The Green's function of the discrete Schödinger operator on a finite graph is considered. This setting reproduces Laplacian and signless Laplacian by adjusting the appropriate potentials. We show two ways of the expression for the Green's function by using graph structures. The first way is based on the factor of the graph by subtrees which have uni-self-loops; the second way is based on that by odd unicycle graphs.
Reliable identification of localized reflection events is essential for diagnosing optical fiber links in high-capacity communication networks. Optical correlation-domain reflectometry (OCDR) enables distributed reflectivity measurements with high spatial selectivity; however, closely spaced reflection points can be difficult to distinguish when their reflection peaks overlap because of insufficient effective spatial resolution or surrounding noise. Here, we propose and experimentally demonstrate a polarization-state-control method for identifying closely spaced reflection points in OCDR. The method exploits the polarization dependence of the beat-signal waveform and selectively enhances the contribution from each reflection point by adjusting the polarization state of the reference light. Experiments were performed using two reflection points with separations of 5.0, 3.0, and 1.3 cm in three OCDR configurations: sinusoidal-modulation OCDR with an acousto-optic modulator (AOM), sinusoidal-modulation OCDR without an AOM, and periodic pseudo-random modulation OCDR. Under polarization-scrambled conditions, the two reflection contributions appeared as a single overlapped response in all configurations. In contrast, reference-polarization adjustment produced states that selectively enhanced either reflection point, enabling their contributions to be identified down to the smallest tested separation of 1.3 cm. For the 5.0-cm condition, the apparent 3-dB peak widths ranged from 8.2 to 12.3 cm and exceeded the physical separation, confirming that the identification did not result from conventional peak-width-limited spatial resolution. The proposed method therefore provides an additional degree of freedom for identifying overlapping reflection events, provided that they exhibit sufficiently distinguishable effective polarization responses.
Quantum reinforcement learning has emerged as a framework combining quantum computation with sequential decision-making, and applications to the multi-armed bandit (MAB) problem have been reported. The graph bandit problem extends the MAB setting by introducing spatial constraints, where the accessibility of arms is restricted by graph connectivity, yet quantum approaches to this setting remain limited. In this paper, we formulate best-arm identification in graph bandits and propose a quantum algorithmic framework, termed quantum spatial best-arm identification, which is applicable to general graph structures. This framework uses quantum walks to encode superpositions over graph-constrained actions, thereby extending amplitude amplification and generalizing the quantum BAI algorithm via Szegedy’s walk framework. We focus our theoretical analysis on complete and bipartite graphs, deriving the maximal success probability of identifying the best arm and the time step at which it is achieved. Our results clarify how quantum walk-based search can be adapted to structurally constrained decision problems and provide a foundation for quantum best-arm identification in graph-structured environments.
Aquatic fungi play an important role in the material cycling, yet the factors structuring the spatial distribution of aquatic fungal communities remain poorly understood. In this study, we investigated fungal community composition across 50 reservoirs in Japan using DNA metabarcoding. Chytridiomycota (chytrids) dominated fungal communities in many reservoirs and constituted a core component of fungal assemblage. Notably, diatom-parasitic taxa were detected in all reservoirs, indicating their ubiquitous occurrence. In contrast, rare and transient components were mainly composed of Dikarya (Ascomycota and Basidiomycota), likely influenced by stochastic processes, such as episodic inputs from terrestrial habitats. Variation partitioning showed that environmental, spatial, and host-related factors each explained only a small proportion of variation in both the total fungal community and chytrids, with spatial effects being slightly stronger for total fungi, whereas environmental and host-related factors contributed relatively more to chytrid communities. Our results indicate reservoir fungal communities are characterized by a ubiquitous chytrid core and substantial unexplained variation reflecting stochastic and within-lake processes.
Tunnel fires pose serious risks to public safety and lead to significant social and economic losses. A key factor in developing effective fire safety and evacuation strategies is understanding the temperature distribution of fire-induced thermal airflow, which influences smoke movement and tenability conditions. This study proposes a unified function to represent the vertical temperature distribution of fire-induced flow from the ceiling to the floor in the tranquil flow region in tunnels with rectangular cross-sections, under naturally ventilated conditions and with no longitudinal gradient. The function parameters are normalized with respect to the tunnel aspect ratio and expressed as functions of distance from the fire source, incorporating both geometric and thermal effects. The proposed function accurately captures the spatial variation of vertical temperature distributions and is applicable to tunnels with various aspect ratios and heat release rates. It also enables reliable estimation of smoke layer thickness, producing values consistent with experimental data. Comparative analyses using small- and full-scale tunnel experimental data, as well as full-scale tunnel numerical simulation data, confirm that the proposed function reasonably captures the vertical temperature distribution from the ceiling to the mid-height of the tunnel, while also naturally representing the distribution from mid-height to the floor, provided that it is applied under conditions where the Froude number is less than 0.9.
