arXiv subjects
Publications and source records attributed to Hiroaki Ito.
We give a concrete construction of a natural extension of $(-β)$-transformation when $β$ is greater than the golden mean. Our construction relies on its Markov diagram and the eigenvectors of the associated countable Markov shifts. Its positive recurrence can be shown by path counting using a special property of the diagram. Our down-to-earth construction elucidates the result of Bruin-Kalle \cite{BruinKalle} by examples.
We study the Reverse algorithm, a multidimensional continued fraction algorithm, which is not unimodular. We show that the Reverse algorithm is ergodic and, by proving that its second Lyapunov exponent is negative, that it is a.e. exponentially convergent. In addition to that, we attach substitutions to this algorithm and study the $S$-adic languages generated by sequences of these substitutions. The negativity of the second Lyapunov exponent implies that almost all of these languages are balanced. By a thorough study of the combinatorics of the substitutions, we are even able to obtain a concrete generic family of balanced languages that is characterized in terms of a simple condition on the underlying sequence of substitutions.
We present a data-driven framework to infer phase-amplitude equations of coupled limit-cycle oscillators directly from waveform measurements. Exploiting the universality of the Stuart-Landau normal form near a supercritical Hopf bifurcation, we reconstruct a near-identity transformation from two independent observables of an isolated oscillator and infer the intrinsic Stuart-Landau parameters. Using this reconstructed transformation, we then estimate linear coupling coefficients from paired measurements. The method accurately recovers parameters for coupled van der Pol oscillators, providing a quantitative benchmark. Applied to a high-dimensional hydrodynamic system of two coupled collapsible-channel oscillators, the inferred Stuart-Landau model captures bistability between in-phase and anti-phase synchronization and reveals that the anti-phase state is destabilized through a Neimark-Sacker bifurcation. Our approach enables quantitative prediction of synchronization transitions involving amplitude dynamics from experimentally accessible waveform data.
Focusing on a two-field Swift-Hohenberg model with linear nonreciprocal interactions, this study investigates how emerging higher-codimension points act as organizing centers for the nonequilibrium phase diagram that features various steady and dynamic phases. Complementing the numerical analysis of the field equations with time simulations and path continuation techniques, we derive a reduced dynamical system corresponding to a one-mode approximation for the critical-wavenumber modes. Furthermore, we derive the normal form equations that are valid in the vicinity of the Takens-Bogdanov bifurcation with O(2)-symmetry, which allows us to draw on corresponding literature results. Comparing results obtained on the different levels of description, we discuss the bifurcation structure relating trivial uniform and inhomogeneous steady states as well as traveling, standing and modulated waves. We also contextualize the relevance of recently highlighted features of the linear mode structure, i.e., of the dispersion relations, termed "critical exceptional points" for the transitions between the nonequilibrium phases.
We execute a numerical simulation on active nematics with particles interacting by an excluded volume effect. The systems with rhomboidal particles and that with elliptical particles are considered in order to investigate the effect of the direct contact of particles. In our simulation, the void regions, where the local number density is almost zero, appear in both systems when the aspect ratio of the particles is high. We focused on the relationship between the void regions and the particle orientation of the bulk. The particle number density, particle orientation, topological defects, and void regions are analyzed for different aspect ratios in both systems. The systems with rhomboidal particles have characteristic void sizes, which increase with an increase in the aspect ratio. In contrast, the distribution of the void-region size in the systems with elliptical particles is broad. The present results suggest that the void size in the systems with rhomboidal particles is determined by the correlation length of the particle orientational field around the void regions, while that might be determined by the system size in the systems with elliptical particles.
We propose a simple mathematical model that describes a pairing-induced motion of active and passive particles in a two-dimensional system, which is motivated by our previous paper [Ishikawa et al., Phys. Rev. E \textbf{106} (2022) 024604]. We assume the following features; the active and passive particles are connected with a linear spring, the active particle is driven in the direction of the current velocity, and the passive particle is repelled from the active particle. A straight motion, a circular motion, and a slalom motion were observed by numerical simulation. Theoretical analysis reproduces the bifurcation between the straight and circular motions depending on the magnitude of self-propulsion.
We investigate the pattern dynamics of the one-dimensional nonreciprocal Swift-Hohenberg model. Characteristic spatiotemporal patterns such as disordered, aligned, swap, chiral-swap, and chiral phases emerge depending on the parameters. We classify the characteristic spatiotemporal patterns obtained in numerical simulation by focusing on the spatiotemporal Fourier spectrum of the order parameters. We derive a reduced dynamical system by using the spatial Fourier series expansion. We analyze the bifurcation structure around the fixed points corresponding to the aligned and chiral phases, and explain the transitions between them. The disordered phase is destabilized either to the aligned phase by the Turing bifurcation or to the chiral phase by the wave bifurcation, while the aligned phase and the chiral phase are connected by the pitchfork bifurcation.
A paraffin droplet containing camphor and oil red O (dye) floating on the water surface shows spontaneous motion and deformation generated by the surface tension gradient around the droplet. We focused on the intermittent motion with a pronounced deformation into a crescent shape observed at specific concentrations of camphor and oil red O. We quantitatively analyzed the time changes in the droplet deformation and investigated the role of the oil red O by measuring the time-dependent paraffin/water interfacial tension with the pendant drop method. The observed effect can be explained by the active role of the oil red O molecules at the paraffin/water interface. The interfacial tension decreases gradually after the interface formation, allowing for the dynamic deformation of the droplet. The combination of the decrease in interfacial tension and the reduction in driving force related to camphor outflow generates intermittent motion with dynamic deformation into a crescent shape.
Learning from label proportions (LLP) is a kind of weakly supervised learning that trains an instance-level classifier from label proportions of bags, which consist of sets of instances without using instance labels. A challenge in LLP arises when the number of instances in a bag (bag size) is numerous, making the traditional LLP methods difficult due to GPU memory limitations. This study aims to develop an LLP method capable of learning from bags with large sizes. In our method, smaller bags (mini-bags) are generated by sampling instances from large-sized bags (original bags), and these mini-bags are used in place of the original bags. However, the proportion of a mini-bag is unknown and differs from that of the original bag, leading to overfitting. To address this issue, we propose a perturbation method for the proportion labels of sampled mini-bags to mitigate overfitting to noisy label proportions. This perturbation is added based on the multivariate hypergeometric distribution, which is statistically modeled. Additionally, loss weighting is implemented to reduce the negative impact of proportions sampled from the tail of the distribution. Experimental results demonstrate that the proportion label perturbation and loss weighting achieve classification accuracy comparable to that obtained without sampling. Our codes are available at https://github.com/stainlessnight/LLP-LargeBags.
In this paper, we address the segmentation of tumor subtypes in whole slide images (WSI) by utilizing incomplete label proportions. Specifically, we utilize `partial' label proportions, which give the proportions among tumor subtypes but do not give the proportion between tumor and non-tumor. Partial label proportions are recorded as the standard diagnostic information by pathologists, and we, therefore, want to use them for realizing the segmentation model that can classify each WSI patch into one of the tumor subtypes or non-tumor. We call this problem ``learning from partial label proportions (LPLP)'' and formulate the problem as a weakly supervised learning problem. Then, we propose an efficient algorithm for this challenging problem by decomposing it into two weakly supervised learning subproblems: multiple instance learning (MIL) and learning from label proportions (LLP). These subproblems are optimized efficiently in the end-to-end manner. The effectiveness of our algorithm is demonstrated through experiments conducted on two WSI datasets.
The PD-L1 rate, the number of PD-L1 positive tumor cells over the total number of all tumor cells, is an important metric for immunotherapy. This metric is recorded as diagnostic information with pathological images. In this paper, we propose a proportion estimation method with a small amount of cell-level annotation and proportion annotation, which can be easily collected. Since the PD-L1 rate is calculated from only `tumor cells' and not using `non-tumor cells', we first detect tumor cells with a detection model. Then, we estimate the PD-L1 proportion by introducing a masking technique to `learning from label proportion.' In addition, we propose a weighted focal proportion loss to address data imbalance problems. Experiments using clinical data demonstrate the effectiveness of our method. Our method achieved the best performance in comparisons.
We investigated self-sustained oscillation in a collapsible channel, in which a part of one rigid wall is replaced by a thin elastic wall, and synchronization phenomena in the two channels connected in parallel. We performed a two-dimensional hydrodynamic simulation in a pair of collapsible channels which merged into a single channel downstream. The stable synchronization modes depended on the distance between the deformable region and the merging point; only an in-phase mode was stable for the large distance, in-phase and antiphase modes were bistable for the middle distance, and again only an in-phase mode was stable for the small distance. An antiphase mode became stable through the subcritical pitchfork bifurcation by decreasing the distance. Further decreasing the distance, the antiphase mode became unstable through the subcritical Neimark-Sacker bifurcation. We also clarified the distance dependences of the amplitude and frequency for each stable synchronization mode.
The Strong Lottery Ticket Hypothesis (SLTH) demonstrates the existence of high-performing subnetworks within a randomly initialized model, discoverable through pruning a convolutional neural network (CNN) without any weight training. A recent study, called Untrained GNNs Tickets (UGT), expanded SLTH from CNNs to shallow graph neural networks (GNNs). However, discrepancies persist when comparing baseline models with learned dense weights. Additionally, there remains an unexplored area in applying SLTH to deeper GNNs, which, despite delivering improved accuracy with additional layers, suffer from excessive memory requirements. To address these challenges, this work utilizes Multicoated Supermasks (M-Sup), a scalar pruning mask method, and implements it in GNNs by proposing a strategy for setting its pruning thresholds adaptively. In the context of deep GNNs, this research uncovers the existence of untrained recurrent networks, which exhibit performance on par with their trained feed-forward counterparts. This paper also introduces the Multi-Stage Folding and Unshared Masks methods to expand the search space in terms of both architecture and parameters. Through the evaluation of various datasets, including the Open Graph Benchmark (OGB), this work establishes a triple-win scenario for SLTH-based GNNs: by achieving high sparsity, competitive performance, and high memory efficiency with up to 98.7\% reduction, it demonstrates suitability for energy-efficient graph processing.
Dynamic lateral transport of lipids, proteins, and self-assembled structures in biomembranes plays crucial roles in diverse cellular processes. In this study, we perform a coarse-grained molecular dynamics simulation on a vesicle composed of a binary mixture of neutral and anionic lipids to investigate the lateral transport of individual lipid molecules and the self-assembled lipid domains upon an applied direct current (DC) electric field. Under the potential force of the electric field, a phase-separated domain rich in the anionic lipids is trapped in the opposite direction of the electric field. The subsequent reversal of the electric field induces the unidirectional domain motion. During the domain motion, the domain size remains constant, but a considerable amount of the anionic lipids is exchanged between the anionic-lipid-rich domain and the surrounding bulk. While the speed of the domain motion (collective lipid motion) shows a significant positive correlation with the electric field strength, the exchange of anionic lipids between the domain and bulk (individual lipid motion) exhibits no clear correlation with the field strength. The mean velocity field of the lipids surrounding the domain displays a two-dimensional (2D) source dipole. We revealed that the balance between the potential force of the applied electric field and the quasi-2D hydrodynamic frictional force well explains the dependence of the domain motions on the electric-field strengths. The present results provide insight into the hierarchical dynamic responses of self-assembled lipid domains to the applied electric field and contribute to controlling the lateral transportation of lipids and membrane inclusions.
We calculate the one-loop correction to the distribution of energy-momentum tensor around a kink in $1+1$ dimensional $ϕ^4$ model. We employ the collective coordinate method to eliminate the zero mode that gives rise to infrared divergence. The ultraviolet divergences are removed by vacuum subtraction and mass renormalization. We obtain an analytic result that is finite and satisfies the momentum conservation. The total energy of the kink obtained from the spatial integral of energy density reproduces the known result. Our result obtained on a finite space has a spatially-uniform term that is inversely proportional to the spatial length.
A density oscillator is a fluid system in which oscillatory flow occurs between different density fluids through the pore connecting them. We investigate the synchronization in coupled density oscillators using two-dimensional hydrodynamic simulation and analyze the stability of the synchronous state based on the phase reduction theory. Our results show that the anti-phase, three-phase, and 2-2 partial-in-phase synchronization modes spontaneously appear as stable states in two, three, and four coupled oscillators, respectively. The phase dynamics of coupled density oscillators is interpreted with their sufficiently large first Fourier components of the phase coupling function.
The superconducting properties and structural parameters, including the Grüneisen parameter (γG), of the BiCh2-based (Ch: S, Se) layered superconductor LaO0.5F0.5BiS2-xSex were investigated. The superconducting transition temperature (Tc) increased with increasing Se concentration (x), and bulk superconductivity was induced by Se substitution. γG exhibited a larger value when x greater than 0.4, where the superconducting properties were improved. These results suggest that the increase of lattice anharmonicity is preferable for superconductivity in LaO0.5F0.5BiS2-xSex. The discussion includes data for related superconductors REO0.5F0.5BiS2 (RE = Pr, Nd), where a positive correlation between γG and Tc is revealed for Se-poor samples. In addition, specific heat analyses suggest the presence of a low-energy optical phonon mode for LaO0.5F0.5BiS2-xSex.
F.~Schweiger introduced the fibred system in \cite{Schweiger-MCF}, to unify and generalize many known continued fraction algorithms. An advantage of a fibred system is that it often provides a systematic construction of absolutely continuous invariant density. In this paper, we define and study the self-duality of fibred systems, a strong symmetry of a given system. We show that explicit algebraic self-duality holds in many systems and presents a curious system with "partial" self-duality.