幾何レヴィ過程に対する局所リスク最小化戦略とその数値解析的研究

早大学位記番号:新7274早稲田大

Monte Carlo simulation for Barndorff-Nielsen and Shephard model under change of measure

The Barndorff-Nielsen and Shephard model is a representative jump-type stochastic volatility model. Still, no method exists to compute option prices numerically for the non-martingale case with infinite active jumps. We develop two simulation methods for such a case under change of measure and conduct some numerical experiments

DialMAT: Dialogue-Enabled Transformer with Moment-Based Adversarial Training

This paper focuses on the DialFRED task, which is the task of embodied instruction following in a setting where an agent can actively ask questions about the task. To address this task, we propose DialMAT. DialMAT introduces Moment-based Adversarial Training, which incorporates adversarial perturbations into the latent space of language, image, and action. Additionally, it introduces a crossmodal parallel feature extraction mechanism that applies foundation models to both language and image. We evaluated our model using a dataset constructed from the DialFRED dataset and demonstrated superior performance compared to the baseline method in terms of success rate and path weighted success rate. The model secured the top position in the DialFRED Challenge, which took place at the CVPR 2023 Embodied AI workshop.Comment: Accepted for presentation at Fourth Annual Embodied AI Workshop at CVP

Development of fast-response PPAC with strip-readout for heavy-ion beams

A strip-readout parallel-plate avalanche counter (SR-PPAC) has been developed aiming at the high detection efficiency and good position resolution in high-intensity heavy-ion measurements. The performance was evaluated using 115 MeV/u $^{132}$Xe, 300 MeV/u $^{132}$Sn, and 300 MeV/u $^{48}$Ca beams. A detection efficiency beyond 99% for these beams is achieved even at an incident beam intensity of 0.7 billion particles per second. The best position resolution achieved is 235 um (FWHM).Comment: 16 pages, 18 figures, 2 table

Quaternifications and Extensions of Current Algebras on S3

Let $\mathbf{H}$ be the quaternion algebra. Let $\mathfrak{g}$ be a complex Lie algebra and let $U(\mathfrak{g})$ be the enveloping algebra of $\mathfrak{g}$. The quaternification $\mathfrak{g}^{\mathbf{H}}=$$\,(\,\mathbf{H}\otimes U(\mathfrak{g}),\,[\quad,\quad]_{\mathfrak{g}^{\mathbf{H}}}\,)$ of $\mathfrak{g}$ is defined by the bracket $\big[\,\mathbf{z}\otimes X\,,\,\mathbf{w}\otimes Y\,\big]_{\mathfrak{g}^{\mathbf{H}}}\,=$$\,(\mathbf{z}\cdot \mathbf{w})\otimes\,(XY)\,-$$\, (\mathbf{w}\cdot\mathbf{z})\otimes (YX)\,,\nonumber$ for $\mathbf{z},\,\mathbf{w}\in \mathbf{H}$ and {the basis vectors $X$ and $Y$ of $U(\mathfrak{g})$.} Let $S^3\mathbf{H}$ be the ( non-commutative) algebra of $\mathbf{H}$-valued smooth mappings over $S^3$ and let $S^3\mathfrak{g}^{\mathbf{H}}=S^3\mathbf{H}\otimes U(\mathfrak{g})$. The Lie algebra structure on $S^3\mathfrak{g}^{\mathbf{H}}$ is induced naturally from that of $\mathfrak{g}^{\mathbf{H}}$. We introduce a 2-cocycle on $S^3\mathfrak{g}^{\mathbf{H}}$ by the aid of a tangential vector field on $S^3\subset \mathbf{C}^2$ and have the corresponding central extension $S^3\mathfrak{g}^{\mathbf{H}} \oplus(\mathbf{C}a)$. As a subalgebra of $S^3\mathbf{H}$ we have the algebra of Laurent polynomial spinors $\mathbf{C}[\phi^{\pm}]$ spanned by a complete orthogonal system of eigen spinors $\{\phi^{\pm(m,l,k)}\}_{m,l,k}$ of the tangential Dirac operator on $S^3$. Then $\mathbf{C}[\phi^{\pm}]\otimes U(\mathfrak{g})$ is a Lie subalgebra of $S^3\mathfrak{g}^{\mathbf{H}}$. We have the central extension $\widehat{\mathfrak{g}}(a)= (\,\mathbf{C}[\phi^{\pm}] \otimes U(\mathfrak{g}) \,) \oplus(\mathbf{C}a)$ as a Lie-subalgebra of $S^3\mathfrak{g}^{\mathbf{H}} \oplus(\mathbf{C}a)$. Finally we have a Lie algebra $\widehat{\mathfrak{g}}$ which is obtained by adding to $\widehat{\mathfrak{g}}(a)$ a derivation $d$ which acts on $\widehat{\mathfrak{g}}(a)$ by the Euler vector field $d_0$. That is the $\mathbf{C}$-vector space $\widehat{\mathfrak{g}}=\left(\mathbf{C}[\phi^{\pm}]\otimes U(\mathfrak{g})\right)\oplus(\mathbf{C}a)\oplus (\mathbf{C}d)$ endowed with the bracket $\bigl[\,\phi_1\otimes X_1+ \lambda_1 a + \mu_1d\,,\phi_2\otimes X_2 + \lambda_2 a + \mu_2d\,\,\bigr]_{\widehat{\mathfrak{g}}} \, =$$(\phi_1\phi_2)\otimes (X_1\,X_2) \, -\,(\phi_2\phi_1)\otimes (X_2X_1)+\mu_1d_0\phi_2\otimes X_2-$ $\mu_2d_0\phi_1\otimes X_1 +$ $(X_1\vert X_2)c(\phi_1,\phi_2)a\,.$ When $\mathfrak{g}$ is a simple Lie algebra with its Cartan subalgebra $\mathfrak{h}$ we shall investigate the weight space decomposition of $\widehat{\mathfrak{g}}$ with respect to the subalgebra $\widehat{\mathfrak{h}}= (\phi^{+(0,0,1)}\otimes \mathfrak{h} )\oplus(\mathbf{C}a) \oplus(\mathbf{C}d)$