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Given a mirror pair of a symplectic manifold $X$ and a Landau-Ginzburg potential $W$, we are interested in the problem whether the quantum cohomology of $X$ and the Jacobian algebra of $W$ are isomorphic. Since those can be equipped with Frobenius algebra structures, we might ask whether they are isomorphic as Frobenius algebras. We show that the Kodaira-Spencer map gives a Frobenius algebra isomorphism for elliptic orbispheres, under the Floer theoretic modification of the residue pairing., Comment: 17 pages, 3 figures

Given a hypersurface singularity (not necessarily isolated) with a finite abelian group action, we develop a method to define an explicit product structure on the twisted Koszul algebra (whose invariant subalgebra is the orbifold Koszul algebra)., Comment: 15 pages

When a Weinstein manifold admits an action of a finite abelian group, we propose its mirror construction following the equivariant TQFT-type construction, and obtain as a mirror the orbifolding of the mirror of the quotient with respect to the induced dual group action. As an application, we construct an orbifold Landau-Ginzburg mirror of a punctured Riemann surface given as an abelian cover of the pair-of-pants, and prove its closed-string mirror symmetry using the (part of) closed-open map twisted by the dual group action., Comment: 42 pages and 11 figures

Despite the common use of rule-based tools for online content moderation, human moderators still spend a lot of time monitoring them to ensure that they work as intended. Based on surveys and interviews with Reddit moderators who use AutoModerator, we identified the main challenges in reducing false positives and false negatives of automated rules: not being able to estimate the actual effect of a rule in advance and having difficulty figuring out how the rules should be updated. To address these issues, we built ModSandbox, a novel virtual sandbox system that detects possible false positives and false negatives of a rule to be improved and visualizes which part of the rule is causing issues. We conducted a user study with online content moderators, finding that ModSandbox can support quickly finding possible false positives and false negatives of automated rules and guide moderators to update those to reduce future errors., Comment: 24 pages, 10 figures

Prior HCI studies often analyzed smartphone app usage data for usability and user experience research purposes. App usage videos are often collected by a screen recording app in order to better analyze the app usage behaviors (e.g., app usage time, screen transition, and notification handling). However, it is difficult to analyze app usage videos along with multiple user interaction stream data. When the length of a video is long, data analysis tends to take a long time due to the volume of user interaction data. This is even more difficult for novice researchers due to a lack of data analysis experience. In this paper, we propose LV-Linker (Log and Video Linker), a visualization tool that helps researchers quickly explore the app usage log and video data by linking multiple time series log data with the video data. We conducted a preliminary user study with eight participants to evaluate the benefits of linking, by measuring task completion time, helpfulness, and subjective task workload. Our results showed that offering a linking feature significantly lowers the task completion time and task workload., Comment: 9 pages, 4 figures, will be published in ACM CHI 2024 after revision

Given a polynomial $W$ with an isolated singularity, we can consider the Jacobian ring as an invariant of the singularity. If in addition we have a group action on the polynomial ring with $W$ fixed, we are led to consider the twisted Jacobian ring which reflects the equivariant structure as well. Our main result is to show that the twisted Jacobian ring is isomorphic to an endomorphism ring of the "twisted diagonal" matrix factorization. As an application, we suggest a way to investigate Floer theory of Lagrangian submanifolds which represent homological mirror functors., Comment: 25 pages, 2 figures. Some parts concerning module structures of morphism spaces were added

A version of mirror symmetry predicts a ring isomorphism between quantum cohomology of a symplectic manifold and Jacobian algebra of the Landau-Ginzburg mirror, and for toric manifolds Fukaya-Oh-Ohta-Ono constructed such a map called Kodaira-Spencer map using Lagrangian Floer theory. We discuss a general construction of Kodaira-Spencer ring homomorphism when LG mirror potential $W$ is given by $J$-holomorphic discs with boundary on a Lagrangian $L$: we find an $A_{\infty}$-algebra $\mathcal{B}$ whose $m_1$-complex is a Koszul complex for $W$ under mild assumptions on $L$. Closed-open map gives a ring homomorphism from quantum cohomology to cohomology algebra of $\mathcal{B}$ which is Jacobian algebra of $W$. We also construct an equivariant version for orbifold LG mirror $(W,H)$. We construct a Kodaira-Spencer map from quantum cohomology to another $A_{\infty}$-algebra $(\mathcal{B}\rtimes H)^H$ whose cohomology algebra is isomorphic to the orbifold Jacobian algebra of $(W,H)$ under an assumption. For the $2$-torus whose mirror is an orbifold LG model given by Fermat cubic with a $\mathbb{Z}/3$-action, we compute an explicit Kodaira-Spencer isomorphism., Comment: 40 pages, 4 figures. Comments are welcome

We investigate how ring isomorphisms between mirror closed states of compact toric Fano manifolds come from homological mirror symmetry. A natural closed-open relation on B-side is also discussed., Comment: 20 pages, 1 figure

We prove an equivalence of two A-infinity functors, via Orlov's Landau-Ginzburg/Calabi-Yau correspondence. One is the Polishchuk-Zaslow's mirror symmetry functor of elliptic curves, and the other is a localized mirror functor from the Fukaya category of the 2-torus to a category of noncommutative matrix factorizations. As a corollary we prove that the noncommutative mirror functor realizes homological mirror symmetry for any translation parameter $t$., Comment: 17 pages, 4 figures. To appear in Kyoto J. Math

We propose a condition-adaptive representation learning framework for the driver drowsiness detection based on 3D-deep convolutional neural network. The proposed framework consists of four models: spatio-temporal representation learning, scene condition understanding, feature fusion, and drowsiness detection. The spatio-temporal representation learning extracts features that can describe motions and appearances in video simultaneously. The scene condition understanding classifies the scene conditions related to various conditions about the drivers and driving situations such as statuses of wearing glasses, illumination condition of driving, and motion of facial elements such as head, eye, and mouth. The feature fusion generates a condition-adaptive representation using two features extracted from above models. The detection model recognizes drivers drowsiness status using the condition-adaptive representation. The condition-adaptive representation learning framework can extract more discriminative features focusing on each scene condition than the general representation so that the drowsiness detection method can provide more accurate results for the various driving situations. The proposed framework is evaluated with the NTHU Drowsy Driver Detection video dataset. The experimental results show that our framework outperforms the existing drowsiness detection methods based on visual analysis., Comment: IEEE Transactions on Intelligent Transportation Systems publication information (2018)

Polishchuk-Zaslow explained the homological mirror symmetry between Fukaya category of symplectic torus and the derived category of coherent sheaves of elliptic curves via Lagrangian torus fibration. Recently, Cho-Hong-Lau found another proof of homological mirror symmetry using localized mirror functor, whose target category is given by graded matrix factorizations. We find an explicit relation between these two approaches., Comment: 25 pages, 7 figures

We find a relation between Lagrangian Floer pairing of a symplectic manifold and Kapustin-Li pairing of the mirror Landau-Ginzburg model under localized mirror functor. They are conformally equivalent with an interesting conformal factor $(vol^{Floer}/vol)^2$, which can be described as a ratio of Lagrangian Floer volume class and classical volume class. For this purpose, we introduce $B$-invariant of Lagrangian Floer cohomology with values in Jacobian ring of the mirror potential function. And we prove what we call a multi-crescent Cardy identity under certain conditions, which is a generalized form of Cardy identity. As an application, we discuss the case of general toric manifold, and the relation to the work of Fukaya-Oh-Ohta-Ono and their $Z$-invariant. Also, we compute the conformal factor $(vol^{Floer}/vol)^2$ for the elliptic curve quotient $\mathbb{P}^1_{3,3,3}$, which is expected to be related to the choice of a primitive form., Comment: 35 pages, 5 figures. Comments are welcome

The complexity of strongly correlated electron physics in vanadium dioxide is exemplified as its rich phase diagrams of all kinds, which in turn shed light on the mechanisms behind its various phase transitions. In this work, we map out the hydrostatic pressure - temperature phase diagram of vanadium dioxide nanobeams by independently varying pressure and temperature with a diamond anvil cell. In addition to the well-known insulating M1 (monoclinic) and metallic R (tetragonal) phases, the diagram identifies the existence at high pressures of the insulating M1' (monoclinic, more conductive than M1) phase, and two metallic phases of X (monoclinic) and O (orthorhombic, at high temperature only). Systematic optical and electrical measurements combined with density functional calculations allow us to delineate their phase boundaries as well as reveal some basic features of the transitions., Comment: 9 pages, 4 figures