Synchronization of non-identical systems by non-invasive mutual time-delayed feedback.

Inspired by time-delayed feedback control, it is shown that synchronization of non-identical systems can be achieved by mutual time-delayed feedback with an asymptotically vanishing interaction. An analytic perturbation scheme is developed, which uncovers the merits as well as the constraints of such an approach. As an application, the use of the concept for a secure communication channel is considered.

Nonlinear dynamics of delay systems: an overview.

Time delays play an important role in many fields such as engineering, physics or biology. Delays occur due to finite velocities of signal propagation or processing delays leading to memory effects and, in general, infinite-dimensional systems. Time delay systems can be described by delay differential equations and often include non-negligible nonlinear effects. This overview article introduces the theme issue 'Nonlinear dynamics of delay systems', which contains new fundamental results in this interdisciplinary field as well as recent developments in applications. Fundamentally, new results were obtained especially for systems with time-varying delay and state-dependent delay and for delay system with noise, which do often appear in real systems in engineering and nature. The applications range from climate modelling over network dynamics and laser systems with feedback to human balancing and machine tool chatter. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

[Branchio-oculo-facial syndrome]. / Syndrome branchio-oculo-facial.

BACKGROUND: Branchio-Oculo-Facial Syndrome (BOFS, MIM#113620) is a rare, polymalformational disorder with cutaneous and ocular abnormalities and characteristic facial anomalies. It is an autosomal dominant developmental disorder caused by mutations or deletions in the transcription factor AP-2 alpha gene (TFAP2A, 6p24). We report a new case of atypical BOFS with a unilateral cervical cutaneous defect. PATIENT AND METHODS: A 5-year-old girl was admitted to our dermatology department for a congenital, linear, erythematous cutaneous anomaly on the right side of her neck. There was no family history. She also presented characteristic facial and ocular anomalies. BOFS was suspected. TFAP2A molecular analysis revealed a heterozygous missense mutation c.767C>T (p.Ala256Val). DISCUSSION: BOFS is variable and remains unknown to dermatologists in spite of distinctive cutaneous features. Identification of this syndrome is important to improving medical care (multidisciplinary care, further tests, genetic counselling). We report a case of atypical BOFS with a unilateral cervical cutaneous defect in one patient and bilateral cutaneous anomalies in the other four patients. In agreement with the literature, there did not appear to be mutation-specific genotype-phenotype correlations.

Beyond the odd number limitation: a bifurcation analysis of time-delayed feedback control.

We investigate the normal form of a subcritical Hopf bifurcation subjected to time-delayed feedback control. Bifurcation diagrams which cover time-dependent states as well are obtained by analytical means. The computations show that unstable limit cycles with an odd number of positive Floquet exponents can be stabilized by time-delayed feedback control, contrary to incorrect claims in the literature. The model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means.

Ellobius lutescens: sex determination and sex chromosome.

The mole vole Ellobius lutescens is an interesting animal, not only concerning its sex determination mechanism without the Y-chromosomal Sry gene, that triggers sex determination in nearly all other mammalian species, but also regarding the karyotype with an odd number of chromosomes, being identical in male and female animals. The odd chromosome represents the X chromosome, and therefore, even males do not have a Y chromosome. We present an overview of a search for candidate genes of male sex determination in the mole vole Ellobius lutescens. A singular X raises questions about the need for X chromosome inactivation in female cells. We present preliminary data that support a hypothesis that the E. lutescens Xist gene may be degenerated and thus non-functional.

Time-delay autosynchronization of the spatiotemporal dynamics in resonant tunneling diodes.

The double barrier resonant tunneling diode exhibits complex spatiotemporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time-delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way. We compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom. The numerically obtained Floquet exponents are explained by analytical results from linear stability analysis.

Self-stabilization of high-frequency oscillations in semiconductor superlattices by time-delay autosynchronization.

We present a scheme to stabilize high-frequency domain oscillations in semiconductor superlattices by a time-delayed feedback loop. Applying concepts from chaos control theory we propose to control the spatiotemporal dynamics of fronts of accumulation and depletion layers which are generated at the emitter and may collide and annihilate during their transit, and thereby suppress chaos. The proposed method only requires the feedback of internal global electrical variables, viz., current and voltage, which makes the practical implementation very easy.

The sex determination in Ellobius lutescens remains bizarre.

Mammalian sex determination and gonad differentiation are the result of a complex interaction of fine-tuned spatial and temporal gene expression with threshold levels of individual genes. The male pathway is initiated by SRY. Some exceptional mammals determine male sex without the SRY gene and even without a Y chromosome. Ellobius lutescens in this report is one example of this "weird" species. We provide key data on the genomic level that there are no coarse differences in the genomes of male and female animals by comparative genomic hybridization. On the gene level we studied the gene Nr5a1 for the orphan nuclear receptor, steroidogenic factor SF-1, a central constituent for gonad differentiation and adrenal gland development. The Ellobius lutescens Nr5a1 gene was mapped to the proximal short arm of chromosome 2 by fluorescence in situ hybridization. In addition, we provide evidence by linkage analysis in two E. lutescens pedigrees that Nr5a1 is not the key male sex-determining gene in Ellobius lutescens.

Comparison of time-delayed feedback schemes for spatiotemporal control of chaos in a reaction-diffusion system with global coupling.

Time-delayed feedback control for stabilizing time periodic spatial patterns is investigated in a generic reaction-diffusion system with global coupling. We focus on the case of low-dimensional chaos where unstable patterns admit only a single unstable mode. Spatial degrees of freedom are taken into account to define different control schemes. The efficiency of these schemes is discussed, where control forces are motivated by physical requirements as well as by the possibility of obtaining analytically exact results. We find that control schemes that contain the full feedback of the inhibitor variable may finally destroy the control performance. Thus schemes that omit the inhibitor might be more efficient. Our numerical findings are explained in terms of Floquet spectra and compared with analytical solutions of particular coupling schemes.

Invariant densities of delayed maps in the limit of large time delay.

The marginal invariant density of chaotic attractors of scalar systems with time delayed feedback has an asymptotic form in the limit of large delay. It is well known that the dimension and the entropy of such attractors obey interesting scaling laws in this limit, but very little has been said about properties of the invariant density. We present general considerations, detailed analytical results in low order perturbation theory for a particular model, and numerics for understanding the asymptotic behavior of the projections of the invariant density. Our approach clarifies how the analytical properties of the model determine the behavior of the marginal invariant densities for large delay times.

Computational complexity of multiple sequence alignment with SP-score.

It is shown that the multiple alignment problem with SP-score is NP-hard for each scoring matrix in a broad class M that includes most scoring matrices actually used in biological applications. The problem remains NP-hard even if sequences can only be shifted relative to each other and no internal gaps are allowed. It is also shown that there is a scoring matrix M(0) such that the multiple alignment problem for M(0) is MAX-SNP-hard, regardless of whether or not internal gaps are allowed.

Spatiotemporal dynamics near a supercritical Turing-Hopf bifurcation in a two-dimensional reaction-diffusion system.

Pattern formation in semiconductor heterostructures is studied on the basis of a spatially two-dimensional model of reaction-diffusion type. In particular, we investigate the neighborhood of a codimension-two Turing-Hopf instability by analytical methods. Amplitude equations are derived which predict the absence of mixed modes but extended ranges of bistability between homogeneous oscillatory states and hexagonal Turing patterns. Our results are confirmed by numerical simulations. The features are not confined to a neighborhood of the bifurcation point so that the conclusions of the weakly nonlinear analysis explain the observations in large portions of the parameter space at least qualitatively

Recurrent mutations in the COL1A2 gene in patients with osteogenesis imperfecta.

A new recurrent point mutation in the COL1A2 gene was found in a patient with type III osteogenesis imperfecta (OI). A G-to-T transversion in nucleotide position 1121 leads to an amino acid substitution Gly238Cys. This is the first report on the most N-terminal cysteine substitution in COL1A2 reported so far. Until now, at this position, only serine substitutions were observed five times in unrelated patients showing a highly variable expression of OI. It is obvious that endogenic and/or exogenic modifiers are involved in this classical autosomal dominant (or rarely recessive) mendelian disorder. An apparent preferential substitution by cysteine and serine residues is discussed with reference to post-transcriptional or post-translational collagen assembly control.

Periodic orbits and topological entropy of delayed maps.

The periodic orbits of a nonlinear dynamical system provide valuable insight into the topological and metric properties of its chaotic attractors. In this paper we describe general properties of periodic orbits of dynamical systems with feedback delay. In the case of delayed maps, these properties enable us to provide general arguments about the boundedness of the topological entropy in the high delay limit. As a consequence, all the metric entropies can be shown to be bounded in this limit. The general considerations are illustrated in the cases of Bernoulli-like and Hénon-like delayed maps.

Exclusion of SOX9 as the testis determining factor in Ellobius lutescens: evidence for another testis determining gene besides SRY and SOX9.

In mammals the initiation of testis determination usually depends on the Y-chromosomal gene SRY. A few species, however, escape from this rule with a testis determination that is independent of SRY. The mole vole Ellobius lutescens is one of these species. It is not known how testis determination is initiated in this species but it has been suggested that a gene from the sex determination cascade usually acting downstream of SRY is mutated and has taken over the testis-determining function. At present SOX9 is the only candidate gene for which a testis-determining function in the absence of SRY has been observed. To test the hypothesis that testis differentiation in E. lutescens is initiated by SOX9, segregation analysis of SOX9 alleles was performed in an E. lutescens family. As there is no marker data available in this species we screened both Ellobius SOX9 introns for polymorphisms suitable for segregation studies. A biallelic polymorphism was found in the second intron of the SOX9 gene and analysis of this marker in the Ellobius family revealed an inheritance pattern completely independent of the sex of the animals. Thus, SOX9 can be excluded from being the testis-determining factor in E. lutescens. These results provide evidence for another possibly yet unknown gene besides SRY and SOX9 able to exert testis-determining function.

Impaired membrane traffic in defective ether lipid biosynthesis.

The first steps of ether lipid biosynthesis are exclusively localized to peroxisomes and hence some peroxisomal disorders are characterized by a severe deficiency of plasmalogens, the main ether lipids in humans. Here we report on gene defects of plasmalogen biosynthesis, chromosomal localization of the corresponding genes and, as a consequence of plasmalogen deficiency, on structural alterations of caveolae, clathrin-coated pits, endoplasmic reticulum and Golgi cisternae, as well as on the reduced rate of transferrin receptor cycling. The data suggest that plasmalogens, analogous to cholesterol, are essential for correct membrane functioning and their deficiency results in impaired membrane trafficking.

A comparison of the expression pattern of five genes of the family of small leucine-rich proteoglycans during mouse development.

For five members of the family of the small leucine-rich proteoglycans (SLRPs), the expression pattern during fetal development was analyzed. RNA in situ hybridization on whole body sections of mouse embryos was performed for biglycan (Bgn), decorin (Dcn), fibromodulin (Fmod), chondroadherin (Chad), and lumican (Lum). Special attention was given to the question of whether these patterns coincide only with sites of collagen secretion in connective tissue during tissue modeling or if expression can be observed at specific sites of organ differentiation also. In general, Fmod, Lum, and Bgn are expressed at sites of cartilage and bone formation and interstitial tissue deposition; Chad is expressed only at sites of cartilage; and Dcn is expressed only at sites of interstitial tissue deposition. However, there are some distinct developmental stages where no collagen secretion is known to occur. For example, this applies for the expression of Fmod in the forming somites of stage 9.5 postconception (p.c.), for Dcn and Lum in later stage embryos in the pituitary gland and dorsal root ganglia, and for Bgn and Dcn during differentiation in the kidney. These studies provide further evidence for a role of these molecules during connective tissue organization but also for an involvement at specific sites of organ differentiation.

Relation between coupled map lattices and kinetic ising models

A spatially one-dimensional coupled map lattice possessing the same symmetries as the Miller-Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity to a symmetry breaking bifurcation point. In parameter space four phases with different ergodic behavior are observed. Although the coupling in the map lattice is diffusive, antiferromagnetic ordering is predominant. Via coarse graining the deterministic model is mapped to a master equation which establishes an equivalence between our system and a kinetic Ising model. Such an approach sheds some light on the dependence of the transient behavior on the system size and the nature of the phase transitions.