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At least 163 records · Page 9

Reinforcement learning in discrete action space applied to inverse defect design

Abstract Reinforcement learning (RL) algorithms that include Monte Carlo Tree Search (MCTS) have found tremendous success in computer games such as Go, Shiga and Chess. Such learning algorithms have demonstrated super-human capabilities in navigating through an exhaustive discrete action search space. Motivated by their success in computer games, we demonstrate that RL can be applied to inverse materials design problems. We deploy RL for a representative case of the optimal atomic scale inverse design of extended defects via rearrangement of chalcogen (e.g. S) vacancies in 2D transition metal dichalcogenides (e.g. MoS 2 ). These defect rearrangements and their dynamics are important from the perspective of tunable phase transition in 2D materials i.e. 2H (semi-conducting) to 1T (metallic) in MoS 2 . We demonstrate the ability of MCTS interfaced with a reactive molecular dynamics simulator to efficiently sample the defect phase space and perform inverse design—starting from randomly distributed S vacancies, the optimal defect rearrangement of defects corresponds a line defect of S vacancies. We compare MCTS performance with evolutionary optimization i.e. genetic algorithms and show that MCTS converges to a better optimal solution (lower objective) and in fewer evaluations compared to GA. We also comprehensively evaluate and discuss the effect of MCTS hyperparameters on the convergence to solution. Overall, our study demonstrates the effectives of using RL approaches that operate in discrete action space for inverse defect design problems.

42 ENGINEERING↗

Novel Z-DNA binding domains in giant viruses

Z-nucleic acid structures play vital roles in cellular processes and have implications in innate immunity due to their recognition by Zα domains containing proteins (Z-DNA/Z-RNA binding proteins, ZBPs). Although Zα domains have been identified in six proteins, including viral E3L, ORF112, and I73R, as well as, cellular ADAR1, ZBP1, and PKZ, their prevalence across living organisms remains largely unexplored. In this study, we introduce a computational approach to predict Zα domains, leading to the revelation of previously unidentified Zα domain-containing proteins in eukaryotic organisms, including non-metazoan species. Our findings encompass the discovery of new ZBPs in previously unexplored giant viruses, members of the Nucleocytoviricota phylum. Through experimental validation, we confirm the Zα functionality of select proteins, establishing their capability to induce the B-to-Z conversion. Additionally, we identify Zα-like domains within bacterial proteins. While these domains share certain features with Zα domains, they lack the ability to bind to Z-nucleic acids or facilitate the B-to-Z DNA conversion. Our findings significantly expand the ZBP family across a wide spectrum of organisms and raise intriguing questions about the evolutionary origins of Zα-containing proteins. Moreover, our study offers fresh perspectives on the functional significance of Zα domains in virus sensing and innate immunity and opens avenues for exploring hitherto undiscovered functions of ZBPs.

59 BASIC BIOLOGICAL SCIENCES↗

The Wormholes Within: A Study of 1, 3, 5–Triamino–2, 4, 6–Trinitrobenzene Crystal Morphology by Micro and Nano–Scale X–Ray Computed Tomography and its Effects Upon the Shock Sensitivity of Detonation

We report that we understand heterogeneous-explosive detonation only to the extent that we can first measure the salient chemical and microstructural features. Barring an inordinate amount of trial and error, we can tailor the detonation properties of our HE formulations only to the extent that we understand (at least qualitatively) the same effects. As an insensitive high explosive, 1, 3, 5-triamino-2, 4, 6-trinitrobenzene (TATB) burns more heterogeneously than conventional high explosives, making its detonation properties sensitive to microstructure. The Benziger route can produce various grain morphologies depending on the amount of water used in the amination step. So-called dry-aminated (DA) TATB crystals are riddled with a void structure called wormholes, which are washed out ammonium chloride (NH4Cl) inclusions that form during synthesis. So-called wet-aminated (WA) TATB crystals do not contain NH 4 Cl inclusions but possess a very convoluted external structure. Using both micro and nano-scale CT, we explore three DA-TATB lots that reflect evolutionary processing changes, plus one WA-TATB material. Micro CT imaged crystal collections show the exterior grain structure, revealing its roughness and providing a crude particle size measurement. The DA-TATB lots that test most sensitively in the LANL ECOT corner-turning test are roughest, having the appearance of being “corroded”. Nano-scale CT reveals both internal NH 4 Cl inclusions and void structures. The DA-TATB lots that tested intermediate and high sensitivity in ECOT exhibited similar wormhole structures, which were more extensive than that of the low-sensitivity lot. The least sensitive DA-TATB lot also retained more NH 4 Cl, consistent with reduced connectivity of voids to the surface.

1, 3, 5-triamino-2,4↗

Implementing the donor–acceptor approach in electronically conducting copolymers via electropolymerization

Electropolymerization has become a convenient method for synthesizing and characterizing complex organic copolymers having intrinsic electronic conductivity, including the donor (D)–acceptor (A) class of electronically conducting polymers (ECPs). This review begins with an introduction to the electrosynthesis of common second-generation ECPs. The information obtainable from electroanalytical studies, charge carriers such as polarons (positive and negative) and bipolarons (positive and negative) and doping will be discussed. The evolutionary chain of ECPs is then presented. ECPs comprising electron-rich D and electron-deficient A moieties have been shown to possess intrinsic electronic conductivity and unique optical and electronic properties. They are third generation ECPs and electropolymerization of mixtures of D and A leads to stoichiometrically controlled block copolymers. These D–A type ECPs are discussed on the basis of selected representative materials. Since the discovery of electropolymerization as a powerful tool to synthesize copolymers of conjugated monomers with a pre-determined ratio of D and A repeat units present in the polymer, the field of D–A type ECPs has grown considerably and the literature available since 2004 to 2021 is summarized and tabulated. Electronic and optical properties of the materials determined by computational chemistry are presented. The data obtained from electrochemical and optical methods are compared with those obtained from computational methods and reasons for discrepancies are given. The literature on the concept of electropolymerization extended to synthesizing triblock and many-block copolymers is reviewed. Finally, applications of D–A polymers in optoelectronic devices (organic solar cells and field-effect transistors) and in bio-imaging are explained quoting appropriate examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A dynamic likelihood approach to filtering transport processes: advection-diffusion dynamics

A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic problems –waves–, and in this paper, it is extended via a split step formulation, to handle advection-diffusion problems. In the dynamic likelihood approach, observations and their statistics are used to propagate probabilities along characteristics, evolving the likelihood in time. The estimate posterior thus inherits phase information. For advection-diffusion the advective part of the time evolution is handled on the basis of observations alone, while the diffusive part is informed through the model as well as observations. We expect, and indeed show here, that in advection-dominated problems, the DLF approach produces better estimates than other assimilation approaches, particularly when the observations are sparse and have low uncertainty. The added computational expense of the method is cubic in the total number of observations over time, which is on the same order of magnitude as a standard Kalman filter and can be mitigated by bounding the number of forward propagated observations, discarding the least informative data.

97 MATHEMATICS AND COMPUTING↗

GenomeFace v1.0

GenomeFace is meta-genome binning software. Metagenomic binning, the process of grouping DNA sequences into taxonomic units, is critical for understanding the functions, interactions, and evolutionary dynamics of microbial communities. We propose a deep learning approach to binning using two neural networks, one based on composition and another on environmental abundance, dynamically weighting the contribution of each based on characteristics of the input data. Trained on over 43,000 prokaryotic genomes, our network for composition-based binning is inspired by metric learning techniques used for facial recognition. Using a task-specific, multi-GPU accelerated algorithm to cluster the embeddings produced by our network, our binner leverages marker genes observed to be universally present in nearly all taxa to grade and select optimal clusters of sequences from a hierarchy of candidates. We evaluate our approach on four simulated datasets with known ground truth. Our linear time integration of marker genes recovers more near complete genomes than state of the art but computationally infeasible solutions using them, while being over an order of magnitude faster. Finally, we demonstrate the scalability and acuity of our approach by testing it on three of the largest metagenome assemblies ever performed. Compared to other binners, we produced 47%-183% more near complete genomes. From these datasets, we find over the genomes of over 3000 new candidate species which have never been previously cataloged, representing a potential 4% expansion of the known bacterial tree of life.

Lettich, Richard [Lawrence Berkeley National Labor↗

Software classification using phylogenetic techniques

Software, such as malware, may be classified using phylogenetic techniques. An evolutionary history of a representative set of software programs may be reconstructed to generate a reference phylogeny. Dynamic traces of the representative software programs may be obtained. The dynamic traces may include time-ordered sequences of execution commands extracted from running software binaries. Metrics may be developed using the dynamic traces. One or more unknown software programs may then be classified against the reference phylogeny using the metrics developed using the dynamic traces of the representative set of software programs.

97 MATHEMATICS AND COMPUTING↗

Comparative genomic analysis of thermophilic fungi reveals convergent evolutionary adaptations and gene losses

Thermophily is a trait scattered across the fungal tree of life, with its highest prevalence within three fungal families (Chaetomiaceae, Thermoascaceae, and Trichocomaceae), as well as some members of the phylum Mucoromycota. We examined 37 thermophilic and thermotolerant species and 42 mesophilic species for this study and identified thermophily as the ancestral state of all three prominent families of thermophilic fungi. Thermophilic fungal genomes were found to encode various thermostable enzymes, including carbohydrate-active enzymes such as endoxylanases, which are useful for many industrial applications. At the same time, the overall gene counts, especially in gene families responsible for microbial defense such as secondary metabolism, are reduced in thermophiles compared to mesophiles. We also found a reduction in the core genome size of thermophiles in both the Chaetomiaceae family and the Eurotiomycetes class. The Gene Ontology terms lost in thermophilic fungi include primary metabolism, transporters, UV response, and O-methyltransferases. Comparative genomics analysis also revealed higher GC content in the third base of codons (GC3) and a lower effective number of codons in fungal thermophiles than in both thermotolerant and mesophilic fungi. Furthermore, using the Support Vector Machine classifier, we identified several Pfam domains capable of discriminating between genomes of thermophiles and mesophiles with 94% accuracy. Using AlphaFold2 to predict protein structures of endoxylanases (GH10), we built a similarity network based on the structures. We found that the number of disulfide bonds appears important for protein structure, and the network clusters based on protein structures correlate with the optimal activity temperature. Thus, comparative genomics offers new insights into the biology, adaptation, and evolutionary history of thermophilic fungi while providing a parts list for bioengineering applications.

59 BASIC BIOLOGICAL SCIENCES↗

Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.

Bayesian optimization↗

Three-dimensional modeling of hyphal fusion, branching, and nutrient transport in filamentous fungi

Fungi exhibit behaviors distinct from other microbes. Filamentous fungi grow by extending complex networks of branched filaments collectively referred to as the mycelium. These networks can expand over large distances and traverse low-nutrient areas by translocating nutrients through the filament network. This spatial characteristic makes filamentous fungi crucial for soil ecosystems, supporting stable microbial communities and promoting plant growth. However, simulating these behaviors is complex. The elongated nature of fungal compartments results in different mechanical interactions compared to the commonly modeled spherical bacteria. These detailed hyphal mechanics require specialized consideration and are often excluded from conventional fungal simulation packages. Additionally, the extensive fungal networks in nature demand computationally intensive simulations, necessitating high-performance algorithms. Therefore, realistic fungi simulations require specialized software. Here, we introduce a fungal modeling expansion to the high-performance biological modelling and interface exchange (bmx) software suite. bmx leverages adaptive mesh refinement in AMReX for chemical diffusion and incorporates a full mechanical model for bacterial cells, accelerated by GPUs. By extending bmx to model filamentous particles, we demonstrate the formation of complex filament networks through interactions like hyphal branching and fusion (anastomosis). We show that the networks produced match real-world fungal structures through various metrics. This work supports computational studies of fungal growth dynamics and can be adapted to investigate the growth of other filamentous structures in biology or materials science. The expanded-BMX package is open-sourced and is available online.

Cell mechanics↗

Chlorophylls as primary electron acceptors in reaction centers

Photosynthetic Reaction Centers (RCs) can be considered blueprints for highly efficient energy transfer. Embedded with an array of cofactors, including (bacterio)chlorophyll ((B)Chl) and (B)pheophytin ((B)Pheo) molecules, RCs function with a high quantum yield that spans a wide spectral range. Understanding the principles that underlie their function can influence the design of the next generation of artificial photosynthetic devices. We are particularly interested in the factors that influence the early stages of light-driven charge separation in RCs. With the recent publication of several highly anticipated RC structures and advanced computational methods available, it is possible to probe both the geometric and electronic structures of an array of RCs. In this chapter, we review the electronic and geometric structures of the (B)Chl and (B)Pheo primary electron acceptors from fiveRCs, comprising both Type I and Type II RCs and representing both heterodimeric and homodimeric systems. We showcase the dimeric A0•- state of Type I RCs, whereby the unpaired electron is delocalized, to various extents, over two (B)Chl molecules (B)Chl2 and (B)Chl3. This delocalization is controlled by several factors, including the structure of the (B)Chls, interactions with the surrounding protein matrix, and the orientation and distances of the cofactors themselves. In contrast, the primary acceptors of Type II RCs are entirely monomeric, with electron density residing solely on the (B)Pheo. We compare the natural design of the primary acceptors of the Type I and Type II RCs from both an evolutionary and application based perspective.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fate of supernova progenitors in massive binary systems

ABSTRACT How massive stars end their lives depends on the core mass, core angular momentum, and hydrogen envelopes at death. However, these key physical facets of stellar evolution can be severely affected by binary interactions. In turn, the effectiveness of binary interactions itself varies greatly depending on the initial conditions of the binaries, making the situation much more complex. We investigate systematically how binary interactions influence core–collapse progenitors and their fates. Binary evolution simulations are performed to survey the parameter space of supernova progenitors in solar metallicity binary systems and to delineate major evolutionary paths. We first study fixed binary mass ratios ($q=M_2/M_1$ = 0.5, 0.7, and 0.9) to elucidate the impacts of initial mass and initial separation on the outcomes, treating separately Type Ibc supernova, Type II supernova, accretion-induced collapse (AIC), rapidly rotating supernova (Ibc-R), black hole formation, and long gamma ray burst (long GRB). We then conduct 12 binary population synthesis model calculations, varying the initial condition distributions and binary evolution parameters, to estimate various supernova fractions. We obtain a Milky Way supernova rate $R_{\rm SN} = (1.78$–$2.47) \times 10^{-2} \, {\rm yr}^{-1}$ which is consistent with observations. We find the rates of AIC, Ibc-R, and long GRB to be $\sim 1/100$ the rate of regular supernovae. Our estimated long GRB rates are higher than the observed long GRB rate and close to the low luminosity GRB rate, although care must be taken considering our models are computed with solar metallicity. Furthering binary modelling and improving the inputs one by one will enable more detailed studies of these and other transients associated with massive stars.

Astronomy & Astrophysics↗

Orbits and Masses of Binaries from Speckle Interferometry at SOAR

We present results from Speckle inteferometric observations of 15 visual binaries and one double-line spectroscopic binary, carried out with the HRCam Speckle camera of the SOAR 4.1 m telescope. These systems were observed as a part of an on-going survey to characterize the binary population in the solar vicinity, out to a distance of 250 pc. We obtained orbital elements and mass sums for our sample of visual binaries. The orbits were computed using a Markov Chain Monte Carlo algorithm that delivers maximum likelihood estimates of the parameters, as well as posterior probability density functions that allow us to evaluate their uncertainty. Their periods cover a range from 5 yr to more than 500 yr; and their spectral types go from early A to mid M, implying total system masses from slightly more than 4M{sub ⊙} down to 0.2M {sub ⊙}. They are located at distances between approximately 12 and 200 pc, mostly at low Galactic latitude. For the double-line spectroscopic binary YSC8, we present the first combined astrometric/radial-velocity orbit resulting from a self-consistent fit, leading to individual component masses of 0.897 ± 0.027 M {sub ⊙} and 0.857 ± 0.026 M {sub ⊙}; and an orbital parallax of 26.61 ± 0.29 mas, which compares very well with the Gaia DR2 trigonometric parallax (26.55 ± 0.27 mas). In combination with published photometry and trigonometric parallaxes, we place our objects on an H-R diagram and discuss their evolutionary status. We also present a thorough analysis of the precision and consistency of the photometry available for them.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Web-Based Tools for Data-Informed Remedy Optimization: Software Theory and User Guide

This report documents the development and application of two web-based decision-support tools for pump-and-treat (P&T) groundwater remediation systems: PTOLEMY (Pump-and-Treat Optimized Location Evaluation to Maximize Yields) and OPTIMA (Optimization for Pump-and-Treat Implementation, Management, & Assessment). These tools enhance remedy design and management by leveraging advanced computational methods – specifically deep learning and multi-objective optimization – within a user-friendly platform. By integrating data-driven models with established hydrogeological knowledge, PTOLEMY and OPTIMA enable more efficient evaluation of well placement and operational strategies, helping site managers balance multiple remediation objectives under complex conditions. Both tools are implemented as modules within the SOCRATES (Suite Of Comprehensive Rapid Analysis Tools for Environmental Sites) web platform, which provides data access, visualization, and analytics to support remedy optimization across sites in the U.S. Department of Energy Office of Environmental Management complex. PTOLEMY is a rapid screening module designed to identify promising locations for new extraction wells. It employs a multi-channel three-dimensional convolutional neural network (MC3D-CNN) trained on high-fidelity simulation data to predict the relative performance (in terms of contaminant mass recovery) of potential well sites. Through an interactive web interface, PTOLEMY visualizes the probability of high performance across a site, highlighting areas where an extraction well is likely to yield above-threshold contaminant removal over a multi-year period. PTOLEMY’s map-based displays and exportable results support transparent communication of screening analyses. By focusing attention on the most favorable candidate locations, the tool augments traditional engineering judgment and physics-based modeling, providing a data informed basis for subsequent detailed evaluations. OPTIMA is a multi objective optimization module designed to find wellfield layouts and operating schedules that meet various cleanup goals. It quickly evaluates thousands of candidate setups – combinations of well locations, timing, and rates – and returns a small set of best trade-off options for comparison. At its core, OPTIMA uses a U-Net-based surrogate model – a deep-learning emulator of a groundwater flow and transport simulator – to dramatically accelerate scenario evaluations. Coupling this fast surrogate with the NSGA-II (Non-dominated Sorting Genetic Algorithm II) evolutionary algorithm, OPTIMA explores a wide decision space of well locations and schedules to identify Pareto-optimal solutions that trade off key objectives (e.g., minimizing cleanup time, maximizing contaminant mass removal, and minimizing plume extent). The tool outputs a family of optimal configurations and visualizes their trade-offs (Pareto frontiers of cleanup metrics and maps of optimized well placements). Site managers can use these results to understand the range of viable strategies and to select candidate designs for more detailed verification. OPTIMA is currently under active development and not yet fully released; this guide provides early documentation to support planning and gather user feedback.

54 ENVIRONMENTAL SCIENCES↗

On Properties of Adjoint Systems for Evolutionary PDEs

We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary partial differential equation has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels. We subsequently address the question of discretize-then-optimize versus optimize-then-discrete for both semi-discretization and time integration, by characterizing the commutativity of discretize-then-optimize methods versus optimize-then-discretize methods uniquely in terms of an adjoint-variational quadratic conservation law. For Galerkin semi-discretizations and one-step time integration methods in particular, we explicitly construct these commuting methods by using structure-preserving discretization techniques.

97 MATHEMATICS AND COMPUTING↗

PyPop: a mature open-source software pipeline for population genomics

Python for Population Genomics (PyPop) is a software package that processes genotype and allele data and performs large-scale population genetic analyses on highly polymorphic multi-locus genotype data. In particular, PyPop tests data conformity to Hardy-Weinberg equilibrium expectations, performs Ewens-Watterson tests for selection, estimates haplotype frequencies, measures linkage disequilibrium, and tests significance. Standardized means of performing these tests is key for contemporary studies of evolutionary biology and population genetics, and these tests are central to genetic studies of disease association as well. Here, we present PyPop 1.0.0, a new major release of the package, which implements new features using the more robust infrastructure of GitHub, and is distributed via the industry-standard Python Package Index. New features include implementation of the asymmetric linkage disequilibrium measures and, of particular interest to the immunogenetics research communities, support for modern nomenclature, including colon-delimited allele names, and improvements to meta-analysis features for aggregating outputs for multiple populations.

59 BASIC BIOLOGICAL SCIENCES↗

Theoretical Investigation of Delafossite-Cu 2 ZnSnO 4 as a Promising Photovoltaic Absorber

In the quest for efficient and cost-effective photovoltaic absorber materials beyond silicon, considerable attention has been directed toward exploring alternatives. One such material, zincblende-derived Cu2ZnSnS4 (CZTS), has shown promise due to its ideal band gap size and high absorption coefficient. However, challenges such as structural defects and secondary phase formation have hindered its development. In this study, we examine the potential of another compound, Cu2ZnSnO4 (CZTO), with a similar composition to CZTS as a promising alternative. Employing ab initio density function theory (DFT) calculations in combination with an evolutionary structure prediction algorithm, we identify that the crystalline phase of delafossite structure is the most stable among the 900 (meta)stable CZTO. Its thermodynamic stability at room temperature is also confirmed by the molecular dynamics study. Excitingly, this new phase of CZTO displays a direct band gap where the dipole-allowed transition occurs, making it a strong candidate for efficient light absorptions. Furthermore, the estimation of spectroscopic limited maximum efficiency (SLME) directly demonstrates the high potential of delafossite-CZTO as a photovoltaic absorber. Our numerical results suggest that delafossite-CZTO holds promise for future photovoltaic applications.

14 SOLAR ENERGY↗

Generating Mixed Patterns of Residential Segregation: An Evolutionary Approach

The Schelling model of residential segregation has demonstrated that even the slightest preference for neighbors of the same race can be amplified into community-wide segregation. However, these models are unable to simulate mixed, coexisting patterns of segregation and integration, which have been seen to exist in cities. Using evolutionary model discovery we demonstrate how including social factors beyond racial bias when modeling relocation behavior enables the emergence of strongly mixed patterns. Our results indicate that the emergence of mixed patterns is better explained by multiple factors influencing the decision to relocate; the most important being the interaction of nonlinear, rapidly diminishing racial bias with a recent, historical tendency to move. Additionally, preference for less isolated neighborhoods or preference for neighborhoods with longer residing neighbors may produce weaker mixed patterns. Finally, this work highlights the importance of exploring the influence of multiple hypothesized factors of decision making, and their interactions, within agent rules, when studying emergent outcomes generated by agent-based models of complex social systems.

97 MATHEMATICS AND COMPUTING↗