Papers by Yoshihiro Mizoguchi
Bulletin of informatics and cybernetics, Mar 1, 1985
We construct a powerset monad, a filter monad and a primefilter monad in the category M-Set of se... more We construct a powerset monad, a filter monad and a primefilter monad in the category M-Set of sets with Mactions. To investigate the categories of algebras of these monads in M-Set, we consider the category of complete semilattices (resp. continuous lattices, compact Hausd orff spaces) with Mactions. We show that if M is a group, this category is isomorphic to the category of algebras of the powerset monad (resp. filter monad, primefilter monad) in M-Set.

arXiv (Cornell University), Mar 14, 2016
The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find ... more The Wang tiling is a classical problem in combinatorics. A major theoretical question is to find a (small) set of tiles which tiles the plane only aperiodically. In this case, resulting tilings are rather restrictive. On the other hand, Wang tiles are used as a tool to generate textures and patterns in computer graphics. In these applications, a set of tiles is normally chosen so that it tiles the plane or its sub-regions easily in many different ways. With computer graphics applications in mind, we introduce a class of such tileset, which we call sequentially permissive tilesets, and consider tiling problems with constrained boundary. We apply our methodology to a special set of Wang tiles, called Brick Wang tiles, introduced by Derouet-Jourdan et al. in 2015 to model wall patterns. We generalise their result by providing a linear algorithm to decide and solve the tiling problem for arbitrary planar regions with holes.
arXiv (Cornell University), Dec 11, 2003
In this paper, in order to investigate natural transformations from discrete CA to QCA, we introd... more In this paper, in order to investigate natural transformations from discrete CA to QCA, we introduce a new formulation of finite cyclic QCA and generalized notion of partitioned QCA. According to the formulations, we demonstrate the condition of local transition functions, which induce a global transition of well-formed QCA. Following the results, extending a natural correspondence of classical cells and quantum cells to the correspondence of classical CA and QCA, we have the condition of classical CA such that CA generated by quantization of its cells is well-formed QCA. Finally we report some results of computer simulations of quantization of classical CA.

arXiv (Cornell University), Oct 26, 2012
In the first part of this paper, we survey results that are associated with three types of Laplac... more In the first part of this paper, we survey results that are associated with three types of Laplacian matrices:difference, normalized, and signless. We derive eigenvalue and eigenvector formulaes for paths and cycles using circulant matrices and present an alternative proof for finding eigenvalues of the adjacency matrix of paths and cycles using Chebyshev polynomials. Even though each results is separately well known, we unite them, and provide uniform proofs in a simple manner. The main objective of this study is to solve the problem of finding graphs, on which spectral clustering methods and normalized cuts produce different partitions. First, we derive a formula for a minimum normalized cut for graph classes such as paths, cycles, complete graphs, double-trees, cycle cross paths, and some complex graphs like lollipop graph LP n,m , roach type graph R n,k , and weighted path P n,k . Next, we provide characteristic polynomials of the normalized Laplacian matrices L(P n,k ) and L(R n,k ). Then, we present counter example graphs based on R n,k , on which spectral methods and normalized cuts produce different clusters.
Bulletin of informatics and cybernetics, Mar 1, 1992
The main objective of this paper is to solve the problem of finding graphs on which the spectral ... more The main objective of this paper is to solve the problem of finding graphs on which the spectral clustering method and the normalized cut produce different partitions. To this end, we derive formulae for minimum normalized cut for graphs in some classes such as paths, cycles, complete graphs, double-trees, lollipop graphs LPn,m, roach type graphs R n,k and weighted paths P n,k .

Formal equivalence classes model of fuzzy relational databases using relational calculus
2017 International Conference on Applied Computer and Communication Technologies (ComCom), 2017
One of our goals is to formalize an equivalence class(FEC) of the fuzzy relational database(FRDB)... more One of our goals is to formalize an equivalence class(FEC) of the fuzzy relational database(FRDB). FRDB, an extension of RDB using a soft computing technique, fuzzy theory. Using our relational formulas of relational calculus, we can denote its properties by simple and correct formulas. Also, we can prove its properties formally using relational calculus. There are many applications of FRDB such as managing hyperlinks of web pages, customer relationship management (CRM), etc. Our motivation is developing formal verification tools for a software system using FEC of FRDB. We also formalize database operations such as “projection”, “selection”, and “natural join”. We prove several elementary properties of natural join operations using our formalization.
Journal of Physics: Conference Series, 2018
In this paper, we propose a design of fuzzy relational database to deal with a conditional probab... more In this paper, we propose a design of fuzzy relational database to deal with a conditional probability relation using fuzzy relational calculus. In the previous, there are several researches about equivalence class in fuzzy database using similarity or approximate relation. It is an interesting topic to investigate the fuzzy dependency using equivalence classes. Our goal is to introduce a formulation of a fuzzy relational database model using the relational calculus on the category of fuzzy relations. We also introduce general formulas of the relational calculus for the notion of database operations such as 'projection', 'selection', 'injection' and 'natural join'. Using the fuzzy relational calculus and conditional probabilities, we introduce notions of equivalence class, redundant, and dependency in the theory fuzzy relational database.
Journal of Mathematical Physics, 1995
This paper studies two-dimensional cellular automata ca−90(m,n) having states 0 and 1 and working... more This paper studies two-dimensional cellular automata ca−90(m,n) having states 0 and 1 and working on a square lattice of size (m−1)×(n−1). All their dynamics, driven by the local transition rule 90, can be simply formulated by representing their configurations with Laurent polynomials over a finite field F2={0,1}. The initial configuration takes the next configuration to a particular configuration whose cells all have the state 1. This paper answers the question of whether the initial configuration lies on a limit cycle or not, and, if that is the case, some properties on period lengths of such limit cycles are studied.
Bulletin of informatics and cybernetics, Mar 1, 1987
To implement Ginzburg's equality check procedure for regular expressions by using personal comput... more To implement Ginzburg's equality check procedure for regular expressions by using personal computers, we propose a new and more efficient axiom system consisting of an axiom and inference rules concerning a new relational symbol C in addition to a part of Salomaa's axiom system.
Relational Graph Rewritings
RIFIS Technical Report, Jul 1, 1991
Finding Clusters in Directed Network Graphs using Spectral Clustering Methods
Linearity of Concept Graph Based on Common Link Occurences in Web Pages
インターネットにおけるダウン症データライブラリの運営と展開
Japan Journal of Medical Informatics, 2001
The Number of Orbits of Periodic Box-Ball Systems
Lecture Notes in Computer Science, 2006
Bipartition of graphs based on the normalized cut and spectral methods
[041] Forum "Math-for-Industry" 2012 "Information Recovery and Discovery
Journal of Computer Chemistry, Japan, 2021
IEICE Transactions on Information and Systems, 2014
We introduce the notion of 'Composition', 'Union' and 'Division' of cellular automata on groups. ... more We introduce the notion of 'Composition', 'Union' and 'Division' of cellular automata on groups. A kind of notions of compositions was investigated by Sato [10] and Manzini [6] for linear cellular automata, we extend the notion to general cellular automata on groups and investigated their properties. We observe the all unions and compositions generated by one-dimensional 2-neighborhood cellular automata over Z 2 including non-linear cellular automata. Next we prove that the composition is right-distributive over union, but is not left-distributive. Finally, we conclude by showing reformulation of our definition of cellular automata on group which admit more than three states. We also show our formulation contains the representation using formal power series for linear cellular automata in Manzini [6].
GRAPH TRANSFORMATION APPROACH FOR THE SHORTEST PATH SEARCH AND LENGTH CALCULATION By
We consider a graph with labels of edges. A label means the length of an edge. We present a metho... more We consider a graph with labels of edges. A label means the length of an edge. We present a method to compute the length of the shortest path between two ver-tices using graph transformations. We introduce graph transformation rules which preserve the length of paths. Reducing to a simple graph which contains two ver-tices, we finally calculate the length of the shortest path of those two vertices. There were several algorithms for computing network reliabilities using graph transfor-mations. We use the same framework as those algorithms for applying the graph transformation rules, but our transformation rules do not calculate the network reliabilities but calculate the length of the shortest path. 1.
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Papers by Yoshihiro Mizoguchi