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Yoshiaki Itoh

Publications and source records attributed to Yoshiaki Itoh.

17 recordsLinked to original sources
arXiv2025

Computational Dating for the Nuzi Cuneiform Archive: The Least Squares Constrained by Family Trees and Synchronisms

We introduce a computational method of dating for an archive in ancient Mesopotamia. We use the name index Nuzi Personal Names (NPN) published in 1943. We made an electronic version of NPN and added the kinships of the two powerful families to NPN to reflect the Nuzi studies after 1943. Nuzi is a town from the 15th - 14th century B.C.E.for a period of some five generations in Arrapha. The cuneiform tablets listed in NPN are for contracts on land transactions, marriage, loans, slavery, etc. In NPN, the kinships and cuneiform tablets (contracts, documents, texts) involved are listed for each person. We reconstruct family trees from the added NPN to formulate the least squares problem with the constraints: a person's father is at least 22.5 years older than the person, contractors were living at the time of the contract, etc. Our results agree with the Assyriological results of M. P. Maidman on the seniority among siblings of a powerful family. Our method could be applied to the other clay tablet archives once we have the name index in the format of NPN.

cs.DL↗
arXiv2025

Paper-Scissors-Stone Model for Interacting Population and its Limit Theorem

This paper treats a random collision model of three species, which is represented by the random time change of three standard Poisson processes. The prey-predator relation in the random collision model looks like paper-scissors-stone game, and the model is called the paper-scissors model. At first, we investigate the stochastic structure of our model. By using stochastic calculus, the model is decomposed into a semi-martingale, and we prove a weak law of large numbers and a central limit theorem. The main purpose of this paper is to obtain an ordinary differential equation from the weak law and a stochastic differential equation from the central limit theorem.

math.PR↗
arXiv2024

Narayana numbers in "explicit sufficient invariants for an interacting particle system ( by Itoh, Mallows, and Shepp)"

We consider an interacting particle system on star graphs. As in the case of the Kdv equation, we have infinitely many invariants ( here, martingale invariants). It enables us to obtain the limiting distribution of the Markov chain. Each of the martingale invariants is a homogeneous polynomial with coefficients of Narayana numbers.The identity for the enumeration of plane unlabeled trees, which gives Narayana numbers, becomes the key identity to obtain the probability of death states by a change of variables.

nlin.SI↗
arXiv2021

Coalescence Model of Rock-Paper-Scissors Particles

The rock-paper-scissors game, commonly played in East Asia, gives a simple model to understand physical, biological, psychological and other problems. The interacting rock-paper-scissors particle system is a point of contact between the kinetic theory of gases by Maxwell and Boltzmann ( collision model) and the coagulation theory by Smoluchowski ( coalescence model). A $2s+1$ types extended rock-paper-scissors collision model naturally introduces a nonlinear integrable system. The time evolution of the $2s+1$ types extended rock-paper-scissors coalescence model is obtained from the logarithmic time change of the nonlinear integrable system. We also discuss the behavior of a discrete rock-paper-scissors coalescence model.

cond-mat.stat-mech↗
arXiv2018

Continuum Cascade Model: Branching Random Walk for Traveling Wave

The food web is a directed graph in which nodes label species and directed links represent the predation between species. The cascade model generates random food webs. The continuum cascade model is a Poisson approximation of the cascade model. The recursion to obtain the probability distribution of the longest chain length generated by the continuum cascade model has the solution with traveling wave. We consider a branching random walk to study the asymptotic probability on the position of wave front.

math.PR↗
arXiv2015

Diffusion on a Hypersphere: Application to the Wright-Fisher model

The eigenfunction expansion by Gegenbauer polynomials for the diffusion on a hypersphere is transformed into the diffusion for the Wright-Fisher model with a particular mutation rate. We use the Ito calculus considering stochastic differential equations. The expansion gives a simple interpretation of the Griffiths eigenfunction expansion for the Wright-Fisher model. Our representation is useful to simulate the Wright-Fisher model as well as Brownian motion on a hypersphere.

math.PR↗
arXiv2014

New results on torus cube packings and tilings

We consider sequential random packing of integral translate of cubes $[0,N]^n$ into the torus $Z^n / 2NZ^n$. Two special cases are of special interest: (i) The case $N=2$ which corresponds to a discrete case of tilings (considered in \cite{cubetiling,book}) (ii) The case $N=\infty$ corresponds to a case of continuous tilings (considered in \cite{combincubepack,book}) Both cases correspond to some special combinatorial structure and we describe here new developments.

math.MG↗
arXiv2013

A binomial splitting process in connection with corner parking problems

A special type of binomial splitting process is studied. Such a process can be used to model a high-dimensional corner parking problem, as well as the depth of random PATRICIA tries (a special class of digital tree data structures). The later also has natural interpretations in terms of distinct values in iid geometric random variables and the occupancy problem in urn models. The corresponding distribution is marked by logarithmic mean and bounded variance, which is oscillating, if the binomial parameter $p$ is not equal to 1/2, and asymptotic to 1 in the unbiased case. Also, the limiting distribution does not exist owing to periodic fluctuations.

math.PR↗
arXiv2013

Logistic Growth for the Nuzi Cuneiform Tablets: Analyzing Family Networks in Ancient Mesopotamia

We reconstruct the year of publication of each cuneiform tablet of the Nuzi society in ancient Mesopotamia. The tablets, are on land transaction, marriage, loan, slavery contracts etc. The number of tablets seem to increase by logistic growth until saturation. It may show the dynamics of concentration of lands or other properties into few powerful families in a period of about twenty years. We reconstruct family trees and social networks of Nuzi and estimate the publication years of cuneiform tablets consistently with the trees and networks, formulating least squares problems with linear inequality constraints.

stat.AP↗
arXiv2012

Continuum Cascade Model of Directed Random Graphs: Traveling Wave Analysis

We study a class of directed random graphs. In these graphs, the interval [0,x] is the vertex set, and from each y\in [0,x], directed links are drawn to points in the interval (y,x] which are chosen uniformly with density one. We analyze the length of the longest directed path starting from the origin. In the large x limit, we employ traveling wave techniques to extract the asymptotic behavior of this quantity. We also study the size of a cascade tree composed of vertices which can be reached via directed paths starting at the origin.

math.PR↗
arXiv2011

Statistical Distribution of Crystallographic Groups for Inorganic Crystal Structure Database

We introduce a method that defines the species (representatives) of inorganic compounds, and studied the statistical distribution of the defined species among space groups (distribution of space groups), by using ICSD (Inorganic Crystal Structure Database). Here we show that the number of formula units in a unit cell gives a natural classification to understand the statistical distribution of crystallographic groups.

stat.AP↗
arXiv2011

Random Sequential Generation of Intervals for the Cascade Model of Food Webs

The cascade model generates a food web at random. In it the species are labeled from 0 to $m$, and arcs are given at random between pairs of the species. For an arc with endpoints $i$ and $j$ ($i<j$), the species $i$ is eaten by the species labeled $j$. The chain length (height), generated at random, models the length of food chain in ecological data. The aim of this note is to introduce the random sequential generation of intervals as a Poisson model which gives naturally an analogous behavior to the cascade model.

nlin.CG↗
arXiv2008

Combinatorial cube packings in cube and torus

We consider sequential random packing of cubes $z+[0,1]^n$ with $z\in \frac{1}{N}\ZZ^n$ into the cube $[0,2]^n$ and the torus $\QuotS{\RR^n}{2\ZZ^n}$ as $N\to\infty$. In the cube case $[0,2]^n$ as $N\to\infty$ the random cube packings thus obtained are reduced to a single cube with probability $1-O(\frac{1}{N})$. In the torus case the situation is different: for $n\leq 2$, sequential random cube packing yields cube tilings, but for $n\geq 3$ with strictly positive probability, one obtains non-extensible cube packings. So, we introduce the notion of combinatorial cube packing, which instead of depending on $N$ depend on some parameters. We use use them to derive an expansion of the packing density in powers of $\frac{1}{N}$. The explicit computation is done in the cube case. In the torus case, the situation is more complicate and we restrict ourselves to the case $N\to\infty$ of strictly positive probability. We prove the following results for torus combinatorial cube packings: We give a general Cartesian product construction. We prove that the number of parameters is at least $\frac{n(n+1)}{2}$ and we conjecture it to be at most $2^n-1$. We prove that cube packings with at least $2^n-3$ cubes are extensible. We find the minimal number of cubes in non-extensible cube packings for $n$ odd and $n\leq 6$.

math.CO↗
arXiv2005

Cube packings, second moment and holes

We consider tilings and packings of $\RR^d$ by integral translates of cubes $[0,2[^d$, which are $4\ZZ^d$-periodic. Such cube packings can be described by cliques of an associated graph, which allow us to classify them in dimension $d\leq 4$. For higher dimension, we use random methods for generating some examples. Such a cube packing is called {\em non-extendible} if we cannot insert a cube in the complement of the packing. In dimension 3, there is a unique non-extendible cube packing with 4 cubes. We prove that $d$-dimensional cube packings with more than $2^d-3$ cubes can be extended to cube tilings. We also give a lower bound on the number $N$ of cubes of non-extendible cube packings. Given such a cube packing and $z\in \ZZ^d$, we denote by $N_z$ the number of cubes inside the $\4t$-cube $z+[0,4[^d$ and call {\em second moment} the average of $N_z^2$. We prove that the regular tiling by cubes has maximal second moment and give a lower bound on the second moment of a cube packing in terms of its density and dimension.

math.CO↗
arXiv2004

Majority Orienting Model for the Oscillation of Market Price

The present paper introduces a majority orienting model in which the dealers' behavior changes based on the influence of the price to show the oscillation of stock price in the stock market. We show the oscillation of the price for the model by applying the van der Pol equation which is a deterministic approximation of our model.

nlin.SI↗
arXiv2001

The Ising Model for Changes in Word Ordering Rule in Natural Language

The order of `noun and adposition' is the important parameter of word ordering rules in the world's languages. The seven parameters, `adverb and verb' and others, have a strong dependence on the `noun and adposition'. Japanese as well as Korean, Tamil and several other languages seem to have a stable structure of word ordering rules, as well as Thai and other languages which have the opposite word ordering rules to Japanese. It seems that each language in the world fluctuates between these two structures like the Ising model for finite lattice.

nlin.AO↗