Strong perturbations in nonlinear systems

A novel case of probabilistic coupling for hybrid stochastic systems with chaotic components via Markovian switching is presented. We study its stability in the norm, in the sense of Lyapunov and present a quantitative scheme for detection of stochastic stability in the mean. In particular we examine the stability of chaotic dynamical systems in which a representative parameter undergoes a Markovian switching between two values corresponding to two qualitatively different attractors. To this end we employ, as case studies, the behaviour of two representative chaotic systems (the classic Rössler and the Thomas-Rössler models) under the influence of a probabilistic switch which modifies stochastically their parameters. A quantitative measure, based on a Lyapunov function, is proposed which detects regular or irregular motion and regimes of stability. In connection to biologically inspired models (Thomas-Rössler models), where strong fluctuations represent qualitative structural changes, we observe the appearance of stochastic resonance-like phenomena i.e. transitions that lead to orderly behavior when the noise increases. These are attributed to the nonlinear response of the system.     

Elastic modulus of a polymer nanodroplet: theory and experiment

We redevelop a theoretical model that, in conjunction with atomic force microscopy (AFM), can be used as a noninvasive method for determination of the elastic modulus of a polymer nanodroplet residing on a flat, rigid substrate. The model is a continuum theory that combines surface and elasticity theories for prediction of the droplet's elastic modulus, given experimental measurement of its adsorbed height. Utilization of AFM-measured heights for relevant droplets reported in the literature and from our own experiments illustrated the following: the significance of both surface and elasticity effects in determining a polymer droplet's spreading behavior; the extent of a continuum theory's validity as one approaches the nanoscale; and a droplet size effect on the elastic modulus.     

Linear Extensions and Comparable Pairs in Partial Orders

We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on n elements, which has close to a third of the pairs comparable with high probability: we show that the number of linear extensions is n! 2^?Θ(n) with high probability.     

Signal classification with a point process distance on the space of persistence diagrams

In this paper, we consider the problem of signal classification. First, the signal is translated into a persistence diagram through the use of delay-embedding and persistent homology. Endowing the data space of persistence diagrams with a metric from point processes, we show that it admits statistical structure in the form of Fréchet means and variances and a classification scheme is established. In contrast with the Wasserstein distance, this metric accounts for changes in small persistence and changes in cardinality. The classification results using this distance are benchmarked on both synthetic data and real acoustic signals and it is demonstrated that this classifier outperforms current signal classification techniques.     

A time-dependent numerical analysis of flow in a mechanical heart valve: Comparison with experimental results

There is a great need to fabricate heart valves that have similar haemodynamic properties with the natural ones. Towards this goal, we examine the dynamics of fluid flow in a mechanical heart valve with one leaflet. The fluid is incompressible and Newtonian and the leaflet is a neo-Hookean material. The Arbitrary Lagrangian Eulerian method is used to model the fluid-leaflet interaction, and the system of equations is solved using the Finite Element method. The pseudo solid approach along with a set of algebraic equations are used to deform the mesh, while care is taken to avoid remeshing of the domain, at the moment of valve closure. The computational results are compared against the experimental results, and we find an excellent agreement for the time period of valve closure, the time the valve is fully opened, and the value of the maximum valve opening angle. This study indicates that the present model is capable of describing the valve dynamics in physiological geometries.     

Hyperchaos of arbitrary order generated by a single feedback circuit, and the emergence of chaotic walks

It is shown that hyperchaos of order m (i.e., with m positive Lyapunov exponents) can be generated by a single feedback circuit in n = 2m + 1 variables. This feedback circuit is constructed such that, dividing phase space into hypercubes, it changes sign wherever the trajectory passes from one hypercube into an adjacent one. Letting the negative diagonal elements in the Jacobian tend to zero, the dynamics becomes conservative. Instead of chaotic attractors, unbounded chaotic walks are then generated. Here we report chaotic walks emerging from a continuous system rather than the well known chaotic walks present in "Lorentz gas" and "couple map lattices."     

Self-affine surface morphology of plastically deformed metals

We analyze the surface morphology of metals after plastic deformation over a range of scales from 10 nm to 2 mm using atomic force microscopy and scanning white-light interferometry. We demonstrate that an initially smooth surface during deformation develops self-affine roughness over almost 4 orders of magnitude in scale. The Hurst exponent H of one-dimensional surface profiles initially decreases with increasing strain and then stabilizes at H approximately 0.75. We show that the profiles can be mathematically modeled as graphs of a fractional Brownian motion. Our findings can be understood in terms of a fractal distribution of plastic strain within the deformed samples.     

Usefulness of event-related potentials in the assessment of mild cognitive impairment

Background  

The aim of this study was to determine if changes in latencies and amplitudes of the major waves of Auditory Event-Related Potentials (AERP), correlate with memory status of patients with mild cognitive impairment (MCI) and conversion to Alzheimer's disease (AD).     

Challenges in optimizing a prostate carcinoma binding peptide, identified through the phage display technology

The transfer of peptides identified through the phage display technology to clinical applications is difficult. Major drawbacks are the metabolic degradation and label instability. The aim of our work is the optimization of DUP-1, a peptide which was identified by phage display to specifically target human prostate carcinoma. To investigate the influence of chelate conjugation, DOTA was coupled to DUP-1 and labeling was performed with 111In. To improve serum stability cyclization of DUP-1 and targeted D-amino acid substitution were carried out. Alanine scanning was performed for identification of the binding site and based on the results peptide fragments were chemically synthesized. The properties of modified ligands were investigated in in vitro binding and competition assays. In vivo biodistribution studies were carried out in mice, carrying human prostate tumors subcutaneously. DOTA conjugation resulted in different cellular binding kinetics, rapid in vivo renal clearance and increased tumor-to-organ ratios. Cyclization and D-amino acid substitution increased the metabolic stability but led to binding affinity decrease. Fragment investigation indicated that the sequence NRAQDY might be significant for target-binding. Our results demonstrate challenges in optimizing peptides, identified through phage display libraries, and show that careful investigation of modified derivatives is necessary in order to improve their characteristics.     

Significant modification of the I(-)3 Lewis base character in the β-cyclodextrin polyiodide inclusion complex with Co2+ ion: an FT-Raman investigation

The β-cyclodextrin (β-CD) polyiodide inclusion complex (β-CD)(2)·Co(0.5)·I(7)·21H(2)O has been synthesized, characterized and further investigated via FT-Raman spectroscopy in the temperature range of 30-120°C. The experimental results point to the coexistence of I(-)(7) units (I(2)·I(-)(3)·I(2)) that seem not to interact with the Co(2+) ions and I(-)(7) units that display such interactions. The former units exhibit a disorder-order transition of both their I(2) molecules above 60°C due to a symmetric charge-transfer interaction with the central I(-)(3) [I(2)←I(-)(3)→I(2)], whereas in the latter units only one of the two I(2) molecules becomes well-ordered above 30°C. The other I(2) molecule remains disordered presenting no charge-transfer phenomena. The Co(2+) ion induces a considerable asymmetry on the geometry of the I(-)(3) anion and a significant modification of its Lewis base character. Complementary dielectric measurements suggest no important involvement of H···I contacts in the observed modification of the I(-)(3) electron-transfer properties.