Finally, we show that this physical framework is generally applicable to the largest instrumented caldera collapse eruptions of the past fifty years.Out of equilibrium, a lack of reciprocity is the rule rather than the exception. selleck Non-reciprocity occurs, for instance, in active matter1-6, non-equilibrium systems7-9, networks of neurons10,11, social groups with conformist and contrarian members12, directional interface growth phenomena13-15 and metamaterials16-20. Although wave propagation in non-reciprocal media has recently been closely studied1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points21. We describe the emergence of these phases using insights from bifurcation theory22,23 and non-Hermitian quantum mechanics24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.The fundamental topology of cellular structures-the location, number and connectivity of nodes and compartments-can profoundly affect their acoustic1-4, electrical5, chemical6,7, mechanical8-10 and optical11 properties, as well as heat1,12, fluid13,14 and particle transport15. Approaches that harness swelling16-18, electromagnetic actuation19,20 and mechanical instabilities21-23 in cellular materials have enabled a variety of interesting wall deformations and compartment shape alterations, but the resulting structures generally preserve the defining connectivity features of the initial topology. Achieving topological transformation presents a distinct challenge for existing strategies it requires complex reorganization, repacking, and coordinated bending, stretching and folding, particularly around each node, where elastic resistance is highest owing to connectivity. Here we introduce a two-tiered dynamic strategy that achieves systematic reversible transformations of the fundamental topology of cellular micrl or localized deformations. We then harness dynamic topologies to develop active surfaces with information encryption, selective particle trapping and bubble release, as well as tunable mechanical, chemical and acoustic properties.At the liquid-gas phase transition in water, the density has a discontinuity at atmospheric pressure; however, the line of these first-order transitions defined by increasing the applied pressure terminates at the critical point1, a concept ubiquitous in statistical thermodynamics2. In correlated quantum materials, it was predicted3 and then confirmed experimentally4,5 that a critical point terminates the line of Mott metal-insulator transitions, which are also first-order with a discontinuous charge carrier density. In quantum spin systems, continuous quantum phase transitions6 have been controlled by pressure7,8, applied magnetic field9,10 and disorder11, but discontinuous quantum phase transitions have received less attention. The geometrically frustrated quantum antiferromagnet SrCu2(BO3)2 constitutes a near-exact realization of the paradigmatic Shastry-Sutherland model12-14 and displays exotic phenomena including magnetization plateaus15, low-lying bound-state excitations16, anomalous thermodynamics17 and discontinuous quantum phase transitions18,19. Here we control both the pressure and the magnetic field applied to SrCu2(BO3)2 to provide evidence of critical-point physics in a pure spin system. We use high-precision specific-heat measurements to demonstrate that, as in water, the pressure-temperature phase diagram has a first-order transition line that separates phases with different local magnetic energy densities, and that terminates at an Ising critical point. We provide a quantitative explanation of our data using recently developed finite-temperature tensor-network methods17,20-22. These results further our understanding of first-order quantum phase transitions in quantum magnetism, with potential applications in materials where anisotropic spin interactions produce the topological properties23,24 that are useful for spintronic applications.The initiation of cell division integrates a large number of intra- and extracellular inputs. D-type cyclins (hereafter, cyclin D) couple these inputs to the initiation of DNA replication1. Increased levels of cyclin D promote cell division by activating cyclin-dependent kinases 4 and 6 (hereafter, CDK4/6), which in turn phosphorylate and inactivate the retinoblastoma tumour suppressor. Accordingly, increased levels and activity of cyclin D-CDK4/6 complexes are strongly linked to unchecked cell proliferation and cancer2,3. However, the mechanisms that regulate levels of cyclin D are incompletely understood4,5. Here we show that autophagy and beclin 1 regulator 1 (AMBRA1) is the main regulator of the degradation of cyclin D. We identified AMBRA1 in a genome-wide screen to investigate the genetic basis of the response to CDK4/6 inhibition. Loss of AMBRA1 results in high levels of cyclin D in cells and in mice, which promotes proliferation and decreases sensitivity to CDK4/6 inhibition. Mechanistically, AMBRA1 mediates ubiquitylation and proteasomal degradation of cyclin D as a substrate receptor for the cullin 4 E3 ligase complex. Loss of AMBRA1 enhances the growth of lung adenocarcinoma in a mouse model, and low levels of AMBRA1 correlate with worse survival in patients with lung adenocarcinoma. Thus, AMBRA1 regulates cellular levels of cyclin D, and contributes to cancer development and the response of cancer cells to CDK4/6 inhibitors.