Ion homeostasis is a crucial process in plants that is closely linked to the efficiency of nutrient uptake, stress tolerance and overall plant growth and development. Nevertheless, our understanding of the fundamental processes of ion homeostasis is still incomplete and highly fragmented. Especially at the mechanistic level, we are still in the process of dissecting physiological systems to analyse the different parts in isolation. However, modelling approaches have shown that it is not individual transporters but rather transporter networks (homeostats) that control membrane transport and associated homeostatic processes in plant cells. To facilitate access to such theoretical approaches, the modelling of the potassium homeostat is explained here in detail to serve as a blueprint for other homeostats. The unbiased approach provided strong arguments for the abundant existence of electroneutral H+/K+ antiporters in plants.

We give explicit formulas witnessing IP, IP$_{\!n}$, or TP2 in fields with Artin–Schreier extensions. We use them to control p-extensions of mixed characteristic henselian valued fields, allowing us most notably to generalize to the NIP$_{\!n}$ context one way of Anscombe–Jahnke’s classification of NIP henselian valued fields. As a corollary, we obtain that NIP$_{\!n}$ henselian valued fields with NIP residue field are NIP. We also discuss tameness results for NTP2 henselian valued fields.

Drylands provide multiple essential services to human society, and dryland vegetation is one of the foundations of these services. There is a paradox, however, in the vegetation productivity–precipitation relationship in drylands. Although water is the most limiting resource in these systems, a strong relationship between precipitation and productivity does not always occur. Such a paradox affects our understanding of dryland vegetation dynamics and hinders our capacity to predict dryland vegetation responses under future climates. In this perspective, we examine the possible causes of the dryland precipitation–productivity paradox. We argue that the underlying reasons depend on the location and scale of the study. Sometimes multiple factors may interact, resulting in a less significant relationship between vegetation growth and water availability. This means that when we observe a poor correlation between vegetation growth and water availability, there are potentially missing sources of water input or a lack of consideration of other important processes. The paradox could also be related to the inaccurate measurement of vegetation productivity and water availability indicators. Incorporating these complexities into predictive models will help us better understand the complex relationship between water availability and dryland ecosystem processes and improve our ability to predict how these ecosystems will respond to the multiple facets of climate change.

A partition calculation method (PCM) for calculating the diffraction efficiency of multilayer Fresnel zone plate with high aspect ratio is proposed. In contrast to the traditional theory, PCM designs and evaluates Fresnel zone plate (FZP) considering material pairs, all zone widths, thicknesses and X-ray energy more completely. The results obtained through PCM are validated by comparing them with the complex amplitude superposition theory and coupled wave theory numerical results. The PCM satisfies the requirements of the theoretical investigation of FZP with small outermost zone width (drN) and large thickness (t). Combining proper numerical analysis with the experimental conditions will present a great potential to break through the imaging performance of X-ray microscopy.

Structure-switching aptamers have become ubiquitous in several applications, notably in analytical devices such as biosensors, due to their ease of supporting strong signaling. Aside from their ability to bind specifically with their respective target, this class of aptamers also undergoes a conformational rearrangement upon target recognition. While several well-studied and early-developed aptamers (e.g., cocaine, ATP, and thrombin) have been found to have this structure-switching property, the vast majority do not. As a result, it is common to try to engineer aptamers into switches. This proves challenging in part because of the difficulty in obtaining structural and functional information about aptamers. In response, we review various readily available biophysical characterization tools that are capable of assessing structure switching of aptamers. In doing so, we delve into the fundamentals of these different techniques and detail how they have been utilized in characterizing structure-switching aptamers. While each of these biophysical techniques alone has utility, their real power to demonstrate the occurrence of structural change with ligand binding is when multiple techniques are used. We hope that through a deeper understanding of these techniques, researchers will be better able to acquire biophysical information about their aptamer–ligand systems and accelerate the translation of aptamers into biosensors.

This paper proves normalisation theorems for intuitionist and classical negative free logic, without and with the operator for definite descriptions. Rules specific to free logic give rise to new kinds of maximal formulas additional to those familiar from standard intuitionist and classical logic. When is added it must be ensured that reduction procedures involving replacements of parameters by terms do not introduce new maximal formulas of higher degree than the ones removed. The problem is solved by a rule that permits restricting these terms in the rules for $\forall $, $\exists $ and to parameters or constants. A restricted subformula property for deductions in systems without is considered. It is improved upon by an alternative formalisation of free logic building on an idea of Jaśkowski’s. In the classical system the rules for require treatment known from normalisation for classical logic with $\lor $ or $\exists $. The philosophical significance of the results is also indicated.

We propose a method for cutting down a random recursive tree that focuses on its higher-degree vertices. Enumerate the vertices of a random recursive tree of size n according to the decreasing order of their degrees; namely, let $(v^{(i)})_{i=1}^{n}$ be such that $\deg(v^{(1)}) \geq \cdots \geq \deg (v^{(n)})$. The targeted vertex-cutting process is performed by sequentially removing vertices $v^{(1)}, v^{(2)}, \ldots, v^{(n)}$ and keeping only the subtree containing the root after each removal. The algorithm ends when the root is picked to be removed. The total number of steps for this procedure, $K_n$, is upper bounded by $Z_{\geq D}$, which denotes the number of vertices that have degree at least as large as the degree of the root. We prove that $\ln Z_{\geq D}$ grows as $\ln n$ asymptotically and obtain its limiting behavior in probability. Moreover, we obtain that the kth moment of $\ln Z_{\geq D}$ is proportional to $(\!\ln n)^k$. As a consequence, we obtain that the first-order growth of $K_n$ is upper bounded by $n^{1-\ln 2}$, which is substantially smaller than the required number of removals if, instead, the vertices were selected uniformly at random.

Safe vaccines are critical for biosecurity protection, yet adverse events—rightly or wrongly attributed to immunization—potentially cause rapid loss of confidence, reduced vaccine uptake, and resurgence of preventable disease. Effective vaccine safety incident management is essential to provide assessment and lead appropriate actions to ensure vaccination programs are safe and mitigate unwarranted crisis escalation that could damage vaccine programs and the effective control of vaccine preventable disease outbreaks or pandemics. Incident management systems (IMS) are used globally to direct emergency management response, particularly for natural disasters of fire, flood, and storm. Public health is equally an emergency response and can therefore benefit from these command control constructs. While examples of IMS for outbreak response and mass immunization logistics exist, there is little to no information on their use in vaccine safety. We describe Australia’s vaccine safety Alert Advisory Group establishment in Victoria during the COVID-19 pandemic and onward embedding into routine practice, anticipant of new vaccines, and the next biosecurity threat.