Mukai’s program in [16] seeks to recover a K3 surface X from any curve C on it by exhibiting it as a Fourier–Mukai partner to a Brill–Noether locus of vector bundles on the curve. In the case X has Picard number one and the curve $C\in |H|$ is primitive, this was confirmed by Feyzbakhsh in [11, 13] for $g\geq 11$ and $g\neq 12$. More recently, Feyzbakhsh has shown in [12] that certain moduli spaces of stable bundles on X are isomorphic to the Brill–Noether locus of curves in $|H|$ if g is sufficiently large. In this paper, we work with irreducible curves in a nonprimitive ample linear system $|mH|$ and prove that Mukai’s program is valid for any irreducible curve when $g\neq 2$, $mg\geq 11$ and $mg\neq 12$. Furthermore, we introduce the destabilising regions to improve Feyzbakhsh’s analysis in [12]. We show that there are hyper-Kähler varieties as Brill–Noether loci of curves in every dimension.

Urinary catheter replacement prior to urinary tract infection assessment, introduced as a quality improvement recommendation in two surgical intensive care units, was associated with (88% and 84%) reduction in catheter-associated urinary tract infections and significant reductions in urine cultures performed.

Since the 1980s, research has linked environmental factors to adult-onset diseases. The DOHaD theory suggests that exposures during development can permanently affect organ function, predisposing individuals to adult diseases. Studies indicate that protein restriction or a high-fat diet (HFD) during this phase impacts adult metabolism since programmed dysfunctions may depend on changes established during puberty, such as the reproductive system. However, there are no studies on the impact of low-protein (LP) or HFD on male testicles during this phase. For this, Male Wistar rats were categorized into three dietary groups: LP (isocaloric low-protein pelletized); HFD; and Control (balanced commercial) until PND 60. This study was approved by the CEUA-UEM. On postnatal day 61, the animals were euthanized for histopathological, sperm count, and oxidative stress assessments in the testis and epididymis. Statistical analyses were conducted following established ethical principles in animal research. The research revealed significant alterations in daily sperm production and transit through the epididymis. Sperm morphology was affected in the experimental groups. Mitochondrial activity increased in the HFD group. Testicular and epididymal histopathology, seminiferous tubule diameter, and germinal epithelium height, as well as the number of Sertoli and Leydig cells, remained unchanged. Stereological analysis revealed tissue remodeling in the epididymis, particularly in the LP group. LP group showed an increase in lipid peroxidation in the oxidative damage test. In conclusion, low-protein and HFD during peripubertal age did not affect postnatal testicular development in rats. However, they impacted sperm quality, potentially affecting fertility and male reproductive system development.

In this article, motivated by the regularity theory of the solutions of doubly nonlinear parabolic partial differential equations, the authors introduce the off-diagonal two-weight version of the parabolic Muckenhoupt class with time lag. Then the authors introduce the uncentered parabolic fractional maximal operator with time lag and characterize its two-weighted boundedness (including the endpoint case) in terms of these weights under an additional mild assumption (which is not necessary for one-weight case). The most novelty of this article exists in that the authors further introduce a new parabolic shaped domain and its corresponding parabolic fractional integral with time lag and, moreover, applying the aforementioned (two-)weighted boundedness of the parabolic fractional maximal operator with time lag, the authors characterize the (two-)weighted boundedness (including the endpoint case) of these parabolic fractional integrals in terms of the off-diagonal (two-weight) parabolic Muckenhoupt class with time lag; as applications, the authors further establish a parabolic weighted Sobolev embedding and a priori estimate for the solution of the heat equation. The key tools to achieve these include the parabolic Calderón–Zygmund-type decomposition, the chaining argument, and the parabolic Welland inequality, which is obtained by making the utmost of the geometrical relation between the parabolic shaped domain and the parabolic rectangle.

We argue that negative references to amicus curiae briefs in high court judgments – instances where a court explicitly signals disagreement with the legal arguments in such briefs – are a significant and understudied feature of judicial reasoning. We theorize that such references may provide courts with a tool for increasing the precision of its case law, fostering its legitimacy, and increasing compliance pressure. Our empirical analysis of the Court of Justice of the European Union indicates that negative references are used both to boost its legitimacy and to specify not only what the law is, but what it is not.

This piece outlines the engagement of the Inter-American Court of Human Rights with the United Nations (UN) Guiding Principles on business and human rights in light of the Advisory Opinion requested by Mexico on the obligations of the firearms industry. It outlines how the Court has relied on the distinction between positive and negative human rights duties, which has led it to constantly find states responsible for omissions (failing to ensure rights) instead of actions (carried out by private actors, including corporations). For the Court, such a distinction translates into the possibility that corporations can violate human rights directly.

Maladaptive daydreaming is a distinct syndrome in which the main symptom is excessive vivid fantasising that causes clinically significant distress and functional impairment in academic, vocational and social domains. Unlike normal daydreaming, maladaptive daydreaming is persistent, compulsive and detrimental to one’s life. It involves detachment from reality in favour of intense emotional engagement with alternative realities and often includes specific features such as psychomotor stereotypies (e.g. pacing in circles, jumping or shaking one’s hands), mouthing dialogues, facial gestures or enacting fantasy events. Comorbidity is common, but existing disorders do not account for the phenomenology of the symptoms. Whereas non-specific therapy is ineffective, targeted treatment seems promising. Thus, we propose that maladaptive daydreaming be considered a formal syndrome in psychiatric taxonomies, positioned within the dissociative disorders category. Maladaptive daydreaming satisfactorily meets criteria for conceptualisation as a psychiatric syndrome, including reliable discrimination from other disorders and solid interrater agreement. It involves significant dissociative aspects, such as disconnection from perception, behaviour and sense of self, and has some commonalities with but is not subsumed under existing dissociative disorders. Formal recognition of maladaptive daydreaming as a dissociative disorder will encourage awareness of a growing problem and spur theoretical, research and clinical developments.

Various minerals have crystallized in centimeter-sized gouges and in adjacent scaly clays of the Main Fault intersecting the Opalinus Clay within the Mont Terri underground rock laboratory (Switzerland). Authigenic illite-type crystals, for instance, formed idiomorphic overgrowths on older detrital mica-type agglomerates in the gouge matrices and in their highly deformed surrounding damage zones. This heterogeneous illite crystallization was induced by local temperature increases due to the friction during faulting and to circulation of hot fluids, more in the highly deformed gouge rims than in the gouge matrices themselves. The aggregation of authigenic illite with detrital counterparts in the size separates made it difficult to do any quantitative distinction, and therefore any direct isotopic age dating. This incomplete separation of the detrital from authigenic illite in size separates of the gouges and the scaly clays, even down to nanometer size, needed a theoretical K-Ar age extrapolation for the authigenic illite fraction at ~8.8±0.9 Ma. This estimated age is based on the K content of a theoretically pure authigenic fraction determined by in situ analysis relative to estimated K contents of the detrital counterparts.

The superposition of the micro-X-ray fluorescence Na and Cl maps visualizes a few veins filled with salts across an examined gouge, showing that fluids flowed through it, as well as through its highly deformed rims, while diffusing discretely into the surrounding matrix. The combined Fe and S micro-X-ray fluorescence maps of the examined materials also showed numerous pyrite agglomerates systematically associated with P, which indicates an occurrence of organic matter related to pyrite alteration. This organic matter induced local reducing conditions that were confirmed by REE spectra in the newly crystallized clay minerals of the fault features, carried by flowing fluids into the gouges. No geochemical argument suggests that the gouges are more or less permeable, at present, than the nearby undeformed Opalinus Clay. However, they were certainly more or less permeable at one point, probably during faulting, as K had to be supplied to explain the illite authigenesis detected in them and, to some extent, in the nearby scaly clays. Such permeability is also demonstrated by the systematic occurrence of salts in the micro-veins throughout the observed gouge and in its highly deformed rims that had to crystallize from fluids flowing during the deformation episode. Clearly, both the shape of the drains in and around the gouges and their systematic infilling by salts exclude technical artifacts claimed sometimes to deny any opening of the gouge volumes.

We are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain and a fine (time-consuming) solver is applied as a corrector in parallel over smaller chunks of the time interval. Moreover, the coarse solver acts on a reduced state variable, which is coupled with the fine state variable through appropriate coupling operators. We first provide a contribution to the convergence analysis of the micro-macro Parareal method for multiscale linear ordinary differential equations. Then, we extend a variant of the micro-macro Parareal algorithm for scalar stochastic differential equations (SDEs) to higher-dimensional SDEs.

Many-valued logics, in general, and real-valued logics, in particular, usually focus on a notion of consequence based on preservation of full truth, typically represented by the value $1$ in the semantics given in the real unit interval $[0,1]$. In a recent paper [Foundations of Reasoning with Uncertainty via Real-valued Logics, Proceedings of the National Academy of Sciences 121(21): e2309905121, 2024], Ronald Fagin, Ryan Riegel, and Alexander Gray have introduced a new paradigm that allows to deal with inferences in propositional real-valued logics based on a rich class of sentences, multi-dimensional sentences, that talk about combinations of any possible truth values of real-valued formulas. They have proved a strong completeness result that allows one to derive exactly what information can be inferred about the combinations of truth values of a collection of formulas given information about the combinations of truth values of a finite number of other collections of formulas. In this paper, we extend that work to the first-order (as well as modal) logic of multi-dimensional sentences. We give a parameterized axiomatic system that covers any reasonable logic and prove a corresponding completeness theorem, first assuming that the structures are defined over a fixed domain, and later for the logics of varying domains. As a by-product, we also obtain a zero-one law for finitely-valued versions of these logics. Since several first-order real-valued logics are known not to have recursive axiomatizations but only infinitary ones, our system is by force akin to infinitary systems.