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A bstract The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas of theoretical physics. While the positive part of the KdV hierarchy is well known, in this paper we consider an affine Lie algebraic construction for its negative part. We show that the original Miura transformation can be extended to a gauge transformation that implies several new types of relations among the negative flows of the KdV and mKdV hierarchies. Contrary to the positive flows, such a “gauge-Miura” correspondence becomes degenerate whereby more than one negative mKdV model is mapped into a single negative KdV model. For instance, the sine-Gordon and another negative mKdV flow are mapped into a single negative KdV flow which inherits solutions of both former models. The gauge-Miura correspondence implies a rich degeneracy regarding solutions of these hierarchies. We obtain similar results for the generalized KdV and mKdV hierachies constructed with the affine Lie algebra s ℓ ̂ r + 1 . In this case the first negative mKdV flow corresponds to an affine Toda field theory and the gauge-Miura correspondence yields its KdV counterpart. In particular, we show explicitly a KdV analog of the Tzitzéica-Bullough-Dodd model. In short, we uncover a rich mathematical structure for the negative flows of integrable hierarchies obtaining novel relations and integrable systems.

The water-soluble extract from vermicompost, also known as vermicompost tea (VT), has attracted interest in sustainable production research due to its potential to increase crop yields. However, information regarding the influence of this bioinput on strawberry cultivation remains limited. This study aimed to evaluate the effects of different VT solution concentrations on the mass fruit, physiology, and fruit quality of the hybrid strawberry cultivar ‘Portola’. The experiment was conducted in a greenhouse, with foliar and substrate applications of VT solutions at varying concentrations (0%, 2%, 4%, 6% and 8%) over 150 days. Evaluations included the chemical composition of the VT, as well as the physiological and agronomic parameters of the strawberry plants, such as gas exchange, biometric data, the physicochemical quality of the fruit and the nutritional composition. Significant differences in gas exchange parameters, particularly intercellular CO2 concentration and stomatal conductance, were observed at the final growth stage. Of the quality and compositional parameters of the strawberries, only the soluble solids/titratable acidity (SS/TA) ratio was affected. The various VT dilutions induced physiological alterations in the strawberry plants, with energy being allocated towards mass fruit at the expense of fruit quality, specifically in terms of the SS/TA ratio.

We set out to develop a simple objective test of functional colour vision based on eye movements made in response to moving patterns. We exploit the finding that while the motion of a colour-defined stimulus can be cancelled by adding a low-contrast luminance-defined stimulus moving in the opposite direction, the “equivalent luminance contrast” required for such cancellation is reduced when colour vision is abnormal. We used a consumer-grade infrared eye-tracker to measure eye movements made in response to coloured patterns drifting at different speeds. An automated analysis of these movements estimated individuals’ red-green equiluminant point and their equivalent luminance contrast. We tested 34 participants: 23 colour vision normal controls, 9 deuteranomalous and 2 protanomalous individuals. We obtained reliable estimates of strength of directed eye movements (i.e. combined optokinetic and voluntary tracking) for stimuli moving at 16 deg/s and could use these data to classify participants’ colour vision status with a sensitivity rate of 90.9% and a specificity rate of 91.3%. We conclude that an objective test of functional colour vision combining a motion-nulling technique with an automated analysis of eye movements can diagnose and assess the severity of protanopia and deuteranopia. The test places minimal demands on patients (who simply view a series of moving patterns for less than 90 s), requires modest operator expertise, and can be run on affordable hardware.

The gauge-Miura correspondence establishes a map between the entire KdV and mKdV hierarchies, including positive and also negative flows, from which new relations besides the standard Miura transformation arise. We use this correspondence to classify solutions of the KdV hierarchy in terms of elementary tau functions of the mKdV hierarchy under both zero and nonzero vacua. We illustrate how interesting nonlinear phenomena can be described analytically from this construction, such as “rogue waves” of a complex KdV system that corresponds to a limit of a vector nonlinear Schrödinger equation.

Congenital hypothyroidism (CH) is a leading preventable cause of neurocognitive impairment. Its incidence appears to be rising in several countries. We analysed 27 years of newborn-screening data (1997–2023) from the largest Chilean screening centre, covering 3,225,216 newborns (51.1% of national births), to characterise temporal trends and potential drivers of CH incidence. Annual CH incidence was modelled with Prais–Winsten regression to correct for first-order autocorrelation; additional models assessed trends in gestational age, sex, biochemical markers, and aetiological subtypes. We identified 1550 CH cases, giving a mean incidence of 4.9 per 10,000 live births and a significant yearly increase of 0.067 per 10,000 (95 % CI 0.037–0.098; p < 0.001). Mild cases (confirmation TSH < 20 mU/L) rose (+0.89 percentage points per year; p = 0.002). The program’s recall was low (0.05%). Over time, screening and diagnostic TSH values declined, total and free T4 concentrations rose, gestational age at diagnosis fell, and a shift from thyroid ectopy toward hypoplasia emerged; no regional differences were detected. The sustained increase in CH incidence, alongside falling TSH thresholds and growing detection of in situ glands, suggests enhanced recognition of milder disease. Ongoing surveillance should integrate environmental, iodine-nutrition, and genetic factors to clarify the causes of this trend.

We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalent Painlevé equations invariant under AN−1(1) symmetry. This formalism identifies rational solutions (as well as special function solutions) with points on orbits of fundamental shift operators of AN−1(1) affine Weyl groups acting on seed configurations defined as first-order polynomial solutions of the underlying dressing chains. This approach clarifies the structure of rational solutions and establishes an explicit and systematic method towards their construction. For the special case of the N=4 dressing chain equations, the method yields all the known rational (and special function) solutions of the Painlevé V equation. The formalism naturally extends to N=6 and beyond as shown in the paper.

The structure of the extended affine Weyl symmetry group of higher Painlevé equations of N periodicity depends on whether N is even or odd. We find that for even N, the symmetry group A^N−1(1) contains the conventional Bäcklund transformations sj,j=1,…,N, the group of automorphisms consisting of cycling permutations but also reflections on a periodic circle of N points, which is a novel feature uncovered in this paper. The presence of reflection automorphisms is connected to the existence of degenerated solutions, and for N=4, we explicitly show how even reflection automorphisms cause degeneracy of a class of rational solutions obtained on the orbit of the translation operators of A^3(1). We obtain the closed expressions for the solutions and their degenerated counterparts in terms of the determinants of the Kummer polynomials.

Background/Objectives: The development of effective oncologic therapies with fewer adverse effects is often limited by the intrinsic and acquired resistance of tumor cells. Hybrid molecules, rationally designed to combine different pharmacophores, represent a promising strategy by providing synergistic effects, dose reduction, and a lower risk of resistance. In this study, the antitumor potential and mechanisms of action of 22 novel hybrid compounds derived from xanthene and pyran scaffolds (SJ022–SJ103) were investigated. The hybrids were initially evaluated through in vitro screening in four breast, three ovarian, and two prostate cancer cell lines, followed by the selection of T-47D, OVCAR-3, and LNCaP cells for detailed assays assessing cytotoxicity, apoptosis, cell cycle distribution, DNA damage, caspase-3/7 activity, morphology, and PI3K/AKT/mTOR pathway modulation. Methods: Cytotoxicity assays were performed in the selected cell lines, while mechanistic studies included apoptosis and cell cycle analysis by flow cytometry, γH2AX detection, Western blotting for PI3K/AKT/mTOR pathway proteins, and 3D spheroid assays. Combinatorial effects with hormone therapies (tamoxifen, fulvestrant, and letrozole) and the AKT inhibitor MK2206 were evaluated. AKT silencing by esiRNA and molecular docking was performed to confirm target engagement. Results: SJ028 demonstrated broad activity across all tested cell lines, whereas SJ064 and SJ078 exhibited higher selectivity. Treatments induced apoptosis, S/G2-M arrest, and DNA damage, accompanied by decreased phospho-AKT levels and stable PI3K and mTOR expression. In 3D models, the hybrids increased caspase-3/7 activity and necrotic core expansion. Co-administration with hormone therapies resulted in synergistic effects in breast and ovarian cancer cells, reducing IC50 values by more than 50% in both parental and resistant models, while combinations with MK2206 were antagonistic across all tumor subtypes. AKT silencing abrogated cytotoxicity, and docking confirmed SJ028 binding to AKT. Conclusions: Xanthene- and pyran-based hybrids—particularly SJ028, SJ064, and SJ078—showed strong antitumor activity through apoptosis induction, cell cycle arrest, and PI3K/AKT pathway modulation. Their preserved efficacy in resistant models and synergistic interactions with hormone therapies contrasted with the antagonism observed with AKT inhibition, highlighting their potential as promising candidates for the treatment of hormone-responsive and -resistant cancers.

Childhood lead exposure through drinking water has long-term effects on cognition and development, and is a significant public health concern. The comprehensive lead testing of public schools entails high expense and time. In prior work, random forest modeling was used successfully to predict the likelihood of lead contamination in the drinking water from schools in the states of California and Massachusetts. In those studies, data from 70% of the schools was used to predict the probability of unsafe water lead levels (WLLs) in the remaining 30%. This study explores how the model predictions degrade, as the training dataset forms a progressively smaller proportion of schools. The size of the training set was varied from 80% to 10% of the total samples in four US states: California, Massachusetts, New York, and New Hampshire. The models were evaluated using the precision-recall area under curve (PR AUC) and area under the receiver operating characteristic curve (ROC AUC). While some states required as few as 10% of the schools to be included in the training set for an acceptable ROC AUC, all four states performed within an acceptable ROC AUC range when at least 50% of the schools were included. The results in New York and New Hampshire were consistent with the prior work that found the most significant predictor in the modeling to be the Euclidean distance to the closest school in the training set demonstrating unsafe WLLs. This study further supports the efficacy of predictive modeling in identifying the schools at a high risk of lead contamination in their drinking water supply, even when the survey data is incomplete on WLLs in all schools.