Search

Nichols algebras are graded Hopf algebra objects in braided tensor categories. They appeared first in a paper by Nichols in 1978 in the search for new examples of Hopf algebras. Rediscovered later several times, they also provide a conceptual explanation of the construction of quantum groups. The aim of the workshop is to review recent developments in the field, initiate collaborations, and discuss new approaches to open problems. [ABSTRACT FROM AUTHOR]

There are confusions about angular momentum propagation in scattering or decay processes involving the transition between particle systems that appear to transform differently under Lorentz transformations. This paper provides an analysis of the transformation properties of the states and interactions for a few typical processes within the standard model of particle physics, and performs explicit calculations showing how angular momentum transfers in these processes. We shall show explicitly (a) how a state with zero angular momentum evolves via interactions mediated by a single vector boson of spin one, and (b) that angular momentum conservation is completely consistent with the calculation in quantum field theory. A discussion is also given about the phenomenological consequences of the theoretical results obtained in this study. [ABSTRACT FROM AUTHOR]

We show that a very general quartic hypersurface in P6k over a field of characteristic different from 2 does not admit a decomposition of the diagonal, hence is not retract rational. This generalizes a result of Nicaise-Ottem, who showed stable irrationality over fields of characteristic zero. To prove our result, we introduce a new cycle-theoretic obstruction that may be seen as an analogue of the motivic obstruction for rationality in characteristic zero, introduced by Nicaise Shinder and Kontsevich-Tschinkel. [ABSTRACT FROM AUTHOR]

The sensation of thirstiness is the desire to drink water. In certain situations, the ingestion of liquid water can be restricted. As a result, thirstiness is not relieved, resulting in an uncomfortable and distressing situation. The present review describes thirstiness and hydration, the food products and beverages that cause thirstiness, and the beverages and food products currently available to quench thirstiness in individuals with restricted access to liquid ingestion. It also discusses how to measure the effectiveness of calming thirstiness. To diminish thirstiness distress, different alternatives to liquids are proposed. Individuals with swallowing disorders are given thickened water, individuals with restricted water ingestion are given ice cubes or ice popsicles of different flavors, and sportspeople are given energy gels. However, current beverage solutions seem not to relieve thirst fully, although some stimuli like iced water, flavors (especially lemon and mint), or acids seem to work better than plain stimuli and could be added to existing products. Therefore, there is still a need to incorporate these strategies into beverage and food formulations and to test their effectiveness. [ABSTRACT FROM AUTHOR]

Objective: To determine the spawning seasonality of two highly targeted jacks (Carangidae; Giant Trevally [known in Hawai'i as ulua aukea] Caranx ignobilis and Bluefin Trevally [known in Hawai'i as 'ōmilu] Caranx melampygus) within Hawai'i through a collaborative effort with local fishers. Methods: By working with volunteer fishers, we collected gonad samples for Giant and Bluefin trevally throughout a 15‐month period on four of the main Hawaiian Islands. Spawning seasonality was assessed using histological gonad samples as well as mean monthly gonadosomatic index (GSI). Result: Fishery involvement proved successful in collecting biological samples needed to understand the spawning seasonality of these species. Participants were able to macroscopically identify when females were spawning versus undeveloped following initial instruction from the researchers. Mature female GSI resulted in similar conclusions as histological analyses. Both species had a spawning season between February and September, with peak spawning occurring from May to July. During the spawning months, a semilunar spawning pattern was observed for Giant Trevally with peak GSI occurring shortly before the full moon. Bluefin Trevally had higher variability, with no distinct lunar periodicity. Conclusion: Training fishers to be a part of the scientific process and collect gonad samples created trust in science and interest in learning more about the biology of their catch. By consistently sharing our progress and results through social media we were able to engage and build trust with the greater fishing community. Impact statementThrough the spawning seasons project, fishers were empowered to contribute to science and be part of the scientific process, which in turn can lead to continuing interest and participation in future management solutions that ensure sustainability. Fishers can use the information learned in this study to practice sustainable fishing by allowing fish to spawn before targeting them. By using science to substantiate traditional management practices based upon observed spawning behaviors, the participants were able to reinforce behaviors that celebrate sustainability within the larger fishing community. [ABSTRACT FROM AUTHOR]

In this paper, the authors study the behavior of the sheaf cohomology functors R ● ind B G − where G is an algebraic group scheme corresponding to a simple classical Lie superalgebra and B is a BBW parabolic subgroup as defined in [GGNW]. We provide a systematic treatment that allows us to study the behavior of these cohomology groups R ● ind B G L f λ where L f λ is an irreducible representation for the detecting subalgebra f. In particular, we prove an analog of Kempf's vanishing theorem and the Bott-Borel-Weil theorem for large weights. [ABSTRACT FROM AUTHOR]

For an integral symmetric matrix κ we construct a new "nonabelian homology localization" of the lattice vertex algebra Lκ on the corresponding loop Grassmannian space 풢κ. We attempt to motivate our construction by presenting related topics in the language of "interaction of particles over algebraic curves". [ABSTRACT FROM AUTHOR]

Let |$Z\to X$| be a closed immersion of smooth affine schemes over a field |$k$|⁠ , and let |$X^h_Z$| denote the henselisation of |$X$| along |$Z$|⁠. We prove that |$E(X^h_Z)\simeq E(Z)$| for every additive presheaf |$E\colon \textbf {SH}(k)^{\textrm {op}}\to \textrm {Ab}$| on the stable motivic homotopy category over |$k$| that is |$l_\varepsilon $| -torsion or |$l$| -torsion, where |$l\in \mathbb Z$| is coprime to |$\operatorname {char} k$|⁠ , and |$l_\varepsilon =\sum _{i=1}^n \langle (-1)^i \rangle $|⁠. More generally, the isomorphism holds for any homotopy invariant |$l_\varepsilon $| -torsion or |$l$| -torsion linear |$\sigma $| -quasi-stable framed additive presheaf on |$\textrm {Sm}_{k}$|⁠. This generalises the result known earlier for local schemes. We prove the above isomorphism by constructing (stable) |${\mathbb {A}}^1$| -homotopies of motivic spaces via algebraic geometry. To achieve this, we replace Quillen's trick with an alternative and more general construction that provides relative curves required in our setting. [ABSTRACT FROM AUTHOR]

Growth rate, longevity, maturity and spawning seasonality were estimated for the endemic Hawaiian hogfish Bodianus albotaeniatus. The sex‐specific von Bertalanffy growth parameters are L∞ = 339 mm fork length (LF) and K = 0.66 year−1 for females and L∞ = 417 mm LF and K = 0.33 year−1 for males. The maximum age is 22 years. Histological gonad analysis and the absence of small and young males indicate a monandric protogynous hermaphrodite. Size and age at maturity for combined sexes are L50 = 238 mm LF and A50 = 1.6 years. [ABSTRACT FROM AUTHOR]

We apply Wildeshaus's theory of motivic intermediate extensions to the motivic decomposition conjecture, formulated by Deninger–Murre and Corti–Hanamura. We first obtain a general motivic decomposition for the Chow motive of an arbitrary smooth projective family |$f:X \rightarrow S$| whose geometric fibers are Tate. Using Voevodsky's motives with rational coefficients, the formula is valid for an arbitrary regular base |$S$|⁠ , without assuming the existence of a base field or even of a prime integer |$\ell $| invertible on |$S$|⁠. This result, and some of Bondarko's ideas, lead us to a generalized formulation of Corti–Hanamura's conjecture. Secondly we establish the existence of the motivic decomposition when |$f:X \rightarrow S$| is a projective quadric bundle over a characteristic |$0$| base, which is either sufficiently general or whose discriminant locus is a normal crossing divisor. This provides a motivic lift of the Bernstein–Beilinson–Deligne decomposition in this setting. [ABSTRACT FROM AUTHOR]

Associated with a reductive algebraic group G and its rational representation (ρ , M) over an algebraically closed filed k , the authors define the enhanced reductive algebraic group G _ := G ⋉ ρ M , which is a product variety G × M and endowed with an enhanced cross product in [5]. If G _ = G L (V) ⋉ η V with the natural representation (η , V) of GL (V) , it is called an enhanced general linear algebraic group. And the authors give a precise classification of finite nilpotent orbits via a finite set of so-called enhanced partitions of n = dim ⁡ V for the enhanced group G _ = GL (V) ⋉ η V in [6, Theorem 3.5]. We will give another way to prove this classification theorem in this paper. Then we focus on the support variety of the Weyl module for G _ = GL (V) ⋉ η V in characteristic p , and obtain that it coinsides with the closure of an enhanced nilpotent orbit under some mild condition. [ABSTRACT FROM AUTHOR]

We generalize Bousfield-Friedlander's Theorem and Hirschhorn's Localization Theorem to settings where the hypotheses are not satisfied at the expense of obtaining semimodel categories instead of model categories. We use such results to answer, in the world of semimodel categories, an open problem posed by May-Ponto about the existence of Bousfield localizations for Hurewicz and mixed type model structures (on spaces and chain complexes). We also provide new applications that were not available before, e.g. stabilization of non-cofibrantly generated model structures or applications to mathematical physics. [ABSTRACT FROM AUTHOR]

Copyright of Cahiers de Topologie et Geometrie Differentielle Categoriques is the property of Andree C. EHRESMANN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We introduce the notion of refined unramified cohomology of algebraic schemes and prove comparison theorems that identify some of these groups with cycle groups. This generalizes to cycles of arbitrary codimension previous results of Bloch–Ogus, Colliot-Thélène–Voisin, Kahn, Voisin, and Ma. We combine our approach with the Bloch–Kato conjecture, proven by Voevodsky, to show that on a smooth complex projective variety, any homologically trivial torsion cycle with trivial Abel–Jacobi invariant has coniveau $1$. This establishes a torsion version of a conjecture of Jannsen originally formulated $\otimes \mathbb {Q}$. We further show that the group of homologically trivial torsion cycles modulo algebraic equivalence has a finite filtration (by coniveau) such that the graded quotients are determined by higher Abel–Jacobi invariants that we construct. This may be seen as a variant for torsion cycles modulo algebraic equivalence of a conjecture of Green. We also prove $\ell$ -adic analogues of these results over any field $k$ which contains all $\ell$ -power roots of unity. [ABSTRACT FROM AUTHOR]

The workshop brought together experts in a rapidly growing field of tensor triangular geometry highlighting applications to and techniques coming from homotopy theory, algebraic geometry, modular representation theory, motivic homotopy theory and noncommutative algebra. [ABSTRACT FROM AUTHOR]

Climate change projections indicate more frequent and severe tropical marine heatwaves (MHWs) and accompanying hypoxia year‐round. However, most studies have focused on peak summer conditions under the assumption that annual maximum temperatures will induce the greatest physiological consequences. This study challenges this idea by characterizing seasonal MHWs (i.e., mean, maximum, and cumulative intensities, durations, heating rates, and mean annual occurrence) and comparing metabolic traits (i.e., standard metabolic rate (SMR), Q10 of SMR, maximum metabolic rate (MMR), aerobic scope, and critical oxygen tension (Pcrit)) of winter‐ and summer‐acclimatized convict tang (Acanthurus triostegus) to the combined effects of MHWs and hypoxia. Fish were exposed to one of six MHW treatments with seasonally varying maximum intensities (winter: 24.5, 26.5, 28.5°C; summer: 28.5, 30.5, 32.5°C), representing past and future MHWs under IPCC projections (i.e., +0, +2, +4°C). Surprisingly, MHW characteristics did not significantly differ between seasons, yet SMR was more sensitive to winter MHWs (mean Q10 = 2.92) than summer MHWs (mean Q10 = 1.81), despite higher absolute summer temperatures. Concurrently, MMR increased similarly among winter +2 and +4°C treatments (i.e., 26.5, 28.5°C) and all summer MHW treatments, suggesting a ceiling for maximal MMR increase. Aerobic scope did not significantly differ between seasons nor among MHW treatments. While mean Pcrit did not significantly vary between seasons, warming of +4°C during winter (i.e., 28.5°C) significantly increased Pcrit relative to the winter control group. Contrary to the idea of increased sensitivity to MHWs during the warmest time of year, our results reveal heightened sensitivity to the deleterious effects of winter MHWs, and that seasonal acclimatization to warmer summer conditions may bolster metabolic resilience to warming and hypoxia. Consequently, physiological sensitivity to MHWs and hypoxia may extend across larger parts of the year than previously expected, emphasizing the importance of evaluating climate change impacts during cooler seasons when essential fitness‐related traits such as reproduction occur in many species. [ABSTRACT FROM AUTHOR]

Victor Snaith was born in Colchester, Essex, on 15 March 1944 and passed away in Bristol on 3 July 2021 at the age of 77. He completed his PhD at the University of Warwick in 1969 under the supervision of Luke Hodgkin. He held faculty positions in Canada, at the University of Western Ontario (1976–88) and McMaster University (1988–98), and became a leading figure in the Canadian mathematical research community during that time. He was named a Fellow of the Royal Society of Canada in 1984, and held the first Britton Professorship at McMaster University. He returned to the United Kingdom in 1998, to professorships at the University of Southampton (1998–2004) and the University of Sheffield (2004–2009) from where he retired in 2009. He was an active member of the Heilbronn Institute from 2006 until the time of his passing. Snaith made significant research contributions in various areas, including the Snaith splitting theorem in stable homotopy theory, the introduction of the Bott periodic form of algebraic K‐theory, and the explicit Brauer induction theorem with its applications in algebraic number theory. He is survived by his wife Carolyn, son Dan, and daughters Anna and Nina. [ABSTRACT FROM AUTHOR]

The workshop Representations of Finite Groups was organised by Olivier Dudas (Marseille), Meinolf Geck (Stuttgart), Radha Kessar (Manchester), and Gabriel Navarro (Valencia). It covered a wide variety of aspects of the representation theory of finite groups and related topics, and showcased several recent breakthrough results. [ABSTRACT FROM AUTHOR]

We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general linear groups GLn, the two-parameter polynomial functors give a new interpretation of (polynomial) representations of the quantum symmetric pair ( U Q , q B (gl n), Uq(gl n)) which specializes to type AIII/AIV quantum symmetric pairs. The coideal subalgebra U Q , q B (gl n) appears in a Schur–Weyl duality with the type B Hecke algebra H Q , q B (d). We endow two-parameter polynomial functors with a cylinder braided structure which we use to construct the two-parameter Schur functors. Our polynomial functors can be precomposed with the quantum polynomial functors of type A producing new examples of action pairs. [ABSTRACT FROM AUTHOR]

The gap between spawning and settlement location of marine fishes, where the larvae occupy an oceanic phase, is a great mystery in both natural history and conservation. Recent genomic approaches provide some resolution, especially in linking parent to offspring with assays of nucleotide polymorphisms. Here, the authors applied this method to the endemic Hawaiian convict tang (Acanthurus triostegus sandvicensis), a surgeonfish with a long pelagic larval stage of c. 54–77 days. They collected 606 adults and 607 juveniles from 23 locations around the island of Oʻahu, Hawaiʻi. Based on 399 single nucleotide polymorphisms, the authors assigned 68 of these juveniles back to a parent (11.2% assignment rate). Each side of the island showed significant population differentiation, with higher levels in the west and north. The west and north sides of the island also had little evidence of recruitment, which may be due to westerly currents in the region or an artefact of uneven sampling. In contrast, the majority of juveniles (94%) sampled along the eastern shore originated on that side of the island, primarily within semi‐enclosed Kāneʻohe Bay. Nearly half of the juveniles assigned to parents were found in the southern part of Kāneʻohe Bay, with local settlement likely facilitated by extended water residence time. Several instances of self‐recruitment, when juveniles return to their natal location, were observed along the eastern and southern shores. Cumulatively, these findings indicate that most dispersal is between adjacent regions on the eastern and southern shores. Regional management efforts for Acanthurus triostegus and possibly other reef fishes will be effective only with collaboration among adjacent coastal communities, consistent with the traditional moku system of native Hawaiian resource management. [ABSTRACT FROM AUTHOR]

We consider finite-dimensional Hopf algebras |$u$| that admit a smooth deformation |$U\to u$| by a Noetherian Hopf algebra |$U$| of finite global dimension. Examples of such Hopf algebras include small quantum groups over the complex numbers, restricted enveloping algebras in finite characteristic, and Drinfeld doubles of height |$1$| group schemes. We provide a means of analyzing (cohomological) support for representations over such |$u$|⁠ , via the singularity categories of the hypersurfaces |$U/(f)$| associated with functions |$f$| on the corresponding parametrization space. We use this hypersurface approach to establish the tensor product property for cohomological support, for the following examples: functions on a finite group scheme, Drinfeld doubles of certain height 1 solvable finite group schemes, bosonized quantum complete intersections, and the small quantum Borel in type |$A$|⁠. [ABSTRACT FROM AUTHOR]

We prove that the Tate conjecture (and its variants) is invariant under homological projective duality. As an application, we obtain a proof, resp. an alternative proof, of the Tate conjecture (and of its variants) in the new case of linear sections of determinantal varieties, resp. in the old cases of Pfaffian cubic fourfolds and complete intersections of quadrics. In addition, we generalize the Tate conjecture (and its variants) from schemes to stacks and prove this generalized conjecture(s) for low-dimensional root stacks and low-dimensional (twisted) orbifolds. [ABSTRACT FROM AUTHOR]

We construct an ungraded version of Beilinson–Ginzburg–Soergel's Koszul duality for Langlands dual flag varieties, inspired by Beilinson's construction of rational motivic cohomology in terms of K$K$‐theory. For this, we introduce and study categories DKS(X)$\hbox{DK}_\mathcal {S}(X)$ of S$\mathcal {S}$‐constructible K$K$‐motivic sheaves on varieties X$X$ with an affine stratification. We show that there is a natural and geometric functor, called Beilinson realisation, from S$\mathcal {S}$‐constructible mixed sheaves DSmix(X)$\hbox{D}^{mix}_\mathcal {S}(X)$ to DKS(X)$\hbox{DK}_\mathcal {S}(X)$. We then show that Koszul duality intertwines the Betti realisation and Beilinson realisation functors and descends to an equivalence of constructible sheaves and constructible K$K$‐motivic sheaves on Langlands dual flag varieties. [ABSTRACT FROM AUTHOR]

We study the interaction between the block decompositions of reduced enveloping algebras in positive characteristic, the Poincaré-Birkhoff-Witt (PBW) filtration, and the nilpotent cone. We provide two natural versions of the PBW filtration on the block subalgebra A λ of the restricted universal enveloping algebra χ () and show these are dual to each other. We also consider a shifted PBW filtration for which we relate the associated graded algebra to the algebra of functions on the Frobenius neighborhood of 0 in the nilpotent cone and the coinvariants algebra corresponding to λ. In the case of = 2 (k) in characteristic p > 2 we determine the associated graded algebras of these filtrations on block subalgebras of 0 ( 2). We also apply this to determine the structure of the adjoint representation of 0 ( 2). [ABSTRACT FROM AUTHOR]

In this paper we determine, for all r$r$ sufficiently large, the irreducible component(s) of maximal dimension of the variety of commuting r$r$‐tuples of nilpotent elements of gln$\mathfrak {gl}_n$. Our main result is that in characteristic ≠2,3$\ne 2,3$, this nilpotent commuting variety has dimension (r+1)⌊n24⌋$(r+1)\lfloor \frac{n^2}{4}\rfloor$ for n⩾4$n\geqslant 4$, r⩾7$r\geqslant 7$. We use this to find the dimension of the (ordinary) r$r$th commuting varieties of gln$\mathfrak {gl}_n$ and sln$\mathfrak {sl}_n$ for the same range of values of r$r$ and n$n$. Our principal motivation is the connection between nilpotent commuting varieties and cohomological complexity of finite group schemes, which we exploit in the last section of the paper to obtain explicit values for complexities of a large family of modules over the r$r$th Frobenius kernel (GLn)(r)$(\operatorname{GL}_n)_{(r)}$. These results indicate an inequality between the complexities of a rational G$G$‐module M$M$ when restricted to G(r)$G_{(r)}$ or to G(Fpr)$G(\mathbb {F}_{p^r})$; we subsequently establish this inequality for every simple algebraic group G$G$ defined over an algebraically closed field of good characteristic, significantly extending the main theorem of Lin and Nakano, Inventiones Mathematicae, 138 (1999), 85–101. [ABSTRACT FROM AUTHOR]

We prove that the stabilization (resp. iterated suspension) functor participates in a derived adjunction comparing pointed spaces with certain (highly homotopy coherent) homotopy coalgebras, in the sense of Blumberg-Riehl, that is a Dwyer-Kan equivalence after restriction to 1-connected spaces, with respect to the associated enrichments. A key ingredient of our proof, of independent interest, is a higher stabilization theorem (resp. higher Freudenthal suspension theorem) for pointed spaces that provides strong estimates for the uniform cartesian-ness of certain cubical diagrams associated to iterating the space level stabilization map (resp. Freudenthal suspension map)—these technical results provide, in particular, new proofs (with strong estimates) of the stabilization and iterated loop-suspension completion results of Carlsson and the subsequent work of Arone-Kankaanrinta, and Bousfield and Hopkins, respectively, for 1-connected spaces; this is the stabilization (resp. Freudenthal suspension) analog of Dundas' higher Hurewicz theorem. [ABSTRACT FROM AUTHOR]

We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal \infty-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories. The result will induce a Dold-Kan correspondence of coalgebras in \infty-categories. Moreover it shows that Shipley's zig-zag of Quillen equivalences provides an explicit symmetric monoidal equivalence of \infty-categories for the stable Dold-Kan correspondence. We study homotopy coherent coalgebras associated to a monoidal model category and we show examples when these coalgebras cannot be rigidified. That is, their \infty-categories are not equivalent to the Dwyer-Kan localizations of strict coalgebras in the usual monoidal model categories of spectra and of connective discrete R-modules. [ABSTRACT FROM AUTHOR]

We show how to use equidimensional algebraic correspondences between complex algebraic varieties to construct pull‐backs and transforms of certain classes of geometric currents. Using this construction we produce explicit formulas at the level of complexes for a regulator map from the higher Chow groups of smooth complex quasi‐projective algebraic varieties to Deligne–Beilinson cohomology with integral coefficients. A distinct aspect of our approach is the use of Suslin's complex n↦ZΔ,eqp(X,n)$n \mapsto \mathcal {Z}^p_{\Delta , \text{eq}}(X,n)$ of equidimensional cycles over Δn$ \Delta ^n$ to compute Bloch's higher Chow groups. We calculate explicit examples involving the Mähler measure of Laurent polynomials. [ABSTRACT FROM AUTHOR]

We introduce an infinite variant of hypersurface support for finite-dimensional, noncommutative complete intersections. We show that hypersurface support defines a support theory for the big singularity category $\operatorname {Sing}(R)$ , and that the support of an object in $\operatorname {Sing}(R)$ vanishes if and only if the object itself vanishes. Our work is inspired by Avramov and Buchweitz' support theory for (commutative) local complete intersections. In the companion piece [27], we employ hypersurface support for infinite-dimensional modules, and the results of the present paper, to classify thick ideals in stable categories for a number of families of finite-dimensional Hopf algebras. [ABSTRACT FROM AUTHOR]

We give an account of the construction of the Bhatt–Morrow–Scholze motivic filtration on topological cyclic homology and related invariants, focusing on the case of equal characteristic p$p$ and the connections to crystalline and de Rham–Witt theory. [ABSTRACT FROM AUTHOR]

Finite tensor categories are, despite their many applications and great interest, notoriously hard to classify. Among them, the semisimple ones (called fusion categories) have been intensively studied. Those with nonintegral dimensions form a remarkable class. Already more than 20 years ago, tilting modules have been proposed as a source of such fusion categories. In this way, the Verlinde categories associated to the pair of a simple complex Lie algebra g and an integer level k have been recovered in a purely algebraic framework-called semisimplification of tensor categories. Recently efforts to understand how to go beyond these examples emerged. This mini-workshop aims at bringing together experts from various branches of representation theory and topological field theory to deepen our understanding of finite tensor categories and to compare new ways to understand semisimplification. [ABSTRACT FROM AUTHOR]

In this paper, we give a survey about L2‐invariants focusing on 3‐manifolds. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study, by using the mathematical tools developed by Chałupnik, Touzé, and Van der Kallen, the effect of the Frobenius twist on |$\operatorname{Ext}$| -group in the category of strict polynomial functors. As an application, we obtain explicit formulas of cohomology of the orthogonal groups and symplectic ones. [ABSTRACT FROM AUTHOR]

We show that several apparently unrelated formulas involving left or right Bousfield localizations in homotopy theory are induced by comparison maps associated with pairs of adjoint functors. Such comparison maps are used in the article to discuss the existence of functorial liftings of homotopical localizations and cellularizations to categories of algebras over monads acting on model categories, with emphasis on the cases of module spectra and algebras over simplicial operads. Some of our results hold for algebras up to homotopy as well; for example, if T is the reduced monad associated with a simplicial operad and ƒ is any map of pointed simplicial sets, then ƒ-localization coincides with Tƒ-localization on spaces underlying homotopy T-algebras, and similarly for cellularizations. [ABSTRACT FROM AUTHOR]

Commutative d-torsion K-theory is a variant of topological K-theory constructed from commuting unitary matrices of order dividing d. Such matrices appear as solutions of linear constraint systems that play a role in the study of quantum contextuality and in applications to operator-theoretic problems motivated by quantum information theory. Using methods from stable homotopy theory, we modify commutative d-torsion K-theory into a cohomology theory that can be used for studying operator solutions of linear constraint systems. This provides an interesting connection between stable homotopy theory and quantum information theory. [ABSTRACT FROM AUTHOR]

Thin-film polymer microelectrode arrays (MEAs) facilitate the high-resolution neural recording with its superior mechanical compliance. However, the densely packed electrodes and interconnects along with the ultra-thin polymeric encapsulation/substrate layers give rise to non-negligible crosstalk, which could result in severe interference in the neural signal recording. Due to the lack of standardized characterization or modeling of crosstalk in neural electrode arrays, to date, crosstalk in polymer MEAs remains poorly understood. In this work, the crosstalk between two adjacent polymer microelectrodes is measured experimentally and modeled using equivalent circuits. Importantly, this study demonstrated a two-well measuring platform and systematically characterized the crosstalk in polymer microelectrodes with true isolation of the victim channel and precise control of its grounding condition. A simple, unified equation from detailed circuit modeling was proposed to calculate the crosstalk in different environments. Finite element analysis (FEA) analysis was conducted further to explore the crosstalk in more aggressively scaled polymer electrode threads. In addition to standardizing neural electrode array crosstalk characterization, this study not only reveals the dependence of the crosstalk in polymer MEAs on a variety of key device parameters but also provides general guidelines for the design of thin polymer MEAs for high-quality neural signal recording. [ABSTRACT FROM AUTHOR]

The purpose of the current study was to assess effects of a hydration management program on the fluid consumption and dehydration parameters (i.e., dehydration risk scores, urine specific gravity, and urine color) of older adults. The study was conducted as a pre-/post-test quasi-experimental study with a control group (intervention group: n = 42, control group: n = 37). The hydration management program applied to the intervention group was completed in 1 week. After the intervention, the knowledge and awareness of the intervention group regarding fluid consumption increased (p = 0.001). The dehydration risk score of the intervention group was significantly lower than that of the control group (p = 0.0001). There was a significant change in average 3-day water intake (p = 0.0001), urine specific gravity value (p = 0.01), and urine color scale score (p = 0.0001) in the intervention group between pre- and post-test. The hydration management program provided a significant improvement in daily water intake and dehydration risk score and increased knowledge and awareness among older adults concerning the importance of fluid intake. [Journal of Gerontological Nursing, 47(9), 40–48.] [ABSTRACT FROM AUTHOR]

We offer short and conceptual re-proofs of some conjectures of Voevodsky's on the slice filtration. The original proofs were due to Marc Levine using the homotopy coniveau tower. Our new proofs use very different methods, namely, recent development in motivic infinite loop space theory together with the birational geometry of Hilbert schemes. [ABSTRACT FROM AUTHOR]

Background: Children 10-20 years old in the US have suboptimal hydration status. Hydration is best assessed using an objective marker, such as urine specific gravity (USG) from a 24-h urine collection. There are limited studies associating hydration from an objective marker with intake assessed from 24-h recalls in children. The objective of the study was to evaluate which foods or beverages are significantly associated with an objective marker of hydration (USG) in a sample of children and adolescents., Methods: Intake was assessed from three 24-h dietary recalls and analyzed using the Nutrition Data System for Research (NDSR). Hydration status was objectively measured using USG via 24-h urine collection. Associations were assessed with logistic regressions., Results: A total of 68 children and adolescents were recruited (50% females). Average overall USG score was 1.020 ± 0.011 uG with 39.7% categorized as dehydrated. After adjusting for age and sex, fruit juice (1.009, 95% CI: 1.001, 1.018) and all beverages (1.001, 95% CI: 1.000, 1.002) were significantly associated with higher odds of being euhydrated., Conclusions: The main predictors of hydration were fruit juice and all beverages intake. Future research should be conducted to explore differences in dietary patterns in a larger, more generalizable sample., Impact: Findings showed that the main predictors of hydration were water and fruit juice intake in children and water intake in adolescents in southern Florida. This is the first study to examine which type of beverages and foods are associated with USG, an objective marker of hydration status, in US children and adolescents. Provides further insight into the use of objective markers to assess hydration status, while providing data to assist epidemiological studies that may have limited resources to examine beverages and foods that contribute to hydration., (© 2023. The Author(s), under exclusive licence to the International Pediatric Research Foundation, Inc.)

Anthrax is a natural foci disease in Inner Mongolia, which poses a severe threat to public health. In this study, the incidence number, rate and constituent ratio were used to describe the epidemiological characteristics of anthrax in the region from 1956–2018. The molecular correlation and genetic characteristics of the strains were investigated using canonical single nucleotide polymorphisms (CanSNP), multiple‐locus variable‐number tandem repeat analysis (MLVA‐15) and whole genome sequencing (WGS). The epidemiological characteristics of anthrax in Inner Mongolia have altered significantly. The incidence of anthrax has decreased annually without vaccination, and the regional distribution of anthrax gradually transferred from central and western regions to the eastern. Moreover, the occupation distribution evolved from multiple early occupations to predominated by farmers and herdsmen. This change is closely related to policy factors and to changes in the means of production and the living habits of the local population. This indicates that reformulating the control and prevention strategies is essential. Both A. Br. Ames and A. Br. 001/002 subgroups were the predominant CanSNP genotypes of Bacillus anthracis in Inner Mongolia. A total of 36 strains constituted six shared MLVA‐15 genotypes, suggesting an epidemiological link between the strains of each shared genotype. The six shared genotypes ([GT1, 9, 11 and 15] and [GT8 and 12]) consisting of 2–7 strains confirmed the occurrence of multiple point outbreaks and cross‐regional transmission caused by multiple common sources of infection. Phylogenetic analysis based on the WGS core genome showed that strains from this study formed an independent clade (C.V.), and they were positioned close to each other, suggesting a common origin. Further comparison analysis should be performed to ascertain the geographic origin of these strains. [ABSTRACT FROM AUTHOR]

The category of framed correspondences Fr*(k) and framed sheaves were invented by Voevodsky in his unpublished notes [ Notes on framed correspondences , 2001, https://www.math.ias.edu/vladimir/publications]. Based on the theory, framed motives are introduced and studied in Garkusha and Panin [J. Amer. Math. Soc. 34 (2021), pp. 261–313]. These are Nisnivich sheaves of S1-spectra and the major computational tool of Garkusha and Panin. The aim of this paper is to show the following result which is essential in proving the main theorem of Garkusha and Panin: given an infinite perfect base field k, any k-smooth scheme X and any n ≥ 1, the map of simplicial pointed Nisnevich sheaves (−,A1//Gm)∧n+ → Tn induces a Nisnevich local level weak equivalence of S1-spectra Mfr(X × (A1//Gm)∧n) → Mfr(X × Tn). Moreover, it is proven that the sequence of S1-spectra Mfr(X ×Tn × Gm) → Mfr(X × Tn × A1) → Mfr(X × Tn+1) is locally a homotopy cofiber sequence in the Nisnevich topology. Another important result of this paper shows that homology of framed motives is computed as linear framed motives in the sense of Garkusha and Panin. This computation is crucial for the whole machinery of framed motives. [ABSTRACT FROM AUTHOR]

Aims and objectives: To investigate the incidence of urinary tract infection and analyse its risk factors among hospitalised patients with spinal cord injury. Background: While the incidence of urinary tract infection varies widely according to the healthcare setting and patients' clinical characteristics, formal reports are limited in quantity. There has been no consensus regarding the risk factors for urinary tract infection. Design: A retrospective descriptive study. Methods: Electronic medical records of 964 subjects between 2010–2017 were reviewed. Urinary tract infection status was examined to identify newly occurred cases. Data included demographic and clinical characteristics, hydration status and length of hospitalisation. The reporting of the study followed the EQUATOR Network's STROBE checklist. Results: Of the sample, 31.7% had urinary tract infection (95% confidence interval: 1.288 to 1.347, p <.001). Sex, completeness of injury, type of bladder emptying, detrusor function and urethral pressure were significant factors affecting urinary tract infection. Patients who were male and those with injury classifications A, B and C had higher risk of urinary tract infection. Patients with urinary or suprapubic indwelling catheters, as well as those with areflexic detrusor combined with normotonic urethral pressure or overactive detrusor combined with normotonic urethral pressure, showed higher risk. Length of hospitalisation in patients with urinary tract infection was greater than that in uninfected patients, which implies the importance of prevention of urinary tract infection. Conclusions: Nurses should carefully assess risk factors to prevent urinary tract infection in patients with spinal cord injury in the acute and sub‐acute stages of the disease trajectory and provide individualised nursing care. Relevance to clinical practice: This study contributes evidence for up‐to‐date clinical nursing practice for the comprehensive management of urinary tract infection. This can lead to improvements in nursing care quality and patient outcomes, including length of hospitalisation. [ABSTRACT FROM AUTHOR]