arXiv subjects

Tatsuro Kawamoto

Publications and source records attributed to Tatsuro Kawamoto.

31 records · Page 2Linked to original sources

arXiv2017

Cross-validation estimate of the number of clusters in a network

Network science investigates methodologies that summarise relational data to obtain better interpretability. Identifying modular structures is a fundamental task, and assessment of the coarse-grain level is its crucial step. Here, we propose principled, scalable, and widely applicable assessment criteria to determine the number of clusters in modular networks based on the leave-one-out cross-validation estimate of the edge prediction error.

cs.SI↗

arXiv2017

Detectability thresholds of general modular graphs

We investigate the detectability thresholds of various modular structures in the stochastic block model. Our analysis reveals how the detectability threshold is related to the details of the modular pattern, including the hierarchy of the clusters. We show that certain planted structures are impossible to infer regardless of their fuzziness.

cs.SI↗

arXiv2016

Localized eigenvectors of the non-backtracking matrix

In the case of graph partitioning, the emergence of localized eigenvectors can cause the standard spectral method to fail. To overcome this problem, the spectral method using a non-backtracking matrix was proposed. Based on numerical experiments on several examples of real networks, it is clear that the non-backtracking matrix does not exhibit localization of eigenvectors. However, we show that localized eigenvectors of the non-backtracking matrix can exist outside the spectral band, which may lead to deterioration in the performance of graph partitioning.

cs.SI↗

arXiv2016

A Tractable Fully Bayesian Method for the Stochastic Block Model

The stochastic block model (SBM) is a generative model revealing macroscopic structures in graphs. Bayesian methods are used for (i) cluster assignment inference and (ii) model selection for the number of clusters. In this paper, we study the behavior of Bayesian inference in the SBM in the large sample limit. Combining variational approximation and Laplace's method, a consistent criterion of the fully marginalized log-likelihood is established. Based on that, we derive a tractable algorithm that solves tasks (i) and (ii) concurrently, obviating the need for an outer loop to check all model candidates. Our empirical and theoretical results demonstrate that our method is scalable in computation, accurate in approximation, and concise in model selection.

cs.LG↗

arXiv2015

Detectability of the spectral method for sparse graph partitioning

We show that modularity maximization with the resolution parameter offers a unifying framework of graph partitioning. In this framework, we demonstrate that the spectral method exhibits universal detectability, irrespective of the value of the resolution parameter, as long as the graph is partitioned. Furthermore, we show that when the resolution parameter is sufficiently small, a first-order phase transition occurs, resulting in the graph being unpartitioned.

cs.SI↗

arXiv2015

Limitations in the spectral method for graph partitioning: detectability threshold and localization of eigenvectors

Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both unnormalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.

cs.SI↗

arXiv2015

Persistence of activity on Twitter triggered by a natural disaster: A data analysis

In this note, we list the results of a simple analysis of a Twitter dataset: the complete dataset of Japanese tweets in the 1-week period after the Great East Japan earthquake, which occurred on March 11, 2011. Our data analysis shows how people reacted to the earthquake on Twitter and how some users went inactive in the long-term.

physics.soc-ph↗

arXiv2015

Estimating the resolution limit of the map equation in community detection

A community detection algorithm is considered to have a resolution limit if the scale of the smallest modules that can be resolved depends on the size of the analyzed subnetwork. The resolution limit is known to prevent some community detection algorithms from accurately identifying the modular structure of a network. In fact, any global objective function for measuring the quality of a two-level assignment of nodes into modules must have some sort of resolution limit or an external resolution parameter. However, it is yet unknown how the resolution limit affects the so-called map equation, which is known to be an efficient objective function for community detection. We derive an analytical estimate and conclude that the resolution limit of the map equation is set by the total number of links between modules instead of the total number of links in the full network as for modularity. This mechanism makes the resolution limit much less restrictive for the map equation than for modularity, and in practice orders of magnitudes smaller. Furthermore, we argue that the effect of the resolution limit often results from shoehorning multi-level modular structures into two-level descriptions. As we show, the hierarchical map equation effectively eliminates the resolution limit for networks with nested multi-level modular structures.

physics.soc-ph↗

arXiv2014

Viral spreading of daily information in online social networks

We explain a possible mechanism of an information spreading on a network which spreads extremely far from a seed node, namely the viral spreading. On the basis of a model of the information spreading in an online social network, in which the dynamics is expressed as a random multiplicative process of the spreading rates, we will show that the correlation between the spreading rates enhances the chance of the viral spreading, shifting the tipping point at which the spreading goes viral.

physics.soc-ph↗

arXiv2012

A stochastic model of the tweet diffusion on the Twitter network

We introduce a stochastic model which describes diffusions of tweets on the Twitter network. By dividing the followers into generations, we describe the dynamics of the tweet diffusion as a random multiplicative process. We confirm our model by directly observing the statistics of the multiplicative factors in the Twitter data.

physics.soc-ph↗

arXiv2011

Microscopic analysis of the microscopic reversibility in quantum systems

We investigate the robustness of the microscopic reversibility in open quantum systems which is discussed by Monnai [arXiv:1106.1982 (2011)]. We derive an exact relation between the forward transition probability and the reversed transition probability in the case of a general measurement basis. We show that the microscopic reversibility acquires some corrections in general and discuss the physical meaning of the corrections. Under certain processes, some of the correction terms vanish and we numerically confirmed that the remaining correction term becomes negligible; the microscopic reversibility almost holds even when the local system cannot be regarded as macroscopic.

cond-mat.stat-mech↗

arXiv2011

A test of "fluctuation theorem" in non-Markovian open quantum systems

We study fluctuation theorems for open quantum systems with a non-Markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems. The approach of Markovian quantum master equations to the fluctuation theorems was developed by Esposito and Mukamel [Phys. Rev. E {\bf73}, 046129 (2006)]. We show that their discussion can be formally generalized to the case of a non-Markovian heat bath when the local system is linearly connected to a Gaussian heat bath with the spectrum distribution of the Drude form. We found by numerically simulating the spin-boson model in non-Markovian regime that the "detailed balance" condition is well satisfied except in a strongly non-equilibrium transient situation, and hence our generalization of the definition of the "entropy production" is almost always legitimate. Therefore, our generalization of the fluctuation theorem seems meaningful in wide regions.

cond-mat.stat-mech↗

arXiv2009

Probabilistic Interpretation of Resonant States

We provide probabilistic interpretation of resonant states. This we do by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of time, and therefore leads to probability conservation. This is in contrast with the conventional employment of a bi-orthogonal basis that precludes probabilistic interpretation, since wave functions of resonant states diverge exponentially in space. On the other hand, resonant states decay exponentially in time, because momentum leaks out of the central scattering area. This momentum leakage is also the reason for the spatial exponential divergence of resonant state. It is by combining the opposite temporal and spatial behaviors of resonant states that we arrive at our probabilistic interpretation of these states. The physical need to normalize resonant wave functions over an expanding spatial domain arises because particles leak out of the region which contains the potential range and escape to infinity, and one has to include them in the total count of particle number.

quant-ph↗