We compute the transition amplitude between the chord number $0$ and $\ell$ states in the double scaled SYK model and interpret it as a Hartle-Hawking wavefunction of the bulk gravitational theory. We observe that the so-called un-crossed matter correlators of double scaled SYK model are obtained by gluing the Hartle-Hawking wavefunctions with an appropriate weight.

As IoT and edge inference proliferate,there is a growing need to simultaneously optimize area and delay in lookup-table (LUT)-based multipliers that implement large numbers of low-bitwidth operations in parallel. This paper proposes a hardwareefficientaccurate 4-bit multiplier design for AMD Xilinx 7-series FPGAs using only 11 LUTs and two CARRY4 blocks. By reorganizing the logic functions mapped to the LUTs, the proposed method reduces the LUT count by one compared with the prior 12-LUT design while also shortening the critical path. Evaluation confirms that the circuit attains minimal resource usage and a critical-path delay of 2.750 ns.

We study the conjecture made by Chang, Minwalla, Sharma, and Yin on the duality between the N=6 Vasiliev higher spin theory on AdS_4 and the N=6 Chern-Simons-matter theory, so-called ABJ theory, with gauge group U(N) x U(N+M). Building on our earlier results on the ABJ partition function, we develop the systematic 1/M expansion, corresponding to the weak coupling expansion in the higher spin theory, and compare the leading 1/M correction, with our proposed prescription, to the one-loop free energy of the N=6 Vasiliev theory. We find an agreement between the two sides up to an ambiguity that appears in the bulk one-loop calculation.

For general one-matrix models in the large $N$ limit, we introduce the cap amplitude $\psi(b)$ as the expansion coefficient of the 1-form $ydx$ on the spectral curve. We find that the dilaton equation for the discrete volume $N_{g,n}$ of the moduli space of genus-$g$ Riemann surfaces with $n$ boundaries is interpreted as gluing the cap amplitude along one of the boundaries. In this process, one of the boundaries is capped and the number of boundaries decreases by one. In a similar manner, the genus-$g$ free energy $F_g$ is obtained by gluing the cap amplitude to $N_{g,1}$.

We study the end of the world (EOW) brane in double scaled SYK (DSSYK) model. We find that the boundary state of EOW brane is a coherent state of the $q$-deformed oscillators and the associated orthogonal polynomial is the continuous big $q$-Hermite polynomial. In a certain scaling limit, the big $q$-Hermite polynomial reduces to the Whittaker function, which reproduces the wavefunction of JT gravity with an EOW brane. We also compute the half-wormhole amplitude in DSSYK and show that the amplitude is decomposed into the trumpet and the factor coming from the EOW brane.

GREX-PLUS (Galaxy Reionization EXplorer and PLanetary Universe Spectrometer) is a mission candidate for a JAXA's strategic L-class mission to be launched in the 2030s. Its primary sciences are two-fold: galaxy formation and evolution and planetary system formation and evolution. The GREX-PLUS spacecraft will carry a 1.2 m primary mirror aperture telescope cooled down to 50 K. The two science instruments will be onboard: a wide-field camera in the 2-8 $\mu$m wavelength band and a high resolution spectrometer with a wavelength resolution of 30,000 in the 10-18 $\mu$m band. The GREX-PLUS wide-field camera aims to detect the first generation of galaxies at redshift $z>15$. The GREX-PLUS high resolution spectrometer aims to identify the location of the water ``snow line'' in proto-planetary disks. Both instruments will provide unique data sets for a broad range of scientific topics including galaxy mass assembly, origin of supermassive blackholes, infrared background radiation, molecular spectroscopy in the interstellar medium, transit spectroscopy for exoplanet atmosphere, planetary atmosphere in the Solar system, and so on.

We study the large $N$ 't Hooft expansion of the chiral partition function of 2d $U(N)$ Yang-Mills theory on a torus. There is a long-standing puzzle that no explicit holomorphic anomaly equation is known for the partition function, although it admits a topological string interpretation. Based on the chiral boson interpretation we clarify how holomorphic anomaly arises and propose a natural anti-holomorphic deformation of the partition function. Our deformed partition function obeys a fairly traditional holomorphic anomaly equation. Moreover, we find a closed analytic expression for the deformed partition function. We also study the behavior of the deformed partition function both in the strong coupling/large area limit and in the weak coupling/small area limit. In particular, we observe that drastic simplification occurs in the weak coupling/small area limit, giving another nontrivial support for our anti-holomorphic deformation.

The widespread adoption of generative AI (GenAI) tools such as GitHub Copilot and ChatGPT is transforming software development. Since generated source code is virtually impossible to distinguish from manually written code, their real-world usage and impact on open-source software development remain poorly understood. In this paper, we introduce the concept of self-admitted GenAI usage, that is, developers explicitly referring to the use of GenAI tools for content creation in software artifacts. Using this concept as a lens to study how GenAI tools are integrated into open-source software projects, we analyze a curated sample of more than 250,000 GitHub repositories, identifying 1,292 such self-admissions across 156 repositories in commit messages, code comments, and project documentation. Using a mixed methods approach, we derive a taxonomy of 32 tasks, 10 content types, and 11 purposes associated with GenAI usage based on 284 qualitatively coded mentions. We then analyze 13 documents with policies and usage guidelines for GenAI tools and conduct a developer survey to uncover the ethical, legal, and practical concerns behind them. Our findings reveal that developers actively manage how GenAI is used in their projects, highlighting the need for project-level transparency, attribution, and quality control practices in the new era of AI-assisted software development. Finally, we examine the impact of GenAI adoption on code churn in 151 repositories with self-admitted GenAI usage and find no general increase, contradicting popular narratives on the impact of GenAI on software development.

We show that the connected correlators of partition functions in double scaled SYK model can be decomposed into ``trumpet'' and the discrete analogue of the Weil-Petersson volume, which was defined by Norbury and Scott. We explicitly compute this discrete volume for the first few orders in the genus expansion and confirm that the discrete volume reduces to the Weil-Petersson volume in a certain semi-classical limit.

It is known that the double-scaled SYK model (DSSYK) reduces to JT gravity with a negative cosmological constant by zooming in on the lower edge $E=-E_0$ of the spectrum. We find that the de Sitter JT gravity (i.e. JT gravity with a positive cosmological constant) is reproduced from DSSYK by taking a scaling limit around the upper edge $E=E_0$ of the spectrum. We also argue that the appearance of de Sitter JT gravity is consistent with the behavior of the classical solution of the sine dilaton gravity.

Implicit gender bias in software development is a well-documented issue, such as the association of technical roles with men. To address this bias, it is important to understand it in more detail. This study uses data mining techniques to investigate the extent to which 56 tasks related to software development, such as assigning GitHub issues and testing, are affected by implicit gender bias embedded in large language models. We systematically translated each task from English into a genderless language and back, and investigated the pronouns associated with each task. Based on translating each task 100 times in different permutations, we identify a significant disparity in the gendered pronoun associations with different tasks. Specifically, requirements elicitation was associated with the pronoun "he" in only 6% of cases, while testing was associated with "he" in 100% of cases. Additionally, tasks related to helping others had a 91% association with "he" while the same association for tasks related to asking coworkers was only 52%. These findings reveal a clear pattern of gender bias related to software development tasks and have important implications for addressing this issue both in the training of large language models and in broader society.

Magnetic skyrmionium is a skyrmion-like spin texture with nanoscale size and high mobility. It is a topologically trivial but dynamically stable structure, which can be used as a non-volatile information carrier for next-generation spintronic storage and computing devices. Here, we study the dynamics of a skyrmionium driven by the spin torque in a ferrimagnetic nanotrack. It is found that the direction of motion is jointly determined by the internal configuration of a skyrmionium and the spin polarization vector. Besides, the deformation of a skyrmionium induced by the intrinsic skyrmion Hall effect depends on both the magnitude of the driving force and the net angular momentum. The ferrimagnetic skyrmionium is most robust at the angular momentum compensation point, whose dynamics is quite similar to the skyrmionium in antiferromagnet. The skyrmion Hall effect is perfectly prohibited, where it is possible to observe the position of the skyrmionium by measuring the magnetization. Furthermore, the current-induced dynamics of a ferrimagnetic skyrmionium is compared with that of a ferromagnetic and antiferromagnetic skyrmionium. We also make a comparison between the motion of a ferrimagnetic skyrmionium and a skyrmion. Our results will open a new field of ferrimagnetic skyrmioniums for future development of ferrimagnetic spintronics devices.

This research extends quantum singular value transformation (QSVT) for general bounded operators embedded in unitary operators on possibly infinite-dimensional Hilbert spaces. Through in-depth mathematical exploration, we have achieved a refined operator-theoretic understanding of QSVT, leading to a more streamlined approach. One of the key discoveries is that polynomial transformations in QSVT inherently apply to the entire operator, rather than being contingent on the selection of a specific basis. We expect that this research will pave the way for applying these insights to a broader range of problems in quantum information processing and provide analytical tools for quantum dynamics, such as quantum walks.

This paper studies spatial patterns formed by a proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility function and an advection-diffusion equation expressing population migration. It is found that diffusion stabilizes a homogeneous stationary solution when transport costs are sufficiently low, and it also inhibits the monotonic facilitation of agglomeration caused by lower transport costs in some cases. When the homogeneous stationary solution is unstable, numerical simulations show spatial patterns having multiple urban areas. Insights into the relation between agglomeration and control parameters (transport costs and preference for variety of consumers) gained from the large-time behavior of solutions confirm the validity of the analysis of linearized equations.

We provide a mathematical framework for identifying the shortest path in a maze using a Grover walk, which becomes non-unitary by introducing absorbing holes. In this study, we define the maze as a network with vertices connected by unweighted edges. Our analysis of the stationary state of the Grover walk on finite graphs, where we strategically place absorbing holes and self-loops on specific vertices, demonstrates that this approach can effectively solve mazes. By setting arbitrary start and goal vertices in the underlying graph, we obtain the following long-time results: (i) in tree structures, the probability amplitude is concentrated exclusively along the shortest path between start and goal; (ii) in ladder-like structures with additional paths, the probability amplitude is maximized near the shortest path.

For eleven examples of one-dimensional quantum mechanics with shape-invariant potentials, the Darboux-Crum transformations in terms of multiple pseudo virtual state wavefunctions are shown to be equivalent to Krein-Adler transformations deleting multiple eigenstates with shifted parameters. These are based upon infinitely many polynomial Wronskian identities of classical orthogonal polynomials, i.e. the Hermite, Laguerre and Jacobi polynomials, which constitute the main part of the eigenfunctions of various quantum mechanical systems with shape-invariant potentials.

The Papanicolaou stain, consisting of eosin Y, hematoxylin, light Green SF yellowish, orange G, and Bismarck brown Y, provides extensive color information essential for cervical cancer screening in cytopathology. However, the visual observation of these colors is subjective and difficult to characterize. In digital image analysis, the RGB intensities are affected by staining and imaging variations, hindering direct quantification of color in Papanicolaou-stained samples. Stain unmixing is a promising alternative that quantifies the amounts of dyes. In previous work, multispectral imaging was utilized to estimate the dye amounts of Papanicolaou stain for quantitative diagnosis. Still, its application to RGB images presents a challenge since the number of dyes exceeds the three RGB channels. This paper proposes a novel Papanicolaou stain unmixing method for RGB images that incorporates three key assumptions: nonnegative stain abundances; a sparse spatial distribution of hematoxylin, which binds to nuclei; and piecewise smoothness of stain abundances. By formulating this as an optimization problem with nonnegativity, weighted nucleus sparsity, and total variation regularizations, our method achieved excellent performance in stain quantification when validated against the results of multispectral imaging. We also adopted the proposed method for discriminating lobular endocervical glandular hyperplasia (LEGH), a precancerous lesion of gastric-type adenocarcinoma of the cervix. The resulting quantification distinctly characterized differences between LEGH and normal endocervical cells with stain abundance, and a classifier based on the quantification results achieved 98.0% accuracy. This demonstrates the significant potential of RGB-based stain unmixing for quantitative diagnosis.

We study the possibility of family unification on the basis of SU(N) gauge theory on the 6-dimensional space-time, $M^4\times T^2/Z_N$. We obtain enormous numbers of models with three families of SU(5) matter multiplets and those with three families of the standard model multiplets, from a single massless Dirac fermion with a higher-dimensional representation of SU(N), through the orbifold breaking mechanism.

This paper proposes an extension to the Generative Adversarial Networks (GANs), namely as ARTGAN to synthetically generate more challenging and complex images such as artwork that have abstract characteristics. This is in contrast to most of the current solutions that focused on generating natural images such as room interiors, birds, flowers and faces. The key innovation of our work is to allow back-propagation of the loss function w.r.t. the labels (randomly assigned to each generated images) to the generator from the discriminator. With the feedback from the label information, the generator is able to learn faster and achieve better generated image quality. Empirically, we show that the proposed ARTGAN is capable to create realistic artwork, as well as generate compelling real world images that globally look natural with clear shape on CIFAR-10.