We investigate a free energy functional that arises in aggregation-diffusion phenomena modelled by nonlocal interactions and local repulsion on the hyperbolic space ${\mathbb H}^n$. The free energy consists of two competing terms: an entropy, corresponding to slow nonlinear diffusion, that favours spreading, and an attractive interaction potential energy that favours aggregation. We establish necessary and sufficient conditions on the interaction potential for ground states to exist on the hyperbolic space ${\mathbb H}^n$. To prove our results, we derived several Hardy–Littlewood–Sobolev (HLS)-type inequalities on general Cartan–Hadamard manifolds of bounded curvature, which have an interest in their own.

In the present notes, we study a generalization of the Peterson subalgebra to an oriented (generalized) cohomology theory which we call the formal Peterson subalgebra. Observe that by recent results of Zhong the dual of the formal Peterson algebra provides an algebraic model for the oriented cohomology of the affine Grassmannian.

Our first result shows that the centre of the formal affine Demazure algebra (FADA) generates the formal Peterson subalgebra. Our second observation is motivated by the Peterson conjecture. We show that a certain localization of the formal Peterson subalgebra for the extended Dynkin diagram of type $\hat A_1$ provides an algebraic model for “quantum” oriented cohomology of the projective line. Our last result can be viewed as an extension of the previous results on Hopf algebroids of structure algebras of moment graphs to the case of affine root systems. We prove that the dual of the formal Peterson subalgebra (an oriented cohomology of the affine Grassmannian) is the zeroth Hochschild homology of the FADA.

This article considers two arguments raised by the Government of Israel to explain why it does not regard the West Bank as occupied territory and may therefore establish Israeli settlements there. The first is that this territory was not the sovereign territory of another state when occupied by Israel in June 1967; the second is that the trust created by the League of Nations Mandate over Palestine still applies in those parts of Mandatory Palestine that did not become the sovereign territory of another state in 1948. After a short introduction, the article argues that in the modern area, in which peoples have the right to self-determination, the law of belligerent occupation may apply in territory that was not the territory of a state before it was occupied. Relying on a large body of historical research, the article then shows that the mandate system was a compromise between the colonial aspirations of Britain and France and the principle of self-determination propagated by US President Woodrow Wilson. The Mandate did not give rights to Jews or the Jewish people. It merely obligated Britain to facilitate its commitment under the Balfour Declaration to create the conditions that ‘will secure the establishment of the Jewish national home’ in Palestine. This obligation, and its parallel right, ended with the termination of the Mandate and the establishment of the State of Israel, which was the ultimate realisation of a national home for the Jewish people in the land of Israel. Even if one were to accept the argument that the trust established by the Mandate continues to apply in the West Bank, in an era in which colonial ideas have been rejected, the conclusion is not that Jewish citizens of Israel have a right to settle there, but that the right of the Palestinian inhabitants of that area to self-determination should be respected.

Physical inactivity is a leading cause globally of noncommunicable diseases such as diabetes, heart attacks, and strokes. Here, we present the results from a 4-week-long experimental test of a nudge designed to promote physical activity among 206 seniors in Abu Dhabi, United Arab Emirates—a population with one of the highest rates of physical inactivity in the world. We find that the “Forever Fit” nudge—a booklet containing a simple exercise program and information about the health benefits of physical activity—has a large positive effect on 93 previously inactive seniors. The nudge increases the time previously inactive participants spend being physically active from about 5 to about 15 minutes per day.

The ability of parties to a multistate contract to choose the law that governs their relationship, once controversial, is now almost universally accepted. So too are the conventional limits on that ability. Most jurisdictions restrict party autonomy in the name of the same set of concerns: Power disparities between the parties that might lead to oppression or unfairness, the policies or interests of the forum, and the policies or interests of the state whose law would govern the contract in the absence of a choice-of-law clause—the state whose law was not selected. This Article adds one more: the interests and policies of the state whose law has been selected. The idea that selecting a state’s law can offend its policies might seem counterintuitive. American scholars, at least, normally think that the way to respect a state’s policies is precisely to select its law, so the idea that those policies might counsel against selecting the law seems odd. But further analysis shows that there are several reasons a state might not want its law selected, and that courts should—and sometimes must—pay attention to those reasons.

Recent years have seen increasing interest in social robots, including pet robots, and their use in the care of people with dementia. Most research has focused on formal care-givers’ perspectives. There is a lack of qualitative research on the use of social robots in embedded practice and how people with dementia react to and interact with social robots. This study explores the use of pet robots in everyday life in a nursing home for people with dementia and how playfulness and disruptions characterized many interactions among the people with dementia, the pet robots and the researcher. It draws on five months of ethnographic fieldwork in a Danish nursing home for people with dementia including 11 residents, 13 staff members and 3 family members. We found that pet robots opened people up for playful interactions, allowing people with dementia to express themselves and have fun in a way that flattened hierarchies and enabled these individuals to be active instigators of joyful interactions. In the article, we argue that agency is distributed and that residents, robots, researchers and other actors both instigate and disrupt playful interactions. Playful interactions in the nursing home can be fun and rebellious in an everyday life that is otherwise focused on fitting in and keeping calm. Therefore, playfulness and fun can be viewed as a way of coping with institutional life. Further, playful interactions with pet robots can provide opportunities for residents to be active instigators rather than merely passive recipients of care and activities.

In Relational Justice, Hanoch Dagan and Avihay Dorfman defend a longstanding intuition of bilateral normativity. They argue that private law, for the most part, should structure legal relationships so that parties show reciprocal respect for each other’s self-determination and substantive equality. In this critical notice, I argue against the plausibility of their account. My main claim is that a commitment to individual self-determination and substantive equality should be societal and not bilateral. Rather than reciprocal respect for each other’s self-determination and equality within bilateral relationships, those who care about these values should require that private law help secure them on a societal scale.