Pairwise Interaction Model Research Articles

The Influence of Mechanical Properties of Laser-Melted Tungsten Carbide Composite with Nickel/Cobalt Ingredients.

This study used statistical tools to optimise WC/Co/Ni welds and model construction to improve the mechanical properties of coatings by laser cladding. The effect of the parameters on the wear performance of the weld was determined by analysis of variance. In addition, a polynomial model was constructed using the response surface method based on the experimental data of the orthogonal array designed by Taguchi. The experimental results show that there are white initial precipitation carbides and grey areas of WC mixed with Co and Ni compounds, while less wear and less plastic deformation are observed with WC/Co/Ni alloys. By adding Co/Ni alloys, the composite coating extension is seen to have good anti-wear performance. Based on the regression model, a pairwise interaction model was successfully constructed and further modelling of the 3D contour of the wear behaviour was explored. Comparing all the experiments, the predictions of the interaction model were found to be reliable, with an average error of 8.75%. The findings show that there is a very close match between the predicted values of RSM for wear performance and the experimental data, which proves the effectiveness of the Taguchi design-based RSM in improving the mechanical properties of laser cladding.

Exploring spatial segregation induced by competition avoidance as driving mechanism for emergent coexistence in microbial communities.

This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge the sufficiency of mean-field pairwise interaction models, and we consider the impact of spatial dynamics. We developed an individual-based spatial simulation depicting bacterial movement through a pattern of random walks influenced by competition avoidance, leading to the formation of spatially segregated clusters. This model was integrated with a Lotka-Volterra metapopulation framework focused on competitive interactions. Our findings reveal that spatial segregation combined with low diffusion rates and high compositional heterogeneity among patches can lead to emergent coexistence in microbial communities. This reveals a novel mechanism underpinning the formation of stable, coexisting microbe clusters, which is nonetheless incapable of promoting coexistence in the case of isolated pairs of species. This study underscores the importance of considering spatial factors in understanding the dynamics of microbial ecosystems.

Gauge fixing for sequence-function relationships.

Quantitative models of sequence-function relationships are ubiquitous in computational biology, e.g., for modeling the DNA binding of transcription factors or the fitness landscapes of proteins. Interpreting these models, however, is complicated by the fact that the values of model parameters can often be changed without affecting model predictions. Before the values of model parameters can be meaningfully interpreted, one must remove these degrees of freedom (called "gauge freedoms" in physics) by imposing additional constraints (a process called "fixing the gauge"). However, strategies for fixing the gauge of sequence-function relationships have received little attention. Here we derive an analytically tractable family of gauges for a large class of sequence-function relationships. These gauges are derived in the context of models with all-order interactions, but an important subset of these gauges can be applied to diverse types of models, including additive models, pairwise-interaction models, and models with higher-order interactions. Many commonly used gauges are special cases of gauges within this family. We demonstrate the utility of this family of gauges by showing how different choices of gauge can be used both to explore complex activity landscapes and to reveal simplified models that are approximately correct within localized regions of sequence space. The results provide practical gauge-fixing strategies and demonstrate the utility of gauge-fixing for model exploration and interpretation.

Stochastic pairwise preference convergence in Bayesian agents.

Beliefs inform the behavior of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to explain how preferences evolve in cases of simple agent interactions. In this paper, we derive a Gaussian, pairwise agent interaction model to study how preferences converge when driven by observation of each other's behaviors. We show that the dynamics of convergence resemble an Ornstein-Uhlenbeck process, a common model in nonequilibrium stochastic dynamics. Using standard analytical and computational techniques, we find that the hyperprior magnitudes, representing the learning time, determine the convergence value and the asymptotic entropy of the preferences across pairs of agents. We also show that the dynamical variance in preferences is characterized by a relaxation time t^{★} and compute its asymptotic upper bound. This formulation enhances the existing toolkit for modeling stochastic, interactive agents by formalizing leading theories in learning theory, and builds towards more comprehensive models of open problems in principal-agent and market theory.

Mixed modifier effect in Na2O·K2O·CaO aluminosilicate glasses: Pairwise and ternary interactions

AbstractThe mixed modifier effect (MME) is one of the most challenging puzzles in the field of oxide glasses, as there exists no universal quantitative theoretical model for accurately describing and predicting the nonlinear deviation of property values. In this paper, pairwise and ternary interactions are examined experimentally to understand the MME in a series of aluminosilicate glasses. By keeping the glass network former concentration constant and adjusting the molar ratios of three network modifiers (Na2O, K2O, and CaO), the MMEs in glass transition temperature (Tg), Vickers hardness (Hv), and activation energy (Ea) for aqueous dissolution for each modifier cation are investigated. We examine whether a pairwise interaction model is sufficient, or if ternary interactions also need to be included to predict the MME in these aluminosilicate glass systems. This work reveals that the pairwise model can be used to predict the MME for Tg in complex multiple‐modifier glass systems using only two‐body interaction factors. However, ternary mixed‐modifier interactions are present in other properties such as Hv and Ea.

Airborne disease transmission during indoor gatherings over multiple time scales: Modeling framework and policy implications

Indoor superspreading events are significant drivers of transmission of respiratory diseases. In this work, we study the dynamics of airborne transmission in consecutive meetings of individuals in enclosed spaces. In contrast to the usual pairwise-interaction models of infection where effective contacts transmit the disease, we focus on group interactions where individuals with distinct health states meet simultaneously. Specifically, the disease is transmitted by infected individuals exhaling droplets (contributing to the viral load in the closed space) and susceptible ones inhaling the contaminated air. We propose a modeling framework that couples the fast dynamics of the viral load attained over meetings in enclosed spaces and the slow dynamics of disease progression at the population level. Our modeling framework incorporates the multiple time scales involved in different setups in which indoor events may happen, from single-time events to events hosting multiple meetings per day, over many days. We present theoretical and numerical results of trade-offs between the room characteristics (ventilation system efficiency and air mass) and the group's behavioral and composition characteristics (group size, mask compliance, testing, meeting time, and break times), that inform indoor policies to achieve disease control in closed environments through different pathways. Our results emphasize the impact of break times, mask-wearing, and testing on facilitating the conditions to achieve disease control. We study scenarios of different break times, mask compliance, and testing. We also derive policy guidelines to contain the infection rate under a certain threshold.

Catalytic effect of graphene on the inversion of corannulene using a continuum approach with the Lennard-Jones potential.

The catalytic effect of graphene on the corannulene bowl-to-bowl inversion is confirmed in this paper using a pair-wise dispersion interaction model. In particular, a continuum approach together with the Lennard-Jones potential are adopted to determine the interaction energy between corannulene and graphene. These results are consistent with previous quantum chemical studies, which showed that a graphene sheet reduces the barrier height for the bowl-to-bowl inversion in corannulene. However, the results presented here demonstrate, for the first time, that the catalytic activity of graphene can be reproduced using pair-wise dispersion interactions alone. This demonstrates the major role that pair-wise dispersion interactions play in the catalytic activity of graphene.

On pairwise interaction multivariate Pareto models

The rich class of multivariate Pareto distributions forms the basis of recently introduced extremal graphical models. However, most existing literature on the topic is focused on the popular parametric family of Hüsler–Reiss distributions. It is shown that the Hüsler–Reiss family is in fact the only continuous multivariate Pareto model that exhibits the structure of a pairwise interaction model, justifying its use in many high‐dimensional problems. Along the way, useful insight is obtained concerning a certain class of distributions that generalize the Hüsler–Reiss family, a result of independent interest.

Simplicial cascades are orchestrated by the multidimensional geometry of neuronal complexes

Cascades over networks (e.g., neuronal avalanches, social contagions, and system failures) often involve higher-order dependencies, yet theory development has largely focused on pairwise-interaction models. Here, we develop a ‘simplicial threshold model’ (STM) for cascades over simplicial complexes that encode dyadic, triadic and higher-order interactions. Focusing on small-world models containing both short- and long-range k-simplices, we explore spatio-temporal patterns that manifest as a frustration between local and nonlocal propagations. We show that higher-order interactions and nonlinear thresholding coordinate to robustly guide cascades along a k-dimensional generalization of paths that we call ‘geometrical channels’. We also find this coordination to enhance the diversity and efficiency of cascades over a simplicial-complex model for a neuronal network, or ‘neuronal complex’. We support these findings with bifurcation theory and data-driven approaches based on latent geometry. Our findings provide fruitful directions for uncovering the multiscale, multidimensional mechanisms that orchestrate the spatio-temporal patterns of nonlinear cascades.

An assessment of statistical models of competitive growth during transient Ostwald ripening in turbine disc nickel-based superalloys

The ability to accurately predict the time evolution of precipitate size distributions is fundamental to optimising heat treatments and mechanical properties of engineering alloys. Mean-field models of the particle growth rates assume that diffusion fields between neighbouring particles are weakly coupled reducing the problem to a single particle embedded in an effective medium. This regime of behaviour is expected to be satisfied for low volume fraction alloys. However, these assumptions are not fulfilled in many applications of interest where strong interactions between precipitates holds. Correction factors are often introduced to account for the accelerated rate of diffusion caused by the overlapping of diffusion fields between neighbouring precipitates. This paper applies the Wang–Glicksman–Rajan–Voorhees (WGRV) discrete point-source/sink model to compare descriptions of competitive growth. This includes assessing correction factors to the mean-field particle growth rate derived by Ardell, Marqusee and Ross, and Svoboda and Fischer in addition to Di Nunzio’s pairwise interaction model. The WGRV model is used as a benchmark to compare different approximations of competitive growth that apply similar assumptions. This is followed by the application of the models to simulate precipitation kinetics during long term aging kinetics observed in the nickel-based superalloys IN738LC and RR1000. It is shown that the competitive growth correction factors are accurate for volume fractions of 20% and under-predict the acceleration of precipitate kinetics predicted at 40%. The WGRV model is able to capture the coarsening kinetics observed in both IN738LC and RR1000 with reasonable accuracy. The WGRV model determines particle growth rates as a function of the immediate neighbourhood and provides an improved prediction of the coarsening behaviour of tertiary particles in RR1000 in comparison to the mean-field approximation, however over-estimates the growth rate of the tertiary particles compared to experimental data.

Score Matching for Compositional Distributions

Compositional data are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. With real data, it is often the case that many of the compositional components are highly right-skewed, with large numbers of zeros. Major limitations of currently available models for compositional data include one or more of the following: insufficient flexibility in terms of distributional shape; difficulty in accommodating zeros in the data in estimation; and lack of computational viability in moderate to high dimensions. In this article, we propose a new model, the polynomially tilted pairwise interaction (PPI) model, for analysing compositional data. Maximum likelihood estimation is difficult for the PPI model. Instead, we propose novel score matching estimators, which entails extending the score matching approach to Riemannian manifolds with boundary. These new estimators are available in closed form and simulation studies show that they perform well in practice. As our main application, we analyse real microbiome count data with fixed totals using a multinomial latent variable model with a PPI model for the latent variable distribution. We prove that, under certain conditions, the new score matching estimators are consistent for the parameters in the new multinomial latent variable model.

Higher order interactions destroy phase transitions in Deffuant opinion dynamics model

Most opinion dynamics models are based on pairwise interactions. However in many real situations, discussions take place within groups of people. Here, we define a higher order Deffuant model by generalizing the original pairwise interaction model for bounded-confidence opinion-dynamics to interactions involving a group of agents of size k. The generalized model is naturally encoded in a hypergraph. We study this dynamics in different hypergraph topologies, from random hypergraph ensembles, to spatially embedded hyper-lattices. We show that including higher order interactions induces a drastic change in the onset of consensus for random hypergraphs; instead of the sharp phase transition, characteristic of the dyadic Deffuant model, the system undergoes a smooth size independent crossover to consensus, as the confidence value increases. This phenomenon is absent from regular hypergraphs, which conserve a phase transition.

Mechanical Torque Promotes Bipolarity of the Mitotic Spindle Through Multi-centrosomal Clustering.

Intracellular forces shape cellular organization and function. One example is the mitotic spindle, a cellular machine consisting of multiple chromosomes and centrosomes which interact via dynamic microtubule filaments and motor proteins, resulting in complicated spatially dependent forces. For a cell to divide properly, it is important for the spindle to be bipolar, with chromosomes at the center and multiple centrosomes clustered into two 'poles' at opposite sides of the chromosomes. Experimental observations show that in unhealthy cells, the spindle can take on a variety of patterns. What forces drive each of these patterns? It is known that attraction between centrosomes is key to bipolarity, but what prevents the centrosomes from collapsing into a monopolar configuration? Here, we explore the hypothesis that torque rotating chromosome arms into orientations perpendicular to the centrosome-centromere vector promotes spindle bipolarity. To test this hypothesis, we construct a pairwise-interaction model of the spindle. On a continuum version of the model, an integro-PDE system, we perform linear stability analysis and construct numerical solutions which display a variety of spatial patterns. We also simulate a discrete particle model resulting in a phase diagram that confirms that the spindle bipolarity emerges most robustly with torque. Altogether, our results suggest that rotational forces may play an important role in dictating spindle patterning.

Statistical energy minimization theory for systems of drop-carrier particles.

Drop-carrier particles (DCPs) are solid microparticles designed to capture uniform microscale drops of a target solution without using costly microfluidic equipment and techniques. DCPs are useful for automated and high-throughput biological assays and reactions, as well as single-cell analyses. Surface energy minimization provides a theoretical prediction for the volume distribution in pairwise droplet splitting, showing good agreement with macroscale experiments. We develop a probabilistic pairwise interaction model for a system of such DCPs exchanging fluid volume to minimize surface energy. This leads to a theory for the number of pairwise interactions of DCPs needed to reach a uniform volume distribution. Heterogeneous mixtures of DCPs with different sized particles require fewer interactions to reach a minimum energy distribution for the system. We optimize the DCP geometry for minimal required target solution and uniformity in droplet volume.

Fast and accurate computation of interactions between linear fiber segments

PurposeFiber networks represent a vast class of materials, which can be modeled by representing its microstructure using one-dimensional fiber embedded in three-dimensional space. Investigating the statics, dynamics and thermodynamics of such structures from computational first principles requires the efficient estimation of cohesive-repulsive energies and forces between interacting fiber segments. This study offers a fast, efficient and effective computational methodology to estimate such interactions which can be coupled with Hamiltonian mechanics to simulate the behavior of fibrous systems.Design/methodology/approachThis method preserves the uniformly continuous distribution of particles on the line segments and utilizes adaptive numerical integration of relevant distance-distribution functions to estimate the effective interaction energy and forces.FindingsThis method is found to be cheaper to compute and more accurate than the corresponding discrete scheme. This scheme is also versatile in the sense that any pair-wise interaction model can be used.Research limitations/implicationsThe scheme depends on the availability of a suitable pair-interaction potential, such as a Lennard-Jones potential or Morse potential. Additionally, it can only be used for systems which are purely fibrous in nature. For example, fiber composites with a non-fibrous matrix are not addressed.Practical implicationsPaper, woven and hair can be represented as purely fibrous at some relevant length scales and are thus excellent candidate systems for this scheme.Originality/valueThis paper presents a novel method which allows rapid and accurate implementation of an otherwise computationally expensive process.

Generalized score matching for general domains.

Estimation of density functions supported on general domains arises when the data are naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching provides a powerful tool for estimating densities with such intractable normalizing constants but as originally proposed is limited to densities on [Formula: see text] and [Formula: see text]. In this paper, we offer a natural generalization of score matching that accommodates densities supported on a very general class of domains. We apply the framework to truncated graphical and pairwise interaction models and provide theoretical guarantees for the resulting estimators. We also generalize a recently proposed method from bounded to unbounded domains and empirically demonstrate the advantages of our method.

Native American Ancestry and Air Pollution Interact to Impact Bronchodilator Response in Puerto Rican Children with Asthma.

Asthma is the most common chronic disease in children. Short-acting bronchodilator medications are the most commonly prescribed asthma treatment worldwide, regardless of disease severity. Puerto Rican children display the highest asthma morbidity and mortality of any US population. Alarmingly, Puerto Rican children with asthma display poor bronchodilator drug response (BDR). Reduced BDR may explain, in part, the increased asthma morbidity and mortality observed in Puerto Rican children with asthma. Gene-environment interactions may explain a portion of the heritability of BDR. We aimed to identify gene-environment interactions associated with BDR in Puerto Rican children with asthma. Genetic, environmental, and psycho-social data from the Genes-environments and Admixture in Latino Americans (GALA II) case-control study. Our discovery dataset consisted of 658 Puerto Rican children with asthma; our replication dataset consisted of 514 Mexican American children with asthma. We assessed the association of pairwise interaction models with BDR using ViSEN (Visualization of Statistical Epistasis Networks). We identified a non-linear interaction between Native American genetic ancestry and air pollution significantly associated with BDR in Puerto Rican children with asthma. This interaction was robust to adjustment for age and sex but was not significantly associated with BDR in our replication population. Decreased Native American ancestry coupled with increased air pollution exposure was associated with increased BDR in Puerto Rican children with asthma. Our study acknowledges BDR's phenotypic complexity, and emphasizes the importance of integrating social, environmental, and biological data to further our understanding of complex disease.

Pairwise interactions in gene expression determine a hierarchical transcriptional profile in the human brain

The orchestrated expression of thousands of genes gives rise to the complexity of the human brain. However, the structures governing these myriad gene-gene interactions remain unclear. By analyzing transcription data from more than 2000 sites in six human brains, we found that pairwise interactions between genes, without considering any higher-order interactions, are sufficient to predict the transcriptional pattern of the genome for individual brain regions and the transcriptional profile of the entire brain consisting of more than 200 areas. These findings suggest a quadratic complexity of transcriptional patterns in the human brain, which is much simpler than expected. In addition, using a pairwise interaction model, we revealed that the strength of gene-gene interactions in the human brain gives rise to the nearly maximal number of transcriptional clusters, which may account for the functional and structural richness of the brain.

Key role of retardation and non-locality in sound propagation in amorphous solids as evidenced by a projection formalism.

We investigate acoustic propagation in amorphous solids by constructing a projection formalism based on separating atomic vibrations into two, "phonon" (P) and "non-phonon" (NP), subspaces corresponding to large and small wavelengths. For a pairwise interaction model, we show the existence of a "natural" separation lengthscale, determined by structural disorder, for which the isolated P subspace presents the acoustic properties of a nearly homogenous (Debye-like) elastic continuum, while the NP one encapsulates all small scale non-affinity effects. The NP eigenstates then play the role of dynamical scatterers for the phonons. However, at variance with a conjecture of defect theories, their spectra present a finite low frequency gap, which turns out to lie around the Boson peak frequency, and only a small fraction of them are highly localized. We then show that small scale disorder effects can be rigorously reduced to the existence, in the Navier-like wave equation of the continuum, of a generalized elasticity tensor, which is not only retarded, since scatterers are dynamical, but also non-local. The full neglect of both retardation and non-locality suffices to account for most of the corrections to Born macroscopic moduli. However, these two features are responsible for sound speed dispersion and have quite a significant effect on the magnitude of sound attenuation. Although it remains open how they impact the asymptotic, large wavelength scaling of sound damping, our findings rule out the possibility of representing an amorphous solid by an inhomogeneous elastic continuum with the standard (i.e., local and static) elastic moduli.

Species dynamics and interactions via metabolically informed consumer-resource models

Quantifying the strength, sign, and origin of species interactions, along with their dependence on environmental context, is at the heart of prediction and understanding in ecological communities. Pairwise interaction models like Lotka-Volterra provide an important and flexible foundation, but notably absent is an explicit mechanism mediating interactions. Consumer-resource models incorporate mechanism, but describing competitive and mutualistic interactions is more ambiguous. Here, we bridge this gap by modeling a coarse-grained version of a species’ true cellular metabolism to describe resource consumption via uptake and conversion into biomass, energy, and byproducts. This approach does not require detailed chemical reaction information, but it provides a more explicit description of underlying mechanisms than pairwise interaction or consumer-resource models. Using a model system, we find that when metabolic reactions require two distinct resources we recover Liebig’s Law and multiplicative co-limitation in particular limits of the intracellular reaction rates. In between these limits, we derive a more general phenomenological form for consumer growth rate, and we find corresponding rates of secondary metabolite production, allowing us to model competitive and non-competitive interactions (e.g., facilitation). Using the more general form, we show how secondary metabolite production can support coexistence even when two species compete for a shared resource, and we show how differences in metabolic rates change species’ abundances in equilibrium. Building on these findings, we make the case for incorporating coarse-grained metabolism to update the phenomenology we use to model species interactions.