Land-use decision-making processes have a long history of producing globally pervasive systemic equity and sustainability concerns. Quantitative, optimization-based planning approaches, e.g. Multi-Objective Land Allocation (MOLA), seemingly open the possibility to improve objectivity and transparency by explicitly evaluating planning priorities by the type, amount, and location of land uses. Here, we show that optimization-based planning approaches with generic planning criteria generate a series of unstable "flashpoints" whereby tiny changes in planning priorities produce large-scale changes in the amount of land use by type. We give quantitative arguments that the flashpoints we uncover in MOLA models are examples of a more general family of instabilities that occur whenever planning accounts for factors that coordinate use on- and between-sites, regardless of whether these planning factors are formulated explicitly or implicitly. We show that instabilities lead to regions of ambiguity in land-use type that we term "gray areas". By directly mapping gray areas between flashpoints, we show that quantitative methods retain utility by reducing combinatorially large spaces of possible land-use patterns to a small, characteristic set that can engage stakeholders to arrive at more efficient and just outcomes.

Despite their ubiquity, variational autoencoders (VAEs) inherently suffer from posterior collapse, a failure mode in which latent variables are effectively ignored. This failure arises because explicit prior imposition drives optimization toward loss landscape regions corresponding to uninformative latent representations. Here, we introduce Entropic Autoencoders (EAEs), a framework in which reconstruction loss is the only explicit objective, and entropy generates the latent variables' prior implicitly through a free energy-minimizing ensemble of encoders. This ensemble biases learning toward high-volume regions of near-optimal solutions, while decoder updates direct the search trajectories toward informative latent representations. We demonstrate that EAEs mitigate posterior collapse by learning non-Gaussian, multimodal latent distributions that yield diverse, data-consistent generations and preserve different forms of underlying structure in the data. As a proof-of-concept, we show that an EAE captures a superposition of the known low-dimensional dynamics of a reaction-diffusion process. Then, we show that an EAE identifies implicit categorical distinctions in MNIST latent representations, and displays a hierarchical understanding of facial structure on the CelebA dataset, from an "all-human" face to individual-dependent features.

Data-driven causal relationship identification is pertinent to advancing understanding of complex systems both within and beyond science. Bayesian networks offer a probabilistic method for modelling generic causal relationships via directed acyclic graphs (DAGs). However, typical techniques for constructing Bayesian networks rely on optimization, which can be ill-suited for learning causal relationships because the underlying data may admit multiple chains of causation. More data-faithful representations of causal relationships would provide frameworks for constructing multiple causal maps that are consistent with the variability that is inherent in underlying data. Here, we show that entropy-based inference generates atlases of plausible causal relationships that are consistent with underlying data. On simulated noisy data of 2- and 20-node linear structural equation models, we sample a maximum-entropy ensemble of graphs that allow us to quantify the inherent structural ambiguity in underlying causal relationships. Our method shows that "optimized" DAGs can contain causal artifacts are not consistent across equivalently accurate topologies.

“Partner number sexuality” (P#S) refers to how many partners individuals have/are interested in having. Those with P#S outside of monogamous desires and/or practices commonly face stigma in North America and elsewhere. Yet theories of sexuality do not always make room for diverse P#S. One theory that does is sexual configurations theory (SCT), which visually models gender/sex and sexuality (van Anders, 2015). In this study, we investigated what insights SCT could provide into P#S, whether SCT was useful to those with minoritized P#S, and how those with minoritized P#S made use of SCT. To do so, we conducted online interviews, asking participants (N = 26) to complete two SCT diagrams and report on their experience. We used template analysis to analyze transcripts and compiled “SCT heatmaps,” aggregates of SCT diagrams. We constructed 11 major themes, including diverse understandings of eroticism and romantic/platonic relationships, the impacts of hermeneutical injustice (the injustice of knowledge systems) on participants’ abilities to conceptualize and discuss their P#S, and how SCT facilitated conversations about P#S. The heatmaps showed that participants made use of most of both SCT diagrams, showing branchedness in P#S between “eroticism” and “nurturance,” and between status, identity, and orientation. Our study highlights that the lived experience of partnering, especially of those with minoritized P#S, extends far beyond commonly understood categories, and that SCT is a useful tool that can accurately reflect diversity in P#S.

The array of neural network training techniques that invoke optimization but rely on ad hoc modification for validity suggests that optimization-based training is misguided. Shortcomings of optimization-based training are brought to strong relief by overfitting, where naive optimization produces spurious outcomes. Here, we introduce simmering, a physics-based method that trains neural networks to generate "good enough" weights and biases, paradoxically outperforming leading optimization-based approaches. Instead of optimizing, simmering systematically samples non-optimal weights and biases to generate an ensemble that provides sufficient representations of the underlying phenomenon. Simmering corrects neural networks that are overfit by optimization, and produces more generalizable predictions if deployed from the outset compared to other overfitting mitigation methods. Our results question optimization as a paradigm for training transformers, and feedforward and convolutional neural networks. We leverage information-geometric arguments to point to the existence of classes of sufficient-training algorithms that do not take optimization as their starting point.

Conceptions of order and disorder date back to antiquity and colour modern understanding of the universe, matter, beauty in art, and social organization. Ancient notions of order and disorder are most precisely operationalized in modern physics where they provide quantitative metrics for the structural organization of matter. Here, we argue that ancient uncertainty- and symmetry-based concepts of disorder have contemporary echoes in physics in the form of entropy and Landau theory. Though many matter systems provide examples in which these two frameworks coincide, we show that recent results in the physics of soft, colloidal matter give a growing, systematically constructed set of discordant examples. The discord between uncertainty- and symmetry-based metrics of disorder we identify in physics casts doubt on the plausibility of drawing precise order--disorder dichotomies in other areas of thought where the concepts of order and disorder have been less precisely defined.

Plurisexuality-sexuality directed toward more than one gender/sex (gender and/or sex)-encompasses a wide array of identities, including "bisexual," "pansexual," "queer," and more. Research on plurisexual labels has found varied accounts of their definitions, with ongoing discussions and tensions. There are also many people who do not identify with plurisexual labels, but who have plurisexual orientations (e.g., attractions) or statuses (e.g., behavior). This research uses an inclusive definition of plurisexuality, recruiting those who are plurisexual by orientation, status, and/or identity, to develop a fuller picture of plurisexuality. Drawing from Sexual Configurations Theory (SCT; van Anders, 2015), this research explores the patterns of plurisexual orientations and statuses that arise within different labels, and how identities, orientations, and statuses can coincide and branch (show homogeneity or heterogeneity, respectively). As part of an online survey, participants (N = 191) completed visual SCT diagrams for their sexual orientations and statuses related to gender/sex, gender, and sex. These diagrams allow participants to visually map out their sexuality without depending on labels. We then created SCT "heatmaps" by identity label to explore visual representations of plurisexuality across identity groups, which highlighted group-level differences and similarities between labels, as well as a great deal of diversity within them. Our results support a multifaceted, tripartite understanding of sexuality, as branchedness occurred between identity, orientation, and status. These results contribute to ongoing discussions about the meaning of different sexuality labels, SCT as a useful way to conceptualize sexuality, and best practices for measuring sexuality in research.

Revolutionary advances in both manufacturing and computational morphogenesis raise critical questions about design sensitivity. Sensitivity questions are especially critical in contexts, such as topology optimization, that yield structures with emergent morphology. However, analyzing emergent structures via conventional, perturbative techniques can mask larger-scale vulnerabilities that could manifest in essential components. Risks that fail to appear in perturbative sensitivity analyses will only continue to proliferate as topology optimization-driven manufacturing penetrates more deeply into engineering design and consumer products. Here, we introduce Laplace-transform based computational filters that supplement computational morphogenesis with a set of nonperturbative sensitivity analyses. We demonstrate how this approach identifies important elements of a structure even in the absence of knowledge of the ultimate, optimal structure itself. We leverage techniques from molecular dynamics and implement these methods in open-source codes, demonstrating their application to compliance minimization problems in both 2D and 3D. Our implementation extends straightforwardly to topology optimization for other problems and benefits from the strong scaling properties observed in conventional molecular simulation.

Emergent design failures are ubiquitous in complex systems, and often arise when system elements cluster. Approaches to systematically reduce clustering could improve a design's resilience, but reducing clustering is difficult if it is driven by collective interactions among design elements. Here, we use techniques from statistical physics to identify mechanisms by which spatial clusters of design elements emerge in complex systems modelled by heterogeneous networks. We find that, in addition to naive, attraction-driven clustering, heterogeneous networks can exhibit emergent, repulsion-driven clustering. We draw quantitative connections between our results on a model system in naval engineering to entropy-driven phenomena in nanoscale self-assembly, and give a general argument that the clustering phenomena we observe should arise in many distributed systems. We identify circumstances under which generic design problems will exhibit trade-offs between clustering and uncertainty in design objectives, and we present a framework to identify and quantify trade-offs to manage clustering vulnerabilities.

Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the structure of the problem and the ultimate solution is the most obscure. The existence of solution with limited insight contrasts with techniques that have been developed for a broad range of engineering problems where integral transform techniques yield solutions and insight in tandem. Here, we present a ``Pareto-Laplace'' integral transform framework that can be applied to problems typically studied via optimization. We show that the framework admits related geometric, statistical, and physical representations that provide new forms of insight into relationships between objectives and outcomes. We argue that some known approaches are special cases of this framework, and point to a broad range of problems for further application.

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

The potential of extreme environmental change driven by a destabilized climate system is an alarming prospect for humanity. But the intricate, subtle ways Earth's climate couples to social and economic systems raise the question of when more incremental climate change signals the need for alarm. Questions about incremental sensitivity are particularly crucial for human systems that are organized by optimization. Optimization is most valuable in resolving complex interactions among multiple factors, however, those interactions can obscure coupling to underlying drivers such as environmental degradation. Here, using Multi-Objective Land Allocation as an example, we show that model features that are common across non-convex optimization problems drive hypersensitivities in climate-induced degradation--loss response. We show that catastrophic losses in human systems can occur well before catastrophic climate collapse. We find punctuated insensitive/hypersensitive degradation--loss response, which we trace to the contrasting effects of environmental degradation on subleading, local versus global optima (SLO/GO). We argue that the SLO/GO response we identify in land-allocation problems traces to features that are common across non-convex optimization problems more broadly. Given the broad range of human systems that rely on non-convex optimization, our results therefore suggest that substantial social and economic risks could be lurking in a broad range in human systems that are coupled to the environment, even in the absence of catastrophic changes to the environment itself.

Creating materials with structure that is independently controllable at a range of scales requires breaking naturally occurring hierarchies. Breaking these hierarchies can be achieved via the decoupling of building block attributes from structure during assembly. Here, we demonstrate, through computer simulations and experiments, that shape and interaction decoupling occur in colloidal cuboids suspended in evaporating emulsion droplets. The resulting colloidal clusters serve as “preassembled” mesoscale building blocks for larger-scale structures. We show that clusters of up to nine particles form mesoscale building blocks with geometries that are independent of the particles’ degree of faceting and dipolar magnetic interactions. To highlight the potential of these superball clusters for hierarchical assembly, we demonstrate, using computer simulations, that clusters of six to nine particles can assemble into high-order structures that differ from bulk self-assembly of individual particles. Our results suggest that preassembled building blocks present a viable route to hierarchical materials design.

Sexual orientation describes sexual interests, approaches, arousals, and attractions. People experience these interests and attractions in a number of contexts, including in-person sexuality, fantasy, and porn use, among others. The extent to which sexual orientation is divergent (branched) and/or overlapping (coincident) across these, however, is unclear. In the present study, a gender/sex and sexually diverse sample (N = 30; 15 gender/sex/ual minorities and 15 majorities) manipulated digital circles representing porn use, in-person sexuality, and fantasy on a tablet during in-person interviews. Participants used circle overlap to represent the degree of shared sexual interests across contexts and circle size to indicate the strength and/or number of sexual interests within contexts. Across multiple dimensions of sexual orientation (gender/sex, partner number, and action/behavior), we found evidence that sexual interests were both branched and coincident. These findings contribute to new understandings about the multifaceted nature of sexual orientations across contexts and provide a novel way to measure, conceptualize, and understand sexual orientation in context.

The gulf between the complexity and diversity of colloidal crystal phases predicted to form in computer simulation and that realized to date in experiment is narrowing, but is still wide. Prior work shows that many synthesized particles are far from optimal "eigenshapes" for target superlattice structures. We use digital alchemy to determine eigenshapes for possible target colloidal crystal structures for eight families of polyhedral nanoparticle shapes already synthesized in the laboratory. Within each family we predict optimal building block shapes to obtain several target superlattice structures, as a guide for future experiments. For three target crystal structures common to multiple families, we identify which of the optimal shapes is most optimal under the same thermodynamic conditions.

Patterns of avoidance, adjacency, and association in complex systems design emerge from the system’s underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and spatial location). Understanding the physical–logical architecture interplay that gives rise to patterns of arrangement requires a quantitative approach that bridges both descriptions. Here, we show that statistical physics reveals patterns of avoidance, adjacency, and association across sets of complex, distributed system design solutions. Using an example arrangement problem and tensor network methods, we identify several phenomena in complex systems design, including placement symmetry breaking, propagating correlation, and emergent localization. Our approach generalizes straightforwardly to a broad range of complex systems design settings where it can provide a platform for investigating basic design phenomena.

Ongoing developments in colloidal particle synthesis show promise for using colloids as building blocks for reconfigurable, functional materials, but their rational design remains a challenge. Recent efforts to inversely design a colloidal particle from a self-assembled target structure at a single state point have proven successful even for complex colloidal crystals, replacing trial-and-error searches. Can such approaches be used to design a particle capable of assembling into multiple target structures under multiple conditions, thereby designing a reconfigurable colloidal crystal? Here we present a computational approach for the design of colloids that exhibit distinct target behaviours under different thermodynamic conditions. By extending the digital alchemy inverse design framework to multiple state points, we design hard particle shapes that entropically self-assemble two different colloidal crystal structures at two different densities; upon a small density change, the system reliably reconfigures between the two solids. We also find that the optimal shape satisfying two constraints is not simply an average of the two optimal shapes from each state point, and therefore is not easily intuited.

Crowded soft-matter and biological systems organize locally into preferred motifs. Locally-organized motifs in soft systems can, paradoxically, arise from a drive to maximize overall system entropy. Entropy-driven local order has been directly confirmed in model, synthetic colloidal systems, however similar patterns of organization occur in crowded biological systems ranging from the contents of a cell to collections of cells. In biological settings, and in soft matter more broadly, it is unclear whether entropy generically promotes or inhibits local organization. Resolving this is difficult because entropic effects are intrinsically collective, complicating efforts to isolate them. Here, we employ minimal models that artificially restrict system entropy to show that entropy drives systems toward local organization, even when the model system entropy is below reasonable physical bounds. By establishing this bound, our results suggest that entropy generically promotes local organization in crowded soft and biological systems of rigid objects.

Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and spatial location). Understanding the physical--logical architecture interplay that gives rise to patterns of arrangement requires a quantitative approach that bridges both descriptions. Here, we show that statistical physics reveals patterns of avoidance, adjacency, and association across sets of complex, distributed system design solutions. Using an example arrangement problem and tensor network methods, we identify several phenomena in complex systems design, including placement symmetry breaking, propagating correlation, and emergent localization. Our approach generalizes straightforwardly to a broad range of complex systems design settings where it can provide a platform for investigating basic design phenomena.