_c$. Extremely low values of the residual Sommerfeld coefficient for pure samples indicate a high volume fraction of the superconducting phase (up to 97%). The electronic contribution to the specific heat in the superconducting state is well described within a single-band BCS model with a temperature dependent gap $\Delta_0 = 27(1)$ K. A broad cusp-like anomaly in the electronic specific heat of samples with suppressed bulk superconductivity is ascribed to a splitting of the ground state of the interstitial Fe$^{2+}$ ions. This contribution is fully suppressed in the ordered state in samples with bulk superconductivity.Comment: 11 pages, 11 figures, 3 table

Magnetic Fields, Relativistic Particles, and Shock Waves in Cluster Outskirts

It is only now, with low-frequency radio telescopes, long exposures with high-resolution X-ray satellites and gamma-ray telescopes, that we are beginning to learn about the physics in the periphery of galaxy clusters. In the coming years, Sunyaev-Zeldovich telescopes are going to deliver further great insights into the plasma physics of these special regions in the Universe. The last years have already shown tremendous progress with detections of shocks, estimates of magnetic field strengths and constraints on the particle acceleration efficiency. X-ray observations have revealed shock fronts in cluster outskirts which have allowed inferences about the microphysical structure of shocks fronts in such extreme environments. The best indications for magnetic fields and relativistic particles in cluster outskirts come from observations of so-called radio relics, which are megaparsec-sized regions of radio emission from the edges of galaxy clusters. As these are difficult to detect due to their low surface brightness, only few of these objects are known. But they have provided unprecedented evidence for the acceleration of relativistic particles at shock fronts and the existence of muG strength fields as far out as the virial radius of clusters. In this review we summarise the observational and theoretical state of our knowledge of magnetic fields, relativistic particles and shocks in cluster outskirts.Comment: 34 pages, to be published in Space Science Review

Correcting palindromes in long reads after whole-genome amplification

Background: Next-generation sequencing requires sufficient DNA to be available. If limited, whole-genome amplification is applied to generate additional amounts of DNA. Such amplification often results in many chimeric DNA fragments, in particular artificial palindromic sequences, which limit the usefulness of long sequencing reads. Results: Here, we present Pacasus, a tool for correcting such errors. Two datasets show that it markedly improves read mapping and de novo assembly, yielding results similar to these that would be obtained with non-amplified DNA. Conclusions: With Pacasus long-read technologies become available for sequencing targets with very small amounts of DNA, such as single cells or even single chromosomes

Whole-genome amplification (WGA) create specific chimeric fragments, which consist mainly of palindrome sequences. We developed the tool Pacasus to detect and correct these palindromic sequences in long reads, for example from PacBio and Nanopore

Next-generation sequencing requires sufficient DNA to be available. If limited, whole-genome amplification is applied to generate additional amounts of DNA. Such amplification often results in many chimeric DNA fragments, in particular artificial palindromic sequences, which limit the usefulness long reads from technologies such as PacBio and Oxford Nanopore unusable for further analysis. We developed Pacasus, a tool for correcting such errors in long reads. With Pacasus long-read technologies become readily available for sequencing targets with very small amounts of DNA

Whole-genome amplification (WGA) create specific chimeric fragments, which consist mainly of palindrome sequences. We developed the tool Pacasus to detect and correct these palindromic sequences in long reads, for example from PacBio and Nanopore

Next-generation sequencing requires sufficient DNA to be available. If limited, whole-genome amplification is applied to generate additional amounts of DNA. Such amplification often results in many chimeric DNA fragments, in particular artificial palindromic sequences, which limit the usefulness long reads from technologies such as PacBio and Oxford Nanopore unusable for further analysis. We developed Pacasus, a tool for correcting such errors in long reads. With Pacasus long-read technologies become readily available for sequencing targets with very small amounts of DNA

Correcting palindromes in long reads after whole-genome amplification

Background: Next-generation sequencing requires sufficient DNA to be available. If limited, whole-genome amplification is applied to generate additional amounts of DNA. Such amplification often results in many chimeric DNA fragments, in particular artificial palindromic sequences, which limit the usefulness of long sequencing reads. Results: Here, we present Pacasus, a tool for correcting such errors. Two datasets show that it markedly improves read mapping and de novo assembly, yielding results similar to these that would be obtained with non-amplified DNA. Conclusions: With Pacasus long-read technologies become available for sequencing targets with very small amounts of DNA, such as single cells or even single chromosomes