Effective multicellularity requires both cooperation and competition between constituent cells. Cooperation involves sacrificing individual fitness in favour of that of the community, but excessive cooperation makes the community susceptible to senescence and ageing. Competition eliminates unfit senescent cells via natural selection and thus slows down ageing, but excessive competition makes the community susceptible to cheaters, as exemplified by cancer and cancer-like phenomena. These observations suggest that an optimal level of intercellular competition in a multicellular organism maximizes organismal vitality by delaying the inevitability of ageing. We quantify this idea using a statistical mechanical framework that leads to a generalized replicator dynamical system for the population of cells that changes their vitality and cooperation due to somatic mutations that make them susceptible to ageing and/or cancer. By accounting for the cost of cooperation and strength of competition in a minimal setting, we show that our model predicts an optimal value of competition that maximizes vitality and delays the inevitability of senescence or cancer. The results have implications for the design of strategies aimed at delaying ageing in biological, technical and social systems that exhibit similar processes.

Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback control theory to explore how a leaf can remain flat while growing. We investigate both in-plane (metric) and out-of-plane (curvature) growth variation and account for both local and nonlocal feedback laws. We show that a linearized feedback theory that accounts for both spatially nonlocal and temporally delayed effects suffices to suppress long wavelength fluctuations effectively and explains recently observed statistical features of growth in tobacco leaves. Our work provides a framework for understanding the regulation of the shape of leaves and other leaflike laminar objects.

There is growing need for hybrid curricula that integrate constructivist methods from Science and Technology Studies (STS) into both engineering and policy courses at the undergraduate and graduate levels. However, institutional and disciplinary barriers have made implementing such curricula difficult at many institutions. While several programs have recently been launched that mix technical training with consideration of “societal” or “ethical issues,” these programs often lack a constructivist element, leaving newly-minted practitioners entering practical fields ill-equipped to unpack the politics of knowledge and technology or engage with skeptical publics. This paper presents a novel format for designing interdisciplinary coursework that combines conceptual content from STS with training in engineering and policy. Courses following this format would ideally be team taught by instructors with advanced training in diverse fields, and hence co-learning between instructors and disciplines is a key element of the format. Several instruments for facilitating both student and instructor collaborative learning are introduced. The format is also designed for versatility: in addition to being adaptable to both technical and policy training environments, topics are modularized around a conceptual core so that issues ranging from biotech to nuclear security can be incorporated to fit programmatic needs and resources.

The presence of incomplete cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension, most beautifully demonstrated in kirigami art-forms. We use numerical experiments to characterize the geometric mechanics of kirigamized sheets as a function of the number, size and orientation of cuts. We show that the geometry of mechanically loaded sheets can be approximated as a composition of simple developable units: flats, cylinders, cones and compressed Elasticae. This geometric construction yields scaling laws for the mechanical response of the sheet in both the weak and strongly deformed limit. In the ultimately stretched limit, this further leads to a theorem on the nature and form of geodesics in an arbitrary kirigami pattern, consistent with observations and simulations. Finally, we show that by varying the shape and size of the geodesic in a kirigamized sheet, we can control the deployment trajectory of the sheet, and thence its functional properties as an exemplar of a tunable structure that can serve as a robotic gripper, a soft light window or the basis for a physically unclonable device. Overall our study of disordered kirigami sets the stage for controlling the shape and shielding the stresses in thin sheets using cuts.

Drawing on elementary invariance principles, we propose that a statistical geometric object, the probability distribution of the normalized contour curvatures (NCC) in the intensity field of a planar image has the potential to categorize objects. We show that NCC is sufficient for discriminating between cognitive categories such as animacy, size and type, and demonstrate the robustness of this metric to variation in illumination and viewpoint, consistent with psychological experiments. A generative model for producing artificial images with the observed NCC distributions highlights the key features that our metric captures, and those that it does not. More broadly, our study points to the need for statistical geometric approaches to cognition that build in both the statistics and the natural invariances of the visual world.

We present an additive approach for the inverse design of kirigami-based mechanical metamaterials by focusing on the empty (negative) spaces instead of the solid tiles. By considering each negative space as a four-bar linkage, we identify a simple recursive relationship between adjacent linkages, yielding an efficient method for creating kirigami patterns. This allows us to solve the kirigami design problem using elementary linear algebra, with compatibility, reconfigurability and rigid-deployability encoded into an iterative procedure involving simple matrix multiplications. The resulting linear design strategy circumvents the solution of a non-convex global optimization problem and allows us to control the degrees of freedom in the deployment angle field, linkage offsets and boundary conditions. We demonstrate this by creating a large variety of rigid-deployable, compact, reconfigurable kirigami patterns. We then realize our kirigami designs physically using two simple but effective fabrication strategies with very different materials. Altogether, our additive approaches present routes for efficient mechanical metamaterial design and fabrication based on ori/kirigami art forms.