arXiv subjects

Akira Ishii

Publications and source records attributed to Akira Ishii.

At least 19 recordsLinked to original sources

arXiv2025

Derived McKay correspondence for real reflection groups of rank three

We describe the derived McKay correspondence for real reflection groups of rank $3$ in terms of a maximal resolution of the logarithmic pair consisting of the quotient variety and the discriminant divisor with coefficient $\frac{1}{2}$. As an application, we verify a conjecture by Polishchuk and Van den Bergh on the existence of a certain semiorthgonal decomposition of the equivariant derived category into the derived categories of affine spaces for any real reflection group of rank $3$.

math.AG↗

arXiv2025

Token-based Decision Criteria Are Suboptimal in In-context Learning

In-Context Learning (ICL) typically utilizes classification criteria from output probabilities of manually selected label tokens. However, we argue that such token-based classification criteria lead to suboptimal decision boundaries, despite delicate calibrations through translation and constrained rotation applied. To address this problem, we propose Hidden Calibration, which renounces token probabilities and uses the nearest centroid classifier on the LM's last hidden states. In detail, we assign the label of the nearest centroid previously estimated from a calibration set to the test sample as the predicted label. Our experiments on 6 models and 10 classification datasets indicate that Hidden Calibration consistently outperforms current token-based baselines by about 20%~50%, achieving a strong state-of-the-art in ICL. Our further analysis demonstrates that Hidden Calibration finds better classification criteria with less inter-class overlap, and LMs provide linearly separable intra-class clusters with the help of demonstrations, which supports Hidden Calibration and gives new insights into the principle of ICL. Our official code implementation can be found at https://github.com/hc495/Hidden_Calibration.

cs.CL↗

arXiv2023

Dimer models and group actions

We construct a consistent dimer model having the same symmetry as its characteristic polygon. This produces examples of non-commutative crepant resolutions of non-toric non-quotient Gorenstein singularities in dimension 3.

math.AG↗

arXiv2021

Exceptional collections on $Σ_{ 2 }$

Structure theorems for exceptional objects and exceptional collections of the bounded derived category of coherent sheaves on del Pezzo surfaces are established by Kuleshov and Orlov. In this paper we propose conjectures which generalize these results to weak del Pezzo surfaces. Unlike del Pezzo surfaces, an exceptional object on a weak del Pezzo surface is not necessarily a shift of a sheaf and is not determined by its class in the Grothendieck group. Our conjectures explain how these complications are taken care of by spherical twists, the categorification of $(-2)$-reflections acting on the derived category. This paper is devoted to solving the conjectures for the prototypical weak del Pezzo surface $Σ_{ 2 }$, the Hirzebruch surface of degree $2$. Specifically, we prove the following results: Any exceptional object is sent to the shift of the uniquely determined exceptional vector bundle by a product of spherical twists which acts trivially on the Grothendieck group of the derived category. Any exceptional collection on $Σ_{ 2 }$ is part of a full exceptional collection. We moreover prove that the braid group on $4$ strands acts transitively on the set of exceptional collections of length $4$ (up to shifts).

math.AG↗

arXiv2021

Rain-Code Fusion : Code-to-code ConvLSTM Forecasting Spatiotemporal Precipitation

Recently, flood damage has become a social problem owing to unexperienced weather conditions arising from climate change. An immediate response to heavy rain is important for the mitigation of economic losses and also for rapid recovery. Spatiotemporal precipitation forecasts may enhance the accuracy of dam inflow prediction, more than 6 hours forward for flood damage mitigation. However, the ordinary ConvLSTM has the limitation of predictable range more than 3-timesteps in real-world precipitation forecasting owing to the irreducible bias between target prediction and ground-truth value. This paper proposes a rain-code approach for spatiotemporal precipitation code-to-code forecasting. We propose a novel rainy feature that represents a temporal rainy process using multi-frame fusion for the timestep reduction. We perform rain-code studies with various term ranges based on the standard ConvLSTM. We applied to a dam region within the Japanese rainy term hourly precipitation data, under 2006 to 2019 approximately 127 thousands hours, every year from May to October. We apply the radar analysis hourly data on the central broader region with an area of 136 x 148 km2 . Finally we have provided sensitivity studies between the rain-code size and hourly accuracy within the several forecasting range.

cs.LG↗

arXiv2020

Generative Damage Learning for Concrete Aging Detection using Auto-flight Images

In order to monitor the state of large-scale infrastructures, image acquisition by autonomous flight drones is efficient for stable angle and high-quality images. Supervised learning requires a large data set consisting of images and annotation labels. It takes a long time to accumulate images, including identifying the damaged regions of interest (ROIs). In recent years, unsupervised deep learning approaches such as generative adversarial networks (GANs) for anomaly detection algorithms have progressed. When a damaged image is a generator input, it tends to reverse from the damaged state to the healthy state generated image. Using the distance of distribution between the real damaged image and the generated reverse aging healthy state fake image, it is possible to detect the concrete damage automatically from unsupervised learning. This paper proposes an anomaly detection method using unpaired image-to-image translation mapping from damaged images to reverse aging fakes that approximates healthy conditions. We apply our method to field studies, and we examine the usefulness of our method for health monitoring of concrete damage.

eess.IV↗

arXiv2020

$G$-constellations and the maximal resolution of a quotient surface singularity

For a finite subgroup $G$ of $\operatorname{GL}(2, \mathbb C)$, we consider the moduli space ${\mathcal M}_θ$ of $G$-constellations. It depends on the stability parameter $θ$ and if $θ$ is generic it is a resolution of singularities of $\mathbb C^2/G$. In this paper, we show that a resolution $Y$ of $\mathbb C^2/G$ is isomorphic to ${\mathcal M}_θ$ for some generic $θ$ if and only if $Y$ is dominated by the maximal resolution under the assumption that $G$ is abelian or small.

math.AG↗

arXiv2019

A study of trends in the effects of TV ratings and social media (Twitter) -- Case study 1

The Japanese TV program 'Drama A' is a drama broadcast from October to December 2016. The audience rating was sluggish, but this drama marked a high audience rating in 2016. Since it was popular from the middle, and it was speculated that there was a part related to social media in the popularity, we considered existing research methods as a case study. In this paper, we used a mathematical model of the hit phenomenon to examine the impact of audience assessment from social media from a sociophysical perspective. We got the same consideration as the audience rating per minute of video research. This paper is IEEE BIGDATA2018's Revised paper(Consideration on TV audience rating and influence of social media).

cs.SI↗

arXiv2019

Consensus formation Online using Sociophysics method

Consensus formation and difference of opinion have long been the subject of research. However, relevant laws and systems within society are being updated to reflect the changes in information networks. Online environment has come to fulfill a major role as a real and concrete place of opposing opinions and consensus formation. In the future, quantitative findings on consensus formation, and findings on relevant trends, must be summarized, and quantitative research related to trends likely to give rise to social and economic risk is required. Thus, the potential for comparing research related to consensus formation using actual data and an approach using a mathematical model was first investigated.

cs.SI↗

arXiv2019

The Influence of Social Media Writing on Online Search Behavior for Seasonal Events: The Sociophysics Approach

Using seasonal topics as the study subject, in this study, we focus on the timing gap between social media writing and online search behavior. To conduct our analysis, we used the mathematical model of search behavior, comprising the sociophysics approach. The seasonal topics selected were St.Valentine's Day, Halloween and New Year countdown. We also picked up the event like Christmas and Halloween. We analyzed the influence of blogs and Twitter on search behavior and found a deviation of interest in terms of timing. We also analyzed Japanese seasonal event of eating Eho-maki in February 3 and eels at the day of the ox in midsummer.

physics.soc-ph↗

arXiv2018

Opinion Dynamics Theory for Analysis of Consensus Formation and Division of Opinion on the Internet

The massive amount of text data on the web has facilitated research on the quantitative analysis of public opinion, which could not be visualized earlier. In this paper, we propose a new opinion dynamics theory. This theory that is intended to explain agreement formation and opinion breakup division in opinion exchanges on social media such as Twitter. With the popularization of the public network, we have become able to communicate with instantaneity and interactivity beyond the temporal and spatial constraints.Research on quantitatively analyzing the distribution of opinion on public opinion that has not been visualized so far utilizing massive web text data is progressing.Our model is based on the Bounded Confidence Model, that expresses opinions in as continuous quantity values. However, in the Bounded Confidence Model, it was assumed that people with different opinions move not in disregard but ignoring opinions. Furthermore, in our theory, it modeled so that it can expresser model incorporates the influence from of the external pressure outside and the phenomenon depending on the surrounding situation.

physics.soc-ph↗

arXiv2018

Analysis of social media content and search behavior related to seasonal topics using the sociophysics approach

We studied the time interval between posting social media content and search action related to seasonal topics. The analysis was performed using a mathematical model of the search behavior as in the theory of sociophysics. As seasonal topics, the word cherry blossom was considered for spring, bikini for summer, autumn leaves for fall, and skiing for winter. We examined the influence of blogs and Twitter posts given the search behavior and found a time deviation of interest on these topics.

physics.soc-ph↗

arXiv2017

Analysis and Predictions of Social Phenomena via social media using Social Physics method

As a method of analyzing and predicting social phenomena using social media as data, we propose a method using a mathematical model of hit phenomenon which is the theory of social physics. I could explain the transition of the number of social media written in movies, TV dramas, Music Concerts, Pokemon GO and proposed a method that can be used for analysis and prediction of social phenomena.

physics.soc-ph↗

arXiv2017

Measurement of human activity using velocity GPS data obtained from mobile phones

Human movement is used as an indicator of human activity in modern society. The velocity of moving humans is calculated based on position information obtained from mobile phones. The level of human activity, as recorded by velocity, varies throughout the day. Therefore, velocity can be used to identify the intervals of highest and lowest activity. More specifically, we obtained mobile-phone GPS data from the people around Shibuya station in Tokyo, which has the highest population density in Japan. From these data, we observe that velocity tends to consistently increase with the changes in social activities. For example, during the earthquake in Kumamoto Prefecture in April 2016, the activity on that day was much lower than usual. In this research, we focus on natural disasters such as earthquakes owing to their significant effects on human activities in developed countries like Japan. In the event of a natural disaster in another developed country, considering the change in human behavior at the time of the disaster (e.g., the 2016 Kumamoto Great Earthquake) from the viewpoint of velocity allows us to improve our planning for mitigation measures. Thus, we analyze the changes in human activity through velocity calculations in Shibuya, Tokyo, and compare times of disasters with normal times.

physics.soc-ph↗

arXiv2017

Position-sensitive propagation of information on social media using social physics approach

The excitement and convergence of tweets on specific topics are well studied. However, by utilizing the position information of Tweet, it is also possible to analyze the position-sensitive tweet. In this research, we focus on bomb terrorist attacks and propose a method for separately analyzing the number of tweets at the place where the incident occurred, nearby, and far. We made measurements of position-sensitive tweets and suggested a theory to explain it. This theory is an extension of the mathematical model of the hit phenomenon.

physics.soc-ph↗

arXiv2016

Extended McKay correspondence for quotient surface singularities

Let $G$ be a finite subgroup of $\mbox{GL}(2)$ acting on $\mathbf{A}^2\setminus\{0\}$ freely. The $G$-orbit Hilbert scheme $G\mbox{-Hilb}(\mathbf{A}^2)$ is a minimal resolution of the quotient $\mathbf{A}^2/G$. We determine the generator sheaf of the ideal defining the universal $G$-cluster over $G\mbox{-Hilb}(\mathbf{A}^2)$, which somewhat strengthens the well-known McKay correspondence for a finite subgroup of $\mbox{SL}(2)$. We also study the quiver structure of $G\mbox{-Hilb}(\mathbf{A}^2)$ at every $G$-cluster $O_{Z_y}=O_{\mathbf{A}^2}/I_y$ in terms of a collection of sort of minimal $G$-submodules of $O_{Z_y}$ (called mono-special $O_{\mathbf{A}^2}$-submodules) and generating $G$-submodules of $I_y$.

math.AG↗

arXiv2015

Mathematical model for hit phenomena and its application to analyze popularity of weekly tv drama

Mathematical model for hit phenomena presented by A Ishii et al in 2012 has been extended to analyze and predict a lot of hit subject using social network system. The equation for each individual consumers is assumed and the equation of social response to each hit subject is derived as stochastic process of statistical physics. The advertisement effect is included as external force and the communication effects are included as two-body and three-body interaction. The applications of this model are demonstrated for analyzing population of weekly TV drama. Including both the realtime view data and the playback view data, we found that the indirect communication correlate strongly to the TV viewing rate data for recent Japanese 20 TV drama.

physics.soc-ph↗

arXiv2013

The special McKay correspondence and exceptional collection

We show that the derived category of coherent sheaves on the quotient stack of the affine plane by a finite small subgroup of the general linear group is obtained from the derived category of coherent sheaves on the minimal resolution by adding a semiorthogonal summand with a full exceptional collection. The proof is based on an explicit construction in the abelian case, together with the analysis of the behavior of the derived categories of coherent sheaves under root constructions.

math.AG↗