Conjugate Points and Shocks in Nonlinear Optimal Control

In this paper the authors use the method of characteristics to extend the Jacobi conjugate points theory to the Bolza problem arising in nonlinear optimal control. This yields necessary and sufficient optimality conditions for weak and strong local minima stated in terms of the existence of a solution to a corresponding matrix Riccati differential equation. The same approach allows to investigate as well smoothness of the value function

Optimality and Characteristics of Hamilton-Jacobi-Bellman Equations

In this paper the authors study the Bolza problem arising in nonlinear optimal control and investigate under what circumstances the necessary conditions for optimality of Pontryagin's type are also sufficient. This leads to the question when shocks do not occur in the method of characteristics applied to the associated Hamilton-Jacobi-Bellman equation. In this case the value function is its (unique) continuously differentiable solution and can be obtained from the canonical equations. In optimal control this corresponds to the case when the optimal trajectory of the Bolza problem is unique for every initial state and the optimal feedback is an upper semicontinuous set-valued map with convex, compact images

Conjugate times and regularity of the minimum time function with differential inclusions

This paper studies the regularity of the minimum time function, $T(\cdot)$, for a control system with a general closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation which guarantees the propagation of the proximal subdifferential of $T$ along any optimal trajectory. Then, we obtain the local $C^2$ regularity of the minimum time function along optimal trajectories by using such a relation to exclude the presence of conjugate times

Homogenization and enhancement for the G-equation

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally we also consider advection depending on position at the integral scale

Registered Replication Report: Dijksterhuis and van Knippenberg (1998)

Dijksterhuis and van Knippenberg (1998) reported that participants primed with a category associated with intelligence ("professor") subsequently performed 13% better on a trivia test than participants primed with a category associated with a lack of intelligence ("soccer hooligans"). In two unpublished replications of this study designed to verify the appropriate testing procedures, Dijksterhuis, van Knippenberg, and Holland observed a smaller difference between conditions (2%-3%) as well as a gender difference: Men showed the effect (9.3% and 7.6%), but women did not (0.3% and -0.3%). The procedure used in those replications served as the basis for this multilab Registered Replication Report. A total of 40 laboratories collected data for this project, and 23 of these laboratories met all inclusion criteria. Here we report the meta-analytic results for those 23 direct replications (total N = 4,493), which tested whether performance on a 30-item general-knowledge trivia task differed between these two priming conditions (results of supplementary analyses of the data from all 40 labs, N = 6,454, are also reported). We observed no overall difference in trivia performance between participants primed with the "professor" category and those primed with the "hooligan" category (0.14%) and no moderation by gender

Registered Replication Report: Dijksterhuis and van Knippenberg (1998)

Dijksterhuis and van Knippenberg (1998) reported that participants primed with a category associated with intelligence ("professor") subsequently performed 13% better on a trivia test than participants primed with a category associated with a lack of intelligence ("soccer hooligans"). In two unpublished replications of this study designed to verify the appropriate testing procedures, Dijksterhuis, van Knippenberg, and Holland observed a smaller difference between conditions (2%-3%) as well as a gender difference: Men showed the effect (9.3% and 7.6%), but women did not (0.3% and -0.3%). The procedure used in those replications served as the basis for this multilab Registered Replication Report. A total of 40 laboratories collected data for this project, and 23 of these laboratories met all inclusion criteria. Here we report the meta-analytic results for those 23 direct replications (total N = 4,493), which tested whether performance on a 30-item general-knowledge trivia task differed between these two priming conditions (results of supplementary analyses of the data from all 40 labs, N = 6,454, are also reported). We observed no overall difference in trivia performance between participants primed with the "professor" category and those primed with the "hooligan" category (0.14%) and no moderation by gender

Neutral sphingomyelinase mediates the co-morbidity trias of alcohol abuse, major depression and bone defects

Mental disorders are highly comorbid and occur together with physical diseases, which are often considered to arise from separate pathogenic pathways. We observed in alcohol-dependent patients increased serum activity of neutral sphingomyelinase. A genetic association analysis in 456,693 volunteers found associations of haplotypes of SMPD3 coding for NSM-2 (NSM) with alcohol consumption, but also with affective state, and bone mineralisation. Functional analysis in mice showed that NSM controls alcohol consumption, affective behaviour, and their interaction by regulating hippocampal volume, cortical connectivity, and monoaminergic responses. Furthermore, NSM controlled bone–brain communication by enhancing osteocalcin signalling, which can independently supress alcohol consumption and reduce depressive behaviour. Altogether, we identified a single gene source for multiple pathways originating in the brain and bone, which interlink disorders of a mental–physical co-morbidity trias of alcohol abuse—depression/anxiety—bone disorder. Targeting NSM and osteocalcin signalling may, thus, provide a new systems approach in the treatment of a mental–physical co-morbidity trias

The Regenerative Lens: A conceptual framework for regenerative social-ecological systems

Societies must transform their dynamics to support the flourishing of life. There is increasing interest in regeneration and regenerative practice as a solution, but also limited cohered understanding of what constitutes regenerative systems at social-ecological scales. In this perspective we present a conceptual, cross-disciplinary, and action-oriented regenerative systems framework, the Regenerative Lens, informed by a wide literature review. The framework emphasizes that regenerative systems maintain positive reinforcing cycles of wellbeing within and beyond themselves, especially between humans and wider nature, such that “life begets life.” We identify five key qualities needed in systems to encourage such dynamics: an ecological worldview embodied in human action; mutualism; high diversity; agency for humans and non-humans to act regeneratively; and continuous reflexivity. We apply the Lens to an envisioned future food system to illustrate its utility as a reflexive tool and for stretching ambition. We hope that the conceptual clarity provided here will aid the necessary acceleration of learning and action toward regenerative systems