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We investigate the role played by curve singularity germs in the enumeration of inflection points in families of curves acquiring singular members. Let

Do demographic shifts in the racial composition of the United States promote positive changes in the nation’s racial dynamics? Change in response to the nation’s growing diversity is likely, but its direction and scope are less clear. This review integrates emerging social-scientific research that examines how Americans are responding to the projected changes in the racial/ethnic demographics of the United States. Specifically, we review recent empirical research that examines how exposure to information that the United States is becoming a “majority-minority” nation affects racial attitudes and several political outcomes (e.g., ideology, policy preferences), and the psychological mechanisms that give rise to those attitudes. We focus primarily on the reactions of members of the current dominant racial group (i.e., white Americans). We then consider important implications of these findings and propose essential questions for future research.

We present a functorial method to define ramification groups, identifying them as inertia groups of an induced action on composite jet algebras. This framework lays the foundation for defining higher ramification groups for actions involving group schemes. To achieve this, we introduce Taylor maps within the category of commutative unitary rings at prime ideals of an$$R$$R -algebra and compute their kernels for algebras of finite type over a field with separably generated residue fields.

For a prime p and a smooth proper p-adic formal scheme X over OK​ where K is a p-adic field, we study a series of conditions (Crs​), s≥0 that partially control the GK​‑action on the image of the associated Breuil–Kisin prismatic cohomologyRΓ△△​(X/S) inside the Ainf​-prismatic cohomologyRΓ△△​(XAinf​​/Ainf​). The condition (Cr0​) is a crystallinity criterion for a Breuil–Kisin–Fargues GK​-module of Gee and Liu, and leads to a proof of crystallinity of Heˊti​(Xη​​,Qp​) that avoids the crystalline comparison. Using the higher conditions (Crs​), we are able to adapt the strategy of Caruso and Liu to establish ramification bounds for the mod p representations Heˊti​(Xη​​,Z/pZ), for arbitrarily large e and i. This extends and/or improves existing bounds in various situations.

We define a motivic conductor for any presheaf with transfers F using the categorical framework developed for the theory of motives with modulus by Kahn, Miyazaki, Saito and Yamazaki. If F is a reciprocity sheaf, this conductor yields an increasing and exhaustive filtration on $F(L)$ , where L is any henselian discrete valuation field of geometric type over the perfect ground field. We show that if F is a smooth group scheme, then the motivic conductor extends the Rosenlicht–Serre conductor; if F assigns to X the group of finite characters on the abelianised étale fundamental group of X, then the motivic conductor agrees with the Artin conductor defined by Kato and Matsuda; and if F assigns to X the group of integrable rank $1$ connections (in characteristic $0$ ), then it agrees with the irregularity. We also show that this machinery gives rise to a conductor for torsors under finite flat group schemes over the base field, which we believe to be new. We introduce a general notion of conductors on presheaves with transfers and show that on a reciprocity sheaf, the motivic conductor is minimal and any conductor which is defined only for henselian discrete valuation fields of geometric type with perfect residue field can be uniquely extended to all such fields without any restriction on the residue field. For example, the Kato–Matsuda Artin conductor is characterised as the canonical extension of the classical Artin conductor defined in the case of a perfect residue field.

John Rognes developed a notion of Galois extension of commutative ring spectra, and this includes a criterion for identifying an extension as unramified. Ramification for commutative ring spectra can be detected by relative topological Hochschild homology and by topological André–Quillen homology. In the classical algebraic context, it is important to distinguish between tame and wild ramification. Noether’s theorem characterizes tame ramification in terms of a normal basis, and tame ramification can also be detected via the surjectivity of the trace map. For commutative ring spectra, we suggest to study the Tate construction as a suitable analog. It tells us at which integral primes there is tame or wild ramification, and we determine its homotopy type in examples in the context of topological K-theory and topological modular forms.

We prove that a formula for the ‘pluricanonical’ double ramification cycle proposed by Janda, Pandharipande, Pixton, Zvonkine, and the second-named author is in fact the class of a cycle constructed geometrically by the first-named author. Our proof proceeds by a detailed explicit analysis of the deformation theory of the double ramification cycle, both to first and to higher order.

COVID-19 had major negative consequences globally for travel for visits to friends and relatives (VFR), which is an under-researched segment of tourism. This paper responds to the need for extended research on VFR travel by examining the impacts of COVID-19 on the VFR sector and its spatial imprint in South Africa. VFR travel sector was second only to business travel in terms of the negative impacts of COVID-19 restrictions imposed in South Africa. An uneven geography is observed of the impact of COVID-19 on VFR travel mobilities. Using data on VFR trips and bednights the analysis discloses the greatest absolute declines in VFR travel occurred in South Africa’s major metropolitan areas. By contrast, in terms of the relative decline and local impacts for destinations of the COVID-19 hollowing out of VFR travel a different pattern emerges. The worst affected spaces were remote, mainly rural localities which are in South Africa’s poorest and most economically distressed areas.

As the digital environment progresses, the complexities of cyber threats also advance, encompassing both hostile cyberattacks and sophisticated cyber espionage. In the face of these difficulties, cooperative endeavours between state and non-state actors have attracted considerable interest as crucial elements in improving global cyber resilience. This study examines cybersecurity governance’s evolving dynamics, specifically exploring non-state actors’ roles and their effects on global security. This highlights the increasing dangers presented by supply chain attacks, advanced persistent threats, ransomware, and vulnerabilities on the Internet of Things. Furthermore, it explores how non-state actors, such as terrorist organisations and armed groups, increasingly utilise cyberspace for strategic objectives. This issue can pose a challenge to conventional state-focused approaches to security management. Moreover, the research examines the crucial influence of informal governance processes on forming international cybersecurity regulations. The study emphasises the need for increased cooperation between governmental and non-governmental entities to create robust and flexible cybersecurity measures. This statement urges policymakers, security experts, and researchers to thoroughly examine the complex relationship between geopolitics, informal governance systems, and growing cyber threats to strengthen global digital resilience.

Extreme climatic events that are expected under global warming expose forest ecosystems to drought stress, which may affect the growth and productivity. We assessed intra-annual growth responses of trees to soil water content in species belonging to different functional groups of tree-ring porosity. We pose the hypothesis that species with contrasting carbon allocation strategies, which emerge from different relationships between wood traits and canopy architecture, display divergent growth responses to drought. We selected two diffuse-porous species ( Acer saccharum and Betula alleghaniensis ) and two ring-porous species ( Quercus rubra and Fraxinus americana ) from the mixed forest of Quebec (Canada). We measured anatomical wood traits and canopy architecture in eight individuals per species and assessed tree growth sensitivity to water balance during 2008–2017 using the standardized precipitation evapotranspiration index (SPEI). Stem elongation in diffuse-porous species mainly depended upon the total number of ramifications and hydraulic diameter of the tree-ring vessels. In ring-porous species, stem elongation mainly depended upon the productivity of the current year, i.e., number of vessels and basal area increment. Diffuse-porous and ring-porous species had similar responses to soil water balance. The effect of soil water balance on tree growth changed during the growing season. In April, decreasing soil temperature linked to wet conditions could explain the negative relationship between SPEI and tree growth. In late spring, greater water availability affected carbon partitioning, by promoting the formation of larger xylem vessels in both functional groups. Results suggest that timings and duration of drought events affect meristem growth and carbon allocation in both functional groups. Drought induces the formation of fewer xylem vessels in ring-porous species, and smaller xylem vessels in diffuse-porous species, the latter being also prone to a decline in stem elongation due to a reduced number of ramifications. Indeed, stem elongation of diffuse-porous species is influenced by environmental conditions of the previous year, which determine the total number of ramifications during the current year. Drought responses in different functional groups are thus characterized by different drivers, express contrasting levels of resistance or resilience, but finally result in an overall similar loss of productivity.