arXiv subjects

Atsushi Tanaka

Publications and source records attributed to Atsushi Tanaka.

7 recordsLinked to original sources

arXiv2026

Lefschetz Fibrations on Knot Traces of Alternating and Extended Alternating Knots

In our previous work, we introduced a simple and explicit method for constructing a positive allowable Lefschetz fibration (PALF) from a $2$-handlebody decomposition of any given compact Stein surface. In this paper, we apply this construction to knot traces whose attaching circles are either alternating knots or \emph{extended alternating knots} (a generalized class introduced herein). We demonstrate that each such knot trace admits a PALF whose regular fiber has a genus exactly equal to the number of white regions in the associated planar graph, yielding PALFs whose regular fibers have a significantly small genus. As immediate corollaries, we prove that knot traces of positive pretzel knots with $s$ rows admit PALFs with regular fibers of genus $s-1$, and those of positive torus knots admit PALFs with regular fibers of genus $1$. Furthermore, we define \emph{positive torus-pretzel knots} by replacing each twist block of a positive pretzel knot with the crossings of a positive torus knot, and we establish that their knot traces also admit PALFs with regular fibers of genus $s-1$.

math.GT↗

arXiv2026

Combinatorial extension of a simple construction of Lefschetz fibrations

In a previous work, we introduced a simple and systematic method for constructing a positive allowable Lefschetz fibration (PALF) from a 2-handlebody decomposition of a given Stein surface. In this paper, we present a combinatorial extension of this construction, focusing on the flexibility of the regular fiber. By introducing variations in the isotopy of the 0-handle during the construction process, we obtain PALFs whose total spaces are diffeomorphic to the original Stein surface but which possess different regular fibers. As a primary application, we prove the existence of PALFs with genus $1$ regular fibers whose total spaces are diffeomorphic to the knot traces of Legendrian positive twist knots and positive torus knots $T_{2, 2n+1}$. Furthermore, we explicitly compare our PALF associated with the positive torus knot $T_{2, 2n+1}$ to the specific open book decomposition generated by Avdek's Algorithm 2, demonstrating that the regular fiber and monodromy of our construction coincide with the page and monodromy of the corresponding open book.

math.GT↗

arXiv2026

A Simple Construction of Lefschetz Fibrations on Compact Stein Surfaces

Loi-Piergallini, Akbulut-Ozbagci, and Akbulut-Arikan showed that every compact Stein surface admits a positive allowable Lefschetz fibration over the disk $D^2$ with bounded fibers (PALF in short), and they provided constructions of PALF's corresponding to compact Stein surfaces. In this paper, we present a simple method for constructing a PALF from a 2-handlebody decomposition of any given compact Stein surface. Our method yields PALF's whose regular fibers have small genus, and it provides an alternative constructive proof of the above result. We also define the minimal genus of a regular fiber of a PALF on the knot trace of a knot $K$ with framing one less than its maximal Thurston-Bennequin number as an invariant of $K$. When the grid number of $K$ is $N$, our construction produces a PALF whose regular fiber has genus at most $(N - 1)/2$, showing that the defined invariant is bounded above by $(N - 1)/2$.

math.GT↗

arXiv2026

Ensemble Machine Learning and Statistical Procedures for Dynamic Predictions of Time-to-Event Outcomes

Dynamic predictions for longitudinal and time-to-event outcomes have become a versatile tool in precision medicine. Our work is motivated by the application of dynamic predictions in the decision-making process for primary biliary cholangitis patients. For these patients, serial biomarker measurements (e.g., bilirubin and alkaline phosphatase levels) are routinely collected to inform treating physicians of the risk of liver failure and guide clinical decision-making. Two popular statistical approaches to derive dynamic predictions are joint modelling and landmarking. However, recently, machine learning techniques have also been proposed. Each approach has its merits, and no single method exists to outperform all others. Consequently, obtaining the best possible survival estimates is challenging. Therefore, we extend the Super Learner framework to combine dynamic predictions from different models and procedures. Super Learner is an ensemble learning technique that allows users to combine different prediction algorithms to improve predictive accuracy and flexibility. It uses cross-validation and different objective functions of performance (e.g., squared loss) that suit specific applications to build the optimally weighted combination of predictions from a library of candidate algorithms. In our work, we pay special attention to appropriate objective functions for Super Learner to obtain the most optimal weighted combination of dynamic predictions. In our primary biliary cholangitis application, Super Learner presented unique benefits due to its ability to flexibly combine outputs from a diverse set of models with varying assumptions for equal or better predictive performance than any model fit separately.

stat.ML↗

arXiv2022

More Tolerant Reconstructed Networks by Self-Healing against Attacks in Saving Resource

Complex network infrastructure systems for power-supply, communication, and transportation support our economical and social activities, however they are extremely vulnerable against the frequently increasing large disasters or attacks. Thus, a reconstructing from damaged network is rather advisable than empirically performed recovering to the original vulnerable one. In order to reconstruct a sustainable network, we focus on enhancing loops so as not to be trees as possible by node removals. Although this optimization is corresponded to an intractable combinatorial problem, we propose self-healing methods based on enhancing loops in applying an approximate calculation inspired from a statistical physics approach. We show that both higher robustness and efficiency are obtained in our proposed methods with saving the resource of links and ports than ones in the conventional healing methods. Moreover, the reconstructed network by healing can become more tolerant than the original one before attacks, when some extent of damaged links are reusable or compensated as investment of resource. These results will be open up the potential of network reconstruction by self-healing with adaptive capacity in the meaning of resilience.

physics.soc-ph↗

arXiv2020

Effective Self-Healing Networks against Attacks or Disasters in Resource Allocation Control

With increasing threats by large attacks or disasters, the time has come to reconstruct network infrastructures such as communication or transportation systems rather than to recover them as before in case of accidents, because many real networks are extremely vulnerable. Thus, we consider self-healing mechanisms by rewirings (reuse or addition of links) to be sustainable and resilient networks even against malicious attacks. In distributed local process for healing, the key strategies are the extension of candidates of linked nodes and enhancing loops by applying a message-passing algorithm inspired from statistical physics. Simulation results show that our proposed combination of ring formation and enhancing loops is particularly effective in comparison with the conventional methods, when more than half damaged links alive or are compensated from reserved ones.

physics.soc-ph↗

arXiv2020

Screw dislocation that converts p-type GaN to n-type: Microscopic study on the Mg condensation and the leakage current in p-n diodes

Recent experiments suggest that Mg condensation at threading dislocations induce current leakage, leading to degradation of GaN-based power devices. To study this issue, we perform first-principles total-energy electronic-structure calculations for various Mg and dislocation complexes. We find that threading screw dislocations (TSDs) indeed attract Mg impurities, and that the electronic levels in the energy gap induced by the dislocations are elevated towards the conduction band as the Mg impurity approaches the dislocation line, indicating that the Mg-TSD complex is a donor. The formation of the Mg-TSD complex is unequivocally evidenced by our atom probe tomography in which Mg condensation and diffusion through [0001] screw dislocations is observed in p-n diodes. These findings provide a novel picture that the Mg being a p-type impurity in GaN diffuses toward the TSD and then locally forms an n-type region. The appearance of this region along the TSD results the reverse leakage current.

cond-mat.mtrl-sci↗