arXiv subjects

Tatsuya Akutsu

Publications and source records attributed to Tatsuya Akutsu.

35 records · Page 2Linked to original sources

arXiv2021

Molecular Design Based on Artificial Neural Networks, Integer Programming and Grid Neighbor Search

A novel framework has recently been proposed for designing the molecular structure of chemical compounds with a desired chemical property using both artificial neural networks and mixed integer linear programming. In the framework, a chemical graph with a target chemical value is inferred as a feasible solution of a mixed integer linear program that represents a prediction function and other requirements on the structure of graphs. In this paper, we propose a procedure for generating other feasible solutions of the mixed integer linear program by searching the neighbor of output chemical graph in a search space. The procedure is combined in the framework as a new building block. The results of our computational experiments suggest that the proposed method can generate an additional number of new chemical graphs with up to 50 non-hydrogen atoms.

cs.LG↗

arXiv2021

New and Improved Algorithms for Unordered Tree Inclusion

The tree inclusion problem is, given two node-labeled trees $P$ and $T$ (the ``pattern tree'' and the ``target tree''), to locate every minimal subtree in $T$ (if any) that can be obtained by applying a sequence of node insertion operations to $P$. Although the ordered tree inclusion problem is solvable in polynomial time, the unordered tree inclusion problem is NP-hard. The currently fastest algorithm for the latter is a classic algorithm by Kilpeläinen and Mannila from 1995 that runs in $O(2^{2d} mn)$ time, where $m$ and $n$ are the sizes of the pattern and target trees, respectively, and $d$ is the degree of the pattern tree. Here, we develop a new algorithm that runs in $O(2^{d} mn^2)$ time, improving the exponential factor from $2^{2d}$ to $2^d$ by considering a particular type of ancestor-descendant relationships that is suitable for dynamic programming. We also study restricted variants of the unordered tree inclusion problem.

cs.DS↗

arXiv2021

Tree Edit Distance with Variables. Measuring the Similarity between Mathematical Formulas

In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas, especially, those appearing in mathematical models of biological systems. We analyze the computational complexities of several variants of this new model. In particular, we show that the problem is NP-complete for ordered trees. We also show for unordered trees that the problem of deciding whether or not the distance is 0 is graph isomorphism complete but can be solved in polynomial time if the maximum outdegree of input trees is bounded by a constant. This distance model is then extended for measuring the difference/similarity between two systems of differential equations, for which results of preliminary computational experiments using biological models are provided.

cs.DS↗

arXiv2020

A novel method for inference of chemical compounds with prescribed topological substructures based on integer programming

Analysis of chemical graphs is becoming a major research topic in computational molecular biology due to its potential applications to drug design. One of the major approaches in such a study is inverse quantitative structure activity/property relationships (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a novel framework has been proposed for inverse QSAR/QSPR using both artificial neural networks (ANN) and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, a feature vector $f(G)$ of a chemical graph $G$ is introduced and a prediction function $ψ_{\mathcal{N}}$ on a chemical property $π$ is constructed with an ANN $\mathcal{N}$. In the second phase, given a target value $y^*$ of the chemical property $π$, a feature vector $x^*$ is inferred by solving an MILP formulated from the trained ANN $\mathcal{N}$ so that $ψ_{\mathcal{N}}(x^*)$ is equal to $y^*$ and then a set of chemical structures $G^*$ such that $f(G^*)= x^*$ is enumerated by a graph enumeration algorithm. The framework has been applied to chemical compounds with a rather abstract topological structure such as acyclic or monocyclic graphs and graphs with a specified polymer topology with cycle index up to 2. In this paper, we propose a new flexible modeling method to the framework so that we can specify a topological substructure of graphs and a partial assignment of chemical elements and bond-multiplicity to a target graph.

cs.CE↗

arXiv2020

Discrimination of attractors with noisy nodes in Boolean networks

Observing the internal state of the whole system using a small number of sensor nodes is important in analysis of complex networks. Here, we study the problem of determining the minimum number of sensor nodes to discriminate attractors under the assumption that each attractor has at most K noisy nodes. We present exact and approximation algorithms for this minimization problem. The effectiveness of the algorithms is also demonstrated by computational experiments using both synthetic data and realistic biological data.

cs.DS↗

arXiv2020

A Novel Method for Inference of Acyclic Chemical Compounds with Bounded Branch-height Based on Artificial Neural Networks and Integer Programming

Analysis of chemical graphs is a major research topic in computational molecular biology due to its potential applications to drug design. One approach is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a framework has been proposed for inverse QSAR/QSPR using artificial neural networks (ANN) and mixed integer linear programming (MILP). This method consists of a prediction phase and an inverse prediction phase. In the first phase, a feature vector $f(G)$ of a chemical graph $G$ is introduced and a prediction function $ψ$ on a chemical property $π$ is constructed with an ANN. In the second phase, given a target value $y^*$ of property $π$, a feature vector $x^*$ is inferred by solving an MILP formulated from the trained ANN so that $ψ(x^*)$ is close to $y^*$ and then a set of chemical structures $G^*$ such that $f(G^*)= x^*$ is enumerated by a graph search algorithm. The framework has been applied to the case of chemical compounds with cycle index up to 2. The computational results conducted on instances with $n$ non-hydrogen atoms show that a feature vector $x^*$ can be inferred for up to around $n=40$ whereas graphs $G^*$ can be enumerated for up to $n=15$. When applied to the case of chemical acyclic graphs, the maximum computable diameter of $G^*$ was around up to around 8. We introduce a new characterization of graph structure, "branch-height," based on which an MILP formulation and a graph search algorithm are designed for chemical acyclic graphs. The results of computational experiments using properties such as octanol/water partition coefficient, boiling point and heat of combustion suggest that the proposed method can infer chemical acyclic graphs $G^*$ with $n=50$ and diameter 30.

cs.DS↗

arXiv2020

On the Compressive Power of Boolean Threshold Autoencoders

An autoencoder is a layered neural network whose structure can be viewed as consisting of an encoder, which compresses an input vector of dimension $D$ to a vector of low dimension $d$, and a decoder which transforms the low-dimensional vector back to the original input vector (or one that is very similar). In this paper we explore the compressive power of autoencoders that are Boolean threshold networks by studying the numbers of nodes and layers that are required to ensure that the numbers of nodes and layers that are required to ensure that each vector in a given set of distinct input binary vectors is transformed back to its original. We show that for any set of $n$ distinct vectors there exists a seven-layer autoencoder with the smallest possible middle layer, (i.e., its size is logarithmic in $n$), but that there is a set of $n$ vectors for which there is no three-layer autoencoder with a middle layer of the same size. In addition we present a kind of trade-off: if a considerably larger middle layer is permissible then a five-layer autoencoder does exist. We also study encoding by itself. The results we obtain suggest that it is the decoding that constitutes the bottleneck of autoencoding. For example, there always is a three-layer Boolean threshold encoder that compresses $n$ vectors into a dimension that is reduced to twice the logarithm of $n$.

cs.LG↗

arXiv2020

Enumerating Chemical Graphs with Two Disjoint Cycles Satisfying Given Path Frequency Specifications

Enumerating chemical graphs satisfying given constraints is a fundamental problem in mathematical and computational chemistry, and plays an essential part in a recently proposed framework for the inverse QSAR/QSPR. In this paper, constraints are given by feature vectors each of which consists of the frequencies of paths in a given set of paths. We consider the problem of enumerating chemical graphs that satisfy the path frequency constraints, which are given by a pair of feature vectors specifying upper and lower bounds of the frequency of each path. We design a branch-and-bound algorithm for enumerating chemical graphs of bi-block 2-augmented structure, that is, graphs that contain two edge-disjoint cycles. We present some computational experiments with an implementation of our proposed algorithm.

cs.DS↗

arXiv2020

Enumerating Chemical Graphs with Mono-block 2-Augmented Tree Structure from Given Upper and Lower Bounds on Path Frequencies

We consider a problem of enumerating chemical graphs from given constraints concerning their structures, which has an important application to a novel method for the inverse QSAR/QSPR recently proposed. In this paper, the structure of a chemical graph is specified by a feature vector each of whose entries represents the frequency of a prescribed path. We call a graph a 2-augmented tree if it is obtained from a tree (an acyclic graph) by adding edges between two pairs of nonadjacent vertices. Given a set of feature vectors as the interval between upper and lower bounds of feature vectors, we design an efficient algorithm for enumerating chemical 2-augmented trees that satisfy the path frequency specified by some feature vector in the set. We implemented the proposed algorithm and conducted some computational experiments.

cs.DS↗

arXiv2016

Maximum margin classifier working in a set of strings

Numbers and numerical vectors account for a large portion of data. However, recently the amount of string data generated has increased dramatically. Consequently, classifying string data is a common problem in many fields. The most widely used approach to this problem is to convert strings into numerical vectors using string kernels and subsequently apply a support vector machine that works in a numerical vector space. However, this non-one-to-one conversion involves a loss of information and makes it impossible to evaluate, using probability theory, the generalization error of a learning machine, considering that the given data to train and test the machine are strings generated according to probability laws. In this study, we approach this classification problem by constructing a classifier that works in a set of strings. To evaluate the generalization error of such a classifier theoretically, probability theory for strings is required. Therefore, we first extend a limit theorem on the asymptotic behavior of a consensus sequence of strings, which is the counterpart of the mean of numerical vectors, as demonstrated in the probability theory on a metric space of strings developed by one of the authors and his colleague in a previous study [18]. Using the obtained result, we then demonstrate that our learning machine classifies strings in an asymptotically optimal manner. Furthermore, we demonstrate the usefulness of our machine in practical data analysis by applying it to predicting protein--protein interactions using amino acid sequences.

stat.ML↗

arXiv2015

Optimal string clustering based on a Laplace-like mixture and EM algorithm on a set of strings

In this study, we address the problem of clustering string data in an unsupervised manner by developing a theory of a mixture model and an EM algorithm for string data based on probability theory on a topological monoid of strings developed in our previous studies. We first construct a parametric distribution on a set of strings in the motif of the Laplace distribution on a set of real numbers and reveal its basic properties. This Laplace-like distribution has two parameters: a string that represents the location of the distribution and a positive real number that represents the dispersion. It is difficult to explicitly write maximum likelihood estimators of the parameters because their log likelihood function is a complex function, the variables of which include a string; however, we construct estimators that almost surely converge to the maximum likelihood estimators as the number of observed strings increases and demonstrate that the estimators strongly consistently estimate the parameters. Next, we develop an iteration algorithm for estimating the parameters of the mixture model of the Laplace-like distributions and demonstrate that the algorithm almost surely converges to the EM algorithm for the Laplace-like mixture and strongly consistently estimates its parameters as the numbers of observed strings and iterations increase. Finally, we derive a procedure for unsupervised string clustering from the Laplace-like mixture that is asymptotically optimal in the sense that the posterior probability of making correct classifications is maximized.

math.ST↗

arXiv2014

Structurally Robust Control of Complex Networks

Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust control engineering has not addressed the problem of structural changes on a large network. Here, we introduce the concept of structurally robust control of complex networks and provide a concrete example using an algorithmic framework that is widely applied in engineering. The developed analytical tools, computer simulations and real network analyses lead herein to the discovery that robust control can be achieved in scale-free networks with exactly the same order of controllers required in a standard non-robust configuration by adjusting only the minimum degree. The presented methodology also addresses the probabilistic failure of links in real systems, such as neural synaptic unreliability in {\it C. elegans}, and suggests a new direction to pursue in studies of complex networks in which control theory has a role.

physics.soc-ph↗

arXiv2013

On the Parameterized Complexity of Associative and Commutative Unification

This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and associative-commutative unification problems are $W[1]$-hard. A fixed-parameter algorithm and a polynomial-time algorithm are presented for special cases of commutative unification in which one input term is variable-free and the number of variables is bounded by a constant, respectively. Related results including those on the string and tree edit distance problems with variables are shown too.

cs.SC↗

arXiv2013

Theoretical estimation of metabolic network robustness against multiple reaction knockouts using branching process approximation

In our previous study, we showed that the branching process approximation is useful for estimating metabolic robustness, measured using the impact degree. By applying a theory of random family forests, we here extend the branching process approximation to consider the knockout of {\it multiple} reactions, inspired by the importance of multiple knockouts reported by recent computational and experimental studies. In addition, we propose a better definition of the number of offspring of each reaction node, allowing for an improved estimation of the impact degree distribution obtained as a result of a single knockout. Importantly, our proposed approach is also applicable to multiple knockouts. The comparisons between theoretical predictions and numerical results using real-world metabolic networks demonstrate the validity of the modeling based on random family forests for estimating the impact degree distributions resulting from the knockout of multiple reactions.

q-bio.MN↗

arXiv2012

Stability and Restoration phenomena in Competitive Systems

A conservation law and stability, recovering phenomena and characteristic patterns of a nonlinear dynamical system have been studied and applied to biological and ecological systems. In our previous study, we proposed a system of symmetric 2n-dimensional conserved nonlinear differential equations with external perturbations. In this paper, competitive systems described by 2-dimensional nonlinear dynamical (ND) model with external perturbations are applied to population cycles and recovering phenomena of systems from microbes to mammals. The famous 10-year cycle of population density of Canadian lynx and snowshoe hare is numerically analyzed. We find that a nonlinear dynamical system with a conservation law is stable and generates a characteristic rhythm (cycle) of population density, which we call the {\it standard rhythm} of a nonlinear dynamical system. The stability and restoration phenomena are strongly related to a conservation law and balance of a system. The {\it standard rhythm} of population density is a manifestation of the survival of the fittest to the balance of a nonlinear dynamical system.

physics.bio-ph↗

arXiv2011

Analysis of the impact degree distribution in metabolic networks using branching process approximation

Theoretical frameworks to estimate the tolerance of metabolic networks to various failures are important to evaluate the robustness of biological complex systems in systems biology. In this paper, we focus on a measure for robustness in metabolic networks, namely, the impact degree, and propose an approximation method to predict the probability distribution of impact degrees from metabolic network structures using the theory of branching process. We demonstrate the relevance of this method by testing it on real-world metabolic networks. Although the approximation method possesses a few limitations, it may be a powerful tool for evaluating metabolic robustness.

q-bio.MN↗

arXiv2007

Structure of n-clique networks embedded in a complex network

We propose the n-clique network as a powerful tool for understanding global structures of combined highly-interconnected subgraphs, and provide theoretical predictions for statistical properties of the n-clique networks embedded in a complex network using the degree distribution and the clustering spectrum. Furthermore, using our theoretical predictions, we find that the statistical properties are invariant between 3-clique networks and original networks for several observable real-world networks with the scale-free connectivity and the hierarchical modularity. The result implies that structural properties are identical between the 3-clique networks and the original networks.

physics.soc-ph↗