Metabolic network dynamics in open chaotic flow

We have analyzed the dynamics of metabolically coupled replicators in open chaotic flows. Replicators contribute to a common metabolism producing energy-rich monomers necessary for replication. The flow and the biological processes take place on a rectangular grid. There can be at most one molecule on each grid cell, and replication can occur only at localities where all the necessary replicators (metabolic enzymes) are present within a certain neighborhood distance. Due to this finite metabolic neighborhood size and imperfect mixing along the fractal filaments produced by the flow, replicators can coexist in this fluid system, even though coexistence is impossible in the mean-field approximation of the model. We have shown numerically that coexistence mainly depends on the metabolic neighborhood size, the kinetic parameters, and the number of replicators coupled through metabolism. Selfish parasite replicators cannot destroy the system of coexisting metabolic replicators, but they frequently remain persistent in the system. (c) 2002 American Institute of Physics.     

An introduction to physical theory of molecular evolution

This work is a tutorial in Molecular Evolution from the point of view of Physics. We discuss Eigen's model, a link between evolutionary theory and physics. We will begin by assuming the existence of (marco) molecules or replicators with the template property, that is, the capacity to self-replicate. According to this assumption, information will be randomly generated and destroyed by mutations in the code (i.e., errors in the copying process) and new bits of information will be fixed (made stable) by the existence of an external pressure on the system (i.e., selection), and the ability of the molecules to replicate themselves. Our aim is to build a model in order to describe molecular evolution from as general a standpoint as possible. As we will see, even very simple models from the theoretical point of view will have surprisingly deep consequences.     

Error thresholds for quasispecies on dynamic fitness landscapes

In this paper we investigate error thresholds on dynamic fitness landscapes. We show that there exists both a lower and an upper threshold, representing limits to the copying fidelity of simple replicators. The lower bound can be expressed as a correction term to the error threshold present on a static landscape. The upper error threshold is a new limit that only exists on dynamic fitness landscapes. We also show that for long genomes and/or highly dynamic fitness landscapes there exists a lower bound on the selection pressure required for the effective selection of genomes with superior fitness independent of mutation rates, i.e. there are distinct nontrivial limits to evolutionary parameters in dynamic environments.     

Evolution of protein synthesis in a lattice model of replicators

The traditional chemical-kinetics approach to the study of prebiotic evolution cannot explain the evolution of protein synthesis in a homogeneous population of self-replicating molecules, because the invasion of a resident population of simpler, template-directed replicators by mutant protein-assisted replicators is deemed impossible. Approaching this problem in a spatial cellular automaton framework, we argue here that in such a setting evolution of protein synthesis is a likely event. In addition, we show that the onset of invasion may be viewed as a nonequilibrium phase transition, that can be characterized quantitatively by a set of critical exponents.     

Dynamics of Finger Formation in Laplacian Growth Without Surface Tension

We study the dynamics of “finger” formation in Laplacian growth without surface tension in a channel geometry (the Saffman–Taylor problem). We present a pedagogical derivation of the dynamics of the conformal map from a strip in the complex plane to the physical channel. In doing so we pay attention to the boundary conditions (no flux rather than periodic) and derive a field equation of motion for the conformal map. We first consider an explicit analytic class of conformal maps that form a basis for solutions in infinitely long channels, characterized by meromorphic derivatives. The great bulk of these solutions can lose conformality due to finite time singularities. By considerations of the nature of the analyticity of these solutions, we show that those solutions which are free of such singularities inevitably result in a single asymptotic “finger” whose width is determined by initial conditions. This is in contradiction with the experimental results that indicate selection of a finger of width 1/2. In the last part of this paper we show that such a solution might be determined by the boundary conditions of a finite body of fluid, e.g. finiteness can lead to pattern selection.     

The comparative analysis of prebiological evolution models

Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models.     

Continuous Selections of Solution Sets of Lipschitzian Quantum Stochastic Differential Inclusions

A multifunction associated with the set of solutions of Lipschitzian quantum stochastic differential inclusion (QSDI) admits a selection continuous from some subsets of complex numbers to the space of the matrix elements of adapted weakly absolutely continuous quantum stochastic processes. In particular, the solution set map as well as the reachable set of the QSDI admit some continuous representations.     

Ordering and growth of Langmuir–Blodgett films: X-ray scattering studies

The interplay of ordering, confinement and growth in ultrathin films gives rise to various interesting phenomena not observed in bulk materials. The nature of ordering and interfacial morphology present in these films, in turn, depends on their growth mechanism. Well-ordered metal–organic films, deposited using an enigmatic Langmuir–Blodgett (LB) technique, are not only ideal systems for understanding the interplay between growth and structure of ultrathin films but also for studying chemical reactions and phase transitions in confined geometries. Studies on these LB films also enhance our understanding of the fundamental interactions of amphiphilic molecules important for biological systems. Advent of grazing incidence X-ray scattering techniques has enabled us to probe the interfacial structure of these multilayer films at very high resolution and as a result has improved our knowledge about the mechanism of growth processes and about physical/chemical properties of ultrathin films. In this review we will focus our attention on recent results obtained using these X-ray scattering techniques to understand the mechanism of growth leading to formation of remarkably well-ordered LB films after giving a brief outline of these scattering techniques. In addition, we also review recent results on growth and structure of nanoparticles formed by suitable chemical processes within the ordered matrix of LB films. Finally, we will discuss the work done on melting of LB films and its implications in our understanding of melting process in lower dimensions. In all these studies, especially those on as-deposited LB films results of atomic force microscopy measurements have provided important complementary morphological information.     

PPT-Inducing,Distillation-Prohibiting,and Entanglement-Binding Quantum Channels

We review the entanglement degradation in open quantum systems in the Choi–Jamio?kowski representation of linear maps. In addition to physical processes of entanglement dissociation and entanglement annihilation, we consider quantum dynamics transforming arbitrary input states into those that remain positive under partial transpose (PPT-inducing channels). Such evolutions form a convex subset of distillation-prohibiting channels. We clarify the relation between the above channels and entanglement-binding channels. We give an example of the distillation-prohibiting map Φ ? Φ, where Φ is not entanglement binding.     

Conditional Granger causality of diffusion processes

The statistical concept of Granger causality is defined by prediction improvement, i.e. the causing time series contains unique information about the future of the caused one. Recently we proposed extending this concept to bivariate diffusion processes by defining Granger causality for each point of the state space as the Granger causality of a process obtained by local linearisation. This provides a Granger causality map, well-defined at least in the vicinity of stable fixed points of the deterministic part of the dynamics. This extension has convenient properties, but carries several important limitations. In the current paper we show how the Granger causality of diffusion processes can be further generalized, incorporating in particular the concept of conditional causality. Moreover, we demonstrate the application potential to systems with a more complex attractor structure such as limit cycles or bistability of fixed points.     

Eigen model version of evolution with directed migration

We consider the two-habitat quasispecies model, which describes evolutionary process with migration on the basis of the Eigen model. In the first habitat there is only one genotype, and here is an influx of the replicators from the first habitat to the second one with the rate h. We solve exactly the case of a single-peak fitness landscape in both habitats, when in the first habitat there are no mutations. The Eigen model version of the model is more adequately describes the real biological experiments than the Crow-Kimura model, as can be related to the serial transfer experiments in chemical reactor.     

The Theory of Individual Based Discrete-Time Processes

A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are hence intrinsic to the system and can induce qualitative changes to the dynamics predicted from the deterministic map. From the Chapman–Kolmogorov equation for the discrete-time Markov process, we derive the analogues of the Fokker–Planck equation and the Langevin equation, which are routinely employed for continuous time processes. In particular, a stochastic difference equation is derived which accurately reproduces the results found from the Markov chain model. Stochastic corrections to the deterministic map can be quantified by linearizing the fluctuations around the attractor of the map. The proposed scheme is tested on stochastic models which have the logistic and Ricker maps as their deterministic limits.     

Spectroscopic Studies of the Hydrogen Bond

Abstract

Since the publication of the proceedings of the Ljubljana symposium on hydrogen bonding by Hadzi [1] and the excellent book on the hydrogen bond by Pimentel and McClellan [2], a very large number of publications on the spectroscopic studies of hydrogen bonding have appeared in the literature. The present authors prepared a review on hydrogen bonding covering the period 1958–1963 for limited circulation [3]. In view of the very enthusiastic reception for this review by a number of workers and also the vast amount of published information on the subject after 1963, it was considered valuable to present an up-to-date review on the subject. The present review covers the period from 1958 to 1967 and embodies most of the studies on the hydrogen bond employing spectroscopic methods. The review does not include studies on crystals and macromolecules; hydrogen bonding in crystals has been recently reviewed by Hamilton and Ibers [4]. Electronic theories of the hydrogen bond have been reviewed by Bratoz [5]. Even though we have attempted to write a comprehensive review to include most of the published work on spectroscopic studies, it is possible that we have missed some of the papers in this field; we apologize for such oversights and omissions which become unavoidable in such an undertaking.     

Dynamical role of the degree of intraspecific cooperation: A simple model for prebiotic replicators and ecosystems

We present a simple mean field model to analyze the dynamics of competition between two populations of replicators in terms of the degree of intraspecific cooperation (i.e., autocatalysis) in one of these populations. The first population can only replicate with Malthusian kinetics while the second one can reproduce with Malthusian or autocatalytic replication or with a combination of both reproducing strategies. The model consists of two coupled, nonlinear, autonomous ordinary differential equations. We investigate analytically and numerically the phase plane dynamics and the bifurcation scenarios of this ecologically coupled system, focusing on the outcome of competition for several degrees of intraspecific cooperation, σ, in the second population of replicators. We demonstrate that the dynamics of both populations can not be governed by a limit cycle, and also that once cooperation is considered, the topology of phase space does not allow for coexistence. Even for low values of the degree of intraspecific cooperation, for large enough autocatalytic replication rates, the second population of replicators is able to outcompete the first one, having a wide basin of attraction in state space. We characterize the same power law dependence between the outcompetition extinction times, τ, and the degree of intraspecific cooperation for both populations, given by τ∼c_iσ⁻¹. Our results suggest that, under some kinetic conditions, the appearance of autocatalysis might be favorable in a population of replicators growing with Malthusian kinetics competing with another population also reproducing exponentially.     

Image Encryption Using a Spectrally Efficient Halton Logistics Tent (HaLT) Map and DNA Encoding for Secured Image Communication

With the advancement of technology worldwide, security is essential for online information and data. This research work proposes a novel image encryption method based on combined chaotic maps, Halton sequence, five-dimension (5D) Hyper-Chaotic System and Deoxyribonucleic Acid (DNA) encoding. Halton sequence is a known low-discrepancy sequence having uniform distribution in space for application in numerical methods. In the proposed work, we derived a new chaotic map (HaLT map) by combining chaotic maps and Halton sequence to scramble images for cryptography applications. First level scrambling was done by using the HaLT map along with a modified quantization unit. In addition, the scrambled image underwent inter- and intra-bit scrambling for enhanced security. Hash values of the original and scrambled image were used for initial conditions to generate a 5D hyper-chaotic map. Since a 5D chaotic map has complex dynamic behavior, it could be used to generate random sequences for image diffusion. Further, DNA level permutation and pixel diffusion was applied. Seven DNA operators, i.e., ADD, SUB, MUL, XOR, XNOR, Right-Shift and Left-Shift, were used for pixel diffusion. The simulation results showed that the proposed image encryption method was fast and provided better encryption compared to ‘state of the art’ techniques. Furthermore, it resisted various attacks.     

Asymptotics of action variables near semi-toric singularities

The presence of focus–focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action–Angle coordinates on such systems. At focus–focus critical points, the Liouville–Arnold–Mineur theorem does not apply. In particular, the affine structure of the image of the moment map around has non-trivial monodromy. In this article, we establish that the singular behavior and the multi-valuedness of the Action integrals is given by a complex logarithm. This extends a previous result by San Vũ Ngọc to any dimension. We also calculate the monodromy matrix for these systems.     

Using Background Knowledge from Preceding Studies for Building a Random Forest Prediction Model: A Plasmode Simulation Study

There is an increasing interest in machine learning (ML) algorithms for predicting patient outcomes, as these methods are designed to automatically discover complex data patterns. For example, the random forest (RF) algorithm is designed to identify relevant predictor variables out of a large set of candidates. In addition, researchers may also use external information for variable selection to improve model interpretability and variable selection accuracy, thereby prediction quality. However, it is unclear to which extent, if at all, RF and ML methods may benefit from external information. In this paper, we examine the usefulness of external information from prior variable selection studies that used traditional statistical modeling approaches such as the Lasso, or suboptimal methods such as univariate selection. We conducted a plasmode simulation study based on subsampling a data set from a pharmacoepidemiologic study with nearly 200,000 individuals, two binary outcomes and 1152 candidate predictor (mainly sparse binary) variables. When the scope of candidate predictors was reduced based on external knowledge RF models achieved better calibration, that is, better agreement of predictions and observed outcome rates. However, prediction quality measured by cross-entropy, AUROC or the Brier score did not improve. We recommend appraising the methodological quality of studies that serve as an external information source for future prediction model development.     

Fitness distributions in exponentially growing asexual populations

We explore a mean-field model for the evolution of exponentially growing populations of mutating replicators. Motivated by recent in vitro experiments devised to analyze phenotypic properties of bacterial and viral populations subjected to serial population transfers, we allow our in silico individuals to undergo unrestricted growth before applying bottleneck events. Different dynamical regimes of our model can be mapped to different experimental situations. Numerical and analytical results for fitness distributions calculated at the statistically stationary states of the dynamics compare favorably with available experimental data. Our model and results provide a common framework to better understand populations evolving under different selection pressures.