Thinking Outside the Euclidean Box: Riemannian Geometry and Inter-Temporal Decision-Making

<div><p>Inter-temporal decisions involves assigning values to various payoffs occurring at different temporal distances. Past research has used different approaches to study these decisions made by humans and animals. For instance, considering that people discount future payoffs at a constant rate (e.g., exponential discounting) or at variable rate (e.g., hyperbolic discounting). In this research, we question the widely assumed, but seldom questioned, notion across many of the existing approaches that the decision space, where the decision-maker perceives time and monetary payoffs, is a Euclidean space. By relaxing the rigid assumption of Euclidean space, we propose that the decision space is a more flexible Riemannian space of Constant Negative Curvature. We test our proposal by deriving a discount function, which uses the distance in the Negative Curvature space instead of Euclidean temporal distance. The distance function includes both perceived values of time as well as money, unlike past work which has considered just time. By doing so we are able to explain many of the empirical findings in inter-temporal decision-making literature. We provide converging evidence for our proposal by estimating the curvature of the decision space utilizing manifold learning algorithm and showing that the characteristics (i.e., metric properties) of the decision space resembles those of the Negative Curvature space rather than the Euclidean space. We conclude by presenting new theoretical predictions derived from our proposal and implications for how non-normative behavior is defined.</p></div

El Diario de Pontevedra : periódico liberal: Ano XXVIII Número 8177 - 1911 agosto 16

Omniphobic surfaces, that is, which repel all known liquids, have proven of value in applications ranging from membrane distillation to underwater drag reduction. A limitation of currently employed omniphobic surfaces is that they rely on perfluorinated coatings, increasing cost and environmental impact and preventing applications in harsh environments. Thus, there is a keen interest in rendering conventional materials, such as plastics, omniphobic by micro/nanotexturing rather than via chemical makeup, with notable success having been achieved for silica surfaces with doubly reentrant micropillars. However, we found a critical limitation of microtextures comprising pillars that they undergo catastrophic wetting transitions (apparent contact angles, θ_r → 0° from θ_r > 90°) in the presence of localized physical damages/defects or on immersion in wetting liquids. In response, a doubly reentrant cavity microtexture is introduced, which can prevent catastrophic wetting transitions in the presence of localized structural damage/defects or on immersion in wetting liquids. Remarkably, our silica surfaces with doubly reentrant cavities could exhibit apparent contact angles, θ_r ≈ 135° for mineral oil, where the intrinsic contact angle, θ_o ≈ 20°. Further, when immersed in mineral oil or water, doubly reentrant microtextures in silica (θ_o ≈ 40° for water) were not penetrated even after several days of investigation. Thus, microtextures comprising doubly reentrant cavities might enable applications of conventional materials without chemical modifications, especially in scenarios that are prone to localized damages or immersion in wetting liquids, for example, hydrodynamic drag reduction and membrane distillation

Doubly Reentrant Cavities Prevent Catastrophic Wetting Transitions on Intrinsically Wetting Surfaces

Omniphobic surfaces, that is, which repel all known liquids, have proven of value in applications ranging from membrane distillation to underwater drag reduction. A limitation of currently employed omniphobic surfaces is that they rely on perfluorinated coatings, increasing cost and environmental impact and preventing applications in harsh environments. Thus, there is a keen interest in rendering conventional materials, such as plastics, omniphobic by micro/nanotexturing rather than via chemical makeup, with notable success having been achieved for silica surfaces with doubly reentrant micropillars. However, we found a critical limitation of microtextures comprising pillars that they undergo catastrophic wetting transitions (apparent contact angles, θ_r → 0° from θ_r > 90°) in the presence of localized physical damages/defects or on immersion in wetting liquids. In response, a doubly reentrant cavity microtexture is introduced, which can prevent catastrophic wetting transitions in the presence of localized structural damage/defects or on immersion in wetting liquids. Remarkably, our silica surfaces with doubly reentrant cavities could exhibit apparent contact angles, θ_r ≈ 135° for mineral oil, where the intrinsic contact angle, θ_o ≈ 20°. Further, when immersed in mineral oil or water, doubly reentrant microtextures in silica (θ_o ≈ 40° for water) were not penetrated even after several days of investigation. Thus, microtextures comprising doubly reentrant cavities might enable applications of conventional materials without chemical modifications, especially in scenarios that are prone to localized damages or immersion in wetting liquids, for example, hydrodynamic drag reduction and membrane distillation

Doubly Reentrant Cavities Prevent Catastrophic Wetting Transitions on Intrinsically Wetting Surfaces

Omniphobic surfaces, that is, which repel all known liquids, have proven of value in applications ranging from membrane distillation to underwater drag reduction. A limitation of currently employed omniphobic surfaces is that they rely on perfluorinated coatings, increasing cost and environmental impact and preventing applications in harsh environments. Thus, there is a keen interest in rendering conventional materials, such as plastics, omniphobic by micro/nanotexturing rather than via chemical makeup, with notable success having been achieved for silica surfaces with doubly reentrant micropillars. However, we found a critical limitation of microtextures comprising pillars that they undergo catastrophic wetting transitions (apparent contact angles, θ_r → 0° from θ_r > 90°) in the presence of localized physical damages/defects or on immersion in wetting liquids. In response, a doubly reentrant cavity microtexture is introduced, which can prevent catastrophic wetting transitions in the presence of localized structural damage/defects or on immersion in wetting liquids. Remarkably, our silica surfaces with doubly reentrant cavities could exhibit apparent contact angles, θ_r ≈ 135° for mineral oil, where the intrinsic contact angle, θ_o ≈ 20°. Further, when immersed in mineral oil or water, doubly reentrant microtextures in silica (θ_o ≈ 40° for water) were not penetrated even after several days of investigation. Thus, microtextures comprising doubly reentrant cavities might enable applications of conventional materials without chemical modifications, especially in scenarios that are prone to localized damages or immersion in wetting liquids, for example, hydrodynamic drag reduction and membrane distillation

Doubly Reentrant Cavities Prevent Catastrophic Wetting Transitions on Intrinsically Wetting Surfaces

Omniphobic surfaces, that is, which repel all known liquids, have proven of value in applications ranging from membrane distillation to underwater drag reduction. A limitation of currently employed omniphobic surfaces is that they rely on perfluorinated coatings, increasing cost and environmental impact and preventing applications in harsh environments. Thus, there is a keen interest in rendering conventional materials, such as plastics, omniphobic by micro/nanotexturing rather than via chemical makeup, with notable success having been achieved for silica surfaces with doubly reentrant micropillars. However, we found a critical limitation of microtextures comprising pillars that they undergo catastrophic wetting transitions (apparent contact angles, θ_r → 0° from θ_r > 90°) in the presence of localized physical damages/defects or on immersion in wetting liquids. In response, a doubly reentrant cavity microtexture is introduced, which can prevent catastrophic wetting transitions in the presence of localized structural damage/defects or on immersion in wetting liquids. Remarkably, our silica surfaces with doubly reentrant cavities could exhibit apparent contact angles, θ_r ≈ 135° for mineral oil, where the intrinsic contact angle, θ_o ≈ 20°. Further, when immersed in mineral oil or water, doubly reentrant microtextures in silica (θ_o ≈ 40° for water) were not penetrated even after several days of investigation. Thus, microtextures comprising doubly reentrant cavities might enable applications of conventional materials without chemical modifications, especially in scenarios that are prone to localized damages or immersion in wetting liquids, for example, hydrodynamic drag reduction and membrane distillation

Doubly Reentrant Cavities Prevent Catastrophic Wetting Transitions on Intrinsically Wetting Surfaces

Omniphobic surfaces, that is, which repel all known liquids, have proven of value in applications ranging from membrane distillation to underwater drag reduction. A limitation of currently employed omniphobic surfaces is that they rely on perfluorinated coatings, increasing cost and environmental impact and preventing applications in harsh environments. Thus, there is a keen interest in rendering conventional materials, such as plastics, omniphobic by micro/nanotexturing rather than via chemical makeup, with notable success having been achieved for silica surfaces with doubly reentrant micropillars. However, we found a critical limitation of microtextures comprising pillars that they undergo catastrophic wetting transitions (apparent contact angles, θ_r → 0° from θ_r > 90°) in the presence of localized physical damages/defects or on immersion in wetting liquids. In response, a doubly reentrant cavity microtexture is introduced, which can prevent catastrophic wetting transitions in the presence of localized structural damage/defects or on immersion in wetting liquids. Remarkably, our silica surfaces with doubly reentrant cavities could exhibit apparent contact angles, θ_r ≈ 135° for mineral oil, where the intrinsic contact angle, θ_o ≈ 20°. Further, when immersed in mineral oil or water, doubly reentrant microtextures in silica (θ_o ≈ 40° for water) were not penetrated even after several days of investigation. Thus, microtextures comprising doubly reentrant cavities might enable applications of conventional materials without chemical modifications, especially in scenarios that are prone to localized damages or immersion in wetting liquids, for example, hydrodynamic drag reduction and membrane distillation

Protonation and Oligomerization of Gaseous Isoprene on Mildly Acidic Surfaces: Implications for Atmospheric Chemistry

In a global process linking the Earth’s climate with its ecosystems, massive photosynthetic isoprene (ISOP) emissions are converted to light-scattering haze. This phenomenon is imperfectly captured by atmospheric chemistry models: predicted ISOP emissions atop forest canopies would deplete the oxidizing capacity of the overhead atmosphere, at variance with field observations. Here we address this key issue in novel laboratory experiments where we apply electrospray mass spectrometry to detect online the products of the reactive uptake of gaseous ISOP on the surface of aqueous jets as a function of acidity. We found that ISOP is already protonated to ISOPH⁺ and undergoes cationic oligomerization to (ISOP)₂H⁺ and (ISOP)₃H⁺ on the surface of pH < 4 water jets. We estimate uptake coefficients, γ_ISOP = (0.5 – 2.0) × 10^–6 on pH = 3 water, which translate into the significant reuptake of leaf-level ISOP emissions in typical (surface-to-volume ∼5 m^–1) forests during realistic (a few minutes) in-canopy residence times. Our findings may also account for the rapid decay of ISOP in forests after sunset and help bring the global budget of volatile organic compounds closer to balance