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Fumitaka Yura

Publications and source records attributed to Fumitaka Yura.

10 recordsLinked to original sources
arXiv2026

Mersenne Representation, the Conolly Sequence, and Soliton Profiles over Finite Fields

We study the Mersenne representation of nonnegative integers and its decomposition into the binary and nonbinary sides. The nonbinary values form A055938, and their successor structure gives a direct proof of the relation between A055938 and A080578 that is recorded as conjectural in the OEIS entry for A080578. The binary-side counting function is identified with a shifted Conolly sequence. We then develop the parent map, truncation blocks, truncation remainders, and the Mersenne tau function associated with this representation. The parent map is conjugate to deletion of the lowest digit. Differences of the Mersenne tau rows recover the parent iterates and the counting function, and they give formulas for digit reconstruction and for a diagonal tau defect. Finally, we revisit a known finite-depth one-soliton family of the finite-field BBS. The Mersenne combinatorics is used directly to reconstruct a global integer-valued traveling-wave profile and to prove an integer window-counting theorem. Reduction modulo 3 yields the corresponding finite-field traveling-wave solutions. We also construct an integer-valued traveling-wave tau function whose front values are given by the Mersenne tau rows. The resulting construction shows how the combinatorics of a number representation can enter directly into the reconstruction of solutions of an integrable system.

math.CO↗
arXiv2024

Solitons in 3-State Mealy Automata

Box--ball systems (BBS) are integrable systems with soliton solutions and other good properties. We will search for automata that belong to the same class as BBS automata by introducing some classes of automata through the features of BBS automaton. In particular, we would like to classify 3-state automata over a 2-letter alphabet.

nlin.SI↗
arXiv2022

Pattern formation of elliptic particles by two-body interactions: a model for dynamics of endothelial cells in angiogenesis

A two-dimensional mathematical model for dynamics of endothelial cells in angiogenesis is investigated. Angiogenesis is a morphogenic process in which new blood vessels emerge from an existing vascular network. Recently a one-dimensional discrete dynamical model has been proposed to reproduce elongation, bifurcation, and cell motility such as cell-mixing during angiogenesis on the assumption of a simple two-body interaction between endothelial cells. The present model is its two-dimensional extension, where endothelial cells are represented as the ellipses with the two-body interactions: repulsive interaction due to excluded volume effect, attractive interaction through pseudopodia and rotation by contact. We show that the oblateness of ellipses and the magnitude of contact rotation significantly affect the shape of created vascular patterns and elongation of branches.

nlin.PS↗
arXiv2014

Hankel Determinant Solution for Elliptic Sequence

We show that the Hankel determinants of a generalized Catalan sequence satisfy the equations of the elliptic sequence. As a consequence, the coordinates of the multiples of an arbitrary point on the elliptic curve are expressed by the Hankel determinants.

nlin.SI↗
arXiv2014

Solitons with nested structure over finite fields

We propose a solitonic dynamical system over finite fields that may be regarded as an analogue of the box-ball systems. The one-soliton solutions of the system, which have nested structures similar to fractals, are also proved. The solitonic system in this paper is described by polynomials, which seems to be novel. Furthermore, in spite of such complex internal structures, numerical simulations exhibit stable propagations before and after collisions among multiple solitons with preserving their patterns.

nlin.SI↗
arXiv2005

Theoretical Analyses of Quantum Counting against Decoherence Errors

In this paper, we analyze the quantum counting under the decoherence, which can find the number of solutions satisfying a given oracle. We investigate probability distributions related to the first order term of the error rate on the quantum counting with the depolarizing channel. We also implement two circuits for the quantum counting -- the ascending-order circuit and the descending-order circuit -- by reversing ordering of application of controlled-Grover operations. By theoretical and numerical calculations for probability distributions, we reveal the difference of probability distributions on two circuits in the presence of decoherence and show that the ascending-order circuit is more robust against the decoherence than the descending-order circuit. This property of the robustness is applicable to the phase estimation such as the factoring.

quant-ph↗
arXiv2002

Fundamental Cycle of a Periodic Box-Ball System

We investigate a soliton cellular automaton (Box-Ball system) with periodic boundary conditions. Since the cellular automaton is a deterministic dynamical system that takes only a finite number of states, it will exhibit periodic motion. We determine its fundamental cycle for a given initial state.

nlin.SI↗
arXiv2001

On a Periodic Soliton Cellular Automaton

We propose a box and ball system with a periodic boundary condition (pBBS). The time evolution rule of the pBBS is represented as a Boolean recurrence formula, an inverse ultradiscretization of which is shown to be equivalent with the algorithm of the calculus for the 2Nth root. The relations to the pBBS of the combinatorial R matrix of ${U'}_q(A_N^{(1)})$ are also discussed.

nlin.SI↗