arXiv subjects

Hiroyuki Miyoshi

Publications and source records attributed to Hiroyuki Miyoshi.

7 recordsLinked to original sources

arXiv2026

Internal geometries regulate the symmetry of defect configurations in cell populations confined to domains with a negative Euler characteristic

Nematic order of confined cell populations plays an important role in determining cell alignment and stable configurations of topological defects, which are related to various biomechanical phenomena. Topological charges (or winding numbers) of topological defects strictly depend on the Euler characteristic of the confining domain, which has typically been non-negative in studies focused on domains without internal obstacles. However, biological tissues often surround two or more internal obstacles or holes, which inherently generate defects with negative charges. To understand the mechanical interaction between cellular tissue and obstacles, it is necessary to elucidate the geometrical effects of obstacles on cell alignment and defects with negative charges. Here, we investigate how cell populations achieve stable defect configurations of two -1/2 defects in a triply connected domain. First, we present experimental observations of C2C12 myoblasts confined by two circular obstacles of varying diameter, demonstrating that two $-1/2$ defects are the most frequent configuration when the obstacles are sufficiently large. Second, to theoretically validate these experimental observations, we perform systematic stability analyses of defect configurations using an explicit expression of cell alignment and numerical minimization of the Frank elastic energy. Our numerical calculations reveal that the most stable configuration shifts continuously from a horizontal, through off-axis, to a vertical configuration as the obstacle size increases. In addition, the experimentally observed defect positions agreed with these theoretical predictions to within 60 $\mu$m. These findings suggest that obstacle sizes control the symmetry of cell alignment, providing insights into how geometric and topological constraints can generate complex force patterns during morphogenesis or organ movements.

physics.bio-ph↗

arXiv2026

Fast computation and convergence analysis of the infinite-product representation of the Schottky--Klein prime function

The Schottky--Klein prime function is a standard tool for boundary-value problems on multiply connected circular domains. Because this function is represented as an infinite product over a Schottky group, numerical evaluation requires truncation to finitely many factors. The standard word-length truncation grows exponentially in cost and becomes inefficient when the boundary circles nearly touch one another or the unit circle. To address this difficulty, we assign to each group element a cross-ratio potential measuring the size of its contribution, and retain only terms below a prescribed threshold. We establish uniform closed-form bounds on the change in this potential when prepending Schottky-group generators, and from these bounds we derive an efficient enumeration algorithm. The resulting relative error decays exponentially with the threshold at a rate determined by the Hausdorff dimension of the limit set of the Schottky group. Numerical experiments demonstrate that the proposed formulation achieves substantial computational speedups over word-length truncation in challenging geometric configurations.

math.NA↗

arXiv2026

Impulse-induced liquid jets from bubbles with arbitrary contact angles

This paper investigates the relationship between the contact angle of a spherical bubble attached to a tube submerged in a container and the jet speed induced by an impulsive acceleration at its base. While it has been well established that bubble geometry strongly influences the ejection speeds of liquid jets, mathematical studies of liquid jets with arbitrary bubble shapes remain limited. In this work, we derive a pressure impulse in the small-cavity limit as a tractable integral of classical Legendre functions. It is shown that the jet speed can be divided into two components: (i) the velocity induced by the hydrostatic pressure impulse distribution created by the curvature of the bubble, and (ii) the velocity induced by the distribution of the submersion of the tube in a container. This decomposition reveals that an optimal bubble curvature emerges only when the tube is submerged: the optimality is absent for non-submerged configurations, where the jet speed increases monotonically with bubble depth. Experiments confirm this non-monotonicity and quantitatively support the predicted shift of the optimal geometry with submersion depth.

physics.flu-dyn↗

arXiv2024

Free energy formulas for confined nematic liquid crystals based on analogies with Kirchhoff-Routh theory in vortex dynamics

Active nematics are influenced by alignment angle singularities called topological defects. The localization of these defects is of major interest for biological applications. The total distortion of alignment angles due to defects is evaluated using Frank free energy, which is one of the criteria used to determine the location and stability of these defects. Previous work used the line integrals of a complex potential associated with the alignments for the energy calculation (Miyazako and Nara, R. Soc. Open Sci., 2022), which has a high computational cost. We propose analytical formulas for the free energy in the presence of multiple topological defects in confined geometries. The formulas derived here are an analogue of Kirchhoff-Routh functions in vortex dynamics. The proposed formulas are explicit with respect to the defect locations and conformal maps, which enables the explicit calculation of the energy extrema. The formulas are applied to calculate the locations of defects in so-called doublets and triplets by solving simple polynomial formulas. A stability analysis is also conducted to detect whether defect pairs with charges $\pm 1/2$ are stable or unstable in triplet regions. Our numerical results are shown to match the experimental results (Ienaga {\em et al.,} Soft Matter, 2023).

physics.flu-dyn↗

arXiv2017

Voice Conversion Using Sequence-to-Sequence Learning of Context Posterior Probabilities

Voice conversion (VC) using sequence-to-sequence learning of context posterior probabilities is proposed. Conventional VC using shared context posterior probabilities predicts target speech parameters from the context posterior probabilities estimated from the source speech parameters. Although conventional VC can be built from non-parallel data, it is difficult to convert speaker individuality such as phonetic property and speaking rate contained in the posterior probabilities because the source posterior probabilities are directly used for predicting target speech parameters. In this work, we assume that the training data partly include parallel speech data and propose sequence-to-sequence learning between the source and target posterior probabilities. The conversion models perform non-linear and variable-length transformation from the source probability sequence to the target one. Further, we propose a joint training algorithm for the modules. In contrast to conventional VC, which separately trains the speech recognition that estimates posterior probabilities and the speech synthesis that predicts target speech parameters, our proposed method jointly trains these modules along with the proposed probability conversion modules. Experimental results demonstrate that our approach outperforms the conventional VC.

cs.SD↗

arXiv2000

Weak $ω$-categories as $ω$-hypergraphs

In this paper, firstly, we introduce a higher-dimensional analogue of hypergraphs, namely $ω$-hypergraphs. This notion is thoroughly flexible because unlike ordinary $ω$-graphs, an n-dimensional edge called an n-cell has many sources and targets. Moreover, cells have polarity, with which pasting of cells is implicitly defined. As examples, we also give some known structures in terms of $ω$-hypergraphs. Then we specify a special type of $ω$-hypergraph, namely directed $ω$-hypergraphs, which are made of cells with direction. Finally, besed on them, we construct our weak $ω$-categories. It is an $ω$-dimensional variant of the weak n-categoreis given by Baez and Dolan. We introduce $ω$-identical, $ω$-invertible and $ω$-universal cells instead of universality and balancedness of Baez-Dolan. The whole process of our definition is in parallel with the way of regarding categories as graphs with composition and identities.

math.CT↗

arXiv1999

Higher dimensional hypercategories

We introduce higher dimensional hypergraphs, which is a generalization of Baez-Dolans's opetopic sets and Hermida-Makkai-Power's multigraphs. This is based on a simple combinatorial structure called shells and the formal composites of pasting diagrams based on the closure of open shells. We give two types of graphical representation of higher dimensional cells which show effectively the relationship of cells of different dimensions. Using the hypergraphs, we define strict hypercategories and illustrate its use by taking Lafont's interaction combinator as an example. We also give a definition of weak $ω$-hypercategories and show that usual category is identified with a special kind of weak hypercategory as an illustration of arguments provided by our framework In the replacement of 9 Aug, an omission of an important condition in the definition of shells is corrected. We are preparing two papers which develop two themes roughly presented in this preprint: (1) Hiroyuki Miyoshi and Toru Tsujishita, Weak $ω$-Categories as $ω$-Hypergraphs, presented at CT99, International Category Theory Meeting Category Theory, July 1999, Coimbra, and (2) Akira Huguchi and Toru Tsujishita, Strict $n$-hypercategories, after completion of which this manuscript will be withdrawn.

math.CT↗