Pairwise Interaction Model Research Articles

Maximization principles for frequency-dependent selection II: the one-locus multiallele case

In this article we study a single-locus multiallele version of the pairwise-interaction model (PIM) in discrete and continuous time and a density-dependent version of this model (D-PIM) in continuous time. The PIM assumes that the fitnesses of genotypes are proportional to the average amount of competition resulting from pairwise interactions. Hence, fitness is frequency dependent. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles analogous to Fisher's Fundamental Theorem for constant selection. We provide a systematic analysis and illustrate our results by concrete examples. We show that in discrete time the mean fitness is nondecreasing along every trajectory provided the interaction coefficients are nonnegative and symmetric. For asymmetric interactions this is in general not true. However, for what we call pseudo-symmetric interactions a function similar to, but in general not identical to, the mean fitness: the adjusted-mean fitness, is nondecreasing along trajectories. For asymmetric interactions, we also provide sufficient conditions for the mean fitness, and more generally for the adjusted-mean fitness, to be nondecreasing and sufficient conditions when it is not. In continuous time, we provide similar but stronger results. If the interaction coefficients are pseudo-symmetric, the adjusted-mean fitness is nondecreasing in the D-PIM.

Partial molar volume of methanol in water: Effect of polarizability

The available pairwise additive intermolecular interaction models used so far in simulations in combination with common combining rules do not seem to be able to reproduce the most distinct feature of aqueous solutions of alcohols, the minimum of the partial molar volume at low alcohol concentrations. Nonetheless, this fundamental failure seems to have been paid little attention to, partly because of very high requirements for accuracy and, hence, CPU time of simulations. As an attempt to go beyond empirical combining rules and account in a more physical and yet simple way for the cross interactions, a feasibility study has been undertaken using a polarizable model of water in molecular simulations of the water–methanol mixture at ambient conditions. It turns out that the inclusion of polarizability may qualitatively change the behavior of the mixture bringing the result in agreement with experiment.

The Generation and Maintenance of Genetic Variation by Frequency-Dependent Selection: Constructing Polymorphisms Under the Pairwise Interaction Model

Frequency-dependent selection remains the most commonly invoked heuristic explanation for the maintenance of genetic variation. For polymorphism to exist, new alleles must be both generated and maintained in the population. Here we use a construction approach to model frequency-dependent selection with mutation under the pairwise interaction model. The pairwise interaction model is a general model of frequency-dependent selection at the genotypic level. We find that frequency-dependent selection is able to generate a large number of alleles at a single locus. The construction process generates multiallelic polymorphisms with a wide range of allele-frequency distributions and genotypic fitness relationships. Levels of polymorphism and mean fitness are uncoupled, so constructed polymorphisms remain permanently invasible to new mutants; thus the model never settles down to an equilibrium state. Analysis of constructed fitness sets reveals signatures of heterozygote advantage and positive frequency dependence.

Maximization principles for frequency-dependent selection I: the one-locus two-allele case

In this article we study the one-locus two-allele version of the pairwise-interaction model of frequency-dependent selection in discrete and continuous time. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles. We provide a systematic approach that covers all possible facets of the dynamical behavior of the model, and we illustrate our results by concrete examples. We show that the mean fitness of the population is nondecreasing if the interaction coefficients are symmetric and positive. Moreover, monotonic convergence to the set of equilibria always occurs, which is not true if we also consider negative interaction coefficients. For asymmetric interaction, we provide necessary conditions when the mean fitness is nondecreasing and sufficient conditions when it is not. Furthermore, in discrete time, we show that limit cycles cannot occur, unless some interaction coefficients are negative.

Unsupervised texture segmentation/classification using 2-D autoregressive modeling and the stochastic expectation-maximization algorithm

The problem of textured image segmentation upon an unsupervised scheme is addressed. In the past two decades, there has been much interest in segmenting images involving complex random or structural texture patterns. However, most unsupervised segmentation techniques generally suffer from the lack of information about the correct number of texture classes. Therefore, this number is often assumed known or given a priori. On the basis of the stochastic expectation-maximization (SEM) algorithm, we try to perform a reliable segmentation without such prior information, starting from an upper bound of the number of texture classes. At a low resolution level, the image model assumes an autoregressive (AR) structure for the class-conditional random field. The SEM procedure is then applied to the set of AR features, yielding an estimate of the true number of texture classes, as well as estimates of the class-conditional AR parameters, and a coarse pre-segmentation. In a final stage, a regularization process is introduced for region formation by the way of a simple pairwise interaction model, and a finer segmentation is obtained through the maximization of posterior marginals. Some experimental results obtained by applying this method to synthetic textured and remote sensing images are presented. We also provide a comparison of our approach with some previously published methods using the same textured image database.

Frequency-Dependent Selection and the Maintenance of Genetic Variation: Exploring the Parameter Space of the Multiallelic Pairwise Interaction Model

When individuals' fitnesses depend on the genetic composition of the population in which they are found, selection is then frequency dependent. Frequency-dependent selection (FDS) is often invoked as a heuristic explanation for the maintenance of large numbers of alleles at a locus. The pairwise interaction model is a general model of FDS via intraspecific competition at the genotypic level. Here we use a parameter-space approach to investigate the full potential for the maintenance of multiallelic equilibria under the pairwise interaction model. We find that FDS maintains full polymorphism more often than classic constant-selection models and produces more skewed equilibrium allele frequencies. Fitness sets with some degree of rare advantage maintained full polymorphism most often, but a wide variety of nonobvious fitness patterns were also found to have positive potential for polymorphism. An example is put forth suggesting possible explanations for multiallelic polymorphisms maintained despite positive FDS on individual alleles.

Interatomic interaction in solid solutions of gold in copper

It is supposed that not only pairwise but also many-particle interaction exists between metal atoms in binary solid solutions. Therefore, the mixing energy in the solid solution V i that is determined from the data on the parameters of short-range order in terms of the model of pairwise interaction has no direct physical sense and proves to be dependent on the concentration of the solute c:V i = V i (c). Only the pair potential h i = V i (0) for impurity atoms to approach each other in the lattice of solvent, which is determined by extrapolation of the V i (c) dependence to zero concentration, is physically meaningful. The potential h i can be used for the calculation of the Wagner interaction parameter and first-order enthalpy parameter. These considerations have been applied to solid solutions of gold in copper. For the Wagner parameter of interaction e Au Au and enthalpy parameter η Au Au in copper-based alloys at 800 K, a satisfactory agreement of the theory and experiment has been obtained.

Study of the Structure, Energetics, and Vibrational Properties of Small Ammonia Clusters (NH3)n (n = 2−5) Using Correlated ab Initio Methods

Equilibrium geometries, interaction energies, and harmonic frequencies of (NH3)n isomers (n = 2-5) have been computed using correlated calculations (MP2) in conjunction with Dunning's aug-cc-pVXZ (X = D, T, Q) basis sets and the Counterpoise procedure. Whenever available, literature values for the binding energy and geometry of dimers and trimers agree well with our data. Low lying isomers for (NH3)4 and (NH3)5 have been found to have similar binding energies (roughly 16 and 20 kcal/mol for the tetramer and pentamer, respectively), perhaps suggesting the presence of a very smooth energy landscape. Using BSSE corrected forces or freezing the monomer structure to its gas phase geometry have been found to have only a weak impact on the energetic and structural properties of the clusters. The effect of zero-point energy (ZPE) on the relative stability of the clusters has been estimated using harmonic frequencies. The latter also highlighted the presence of vibrational fingerprints for the presence of double acceptor ammonia molecules. Many-body effects for (NH3)n isomers (n = 2-4) have been investigated to explore the possibility of building a pairwise interaction model for ammonia. In the frame of the work presented, we have found the 3-body effect to account for 10-15% of the total interaction energy, whereas the 4-body effects may be neglected as first approximation.

The analysis of marked point patterns evolving through space and time

A maximum pseudo-likelihood approach has previously been developed for fitting pairwise interaction models to patterns generated by growth–interaction processes that are sampled at fixed time points. This approach is now extended, not only by estimating the parameters of the process through time, but also by employing least squares estimation since likelihood based approaches are much more computationally demanding. First, simple stochastic models are used to demonstrate that least squares methods are as powerful as likelihood-based approaches, as well as being mathematically and computationally simpler. The algorithm generates simulations of the deterministic growth–interaction and stochastic immigration–death process, and through these the parameter estimates are determined. Logistic and linear growth are then combined with (symmetric) disc-interaction and (asymmetric) area-interaction processes, and between them these generate a variety of mark–point spatial structures. A robustness study shows that the procedure works well in that the presence, structure and strength of a growth–interaction process can be determined even when an incorrectly presumed model is employed. Thus, the technique is likely to prove to be very useful in general practical applications where the underlying process generating mechanism is almost certain to be unknown. Finally, the procedure is applied to the analysis of a new Swedish pine forest data set for which tree location and diameter at breast height were recorded in 1985, 1990 and 1996.

From all-atom vision to molecular pairwise-interactions: the mean-field approach in molecular alloys

The pairwise-interaction model for molecular alloys has been improved by using all-atom potential functions. Both descriptions have been correlated under a more general approach, the mean-field. Expressions for the excess internal energy have been obtained. Two sources of non-thermodynamical regularity arose: the differences in the geometry and chemical nature of the molecules and the non-transferability of the interaction potentials from pure components to alloys. The p-dichlorobenzene (1,4-C6H4Cl2)/p-dibromobenzene (1,4-C6H4Br2) molecular system has been used to illustrate the theoretical treatments.

The Dynamics of Trustworthiness Among the Few

Conventional stochastic models of evolutionary processes with infinitely many agents are deterministic models in disguise. Only finite population models become truly stochastic. Therefore this paper focuses on an indirect evolutionary model of pair wise interaction in a pool of three (corresponding to analysing oligopolies in terms of duopoly markets). The outcomes of the process over the long haul are characterized by the stationary distribution of the underlying Markov process. Our example indicates that intermediate cases cannot be seen as convex combinations of the two polar non-stochastic cases of two or infinitely many individuals. JEL Classification Numbers: C72, C73.

Beyond second-order statistics for learning: A pairwise interaction model for entropy estimation

Second order statistics have formed the basis of learning and adaptation due to its appeal and analytical simplicity. On the other hand, in many realistic engineering problems requiring adaptive solutions, it is not sufficient to consider only the second order statistics of the underlying distributions. Entropy, being the average information content of a distribution, is a better-suited criterion for adaptation purposes, since it allows the designer to manipulate the information content of the signals rather than merely their power. This paper introduces a nonparametric estimator of Renyi's entropy, which can be utilized in any adaptation scenario where entropy plays a role. This nonparametric estimator leads to an interesting analogy between learning and interacting particles in a potential field. It turns out that learning by second order statistics is a special case of this interaction model for learning. We investigate the mathematical properties of this nonparametric entropy estimator, provide batch and stochastic gradient expressions for off-line and on-line adaptation, and illustrate the performance of the corresponding algorithms in examples of supervised and unsupervised training, including time-series prediction and ICA.

Ab initio pair potentials and phase equilibria predictions of halogenated compounds

Ab initio pair potentials are developed for two fluorinated compounds, hydrogen fluoride and methyl fluoride, using symmetry-adapted perturbation theory (SAPT) by considering several hundreds of configurations between a pair of molecules. The interaction energies were fitted to a site–site pair potential model. Also, a pairwise interaction model for a chlorinated compound, hydrogen chloride, was taken from the literature. These pair potentials were then used to predict the second virial coefficients and, using Gibbs ensemble Monte Carlo (GEMC) simulations, the vapor–liquid equilibria of each of the compounds. The properties of methyl fluoride and hydrogen chloride were found to be very well described with the ab initio pair potentials, resulting in predicted second virial coefficients, liquid densities and vapor pressures in good agreement with experimental data. Estimated critical temperatures and densities deviate by only few percent from reported values. However, for hydrogen fluoride, the ab initio pair potential results in a poor description of its phase behavior, but this is not unexpected since hydrogen fluoride is a strong hydrogen-bonding fluid and multi-body effects play a large role in the molecular interactions.

Modelling of spatial point processes derived from a sequence of auto-Poisson lattice schemes

Spatial point processes form a set of statistical tools capable of modelling many environmental processes. They can deal with spatial interactions and dependencies between individuals which is an essential framework in environmental modelling. In this context, we focus on inhibitory pairwise interaction point processes that can be obtained as the limit of a suitable sequence of auto-Poisson lattice schemes. We review the limit theorems concerned, present a computer software (SPPA) and analyze the results of a Monte Carlo simulation study based on a particular pairwise interaction model.

Reversible frequency-dependent switches in male mate choice.

Current sexual-selection theories predict that mating should occur preferentially with the highest-quality partner, and assume that for distinguishing among potential mates the choosy sex applies an internal representation of the characteristics of the desired mate, i.e. a template. Binary choice experiments were performed to test male mate choice between two different female colour morphs in the damselfly Ischnura elegans. Choice experiments were conducted before and after an habituation period, during which males were exposed to only one female colour morph. Given the choice between the two female morphs, males did exhibit a choice for the most recently experienced female morph. This is the first evidence for a reversible switch in mate choice in a frequency-dependent way. In contrast with previous studies on mate choice, template formation in male I. elegans seems not to be based on quality. Switching mate choice in a frequency-dependent manner, choosing the most common morph, probably allows males to minimize their search efforts and to maximize fitness.

On the design and analysis of protein folding potentials.

Pairwise interaction models to recognize native folds are designed and analyzed. Different sets of parameters are considered but the focus was on 20 x 20 contact matrices. Simultaneous solution of inequalities and minimization of the variance of the energy find matrices that recognize exactly the native folds of 572 sequences and structures from the protein data bank (PDB). The set includes many homologous pairs, which present a difficult recognition problem. Significant recognition ability is recovered with a small number of parameters (e.g., the H/P model). However, full recognition requires a complete set of amino acids. In addition to structures from the PDB, a folding program (MONSSTER) was used to generate decoy structures for 75 proteins. It is impossible to recognize all the native structures of the extended set by contact potentials. We therefore searched for a new functional form. An energy function U, which is based on a sum of general pairwise interactions limited to a resolution of 1 angstrom, is considered. This set was infeasible too. We therefore conjecture that it is not possible to find a folding potential, resolved to 1 angstrom, which is a sum of pair interactions.

Chromosome Aberrations Induced in Human Lymphocytes by 3.45 MeV Alpha Particles Analyzed by Premature Chromosome Condensation

Premature chromosome condensation (PCC) experiments using human lymphocytes with centromere staining have shown that after exposure to 3.45 MeV alpha-particle radiation, the full number of dicentric chromosomes appears when the cell fusion protocol is applied immediately after irradiation. In this case, the time available for repair and misrepair of DNA damage is only about 30 min. The number of dicentrics does not change with a further increase in the time available for chromatin rearrangement. This fast response confirms the expectation based on our previous experiments using PCC with 150 kV X rays in which the alpha component of the yield of dicentrics was found to appear when the cell fusion protocol was applied immediately after irradiation, whereas the beta component was delayed by several hours. The time constant for rejoining of the excess acentric chromosome fragments is found to be donor-specific and not to differ for alpha particles and X rays, but alpha-particle radiation leaves a larger fraction of the excess acentric fragments unrejoined. The RBEs of the 3.45 MeV alpha-particle radiation compared to 150 kV X rays, evaluated for the alpha component for the yield of dicentrics and for the yield of unrepaired acentric fragments, have almost equal values of about 4. This is consistent with data in the literature on chromosome aberrations observed in metaphase that show the equality of the RBE values for production of dicentrics and acentric fragments. Our experimental results concerning the fast kinetics of the alpha component of the yield of exchange-type chromosome aberrations are not consistent with Lea's pairwise lesion interaction model, and they support the proposed alternative mechanism of lesion-nonlesion interaction between chromatin regions carrying clustered DNA damage and intact chromatin regions.

Atomistic modelling of diffusion-controlled interfacial decohesion

Abstract This article reviews the atomistic aspects and the available atomistic modelling methods for studying diffusion-controlled interfacial decohesion. This comprises models for the atomic interaction that fall into two categories: materials-specific models that mostly contain some of the quantum-mechanical characteristics of the bonding, or generic simple pairwise or density-dependent interaction models. Furthermore, atomistic-simulation techniques and boundary conditions are discussed with regard to their importance for studying segregation phenomena and fracture. While reliable atomic-interaction models are still not generally available, it is shown that all the main simulation tools for the study of segregation, diffusion, and fracture along grain boundaries are available today. Consequently, a concerted effort to study all these effects in some model systems on the atomic scale and to combine the individual studies into a realistic model for the fracture process seems feasible.

Mean fields and two-dimensional Markov random fields in image analysis

In this paper we compare two iterative approaches to the problem of pixel-level image restoration when the model contains unknown parameters. Pairwise interaction models are assumed to represent the local associations in the true scene. The first approach is a variation on the EM algorithm in which Mean-field approximations are used in the E-step and a variational approximation is used in the M-step. In the second approach, each iteration involves first restoring the image using the Iterated Conditional Modes (ICM) algorithm and then updating the parameter estimates by maximising the so-called pseudolikelihood. In addition, refinemenrs are made to the Mean-field approximation, and these are also used for restoration. The methods are compared empirically using both artificial and real noise-corrupted binary scenes. Within the comparisons the effects of using different convergence criteria for deciding when to stop the algorithms are also investigated.

Particle-phase pressure in a slow shearing flow based on the numerical simulation of a planar suspension of rough contacting cylinders

Planar Stokes flow of a concentrated planar suspension of rigid cylinders is simulated using the finite-element method. A constraint condition, limiting cylinder approach to a specified distance, is applied to simulate interparticle contacts. The results of these simulations reveal a stress response and ordering of the cylinders which is similar to experimental observations of suspensions of nominally spherical particles. These results include direct observations of anisotropic structure, as well as the development of a distinct particle-phase pressure resulting from the asymmetry of interparticle contacts and the consequent developed anisotropy. A simple pair-wise interaction model is proposed for ab initio prediction of the particle-phase pressure for these planar suspensions of cylinders.