arXiv subjects

Toru Ohira

Publications and source records attributed to Toru Ohira.

At least 19 recordsLinked to original sources

arXiv2025

Local Ridge Formation and Domain Delimitation in Aggregation-Diffusion Equations

On the carapace of turtles such as Mauremys japonica, raised linear structures called keels form along the midline during embryonic development. This study investigates the underlying mechanisms of keel formation and domain delimitation on the carapace using a theoretical framework based on aggregation-diffusion equations. In this model, outward tissue growth is represented by density-dependent diffusion, while local ridge formation is modeled as distance-dependent aggregation potentially driven by haptotaxis. Analytical and numerical investigations reveal that distance sensitivity in aggregation plays a critical role in shaping ridge patterns and domain boundaries: low sensitivity promotes uniform density, whereas high sensitivity leads to localized high-density regions. The model may reproduce species-specific variations in keel formation, including the emergence of single or multiple keels, and accounts for the consistent appearance of the midline keel across diverse turtle species. Furthermore, the emergence of multiple high-density regions is shown to occur at points where the aggregation flux changes sign. These findings imply that cellular responses to structural gradients may underlie both ridge formation and boundary determination. This study helps possibly providing new insight into morphogenetic patterning on the turtle carapace and highlighting the role of distance-dependent cell aggregation in shaping complex biological structures.

physics.bio-ph↗

arXiv2024

Amplitude Enhancements through rewiring of a non-autonomous delay system

Complex systems, such as biological networks, often exhibit intricate rhythmic behaviors that emerge from simple, small-amplitude dynamics in individual components. This study explores how significant oscillatory signals can arise from a minimal system consisting of just two interacting units, each governed by a simple non-autonomous delay differential equation with a recently obtained exact analytical solution. Contrary to the common assumption that large-scale oscillations require numerous units, our model demonstrates that rewiring two units from self-feedback to cross-feedback can generate robust, finite-amplitude oscillations. With time delay, these interacting units produce strongly amplified oscillatory packets compared to self-feedback configurations. Our findings highlight the potential of this minimalistic mechanism for generating complex rhythmic outputs, with implications for oscillatory signal processing and various other applications.

nlin.AO↗

arXiv2024

Separation out of Entanglement

We investigate the separability properties of quantum states described by an extended Werner density matrix, where the classical component exhibits statistical dependence. By generalizing the classical part to allow correlations, we demonstrate that within a specific parameter range the separable region expands compared to the standard Werner state with an independent classical component. This result suggests that increasing classical correlation can enhance the separability of the overall quantum state, providing new insights into the interplay between classical and quantum correlations.

physics.gen-ph↗

arXiv2024

The Bifurcation Growth Rate for the Robust Pattern Formation in the Reaction-Diffusion System on the Growing Domain

Among living organisms, there are species that change their patterns on their body surface during their growth process and those that maintain their patterns. Theoretically, it has been shown that large-scale species do not form distinct patterns. However, exceptionally, even large-scale species like giraffes form and maintain patterns, and previous studies have shown that the growth plays a crucial role in pattern formation and transition. Here we show how the growth of the domain contributes to Turing bifurcation based on the reaction-diffusion system by applying the Gray-Scott model to the reaction terms, both analytically and numerically, focusing on the phenomenon of pattern formation and maintenance in large species like giraffes, where melanocytes are widely distributed. After analytically identifying the Turing bifurcation related to the growth rate, we numerically verify the pattern formation and maintenance in response to the finite-amplitude perturbations of the blue state specific to the Gray-Scott model near the bifurcation. Furthermore, among pairs of the parameters that form Turing patterns in a reaction-diffusion system on a fixed domain, we determine a pair of the parameters that maximizes the growth rate for the Turing bifurcation in a reaction-diffusion system on a time-dependently growing domain. Specifically, we conduct a numerical analysis to pursue the pair of the parameters in the Turing space that can be the most robust in maintaining the patterns formed on the fixed domain, even as the domain grows. This study may contribute to specifically reaffirming the importance of growth rate in pattern formation and understanding patterns that are easy to maintain even during growth.

physics.bio-ph↗

arXiv2024

The Turing Pattern Transition with the Growing Domain and Metabolic Rate Effects

This study examines how patterns on mammal body surfaces change as they transition from juveniles to adults and with seasonal variations. Our previous research suggests that patterns formed in infancy may fade due to the growing domain effects, typically linked to the body's surface expanding as it grows, but this transition is influenced by various factors. Here, we focus on how heat, which can change with body growth, affects this process. Generally, smaller organisms lose heat more easily due to their higher surface area-to-volume ratio, while larger organisms retain heat more effectively. In fact, thermoregulation during infancy is a crucial factor directly influencing survival. We propose a theoretical model that incorporates both growing domain and metabolic rate effects to explain the mechanisms behind these pattern transitions. The model suggests that Turing patterns formed during juvenile stages disperse in adulthood due to domain growth and changes in metabolic rates affecting reaction rates. Numerical analysis shows that when both growing domain and metabolic rate effects are considered, patterns disperse more rapidly than when only growing domain effects are accounted for. Furthermore, we discuss potential correlations among pattern transitions, growth, and thermoregulation mechanisms, emphasizing the role of metabolic rates in maintaining body temperature. Our findings shed light on the intricate relationship between growth, thermoregulation, and pattern transitions in mammals, possibly useful for further research in this field.

physics.bio-ph↗

arXiv2024

Solving a Delay Differential Equation through Fourier Transform

In this study, we introduce and explore a delay differential equation that lends itself to explicit solutions in the Fourier-transformed space. Through the careful alignment of the initial function, we can construct a highly accurate solution to the equation. These findings open new avenues for understanding delay systems, demonstrating the efficacy of Fourier transform techniques in capturing transient oscillatory dynamics.

nlin.AO↗

arXiv2023

Transient Reviving Dynamics with an Exact Solution for Delay Differential Equations

We present a new approach to examine transient dynamics in a class of non-autonomous delay differential equations. Exact solutions for these equations are obtained using the Lambert W function alongside an appropriately chosen initial function. These solutions provide a reliable approximation for transient dynamics when the initial functions are not markedly distinct. We explore a non-autonomous equation that exhibits a distinctive phenomenon of reviving dynamics as an illustrative example. The derived exact solutions effectively encapsulate the qualitative characteristics of this reviving dynamics over various delay values.

nlin.AO↗

arXiv2023

The Mechanism of Pattern Transitions between Formation and Dispersion

The patterns observed on the body surface of living organisms have traditionally been attributed solely to ecological strategies. However, this study investigates a fascinating phenomenon in Pelodiscus sinensis, where patterns formed on the plastron during embryonic and juvenile stages, which are not externally visible, ultimately disappear in adulthood. This exploration suggests the existence of mechanisms beyond ecological purposes in the formation of body surface patterns in living organisms. While numerous studies have examined pattern formation mechanisms, limited research has focused on the dispersion of preexisting patterns. This study aims to investigate the actual dispersion of patterns on the plastron of P.sinensis.Our research explores the role of osteoblasts expressing the enzyme cyp26b1, retinoic acid, and melanoblasts/melanophores on the ventral part of the plastron. We propose a hypothesis based on a reaction-diffusion system with a time-dependent growing spatial domain. This mathematical framework suggests the occurrence of the dispersion phenomenon. Specifically, we focus on the dilution term within the system under the growing-domain condition. In the context of black-pattern formation, we propose that variations in retinoic acid concentration, indirectly influenced by osteoblasts expressing the enzyme cyp26b1 during the embryonic/juvenile stage, contribute to the observed patterns. This hypothesis is grounded in the concept of prioritized osteogenesis and ossification during the embryonic/juvenile phase. This study expands our understanding of the species' survival strategy, highlighting the significance of bone biology and retinoic acid regulation. The findings have broader implications beyond P.sinensis, contributing to our knowledge of pattern formation and bone development in other organisms.

physics.bio-ph↗

arXiv2023

Delay, resonance and the Lambert W function

We discuss a new type of delay differential equation that exhibits resonating transient oscillations. The power spectrum peak of the dynamical trajectory reaches its maximum height when the delay is suitably tuned. Furthermore, our analysis of the resonant conditions for this equation has revealed a new connection between the solutions of the transcendental trigonometric equation and the Lambert W function. These results offer fresh insights into the nonlinear dynamics induced by delayed feedback.

nlin.AO↗

arXiv2022

Delayed Dynamics with Transient Resonating Oscillations

Recently, we have studied a delay differential equation which has a coefficient that is a linear function of time. The equation has shown the oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. We here propose and study another equation that shows similar transient oscillations. It has an extra exponential gaussian factor on the delayed feedback term. It is shown that this equation is analytically tractable with the use of the Lambert $W$ function. This equation is also studied numerically to confirm some of the properties inferred from the analytical solution. We also have found that the amplitude of transient oscillation changes and goes through a maximum as we increase the value of the delay. In this sense, the proposed equation is one of the simplest dynamical equations that brings out a resonant behavior without any external oscillating inputs.

nlin.AO↗

arXiv2021

Binary Correlation Measurements

We search a simplest and minimal way to determine whether a given quantum system is entangled or separable. For this end, we propose binary correlation measurements in which restricted knowledge of only zero or non-zero correlations is available. We consider the concrete investigation on a pure state for two particles, each particle having two basis states (the 2x2 system). We show that, even with this limited information from the binary correlation measurements, we can still reach the known minimum of three measurements for entanglement detection. We next consider the comparable problem applied to the mixed density matrix. The mixed quantum case appears to require more detailed information, which we illustrate by studying the concrete example of the Werner density matrix.

quant-ph↗

arXiv2020

Zero-Correlation Entanglement

We consider a quantum entangled state for two particles, each particle having two basis states, which includes an entangled pair of spin 1/2 particles. We show that, for any quantum entangled state vectors of such systems, one can always find a pair of observable operators X, Y with zero-correlations = . At the same time, if we consider the analogous classical system of a "classically entangled" (statistically non-independent) pair of random variables taking two values, one can never have zero correlations (zero covariance, E[XY] - E[X]E[Y] = 0). We provide a general proof to illustrate the different nature of entanglements in classical and quantum theories.

quant-ph↗

arXiv2018

On Statistical Independence and No-Correlation for a Pair of Random Variables Taking Two Values: Classical and Quantum

It is well known that when a pair of random variables is statistically independent, it has no-correlation (zero covariance, $E[XY] - E[X]E[Y] = 0$), and that the converse is not true. However, if both of these random variables take only two values, no-correlation entails statistical independence. We provide here a general proof. We subsequently examine whether this equivalence property carries over to quantum mechanical systems. A counter-example is explicitly constructed to show that it does not. This observation provides yet another simple theorem separating classical and quantum theories.

quant-ph↗

arXiv2017

A Neural Network model with Bidirectional Whitening

We present here a new model and algorithm which performs an efficient Natural gradient descent for Multilayer Perceptrons. Natural gradient descent was originally proposed from a point of view of information geometry, and it performs the steepest descent updates on manifolds in a Riemannian space. In particular, we extend an approach taken by the "Whitened neural networks" model. We make the whitening process not only in feed-forward direction as in the original model, but also in the back-propagation phase. Its efficacy is shown by an application of this "Bidirectional whitened neural networks" model to a handwritten character recognition data (MNIST data).

stat.ML↗

arXiv2017

Delayed Random Relays

We present here a system with collection of random walks relaying a signal in one dimension in the presence of delays. We are interested in the time for a signal to travel from one end (start) to the other end (finish) of the lined group of random walkers. The delay is introduced at the point when the signal is transferred from each walker to the next one. It is found that there is an optimal number of walkers for the signal to travel fastest when delays are present. We discuss implications of this model and associated behaviors to physical and biological systems.

physics.gen-ph↗

arXiv2016

Delayed Gambler's Ruin

We present here a new extended model of the gambler's ruin problem by incorporating delays in receiving of rewards and paying of penalties. When there is a difference between two delays, an exact analysis of the ruin probability is difficult. We derive an approximate scheme to find an effective shift in the initial assets of the gambler. Through comparison against computer simulations, this approximation is shown to work for small differences between the two delays.

physics.soc-ph↗

arXiv2014

Chases and Escapes, and Optimization Problems

We propose a new approach for solving combinatorial optimization problem by utilizing the mechanism of chases and escapes, which has a long history in mathematics. In addition to the well-used steepest descent and neighboring search, we perform a chase and escape game on the "landscape" of the cost function. We have created a concrete algorithm for the Traveling Salesman Problem. Our preliminary test indicates a possibility that this new fusion of chases and escapes problem into combinatorial optimization search is fruitful.

cs.AI↗

arXiv2013

Stochastic Modelings of Social Phenomena: Pedestrian Counter Flow and Tournaments

We present here two examples of stochastic modelings of social phenomena. The first topic is pedestrian counter flow. Two groups of model pedestrians move in opposite directions and create congestions. It will be shown that this congestion becomes worst where individuals are given certain stochastic freedom to avoid another in front compared to the case that they are bound to more strict rules. The second example model tournaments. We present here a rather unexpected feature of tournaments that the probability to reach the top position is higher than that of finishing up at lower positions for not only the number one ranked player, but also for a range of top players. This "inversion characteristics" are shown to be observed with simple mathematical model tournaments as well as in the real tournaments.

physics.soc-ph↗