Abstract We prove that every element of the special linear group can be represented as the product of at most six block unitriangular matrices, and that there exist matrices for which six products are necessary, independent of indexing. We present an analogous result for the general linear group. These results serve as general statements regarding the representational power of alternating linear updates. The factorizations and lower bounds of this work immediately imply tight estimates on the expressive power of linear affine coupling blocks in machine learning.
Abstract Graph clustering is a fundamental problem in machine learning with numerous applications in data science. State-of-the-art approaches to the problem, Louvain and Leiden, aim at optimizing the modularity function. However, their greedy nature leads to fast convergence to sub-optimal solutions. Here, we design a new approach to graph clustering, Tel-Aviv University (TAU), that efficiently explores the solution space using a genetic algorithm. We benchmark TAU on synthetic and real data sets and show its superiority over previous methods both in terms of the modularity of the computed solution and its similarity to a ground-truth partition when such exists. TAU is available at https://github.com/GalGilad/TAU.
Abstract Biological or biomimetic membranes are examples within the larger material class of flexible ultrathin lamellae and contoured fluid sheets that require work or energy to impose bending deformations. Bending elasticity also dictates the interactions and assembly of integrated phases or molecular clusters within fluid lamellae, for instance enabling critical cell functions in biomembranes. More broadly, lamella and other thin fluids that integrate dispersed objects, inclusions, and phases behave as contoured 2D colloidal suspensions governed by elastic interactions. To elucidate the breadth of interactions and assembled patterns accessible through elastic interactions, we consider the bending elasticity-driven assembly of 1–10 μm solid plate-shaped Brownian domains (the 2D colloids), integrated into a fluid phospholipid membrane (the 2D fluid). Here, the fluid membranes of giant unilamellar vesicles, 20–50 μm in diameter, each contain 4–100 monodisperse plate-domains at an overall solid area fraction of 17 ± 3%. Three types of reversible plate arrangements are found: persistent vesicle-encompassing quasi-hexagonal lattices, persistent closely associated chains or concentrated lattices, and a dynamic disordered state. The interdomain distances evidence combined attractive and repulsive elastic interactions up to 10 μm, far exceeding the ranges of physio-chemical interactions. Bending contributions are controlled through membrane slack (excess area) producing, for a fixed composition, a sharp cooperative multibody transition in plate arrangement, while domain size and number contribute intricacy.
Abstract The August 8, 2023 Lahaina fire refocused attention on wildfires, public alerts, and emergency management. Wildfire risk is on the rise, precipitated through a combination of climate change, increased development in the wildland–urban interface (WUI), decades of unmitigated biomass accumulation in forests, and a long history of emphasis on fire suppression over hazard mitigation. Stemming the tide of wildfire death and destruction will involve bringing together diverse scientific disciplines into policy. Renewed emphasis is needed on emergency alerts and community evacuations. Land management strategies need to account for the impact of climate change and hazard mitigation on forest ecosystems. Here, we propose a long-term strategy consisting of integrating wildfire risk management in wider-scope forest land management policies and strategies, and we discuss new technologies and possible scientific breakthroughs.
Abstract How likely are engineering PhD graduates to get a tenure-track faculty position in the United States? To answer this question, we analyzed aggregated yearly data on PhD graduates and tenure-track/tenured faculty members across all engineering disciplines from 2006 to 2021, obtained from the American Society of Engineering Education. The average likelihood for securing a tenure-track faculty position for engineering overall during this 16-year period was 12.4% (range = 10.9–18.5%), implying that roughly 1 in 8 PhD graduates attain such positions. After a significant decline from 18.5 to 10.9% between 2006 and 2014 (R2 = 0.62; P < 0.05), a trend consistent with a period of rising competition, the outlook has since stabilized between 11.3 and 12% (R2 = 0.04; P > 0.05). Given that most engineering PhD graduates will never secure a tenure-track faculty position, emphasizing alternative career tracks during doctoral training could align expectations better with reality.
Abstract In fluid mechanics, dimensionless numbers like the Reynolds number help classify flows. We argue that such a classification is also relevant for crowd flows by putting forward the dimensionless Intrusion and Avoidance numbers, which quantify the intrusions into the pedestrians' personal spaces and the imminency of the collisions that they face, respectively. Using an extensive dataset, we show that these numbers delineate regimes where distinct variables characterize the crowd's arrangement, namely, Euclidean distances at low Avoidance number and times-to-collision at low Intrusion number. On the basis of these findings, a perturbative expansion of the individual pedestrian dynamics is carried out around the noninteracting state, in quite general terms. Simulations confirm that this expansion performs well in its expected regime of applicability.
Abstract Climate change mitigation will trigger major changes in human activity, energy systems, and material use, potentially shifting pressure from climate change to other environmental problems. We provide a comprehensive overview of such "environmental problem shifting" (EPS). While there is considerable research on this issue, studies are scattered across research fields and use a wide range of terms with blurred conceptual boundaries, such as trade-off, side effect, and spillover. We identify 506 relevant studies on EPS of which 311 are empirical, 47 are conceptual–theoretical, and 148 are synthetic studies or reviews of a particular mitigation option. A systematic mapping of the empirical studies reveals 128 distinct shifts from 22 categories of mitigation options to 10 environmental impacts. A comparison with the recent IPCC report indicates that EPS literature does not cover all mitigation options. Moreover, some studies systematically overestimate EPS by not accounting for the environmental benefits of reduced climate change. We propose to conceptually clarify the different ways of estimating EPS by distinguishing between gross, net, and relative shifting. Finally, the ubiquity of EPS calls for policy design which ensures climate change mitigation that minimizes unsustainability across multiple environmental dimensions. To achieve this, policymakers can regulate mitigation options—for example, in their choice of technology or location—and implement complementary environmental policies.
Abstract Planetary radiometric observations enable remote sensing of biogeochemical parameters to describe spatiotemporal variability in aquatic ecosystems. For approximately the last half century, the science of aquatic radiometry has established a knowledge base using primarily, but not exclusively, visible wavelengths. Scientific subdisciplines supporting aquatic radiometry have evolved hardware, software, and procedures to maximize competency for exploiting visible wavelength information. This perspective culminates with the science requirement that visible spectral resolution must be continually increased to extract more information. Other sources of information, meanwhile, remain underexploited, particularly information from nonvisible wavelengths. Herein, absolute radiometry is used to evaluate spectral limits for deriving and exploiting aquatic data products, specifically the normalized water-leaving radiance, Γ(λ), and its derivative products. Radiometric observations presented herein are quality assured for individual wavebands, and spectral verification is conducted by analyzing celestial radiometric results, comparing agreement of above- and in-water observations at applicable wavelengths, and evaluating consistency with bio-optical models and optical theory. The results presented include the first absolute radiometric field observations of Γ(λ) within the IR-B spectral domain (i.e. spanning 1400–3000 nm), which indicate that IR-B signals confer greater and more variable flux than formerly ascribed. Black-pixel processing, a routine correction in satellite and in situ aquatic radiometry wherein a spectrum is offset corrected relative to a nonvisible waveband (often IR-B or a shorter legacy waveband) set to a null value, is shown to degrade aquatic spectra and derived biogeochemical parameters.
Abstract Projections of granular energy technology diffusion can support decision-making on climate mitigation policies and infrastructure investments. However, such projections often do not account for uncertainties and have low spatial resolution. S-curve models of technology diffusion are widely used to project future installations, but the results of the different models can vary significantly. We propose a method to create probabilistic projections of granular energy technology diffusion at subnational level based on historical time series data and testing how various projection models perform in terms of accuracy and uncertainty to inform the choice of models. As a case study, we investigate the growth of solar photovoltaics, heat pumps, and battery electric vehicles at municipality level throughout Switzerland in 2000–2021 (testing) and until 2050 (projections). Consistently for all S-curve models and technologies, we find that the medians of the probabilistic projections anticipate the diffusion of the technologies more accurately than the respective deterministic projections. While accuracy and probabilistic density intervals of the models vary across technologies, municipalities, and years, Bertalanffy and two versions of the generalized Richards model estimate the future diffusion with higher accuracy and sharpness than logistic, Gompertz, and Bass models. The results also highlight that all models come with trade-offs and eventually a combination of models with weights is needed. Based on these weighted probabilistic projections, we show that, given the current dynamics of diffusion in solar photovoltaics, heat pumps, and battery electric vehicles in Switzerland, the net-zero emissions target would be missed by 2050 with high certainty.
AbstractThe jamming transition, generally manifested by a rapid increase of rigidity under compression (i.e. compression hardening), is ubiquitous in amorphous materials. Here we study shear hardening in deeply annealed frictionless packings generated by numerical simulations, reporting critical scalings absent in compression hardening. We demonstrate that hardening is a natural consequence of shear-induced memory destruction. Based on an elasticity theory, we reveal two independent microscopic origins of shear hardening: (i) the increase of the interaction bond number and (ii) the emergence of anisotropy and long-range correlations in the orientations of bonds—the latter highlights the essential difference between compression and shear hardening. Through the establishment of physical laws specific to anisotropy, our work completes the criticality and universality of jamming transition, and the elasticity theory of amorphous solids.
Abstract Erythrocyte sedimentation rate (ESR) is a clinical parameter used as a nonspecific marker for inflammation, and recent studies have shown that it is linked to the collapse of the gel formed by red blood cells (RBCs) at physiological hematocrits (i.e. RBC volume fraction). Previous research has suggested that the observation of a slower initial dynamics is related to the formation of fractures in the gel. Moreover, RBC gels present specific properties due to the anisotropic shape and flexibility of the RBCs. Namely, the onset of the collapse is reached earlier and the settling velocity of the gel increases with increasing attraction between the RBCs, while the gel of spherical particles shows the opposite trend. Here, we report experimental observations of the gel structure during the onset of the collapse. We suggest an equation modeling this initial process as fracturing of the gel. We demonstrate that this equation provides a model for the motion of the interface between blood plasma and the RBC gel, along the whole time span. We also observe that the increase in the attraction between the RBCs modifies the density of fractures in the gel, which explains why the gel displays an earlier onset when the aggregation energy between the RBCs increases. Our work uncovers the detailed physical mechanism underlying the ESR and provides insights into the fracture dynamics of an RBC gel. These results can improve the accuracy of clinical measurements.
Abstract The inherent coupling of chemical and mechanical behavior in fluid-filled microchambers enables the fluid to autonomously perform work, which in turn can direct the self-organization of objects immersed in the solution. Using theory and simulations, we show that the combination of diffusioosmotic and buoyancy mechanisms produce independently controlled, respective fluid flows: one generated by confining surfaces and the other in the bulk of the solution. With both flows present, the fluid can autonomously join 2D, disconnected pieces to a chemically active, "sticky" base and then fold the resulting layer into regular 3D shapes (e.g. pyramids, tetrahedrons, and cubes). Here, the fluid itself performs the work of construction and thus, this process does not require extensive external machinery. If several sticky bases are localized on the bottom surface, the process can be parallelized, with the fluid simultaneously forming multiple structures of the same or different geometries. Hence, this approach can facilitate the relatively low-cost, mass production of 3D micron to millimeter-sized structures. Formed in an aqueous solution, the assembled structures could be compatible with biological environments, and thus, potentially useful in medical and biochemical applications.
Abstract Topological transitions of lipid membranes are ubiquitous in key biological processes for cell life, like neurotransmission, fertilization, morphogenesis, and viral infections. Despite this, they are not well understood due to their multiscale nature, which limits the use of molecular models and calls for a mesoscopic approach such as the celebrated Canham–Helfrich one. Unfortunately, such a model cannot handle topological transitions, hiding the crucial involved forces and the appearance of the experimentally observed hemifused intermediates. In this work, we describe the membrane as a diffuse interface preserving the Canham–Helfrich elasticity. We show that pivotal features of the hemifusion pathway are captured by this mesoscopic approach, e.g. a (meta)stable hemifusion state and the fusogenic behavior of negative monolayer spontaneous curvatures. The membrane lateral stress profile is calculated as a function of the elastic rigidities, yielding a coarse-grained version of molecular models findings. Insights into the fusogenic mechanism are reported and discussed.
Abstract Enabling widespread electric vehicle (EV) adoption requires a substantial build-out of charging infrastructure in the coming decade. We formulate the charging infrastructure needs as a scaling analysis problem and use it to estimate the EV infrastructure needs of the USA at a county-level resolution. We find that gasoline and EV charging stations scale sub-linearly with their respective vehicle registrations, recovering the sub-linear scaling typical of infrastructure. Surprisingly, we find that EV charging stations scale super-linearly with population size within counties, deviating from the sub-linear scaling of gasoline stations. We discuss how this demonstrates the infancy of both EVs and EV infrastructure while providing a framework for estimating future EV infrastructure demands. By considering the power delivery of existing gasoline stations, and appropriate EV efficiencies, we estimate the EV infrastructure gap at the county level, providing a road map for future EV infrastructure expansion.
Abstract The Industrial Revolution precipitated a pivotal shift from waterpower to coal-fueled steam power in British textile mills. Although it is now widely accepted that steam was chosen to power factories despite the availability of sufficient waterpower resources across most of Britain, the location and suitability of that waterpower during the early 19th century remain underexplored. Here, we employ quantitative fluvial geomorphology alongside historical climate data, factory records, and a catalog of over 26,000 mill sites to reveal that waterpower was abundant for most of early 19th century Britain, except in the central hub of British cotton production: Greater Manchester in the Mersey Basin. Our findings show that surging factory mechanization and overcrowding on key waterways in the Mersey Basin compounded waterpower scarcity arising from a drier 19th century climate. Widespread adoption of coal-fueled steam engines in certain key industrial centers of Britain was a strategy aimed at ameliorating some of the reduced reliability of waterpower. The fact that steam engines were frequently used in water-powered factories in many industrial regions until the third quarter of the 19th century to recirculate water to provide that power, or as a power supplement when waterpower availability was restricted, adds further weight to our argument. Rapid adoption of coal-powered steam engines reshaped the social and structural landscape of industrial work, firmly established Britain's prominence as an industrial powerhouse, and had lasting global industrial and environmental impacts.
