Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics

We consider a nonlinear diffusion equation proposed by Shigesada and Okubo which describes phytoplankton growth dynamics with a selfs-hading effect.We show that the following alternative holds: Either (i) the trivial stationary solution which vanishes everywhere is a unique stationary solution and is globally stable, or (ii) the trivial solution is unstable and there exists a unique positive stationary solution which is globally stable. A criterion for the existence of positive stationary solutions is stated in terms of three parameters included in the equation.     

Spatial distribution of dispersing animals

Summary A mathematical model for the dispersal of an animal population is presented for a system in which animals are initially released in the central region of a uniform field and migrate randomly, exerting mutually repulsive influences (population pressure) until they eventually become sedentary. The effect of the population pressure, which acts to enhance the dispersal of animals as their density becomes high, is modeled in terms of a nonlinear-diffusion equation. From this model, the density distribution of animals is obtained as a function of time and the initial number of released animals. The analysis of this function shows that the population ultimately reaches a nonzero stationary distribution which is confined to a finite region if both the sedentary effect and the population pressure are present. Our results are in good agreement with the experimental data on ant lions reported by Morisita, and we can also interpret some general features known for the spatial distribution of dispersing insects.     

Temporal oscillations in neuronal nets

Summary A model for the interactions of cortical neurons is derived and analyzed. It is shown that small amplitude spatially inhomogeneous standing oscillations can bifurcate from the rest state. In a periodic domain, traveling wave trains exist. Stability of these patterns is discussed in terms of biological parameters. Homoclinic and heteroclinic orbits are demonstrated for the space-clamped system.The research reported in this paper was supported in part by NIH GM2037     

Planarian activity differences when maintained in water pre-treated with magnetic fields: a nonlinear effect

There have been multiple claims that exposing water to a static magnetic field affects its properties which influence living systems. To test this hypothesis, planarian subsequent to dissection were maintained in spring water that had been previously exposed for only one day to one of three (16, 160, or 1,600 G) intensity static magnetic fields or to a reference condition. Although there was no significant difference in regeneration rates over the subsequent seven-day period, there was a statistically significant nonlinear effect for planarian mobility and diffusion rates. Both mobility rates and diffusion velocity of a liquid within the water that had been exposed to the 16 G field was about twice that for water exposed to the other intensities. These results imply that nonlinear biophysical effects may emerge under specific conditions of intensity ranges for particular volumes of water.     

Applications of second harmonic generation (SHG)/sum-frequency generation (SFG) imaging for biophysical characterization of the plasma membrane

The plasma membrane is a lipid bilayer of < 10 nm width that separates intra- and extra-cellular environments and serves as the site of cell-cell communication, as well as communication between cells and the extracellular environment. As such, biophysical phenomena at and around the plasma membrane play key roles in determining cellular physiology and pathophysiology. Thus, the selective visualization and characterization of the plasma membrane are crucial aspects of research in wide areas of biology and medicine. However, the specific characterization of the plasma membrane has been a challenge using conventional imaging techniques, which are unable to effectively distinguish between signals arising from the plasma membrane and those from intracellular lipid structures. In this regard, interface-specific second harmonic generation (SHG) and sum-frequency generation (SFG) imaging demonstrate great potential. When combined with exogenous SHG/SFG active dyes, SHG/SFG can specifically highlight the plasma membrane as the most prominent interface associated with cells. Furthermore, SHG/SFG imaging can be readily extended to multimodal multiphoton microscopy with simultaneous occurrence of other multiphoton phenomena, including multiphoton excitation and coherent Raman scattering, which shed light on the biophysical properties of the plasma membrane from different perspectives. Here, we review traditional and current applications, as well as the prospects of long-known but unexplored SHG/SFG imaging techniques in biophysics, with special focus on their use in the biophysical characterization of the plasma membrane.     

Non-identifiability of the Rayleigh damping material model in Magnetic Resonance Elastography

Magnetic Resonance Elastography (MRE) is an emerging imaging modality for quantifying soft tissue elasticity deduced from displacement measurements within the tissue obtained by phase sensitive Magnetic Resonance Imaging (MRI) techniques. MRE has potential to detect a range of pathologies, diseases and cancer formations, especially tumors. The mechanical model commonly used in MRE is linear viscoelasticity (VE). An alternative Rayleigh damping (RD) model for soft tissue attenuation is used with a subspace-based nonlinear inversion (SNLI) algorithm to reconstruct viscoelastic properties, energy attenuation mechanisms and concomitant damping behavior of the tissue-simulating phantoms. This research performs a thorough evaluation of the RD model in MRE focusing on unique identification of RD parameters, _μI${\mu }_I$ and _ρI${\rho }_I$.     

Dynamic stability of a human standing on a balance board

The neuromuscular system used to stabilize upright posture in humans is a nonlinear dynamical system with time delays. The analysis of this system is important for improving balance and for early diagnosis of neuromuscular disease. In this work, we study the dynamic coupling between the neuromuscular system and a balance board—an unstable platform often used to improve balance in young athletes, and older or neurologically impaired patients. Using a simple inverted pendulum model of human posture on a balance board, we describe a surprisingly broad range of divergent and oscillatory CoP/CoM responses associated with instabilities of the upright equilibrium. The analysis predicts that a variety of sudden changes in the stability of upright postural equilibrium occurs with slow continuous deterioration in balance board stiffness, neuromuscular gain, and time delay associated with the changes in proprioceptive/vestibular/visual-neuromuscular feedback. The analysis also provides deeper insight into changes in the control of posture that enable stable upright posture on otherwise unstable platforms.     

Voice disorders assessed by (cross-) Sample Entropy of electroglottogram and microphone signals

The quantitative analysis of vocal disorders by nonlinear signal processing methods has been extensively used in the last two decades. In this work, two algorithms for nonlinear time-series analysis, Sample Entropy and cross-Sample Entropy, are used on electroglottogram (EGG) and microphone (MIC) signals recorded from 51 normal and 80 dysphonic subjects, to obtain summary measures of voice disorders through SampEn and cross-SampEn indices. Such parameters quantify, respectively, the degree of irregularity (in the sense of self-dissimilarity) within a time-series and of asynchrony (in the sense of cross-dissimilarity) between two distinct time-series. The aims of this work are: to determine if statistically significant differences in terms of signal irregularity quantified by SampEn occur between normal and pathological subjects, investigating whether or not such differences can be equally seen in EGG and MIC; to assess if cross-SampEn reveals different degrees of asynchrony between EGG and MIC signals in the two groups. Results show that SampEn in pathological subjects is higher than in normal subjects for both EGG and MIC time-series, with a statistically significant difference detectable from both signals (Pe < 10^?4 for EGG and Pe < 10^?7 for MIC). Cross-SampEn exhibits a statistically significant difference too, showing a higher degree of cross-dissimilarity between EGG and MIC time-series for pathological subjects (Pe < 10^?4). In conclusion, SampEn and cross-SampEn well quantify the increase of complexity of both EGG and MIC signals and the decrease of their cross-similarity in presence of vocal disorders. Thanks to the complementarity of nonlinear indicators to the traditionally considered linear ones, SampEn and cross-SampEn appear as suitable candidates to enter the pool of approaches to investigate speech pathologies and to obtain potentially new insights on their nature.     

Brain structure and spatial sensitivity profile assessing by near‐infrared spectroscopy modeling based on 3D MRI data

The goal of this study is to prove that the light propagation in the head by used the 3‐D optical model from in vivo MRI data set can also provide significant characteristics on the spatial sensitivity of cerebral cortex folding geometry based on Monte Carlo simulation. Thus, we proposed a MRI based approach for 3‐D brain modeling of near‐infrared spectroscopy (NIRS). In the results, the spatial sensitivity profile of the cerebral cortex folding geometry and the arrangement of source‐detector separation have being necessarily considered for applications of functional NIRS. The optimal choice of source‐detector separation is suggested within 3–3.5 cm by the received intensity with different source‐detector separations and the ratio of received light from the gray and white matter layer is greater than 50%. Additionally, this study has demonstrated the capability of NIRS in not only assessing the functional but also detecting the structural change of the brain by taking advantage of the low scattering and absorption coefficients observed in CSF of sagittal view. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements

When a laser is mode-locked, it emits a train of ultra-short pulses at a repetition rate determined by the laser cavity length. This article outlines a new and inexpensive procedure to force mode locking in a pre-adjusted nonlinear polarization rotation fiber laser. This procedure is based on the detection of a sudden change in the output polarization state when mode locking occurs. This change is used to command the alignment of the intra-cavity polarization controller in order to find mode-locking conditions. More specifically, the value of the first Stokes parameter varies when the angle of the polarization controller is swept and, moreover, it undergoes an abrupt variation when the laser enters the mode-locked state. Monitoring this abrupt variation provides a practical easy-to-detect signal that can be used to command the alignment of the polarization controller and drive the laser towards mode locking. This monitoring is achieved by feeding a small portion of the signal to a polarization analyzer measuring the first Stokes parameter. A sudden change in the read out of this parameter from the analyzer will occur when the laser enters the mode-locked state. At this moment, the required angle of the polarization controller is kept fixed. The alignment is completed. This procedure provides an alternate way to existing automating procedures that use equipment such as an optical spectrum analyzer, an RF spectrum analyzer, a photodiode connected to an electronic pulse-counter or a nonlinear detecting scheme based on two-photon absorption or second harmonic generation. It is suitable for lasers mode locked by nonlinear polarization rotation. It is relatively easy to implement, it requires inexpensive means, especially at a wavelength of 1550 nm, and it lowers the production and operation costs incurred in comparison to the above-mentioned techniques.