The steady-state current–voltage response of ion-selective systems varies as the number of ion-selective components is varied. For the highly investigated unipolar system, including only one ion-selective component, it has been shown that above a supercritical voltage, an electroosmotic instability is triggered, leading to overlimiting currents. In contrast, the effects of this instability on the current–voltage response of the second most common system of a bipolar system, including two oppositely charged permselective regions, have yet to be reported. Using numerical simulations, we investigate the steady-state electrical response of bipolar systems as we vary the ratio of the charge within the two oppositely charged regions. The responses are divided into those with an internal symmetry related to the surface charge and those without. In contrast to the unipolar systems, bipolar systems with the internal symmetry do not exhibit overlimiting currents and their steady-state response is identical to the convectionless steady-state response. In contrast, the systems without the internal symmetry exhibit much more complicated behaviour. For positive voltages, they have overlimiting currents, while for negative voltages, they do not have overlimiting currents. Our findings contribute to a more profound understanding of the behaviour of the current–voltage response in bipolar systems.

We study the geometry of tropical extensions of hyperfields, including the ordinary, signed, and complex tropical hyperfields. We introduce the framework of ‘enriched valuations’ as hyperfield homomorphisms to tropical extensions and show that a notable family of them are relatively algebraically closed. Our main results are hyperfield analogues of Kapranov’s theorem and the Fundamental theorem of tropical geometry. Utilizing these theorems, we introduce fine tropical varieties and prove a structure theorem for them in terms of their initial ideals.

This paper delves into the influence of network media on the efficacy of emergency response during natural disasters. Given the frequent occurrence of disasters that pose significant risks to urban areas, effective emergency response mechanisms are paramount. Leveraging the Data Envelopment Analysis (DEA) model, this study assesses disaster response efficiency by analyzing network information. It explores the distinct characteristics of disaster response across different types of natural disasters and their various occurrence stages. To this end, three emblematic disasters are chosen for empirical analysis: the 2021 Zhengzhou heavy rainstorm, the 2022 Super Typhoon Chaba, and the 2022 Luding earthquake. Our findings reveal disparities in response efficiency among these disaster types, with Zhengzhou’s rainstorm response demonstrating the highest efficiency, followed by the Super Typhoon Chaba, and the Luding earthquake yielding the lowest efficiency. Furthermore, this study meticulously discusses the pivotal factors that shape response efficiency, encompassing government decision-making, emergency rescue operations, and social assistance. By pinpointing optimal response strategies tailored to distinct disaster stages, this paper underscores its contribution toward augmenting disaster response efficiency and fostering urban safety and disaster preparedness.

In this article, we investigate the topological structure of large-scale interacting systems on infinite graphs, by constructing a suitable cohomology which we call the uniform cohomology. The central idea for the construction is the introduction of a class of functions called uniform functions. Uniform cohomology provides a new perspective for the identification of macroscopic observables from the microscopic system. As a straightforward application of our theory when the underlying graph has a free action of a group, we prove a certain decomposition theorem for shift-invariant closed uniform forms. This result is a uniform version in a very general setting of the decomposition result for shift-invariant closed $L^2$-forms originally proposed by Varadhan, which has repeatedly played a key role in the proof of the hydrodynamic limits of nongradient large-scale interacting systems. In a subsequent article, we use this result as a key to prove Varadhan’s decomposition theorem for a general class of large-scale interacting systems.

Observers have noted that world politics is replete with shame. Whether they observe this concerning the apologies regarding past atrocities, the felt necessity for revenge after a humiliating defeat, the feelings that populist leaders find antithetical to the greatness of their nation, or the affective responses to the latter's election, shame seems to be ubiquitous. Vital to understanding the particular politics of this emotion is the concept of state shame. However, the origins, divergent effects, and social and moral roles of state shame are left obscure in International Relations (IR) scholarship, making the concept undertheorized and in need of further elaboration. The primary goal of this research is to (re)conceptualize state shame as a narrative on the social position of the state by building on insights developed by IR theory, sociology, and social psychology. Moreover, the article proposes four types of state shame narratives, namely situational shame, narcissistic shame, aggressive shame, and deferential shame, that can separately account for the divergent effects and social and moral roles that the emotion can be attributed with. These four types, and the politics that characterize them, aim to capture and explain lived practices and meanings that state shame can come to hold.

We study the mixing time of the single-site update Markov chain, known as the Glauber dynamics, for generating a random independent set of a tree. Our focus is obtaining optimal convergence results for arbitrary trees. We consider the more general problem of sampling from the Gibbs distribution in the hard-core model where independent sets are weighted by a parameter $\lambda \gt 0$; the special case $\lambda =1$ corresponds to the uniform distribution over all independent sets. Previous work of Martinelli, Sinclair and Weitz (2004) obtained optimal mixing time bounds for the complete $\Delta$-regular tree for all $\lambda$. However, Restrepo, Stefankovic, Vera, Vigoda, and Yang (2014) showed that for sufficiently large $\lambda$ there are bounded-degree trees where optimal mixing does not hold. Recent work of Eppstein and Frishberg (2022) proved a polynomial mixing time bound for the Glauber dynamics for arbitrary trees, and more generally for graphs of bounded tree-width.

We establish an optimal bound on the relaxation time (i.e., inverse spectral gap) of $O(n)$ for the Glauber dynamics for unweighted independent sets on arbitrary trees. We stress that our results hold for arbitrary trees and there is no dependence on the maximum degree $\Delta$. Interestingly, our results extend (far) beyond the uniqueness threshold which is on the order $\lambda =O(1/\Delta )$. Our proof approach is inspired by recent work on spectral independence. In fact, we prove that spectral independence holds with a constant independent of the maximum degree for any tree, but this does not imply mixing for general trees as the optimal mixing results of Chen, Liu, and Vigoda (2021) only apply for bounded-degree graphs. We instead utilize the combinatorial nature of independent sets to directly prove approximate tensorization of variance via a non-trivial inductive proof.

The fixed points of the generalized Ricci flow are the Bismut Ricci flat (BRF) metrics, i.e., a generalized metric (g, H) on a manifold M, where g is a Riemannian metric and H a closed 3-form, such that H is g-harmonic and $\operatorname{Rc}(g)=\tfrac{1}{4} H_g^2$. Given two standard Einstein homogeneous spaces $G_i/K$, where each Gi is a compact simple Lie group and K is a closed subgroup of them holding some extra assumption, we consider $M=G_1\times G_2/\Delta K$. Recently, Lauret and Will proved the existence of a BRF metric on any of these spaces. We proved that this metric is always asymptotically stable for the generalized Ricci flow on M among a subset of G-invariant metrics and, if $G_1=G_2$, then it is globally stable.