arXiv subjects

Shota Takahashi

Publications and source records attributed to Shota Takahashi.

17 recordsLinked to original sources

arXiv2026

Color Complexity of Recolorable Graph Exploration: Upper and Lower Bounds via Block Structure

We study exploration of anonymous, port-free graphs by a single agent with no internal memory. To compensate for the lack of memory, the agent uses writable vertex colors as external memory. From every starting vertex, the agent must visit all vertices, return to its start, and terminate there. Throughout, recoloring is unrestricted, and the color count includes the common initial color. However, to our knowledge, no nontrivial color lower bound was known for unrestricted recoloring. We determine the optimal number of colors on two classes defined by block structure and prove the first nontrivial color lower bounds for unrestricted recoloring. First, a single three-color algorithm explores every tree and every simple cycle in $O(n)$ moves, and no algorithm with at most two colors explores $P_3$, the path on three vertices. Second, we give a four-color algorithm that explores every graph whose blocks are cycles or complete bipartite graphs in $O(n)$ moves, and we prove that no algorithm with at most three colors explores all subcubic pseudotrees. Hence four colors are optimal for every class between subcubic pseudotrees and this block-defined class. On cacti, this improves the previous five-color upper bound to a tight four. The lower bound reduces the possible initial actions by hand and rules out the remaining cases by a machine-checked SAT certificate on nine graphs with at most five vertices. Finally, we extend the known five-color algorithm for triangle-free graphs to graphs whose blocks are cliques or triangle-free, using $O(nΔ)$ moves, where $Δ$ is the maximum degree.

cs.DC↗

arXiv2026

Tip-Enhanced Vibrational Ladder Climbing in Surface Molecular System

Achieving high-lying vibrational states is essential for actively controlling molecular reactions. We demonstrate vibrational ladder climbing of CO adsorbed on Pt(111) within the plasmonic tip-substrate nanogap formed in a scanning tunneling microscope, detected via tip-enhanced sum-frequency generation (TE-SFG). As the infrared pulse energy increases, hot-band peaks appear sequentially up to the 3-4 transition, indicating the stepwise population of higher vibrational states. Numerical analysis using the optical Bloch equations captures the observed energy dependence of these features. These results demonstrate the capability of TE-SFG to probe vibrational ladder climbing in surface molecular systems and suggest a promising route toward accessing high-lying vibrational states and controlling vibrational excitation at the nanoscale.

physics.optics↗

arXiv2026

Dynamic Competition of Fast and Collisional Neutrino Flavor Instabilities with Collisional Damping in Spatially Inhomogeneous Systems

Neutrino flavor evolution in dense astrophysical environments such as core-collapse supernova (CCSN) is influenced by collective effects. While the Fast Flavor Instability (FFI) and the Collisional Flavor Instability (CFI) are recognized as key drivers of rapid flavor conversion, their non-linear competition with collisional damping in spatially inhomogeneous systems remains poorly understood. Motivated by recent findings that FFI and resonance-like CFI co-occur in the post-bounce phase in CCSN, we scrutinize their dynamic competitions and asymptotic states. To this end, we perform numerical simulations of the quantum kinetic neutrino transport, incorporating both spatial advection and the collision terms. We demonstrate that the interplay between these coexisting neutrino flavor instabilities and collisions leads to rich dynamics. Rather than merely inducing simple decoherence, collisional damping can substantially alter the overall dynamics of collective flavor oscillations, driving the system through complex evolutionary pathways. In all cases where flavor instability develops, we find that the system converges to the same flavor-equilibrated asymptotic state, despite the diversity of intermediate dynamics. Our results suggest that realistic collisional effects drive the system to an asymptotic state distinct from the one predicted by the collisionless FFI picture. This highlights the importance of incorporating collisional effects when modeling the asymptotic outcome of flavor conversion in CCSN models.

astro-ph.HE↗

arXiv2026

Adaptive Conditional Gradient Sliding: Projection-Free and Line-Search-Free Acceleration

We study convex optimization problems over a compact convex set where projections are expensive but a linear minimization oracle (LMO) is available. We propose the adaptive conditional gradient sliding method (AdCGS), a projection-free and line-search-free method that retains Nesterov's acceleration with adaptive stepsizes based on local Lipschitz estimates. AdCGS combines an accelerated outer scheme with an LMO-based inner routine. It reuses gradients across multiple LMO calls to reduce gradient evaluations, while controlling the subproblem inexactness via a prescribed accuracy level coupled with adaptive stepsizes. We prove accelerated rates for convex objective functions, matching projection-based methods, without relying on a projection oracle. For locally strongly convex objective functions, we further establish linear convergence without additional geometric assumptions on the constraint set, such as polytopes or strongly convex sets. Experiments on constrained $\ell_p$ regression, logistic regression, and least-squares problems demonstrate that AdCGS improves over projection-free baselines and provides competitive performance when projections are inexpensive.

math.OC↗

arXiv2026

Approximate Bregman proximal gradient algorithm with variable metric Armijo--Wolfe line search

We propose a variant of the approximate Bregman proximal gradient (ABPG) algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function. ABPG is known to converge globally to a stationary point even when the smooth part of the objective function does not have a globally Lipschitz continuous gradient, and its iterates can often be expressed in closed form. However, ABPG relies on an Armijo line search to guarantee global convergence, which can slow down its practical performance. To address this issue, we propose a variant of ABPG with a variable metric Armijo--Wolfe line search. Under the variable metric Armijo--Wolfe condition, we establish global subsequential convergence of the algorithm. Moreover, assuming the Kurdyka--Łojasiewicz property, we also prove that the algorithm globally converges to a stationary point. Numerical experiments on $\ell_p$-regularized least squares problems and nonnegative linear inverse problems demonstrate that the proposed algorithm outperforms existing algorithms.

math.OC↗

arXiv2026

Plasmonic- and Electronic-Enhancement-Free Coherent Raman Detection of Ångström-Scale Molecular Layers at Metal Interfaces

Coherent Raman scattering provides highly sensitive vibrational analysis through nonlinear light-matter interactions. However, its application to metal interfaces has remained challenging because the intrinsically large non-resonant background (NRB) of metals overwhelms weak interfacial molecular vibrational signals, making direct Raman detection without plasmonic or electronic enhancement highly challenging. Here, we report a time-frequency hybrid coherent Raman spectroscopy approach that overcomes this limitation and enables sensitive detection of ångström-thick molecular systems even on atomically flat metal surfaces. Our method employs a time-frequency engineered detection scheme that combines femtosecond pump and Stokes pulses with a time-delayed, asymmetrically shaped picosecond probe pulse. By exploiting instantaneous temporal response of the metal NRB, this pulse configuration effectively filters out the dominant metal NRB in the time domain while retaining a controlled residual NRB that acts as an internal local oscillator, enabling strong interferometric amplification of weak interfacial vibrational signatures. This all-optical coherent enhancement strategy establishes a new route for direct, non-invasive Raman detection of interfacial molecular systems across a wide range of surfaces without requiring structure- and material-specific plasmonic and electronic enhancement mechanisms.

physics.optics↗

arXiv2026

Fast Frank--Wolfe Algorithms with Adaptive Bregman Step-Size for Weakly Convex Functions

We propose Frank--Wolfe (FW) algorithms with an adaptive Bregman step-size strategy for smooth adaptable (also called: relatively smooth) (weakly-) convex functions. This means that the gradient of the objective function is not necessarily Lipschitz continuous, and we only require the smooth adaptable property. Compared with existing FW algorithms, our assumptions are less restrictive. We establish convergence guarantees in various settings, including convergence rates ranging from sublinear to linear, depending on the assumptions for convex and nonconvex objective functions. Assuming that the objective function is weakly convex and satisfies the local quadratic growth condition, we provide both local sublinear and local linear convergence with respect to the primal gap. We also propose a variant of the away-step FW algorithm using Bregman distances over polytopes. We establish faster global convergence (up to a linear rate) for convex optimization under the Hölder error bound condition and local linear convergence for nonconvex optimization under the local quadratic growth condition. Numerical experiments demonstrate that our proposed FW algorithms outperform existing methods.

math.OC↗

arXiv2025

Phase-sensitive tip-enhanced sum frequency generation spectroscopy using temporally asymmetric pulse for detecting weak vibrational signals

Vibrational sum frequency generation (SFG) spectroscopy is a powerful technique for investigating molecular structures, orientations, and dynamics at surfaces. However, its spatial resolution is fundamentally restricted to the micrometer scale by the optical diffraction limit. Tip-enhanced SFG (TE-SFG) using a scanning tunneling microscope has been developed to overcome this limitation. The acquired spectra exhibit characteristic dips originating from vibrational responses located within the strong broadband non-resonant background (NRB), which distorts and obscures the molecular signals. By making the second pulse temporally asymmetric and introducing a controlled delay between the first and second laser pulses, the NRB was effectively suppressed, which in turn amplified the vibrational response through interference and facilitated the detection of weak vibrational signals. This interference also made the technique phase-sensitive, enabling the determination of absolute molecular orientations. Furthermore, forward- and backward-scattered signals were simultaneously detected, conclusively confirming that the observed signals originated from tip enhancement rather than far-field contributions. Finally, the signal enhancement factor in TE-SFG was estimated to be $6.3\times 10^6-1.3\times 10^7$, based on the experimental data. This phase-sensitive TE-SFG technique overcomes the optical diffraction limit and enables the investigation of molecular vibrations at surfaces with unprecedented detail.

physics.optics↗

arXiv2025

Giant near-field nonlinear electrophotonic effects in an angstrom-scale plasmonic junction

Plasmons facilitate a strong confinement and enhancement of near-field light, offering exciting opportunities to enhance nonlinear optical responses at the nanoscale. However, despite significant advancements, the electrically tunable range of the nonlinear optical responses at nanometer-scale plasmonic structures remains limited to a few percents per volt. Here, we transcend the limitation of the nanometer regime by expanding the concept of electrophotonics into angstrom-scale platform, enabling high-performance modulation of near-field nonlinear optical responses inaccessible in prior architectures. We demonstrate ~2000% enhancement in second-harmonic generation (SHG) within 1 V of voltage application by utilizing an angstrom-scale plasmonic gap between a metallic tip and a flat metal substrate in a scanning tunneling microscope. Extending this near-field SHG scheme to sum-frequency generation that is accompanied by large frequency upconversion, we also found that such giant electrical modulation of plasmon-enhanced nonlinear optical phenomena is effective over mid-infrared to visible broad wavelength range. Our results and concepts lay the foundation for developing near-field-based angstrom-scale nonlinear electrophotonics with significant modulation depth at low driving voltage.

physics.optics↗

arXiv2025

Diffraction-Unlimited Tip-Enhanced Sum-Frequency Vibrational Nanoscopy

Sum-frequency generation (SFG) is a powerful second-order nonlinear spectroscopic technique that provides detailed insights into molecular structures and absolute orientations at surfaces and interfaces. However, conventional SFG based on far-field schemes suffers from the diffraction limit of light, which inherently averages spectroscopic information over micrometer-scale regions and obscures nanoscale structural inhomogeneity. Here, we overcome this fundamental limitation by leveraging a highly confined optical near field within a tip-substrate nanogap of a scanning tunneling microscope (STM), pushing the spatial resolution of SFG down to ~10 nm, a nearly two-orders-of-magnitude improvement over conventional far-field SFG. By capturing tip-enhanced SFG (TE-SFG) spectra concurrently with STM scanning, we demonstrate the capability to resolve nanoscale variation in molecular adsorption structures across distinct interfacial domains. To rigorously interpret the observed TE-SFG spectra, we newly developed a comprehensive theoretical framework for the TE-SFG process and confirm via numerical simulations that the TE-SFG response under our current experimental conditions is dominantly governed by the dipole-field interactions, with negligible contributions from higher-order multipole effects. The dominance of the dipole mechanism ensures that the observed TE-SFG spectra faithfully reflect not only nanoscale interfacial structural features but also absolute up/down molecular orientations. This study presents the first experimental realization of diffraction-unlimited second-order nonlinear vibrational SFG nanoscopy, opening a new avenue for nanoscale domain-specific investigation of molecular structures and dynamics within inhomogeneous interfacial molecular systems beyond the conventional far-field SFG and STM imaging.

physics.optics↗

arXiv2025

Majorization-minimization Bregman proximal gradient algorithms for NMF with the Kullback--Leibler divergence

Nonnegative matrix factorization (NMF) is a popular method in machine learning and signal processing to decompose a given nonnegative matrix into two nonnegative matrices. In this paper, we propose new algorithms, called majorization-minimization Bregman proximal gradient algorithm (MMBPG) and MMBPG with extrapolation (MMBPGe) to solve NMF. These iterative algorithms minimize the objective function and its potential function monotonically. Assuming the Kurdyka--Łojasiewicz property, we establish that a sequence generated by MMBPG(e) globally converges to a stationary point. We apply MMBPG and MMBPGe to the Kullback--Leibler (KL) divergence-based NMF. While most existing KL-based NMF methods update two blocks or each variable alternately, our algorithms update all variables simultaneously. MMBPG and MMBPGe for KL-based NMF are equipped with a separable Bregman distance that satisfies the smooth adaptable property and that makes its subproblem solvable in closed form. Using this fact, we guarantee that a sequence generated by MMBPG(e) globally converges to a Karush--Kuhn--Tucker (KKT) point of KL-based NMF. In numerical experiments, we compare proposed algorithms with existing algorithms on synthetic data and real-world data.

math.OC↗

arXiv2025

Recolorable Graph Exploration by an Oblivious Agent with Fewer Colors

Recently, Böckenhauer, Frei, Unger, and Wehner (SIROCCO 2023) introduced a novel variant of the graph exploration problem in which a single memoryless agent must visit all nodes of an unknown, undirected, and connected graph before returning to its starting node. Unlike the standard model for mobile agents, edges are not labeled with port numbers. Instead, the agent can color its current node and observe the color of each neighboring node. To move, it specifies a target color and then moves to an adversarially chosen neighbor of that color. Böckenhauer~et al.~analyzed the minimum number of colors required for successful exploration and proposed an elegant algorithm that enables the agent to explore an arbitrary graph using only eight colors. In this paper, we present a novel graph exploration algorithm that requires only six colors. Furthermore, we prove that five colors are sufficient if we consider only a restricted class of graphs, which we call the $φ$-free graphs, a class that includes every graph with maximum degree at most three and every cactus.

cs.DC↗

arXiv2025

An Extended Closure Relation by LightGBM for Neutrino Radiation Transport in Core-collapse Supernovae

We developed a machine learning model using LightGBM, one of the most popular gradient-boosting decision tree methods these days, to predict the Eddington tensor, or the second-order angular moment, for neutrino radiation transport in core-collapse supernova simulations. We use not only the zeroth and first moments of the neutrino distribution function in momentum space as in ordinary closure relations but also information on the background matter configuration extensively. For training the model, we utilize some post-bounce snapshots from one of our previous Boltzmann radiation-hydrodynamics simulations; the Eddington tensor as well as the zeroth and first angular moments are calculated from the neutrino distribution function obtained in the simulation. LightGBM is light indeed, and its high efficiency in training enables us to feed a large number of features and figure out which features are more important than others. In this paper, we report the results of this feature engineering in addition to those of the training, validation, and generalization of our model. We find that the flux factor and non-local features are among the most relevant features; our LightGBM model can reproduce the Eddington factor better in general than the M1 closure relation, one of the most commonly employed algebraic closure relations at present; the generalization performance is also much improved from our previous model based on the deep neural network.

hep-ph↗

arXiv2024

Tip-Enhanced Sum Frequency Generation for Molecular Vibrational Nanospectroscopy

Vibrational sum frequency generation (SFG) is a nonlinear spectroscopic technique widely used to study the molecular structure and dynamics of surface systems. However, the spatial resolution achieved by far-field observations is constrained by the diffraction limit, obscuring molecular details in inhomogeneous structures smaller than the wavelength of light. To overcome this limitation, we developed a system for tip-enhanced SFG (TE-SFG) spectroscopy based on a scanning tunneling microscope. We successfully detected vibrational TE-SFG signals from adsorbed molecules on a gold substrate under ambient conditions. The phase analysis of interferometric SFG spectra provided information on molecular orientation. Furthermore, the observed TE-SFG signal was confirmed to originate from a highly localized region within a gap between the tip apex and the sample substrate. This method offers a novel platform for nonlinear optical nanospectroscopy, paving the way for the investigation of surface molecular systems beyond the diffraction limit.

physics.optics↗

arXiv2024

Approximate Bregman Proximal Gradient Algorithm for Relatively Smooth Nonconvex Optimization

In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG simpler to solve compared to existing Bregman-type algorithms. The subproblem of ABPG is often expressed in a closed form. Similarly to existing Bregman-type algorithms, ABPG does not require the global Lipschitz continuity for the gradient of the smooth part. Instead, assuming the smooth adaptable property, we establish the global subsequential convergence under standard assumptions. Additionally, assuming that the Kurdyka--Łojasiewicz property holds, we prove the global convergence for a special case. Our numerical experiments on the $\ell_p$ regularized least squares problem, the $\ell_p$ loss problem, and the nonnegative linear system show that ABPG outperforms existing algorithms especially when the gradient of the smooth part is not globally Lipschitz or even local Lipschitz continuous.

math.OC↗

arXiv2022

Blind Deconvolution with Non-smooth Regularization via Bregman Proximal DCAs

Blind deconvolution is a technique to recover an original signal without knowing a convolving filter. It is naturally formulated as a minimization of a quartic objective function under some assumption. Because its differentiable part does not have a Lipschitz continuous gradient, existing first-order methods are not theoretically supported. In this paper, we employ the Bregman-based proximal methods, whose convergence is theoretically guaranteed under the $L$-smooth adaptable ($L$-smad) property. We first reformulate the objective function as a difference of convex (DC) functions and apply the Bregman proximal DC algorithm (BPDCA). This DC decomposition satisfies the $L$-smad property. The method is extended to the BPDCA with extrapolation (BPDCAe) for faster convergence. When our regularizer has a sufficiently simple structure, each iteration is solved in a closed-form expression, and thus our algorithms solve large-scale problems efficiently. We also provide the stability analysis of the equilibrium and demonstrate the proposed methods through numerical experiments on image deblurring. The results show that BPDCAe successfully recovered the original image and outperformed other existing algorithms.

math.OC↗

arXiv2022

New Bregman proximal type algorithms for solving DC optimization problems

Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of the objective function have $L$-smoothness. In this article, we propose the Bregman Proximal DC Algorithm (BPDCA) for solving large-scale DC optimization problems that do not possess $L$-smoothness. Instead, it requires that the convex part of the objective function has the $L$-smooth adaptable property that is exploited in Bregman proximal gradient algorithms. In addition, we propose an accelerated version, the Bregman Proximal DC Algorithm with extrapolation (BPDCAe), with a new restart scheme. We show the global convergence of the iterates generated by BPDCA(e) to a limiting critical point under the assumption of the Kurdyka-Łojasiewicz property or subanalyticity of the objective function and other weaker conditions than those of the existing methods. We applied our algorithms to phase retrieval, which can be described both as a nonconvex optimization problem and as a DC optimization problem. Numerical experiments showed that BPDCAe outperformed existing Bregman proximal-type algorithms because the DC formulation allows for larger admissible step sizes.

math.OC↗