Equilibrium Stochastic Delay Processes

Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is available for linear models only. We introduce a class of stochastic delay processes with nonlinear time-local forces and linear time-delayed forces that obey fluctuation theorems and converge to a Boltzmann equilibrium at long times. From the point of view of control theory, such ``equilibrium stochastic delay processes'' are stable and energetically passive, by construction. Computationally, they provide diverse exact constraints on general nonlinear stochastic delay problems and can, in various situations, serve as a starting point for their perturbative analysis. Physically, they admit an interpretation in terms of an underdamped Brownian particle that is either subjected to a time-local force in a non-Markovian thermal bath or to a delayed feedback force in a Markovian thermal bath. We illustrate these properties numerically for a setup familiar from feedback cooling and point out experimental implications.

Analytical calculation of the parameters of light bullets propagating in the tunnel ionization regime

Analytic estimation of the parameters of light bullets formed in the anomalous group dispersion region of transparent dielectrics under conditions of tunneling photoionization was performed. For this purpose, the system of the ordinary differential equations for the laser pulse’s parameters such as amplitude, temporal duration, chirp parameter, temporal delay, frequency shift, radius and curvature were obtained. The stationary solution of this system and conditions of the quasi-stable regime of propagation were found.

Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique

The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt. But it estimates Rt with a significant temporal delay. Here, we propose a method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it. Our signal-processing approach to this problem yields both Rt and a restored it corrected for the “weekend effect” by applying a deconvolution and denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open source and can be run in real time on every country in the world and every US state.

Experimental evidence for delayed post-conflict management behaviour in wild dwarf mongooses

In many species, within-group conflict leads to immediate avoidance of potential aggressors or increases in affiliation, but no studies have investigated delayed post-conflict management behaviour. Here, we experimentally test that possibility using a wild but habituated population of dwarf mongooses (Helogale parvula). First, we used natural and playback-simulated foraging displacements to demonstrate that bystanders take notice of the vocalisations produced during such within-group conflict events but that they do not engage in any immediate post-conflict affiliative behaviour with the protagonists or other bystanders. We then used another playback experiment to assess delayed effects of within-group conflict on grooming interactions: we examined affiliative behaviour at the evening sleeping burrow, 30–60 min after the most recent simulated foraging displacement. Overall, fewer individuals groomed on evenings following an afternoon of simulated conflict, but those that did groomed more than on control evenings. Subordinate bystanders groomed with the simulated aggressor significantly less, and groomed more with one another, on conflict compared to control evenings. Our study provides experimental evidence that dwarf mongooses acoustically obtain information about within-group contests (including protagonist identity), retain that information, and use it to inform conflict-management decisions with a temporal delay.

Optogenetic suppression of the medial septum impairs working memory maintenance

Spatial working memory (SWM) is the ability to encode, maintain, and retrieve spatial information over a temporal gap, and relies on a network of structures including the medial septum (MS), which provides critical input to the hippocampus. Although the role of the MS in SWM is well-established, up until recently, we have been unable to use temporally precise circuit manipulation techniques to examine the specific role of the MS in SWM, particularly to distinguish between encoding, maintenance, and retrieval. Here, we test the hypothesis that the MS supports the maintenance of spatial information over a temporal gap using precisely timed optogenetic suppression delivered during specific portions of three different tasks, two of which rely on SWM and one that does not. In experiment 1, we found that MS optogenetic suppression impaired choice accuracy of a SWM dependent conditional discrimination task. Moreover, this deficit was only observed when MS suppression was delivered during the cue-sampling, but not the cue-retrieval, portion of the trial. There was also no deficit when MS neurons were optogenetically suppressed as rats performed a SWM-independent variant of the task. In experiment 2, we tested whether MS suppression affected choice accuracy on a delayed nonmatch to position (DNMP) task when suppression was limited to the sample, delay, and choice phases of the task. We found that MS suppression delivery during the delay phase of the DNMP task, but not during the sample or choice phases, impaired choice accuracy. Our results collectively suggest that the MS plays an important role in SWM by maintaining task-relevant information over a temporal delay.

Distribution of Responsibility for Climate Change within the Milieu

This article approaches the challenges of the distribution of responsibility for climate change on a local level using the framework of the milieu. It suggests that the framework of the milieu, inspired by Japanese and cross-cultural environmental philosophy, provides pathways to address the four challenges of climate change (global dispersion, fragmentation of agency, institutional inadequacy, temporal delay). The framework of the milieu clarifies the interrelations between the individual, the community, and the local milieu and is open to a conservative view of human communities and an inclusive view of multispecies communities. On this basis, an account of individual responsibility that is anchored in the local milieu and includes a responsibility to collaborate across milieus is developed. It consists of a forward-looking responsibility that balances a degree of contributory responsibility for one’s imprints on the milieu with a degree of capacity-responsibility that varies regarding the individual’s knowledge and powers, and the acceptability of practices within the local milieu.