We study the Cauchy problem for multidimensional scalar conservation laws with bounded initial data and locally Lipschitz continuous flux functions. We focus on the entropy solutions to the Cauchy problem and construct the approximate solutions using a combination of the front tracking and the fractional step methods. Our approach extends previous works by allowing more general initial data, beyond functions of bounded variation. We prove the local stability of the approximate solutions and show that they converge to the unique entropy solution. This provides a simple and effective method for approximating solutions to multidimensional conservation laws.
Unsupervised explainable AI identifies ∼2,000 oligonucleotide-usage zones in the human genome and predicts high-resolution chromosome banding from genome sequences, bridging genomics and cytogenetics. Unsupervised and explainable AI can uncover genomic features beyond human expectations. Oligonucleotides such as penta- and hexanucleotides often function as core binding motifs for regulatory proteins, and their usage provides powerful tools in functional genomics. We applied an unsupervised, explainable AI to their odds-ratio profiles of all 1-Mb euchromatic fragments in the human genome. Clustering using penta- or hexanucleotide odds ratios (1,024 or 4,096 variables) unexpectedly revealed nearly 2,000 distinct zones. CG-containing penta- and hexanucleotides (244 and 1,185 variables) produced comparable ∼2,000 zones, indicating fundamental genomic segmental structures. Human chromosomes exhibit Giemsa-banding patterns comprising 850 bands at prometaphase and ∼2,000 at prophase. Using single-nucleotide coordinates available for the 850 bands, we identified diagnostic oligonucleotides distinguishing Giemsa-negative and Giemsa-positive regions. Computational pseudo-band reconstruction based on these oligonucleotides generated genome segmentations that more closely paralleled the AI-derived ∼2,000 zones than the 850 bands. These findings indicate that AI captures characteristic sequence features of chromosomal bands and can predict high-resolution banding from genome sequences alone, thereby bridging classical cytogenetics and modern AI-based genomics.
It is known that any optimal 1-planar graph has a K6-minor, while those having a K7-minor have been completely characterized. Furthermore, one of the authors showed that for any graph H there exists an optimal 1-planar graph having H as a topological minor. In this paper, we study optimal 1-embedded graphs on general closed surfaces and investigate the minors contained in them. In particular, we prove that for any graph H, every optimal 1-embedded graph on a closed surface F2 whose quadrangular subgraph has sufficiently large representativity has H as a minor. Note that H in our result is not necessarily 1-embeddable on F2.
Wind-farm planning requires practical methods for identifying potential ecological conflicts before detailed project-level surveys. Existing seabird sensitivity assessments are less suitable for species whose breeding distributions shift among years and whose marine use areas are difficult to delineate, because space use depends on colony location and central-place foraging constraints. Here, we present a screening framework for such species, using Little Tern Sternula albifrons in Japan as a case study. The framework integrates three components: (1) MaxEnt-based nesting suitability from 95 occupied 500-m grid cells, (2) energetically constrained foraging accessibility derived from a central-place foraging model parameterised with field observations and prey-energy data, and (3) wind-turbine response quantified from three-dimensional flight tracking. The MaxEnt model identified bare land as the strongest positive predictor of suitable nesting area, highlighting extensive high-potential coastal habitat. The foraging model estimated a maximum one-way foraging distance of 8.92 km from nesting colonies under the median prey-energy scenario, allowing marine use areas to be mapped from suitable nesting sites. Mapped areas overlapped with offshore wind projects under environmental impact assessment, and with government-designated pre-EIA planning areas. Ornithodolite tracking showed clear horizontal turbine avoidance, with significantly fewer approaches at radii of 60-140 m from turbine tower centres and no trajectories recorded within 70 m. Together, these components provide a first-pass spatial screen of potential conflict between offshore wind development and breeding Little Terns, identifying areas requiring detailed site-specific surveys. The framework is intended for early-stage screening and does not estimate collision mortality or population-level consequences.
The anterior cingulate cortex (ACC), crucial for executive function, is frequently impaired in progressive supranuclear palsy (PSP), yet mechanisms underlying this selective vulnerability remain unclear. Given the integration of astrocytes into neural circuits, we hypothesized that astrocyte dysfunction and altered astrocyte–neuron crosstalk contribute to functional abnormalities in the ACC in PSP. To test this hypothesis, we conducted a multimodal analysis integrating SWATH-MS-based proteomics, histopathology, and in vivo magnetic resonance spectroscopy (MRS) in postmortem and living brains of patients with PSP and healthy controls (HCs). The astrocytic markers glial fibrillary acidic protein (GFAP) and aquaporin-4 (AQP4) were significantly elevated in the ACC of patients with PSP compared with those in HCs. Enhanced astrocytic Ca2⁺ signaling through the IP3-Ca2⁺ cascade was suggested in the ACC of patients with PSP, consistent with elevated myo-inositol levels on MRS. Proteomic data revealed reduced expression of pyruvate dehydrogenase complex components (DLD and PDHX) and oxidative phosphorylation-related proteins, including astrocyte-enriched genes such as ETFDH and UQCRC1. MRS also revealed significantly increased levels of lactate and glutamate in the ACC of patients with PSP compared with those in HCs. Notably, myo-inositol, lactate, and glutamate levels were positively correlated, indicating astrocyte-associated metabolic dysfunction. Expression of glutamate–glutamine cycle-related molecules and neuronal markers was negatively correlated with GFAP and AQP4 levels, suggesting that astrocytic dysfunction is associated with alterations in the excitatory/inhibitory balance in the ACC of patients with PSP. These findings demonstrate that multiple aspects of astrocyte–neuron crosstalk, including AQP4-mediated glymphatic clearance, energy metabolism, and neurotransmitter cycling, are altered in the ACC of patients with PSP. Such disruptions may contribute to neuronal dysfunction. Our study highlights astrocyte dysfunction as a central feature of the PSP pathophysiology.
