The Gilbert–Steiner problem is a generalization of the Steiner tree problem and specific optimal mass transportation, which allows the use additional (branching) point in a transport plan. A specific feature of the problem is that the cost of transporting a mass m along a segment of length l is equal to l × m^p for a fixed 0 < p < 1 and segments may end at points not belonging to the supports of given measures (branching points). Main result of this paper determines all pairs of (p,d) for which the Gilbert–Steiner problem in ℝ^d admits only branching points of degree 3. Namely, it happens if and only if d = 2 or p < 1/2.
The paper considers the construction of two new orthogonal multiwavelets with supercompact support by using the Fast Bauer's method for matrix spectral factorization on the matrix product filter of the orthogonal CL multiwavelet filter. The new multiwavelets possess orthogonality, symmetry/antisymmetry, and one of them provides better coding and smoothness than other supercompact multiwavelets. The performance of the new multiwavelet filters in subband-based edge detection, grayscale and color image compression and 1D and 2D signal denoising is compared with the GHM, SA4, CL, Integer Haar and Alpert multifilters. The comparative analysis shows that new multiwavelets can provides better human visual measures, SSIM and MS-SSIM in image compression and denoising applications.
Let \partial \,\mathcal{C} ∂ C be the boundary of a compact convex body \mathcal{C} C in \mathbb{R}^n,\, n\geq 2 R n , n ≥ 2 , and O O be an interior point of \mathcal C C . Every straight line l l containing O O cuts from \mathcal{C} C a segment [AB] [ A B ] with end-points on \partial \,\mathcal{C} ∂ C . It is shown that if [AB] [ A B ] is the shortest such segment, then \partial \,\mathcal{C} ∂ C is smooth at the points A A and B B (i.e. at both of them there is only one supporting hyperplane for \mathcal{C} C ) and, something more, the normals to the unique supporting hyperplanes at the points A A and B B intersect at a point belonging to the hyperplane through O O which is orthogonal to [AB] [ A B ] . If \mathcal{C} C is a smooth compact convex body in \mathbb{R}^n,\, n\geq 2 R n , n ≥ 2 , the above property holds also when [AB] [ A B ] is the longest such segment. Similar results are also valid when O O is outside the set \mathcal{C} C . The “local versions” of these results (when the length |AB| ∣ A B ∣ of the segment [AB] [ A B ] is locally maximal or locally minimal) are valid as well. More specific results are obtained in the particular case when \mathcal{C} C is a convex polytope
Maternal exposure to constant light during pregnancy (CLE) is associated with disrupted circadian organization and persistent behavioral alterations in adult offspring. This study examined behavioural performance and 24-hour locomotor activity patterns, as well as hippocampal pCREB and BDNF levels, in adult male and female offspring following prenatal CLE and maternal treatment with piromelatine (pir), which acts as an agonist at melatonin MT1/MT2 and serotonin 5-HT1A/5-HT1D receptors. Pregnant Wistar rats under light-dark regime received vehicle (veh), whereas dams exposed to CLE received vehicle (LL-veh), pir (10 mg/kg), or melatonin. Compared to the LL-veh groups, offspring from pir-treated dams exhibited reduced anxiety- and depression-like responses and improved working memory in both sexes. Individual-subject cosinor analysis revealed heterogeneous 24-hour locomotor rhythmicity within and between groups. No significant treatment-group effect was detected for MESOR or amplitude, and the descriptive acrophase patterns did not provide evidence of treatment-induced restoration or normalization of circadian organization. Maternal pir treatment was associated with higher hippocampal pCREB and BDNF levels in male, but not female offspring relative to the LL-veh group. While the behavioral and molecular differences occurred concurrently in males, these findings do not prove that pCREB/BDNF signaling mediated the behavioral outcomes. Furthermore, the study cannot distinguish the direct developmental effects of maternal pir exposure from those mediated through maternal or offspring circadian rhythm. Therefore, the findings should be interpreted as long-term behavioral and sex-specific molecular differences associated with maternal pir treatment rather than as evidence of circadian-independent antidepressant, anxiolytic, cognitive-enhancing, or BDNF-enhancing actions.
Microplastic (MP) in marine ecosystems poses an increasing risk to the environment and human health. However standardized rapid methods for monitoring large numbers of samples are still lacking. This study validates a semi-automated Nile Red dye (NRD) fluorescence method combined with a two-step KOH/H₂O₂ digestion protocol for MP detection in marine molluscs. Twelve reference materials, including six synthetic polymer types (PE [two size fractions], PP, PA-66, PET, PMMA) and six natural materials (cotton, hemp, cellulose, wool, viscose, olive stone powder), were evaluated before and after digestion. Treatment resulted in 83.2 (± 4.8%) digestion of the natural reference, and reduced fluorescence intensity by 83.9 (± 14.9%). In comparison, the synthetic polymers lost only 13.0 ± 11.6% of their initial mass and 42.7 ± 18.4% of their fluorescence intensity, thus increasing the fluorescence discrimination ratio between synthetic and natural materials from 3-fold to 16.9-fold. The protocol retains the chemical integrity of the synthetic polymers (FTIR Hit Quality Index: 89.7–99.3%), which allows further reliable identification of the particles by FTIR. The protocol was applied to samples of Black Sea invertebrate organisms (M. galloprovincialis and R. venosa, 67 specimens) and achieved near-complete organic matter removal (>99.8%). The MP load was higher in M. galloprovincialis (median: 1.3 MPs g−1 WW; Q1-Q3: 0–3.2; n = 27) than in Rapana venosa (median: 0 MPs g−1 WW; Q1-Q3: 0–0.2; n = 40). This validated workflow provides a reproducible and cost-effective approach for large-scale MP monitoring in marine bioindicator species.
