The δ-function counterion condensate around a line charge derived from the Fuoss,Katchalsky, and Lifson polyelectrolyte theory

It has recently been proven that the counterion condensate around an isolated line charge in an electrolyte, as characterized by nonlinear Poisson-Boltzmann theory, is an encapsulating δ-function. Here the identical result is shown to hold in the framework of the polyelectrolyte theory of Fuoss, Katchalsky, and Lifson. The proof fully exploits analytic solutions to the differential equation which are not available for the nonlinear, cylindrical Poisson-Boltzmann equation.     

The relationship of the slope of the heart rate graph regression with linear and nonlinear heart rate dynamics in stationary short-time series

The relationship of the slope of the heart rate graph regression curve (b ₁) with periodic (linear) and nonlinear heart rate dynamics has been studied in stationary short-time series (256 points). For estimating nonlinear dynamics, a parameter derived from correlation dimension has been used, which has made it possible to estimate chaotic processes in short-time series. According to the results of the study, the heart rate dynamics in short-time series may be represented as a sum of linear (periodic) and nonlinear (stochastic) processes. The relationships of b ₁ with both the linear and the nonlinear heart rate dynamics have been demonstrated. Equations for calculating the absolute and relative (to the periodic oscillation amplitude) noises in the heart rate dynamics in short-time series are proposed. Stochastic nonlinear dynamics in different physiological states of humans have been compared. It has been found that the increase in the relative noise intensity in the heart rate dynamics with an increase in respiration rate is determined not only by the decrease in the amplitude of respiratory waves, but also by an increase in the amplitude of the noise itself. The absolute noise intensity is decreased in the states of neurotic excitement, fatigue, and, especially, mental stress. In the state of rest, nonlinear (stochastic) processes dominate over linear (periodic) ones.     

A specific radiochemical assay for pyrroline-5-carboxylate dehydrogenase

Previous studies of pyrroline-5-carboxylate dehydrogenase have been conducted using a spectrophotometric method to monitor substrate-dependent NAD(P)H production. For the assay of the mammalian enzyme, the spectrophotometric assay was found to be unacceptable for kinetic studies as the production of NAD(P)H was nonlinear with time and protein concentration. An assay which measures radiolabeled glutamate production by this enzyme in the presence of NAD+ from radiolabeled pyrroline-5-carboxylate has been developed. Separation of substrate from product is achieved by column chromatography using Dowex 50 cation-exchange resin. The product isolated by this procedure was identified as glutamate. This new assay is linear with time and protein concentration and gives reproducible results. The assay is not influenced by competing enzyme activities, such as glutamate dehydrogenase, in a liver homogenate so that quantitative conversion of pyrroline-5-carboxylate to glutamate is observed.     

Nonlinear dynamics of heart rate variability during experimental hemorrhage in ketamine-anesthetized rats

Indexes of heart rate variability (HRV) based on linear stochastic models are independent risk factors for arrhythmic death (AD). An index based on a nonlinear deterministic model, a reduction in the point correlation dimension (PD2i), has been shown in both animal and human studies to have a higher sensitivity and specificity for predicting AD. Dimensional reduction subsequent to transient ischemia was examined previously in a simple model system, the intrinsic nervous system of the isolated rabbit heart. The present study presents a new model system in which the higher cerebral centers are blocked chemically (ketamine inhibition of N-methyl-D-aspartate receptors) and the system is perturbed over a longer 15-min interval by continuous hemorrhage. The hypothesis tested was that dimensional reduction would again be evoked, but in association with a more complex relationship between the system variables. The hypothesis was supported, and we interpret the greater response complexity to result from the larger autonomic superstructure attached to the heart. The complexities observed in the nonlinear heartbeat dynamics constitute a new genre of autonomic response, one clearly distinct from a hardwired reflex or a cerebrally determined defensive reaction.     

Nonlinear transient computation as a potential "kernel trick" in cortical processing

Evidence has been found for the presence of chaotic dynamics at all levels of the mammalian brain. This has led to some searching questions about the potential role that nonlinear dynamics may have in neural information processing. We propose that chaos equips the brain with the equivalent of a kernel trick for solving hard nonlinear problems. The approach presented, which is described as nonlinear transient computation, uses the dynamics of a well known chaotic attractor. The paper provides experimental results to show that this approach can be used to solve some challenging pattern recognition tasks. The paper also offers evidence to suggest that the efficacy of nonlinear transient computation for nonlinear pattern classification is dependent only on the generic properties of chaotic attractors and is not sensitive to the particular dynamics of specific sub-regions of chaotic phase space. If, as this work suggests, nonlinear transient computation is independent of the particulars of any given chaotic attractor, then it could be offered as a possible explanation of how the chaotic dynamics that have been observed in brain structures contribute to neural information processing tasks.     

Neurodynamics: nonlinear dynamics and neurobiology

The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.     

Thermoelastic excitation of acoustic waves in biological models under the effect of the high peak-power pulsed electromagnetic radiation of extremely high frequency

The capability of high peak-power pulsed electromagnetic radiation of extremely high frequency (35,27 GHz, pulse widths of 100 and 600 ns, peak power of 20 kW) to excite acoustic waves in model water-containing objects and muscular tissue of animals has been experimentally shown for the first time. The amplitude and duration of excited acoustic pulses are within the limits of accuracy of theoretical assessments and have a complex nonlinear dependence on the energy input of electromagnetic radiation supplied. The velocity of propagation of acoustic pulses in water-containing models and isolated muscular tissue of animals was close to the reference data. The excitation of acoustic waves in biological systems under the action of high peak-power pulsed electromagnetic radiation of extremely high frequency is the important phenomenon, which essentially contributes to the understanding of the mechanisms of biological effects of these electromagnetic fields.     

Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control

In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear measurements of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. Choosing the right nonlinear observable functions to form an invariant subspace where it is possible to obtain linear reduced-order models, especially those that are useful for control, is an open challenge. Here, we investigate the choice of observable functions for Koopman analysis that enable the use of optimal linear control techniques on nonlinear problems. First, to include a cost on the state of the system, as in linear quadratic regulator (LQR) control, it is helpful to include these states in the observable subspace, as in DMD. However, we find that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not globally topologically conjugate to a finite-dimensional linear system, and cannot be represented by a finite-dimensional linear Koopman subspace that includes the state. We then present a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ₁-regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.     

On the Question of Self-Organization of Population Dynamics on Earth

Biophysics - A new mathematical model based on the predator–prey interactions has been proposed. Strictly analytical solution has been found for a system of nonlinear differential equations...     

Isolation of highly heat-resistant Listeria monocytogenes variants by use of a kinetic modeling-based sampling scheme

Stable high-hydrostatic-pressure (HHP)-resistant Listeria monocytogenes LO28 variants were previously isolated and characterized. These HHP variants were also more resistant to heat. In addition, nonlinear heat inactivation kinetics pointed toward the existence of heat-resistant variants, although these could not be isolated so far. In this study, we used kinetic modeling of inactivation curves of two isolated HHP variants and their wild type, and this revealed that the probability of finding resistant variants should depend on the nature of the inactivation treatment and the time of exposure. At specific heat and HHP conditions, resistant LO28 and EGDe variants were indeed isolated. Resistant LO28 variants were even isolated after a heat inactivation at 72°C in milk, and these variants showed high resistance to standard pasteurization conditions. The increased resistance of part of the isolated LO28 and EGDe variants was due to mutations in their ctsR genes. For the variants whose ctsR genes and upstream regions were not altered, the mechanisms leading to increased resistance remain to be elucidated. This research showed the strength of kinetic modeling in unraveling the causes of nonlinear inactivation and facilitating the isolation of heat-resistant L. monocytogenes variants.     

Influence of the PCR artifacts on the genotyping efficiency by the microsatellite loci using native polyacrylamide gel electrophoresis

Formation of different types of artifacts during amplification has been studied using different classes of molecular-genetic markers (Indel and SSR). It has been shown that DNA heteroduplexes are formed during amplification of heterozygous samples as fragments of both target genes and microsatellite loci. Electrophoresis of the amplification products of homozygous samples by microsatellite loci in native polyacrylamide gel has revealed specific additional fragments that do not belong to the class of heteroduplex DNA. It has been supposed that the additional fragments belong to a special type of homoduplex DNA—nonlinear homoduplexes. The analysis has revealed that the formation of nonlinear homoduplex DNA takes place on the 20–25 cycle of the PCR at the amplification of both experimental samples and individual DNA fragments cut from the gel.     

Mathematical and computation modeling of self-organizing sarcomere with chaotic dynamics of the order parameter

The results of constructing a nonlinear model of sarcomere contraction are summarized. A strange attractor has been obtained, which is related to the randomness of the dynamics of the order parameter during sarcomere deformation. A hypothesis is proposed that upon fixation of the actin filaments in the sarcomere the myosin system undergoes nonlinear oscillations with dissipation, which leads to elevation of solution temperature. The increase in temperature has been determined for pulsations of the inertial range. Normalized power spectra of the pulsations of the order parameter have been constructed for the model by Fourier transform. The thermodynamics of sarcomere contraction is considered.     

Enhanced Nonlinear Optical Response of Resonantly Coupled Silver Nanoparticle–Organic Dye Complexes

The influence of metal nanoparticles on linear and nonlinear optical properties of surrounding organic molecules has been widely investigated, whereas much less attention has been paid to the influence of molecules on properties of nanoparticles. Here, we employ transient absorption spectroscopy to address the nonlinear optical responses of the resonantly coupled silver nanoparticle–organic dye systems and demonstrate that silver nanoparticles covered with dye molecules show enhanced and spectrally different nonlinear extinction changes from pristine nanoparticles. We identify changes of the plasmon resonance band of nanoparticles induced by excitation of surrounding dye. We attribute these exciton–plasmon coupling effects to the excitation-induced refractive index modifications of the dye layer surrounding a nanoparticle and to the back-transfer of the oscillator strength borrowed by the dye from the nanoparticle.     

Nonlinear Dynamics of the Movement of the Venus Flytrap

The Venus flytrap has long been regarded as one of the most amazing examples of movement in the plant kingdom. The trapping ability of the flytrap consists of three unique features. First, trap closure represents one of the fastest movements in the plant kingdom. Second, a decision-making stage allows the plant to "decide" whether to completely close or open the trap, based on stimuli provided from the trapped object. Finally, the Venus flytrap contains a "memory function" that requires two mechanical stimuli within about 30 seconds to initiate trap closure. The movement involved in trap closure consists of nonlinear dynamics that have not been well understood. By understanding the movement, through nonlinear dynamics analysis, it will be possible to better understand this biological process. A mathematical model describing the movement of the Venus flytrap was first proposed by the authors in Yang et?al., Plant Signal. Behav. 5(8), 968-978 (2010). In the current work, the earlier research has been advanced and an in-depth nonlinear and control analysis of the dynamic process has been provided.     

An immunological analysis of the hemagglutinin from the influenza A virus (H1N1) isolated by using various detergents

Immunogenic properties of influenza virus hemagglutinin, isolated by new detergents O-14 (desintegron-O) and B-14 (desintegron-B) have been studied. Hemagglutinin isolated by desintegron-O has been found to be more immunogenic than virions. It has been shown that hemagglutinin isolated by desintegron-B induces a lower humoral immune response than the influenza virus.     

ISOLATION AND PROPERTIES OF LIVER CELL NUCLEOLI

1. The significance of the term nucleolus has been discussed. 2. A detailed method for the isolation of nucleoli from already isolated rat or cat liver nuclei has been presented. 3. The presence of DNA in isolated liver cell nucleoli has been indicated by histochemical methods. 4. The percentages of DNA and RNA in the isolated nucleoli have been determined by chemical analysis. 5. The specific activities of aldolase, arginase, and catalase have been determined for two subnuclear fractions and for the isolated nucleoli of rat and cat liver, and the relative amounts of these enzymes in the same subnuclear fractions and nucleoli of rat liver have been measured. 6. The significance of the above findings has been discussed and consideration has been given to what types of isolated nuclei might best serve as starting material for the isolation of nucleoli. 7. A new hypothesis has been presented that nucleoli of the liver cell type may function primarily in furnishing (directly or indirectly) templates for the synthesis of the particular enzymes that must govern the chemistry of mitosis.     

Membrane structure in isolated and intact myelins.

The biochemical composition of myelin and the topology of its constituent lipids and proteins are typically studied using membranes that have been isolated from whole, intact tissue using procedures involving hypotonic shock and sucrose density gradient centrifugation. To what extent, however, are the structure and intermembrane interactions of isolated myelin similar to those of intact myelin? We have previously reported that intact and isolated myelins do not always show identical myelin periods, indicating a difference in membrane-membrane interactions. The present study addresses the possibility that this is due to altered membrane structure. Because x-ray scattering from isolated myelin sometimes consists of overlapping Bragg reflections or is continuous, we developed nonlinear least squares procedures for analyzing the total intensity distribution after film scaling, background subtraction, and Lorentz correction. We calculated electron density profiles of isolated myelin for comparison with membrane profiles from intact myelin. The change in the width of the extracellular space and the relative invariance of the cytoplasmic space as a function of pH and ionic strength that we previously found for intact nerve was largely paralleled by isolated myelin. There were two exceptions: isolated CNS myelin was resistant to swelling under all conditions, and isolated PNS myelin in hypotonic saline showed indefinite swelling at the extracellular apposition. However, electron density profiles of isolated myelins, calculated to 30 A resolution, did not show any major change in structure compared with intact myelin that could account for the differences in interactions.     

Theoretical models of the influence of genomic architecture on the dynamics of speciation

A long‐standing problem in evolutionary biology has been determining whether and how gradual, incremental changes at the gene level can account for rapid speciation and bursts of adaptive radiation. Using genome‐scale computer simulations, we extend previous theory showing how gradual adaptive change can generate nonlinear population transitions, resulting in the rapid formation of new, reproductively isolated species. We show that these transitions occur via a mechanism rooted in a basic property of biological heredity: the organization of genes in genomes. Genomic organization of genes facilitates two processes: (i) the build‐up of statistical associations among large numbers of genes and (ii) the action of divergent selection on persistent combinations of alleles. When a population has accumulated a critical amount of standing, divergently selected variation, the combination of these two processes allows many mutations of small effect to act synergistically and precipitously split one population into two discontinuous, reproductively isolated groups. Periods of allopatry, chromosomal linkage among loci, and large‐effect alleles can facilitate this process under some conditions, but are not required for it. Our results complement and extend existing theory on alternative stable states during population divergence, distinct phases of speciation and the rapid emergence of multilocus barriers to gene flow. The results are thus a step towards aligning population genomic theory with modern empirical studies.     

Plasmon-Enhanced Second Harmonic Generation: from Individual Antennas to Extended Arrays

We analyze the emission yield of the second harmonic generation (SHG) from dense ordered arrays of L-shaped Au nanoantennas within a well-defined collection angle and compare it to that of the isolated nanostructures designed with the same geometrical parameters. Thanks to the high antenna surface density, arrays display one order of magnitude higher SHG yield per unit surface with respect to isolated nanoantennas. The difference in the collected nonlinear signals becomes even more pronounced by reducing the collection angle, because of the efficient angular filtering that can be attained in dense arrays around the zero order. Albeit this key-enabling feature allows envisioning application of these platforms to nonlinear sensing, a normalization of the SHG yield to the number of excited antennas in the array reveals a reduced nonlinear emission from each individual antenna element. We explain this potential drawback in terms of resonance broadening, commonly observed in densely packed arrays, and angular filtering of the single antenna emission pattern provided by the array 0th order.