arXiv subjects

Takashi Sato

Publications and source records attributed to Takashi Sato.

At least 19 recordsLinked to original sources

arXiv2026

Mean-field games with unbounded controls: a weak formulation approach to global solutions

We establish an existence of equilibrium result for a class of non-Markovian mean-field games with unbounded control space in weak formulation. Our result is based on new existence and stability results for quadratic-growth generalized McKean-Vlasov BSDEs. Unlike earlier approaches, our approach does not require boundedness assumptions on the model parameters or time horizons and allows for running costs that are quadratic in the control variable.

math.OC↗

arXiv2026

3D-Printing Water-Soluble Channels Filled with Liquid Metal for Recyclable and Cuttable Wireless Power Sheet

A recyclable and cuttable wireless power transfer (WPT) sheet is proposed, enabled by H-tree wiring and water-soluble channels filled with liquid metal (LM). Conventional 2D WPT systems lose their functionality when physically damaged or modified. The H-tree wiring pattern maintains the operation of the remaining coils even after the outer region of the sheet is cut away. The LM can be recovered by dissolving 3D-printed polyvinyl alcohol (PVA) channels in water. The sheet dimensions were experimentally optimized, and a Q-factor over 55 was achieved at 6.78 MHz. The sheet maintained its bending stiffness and electrical resistance during 100 bending cycles. After four dissolution-refabrication cycles, 98 percent of the LM was recovered with stable electrical properties. The WPT sheet can be integrated into everyday objects and enables long-term, continuous operation of surrounding electronic devices, contributing to IoT applications and ambient computing.

cs.HC↗

arXiv2026

Six-dimensional GKM manifolds with four fixed points

In this paper, we study $6$-dimensional GKM manifolds with $4$ fixed points. We classify all possible GKM graphs, and for each type of graph we construct a manifold, proving the existence. We show that six types occur. (P1) complex projective space $\mathbb{C} P^3$ with standard complex structure (P2) blow up of $S^6$ at a fixed point, diffeomorphic to $\mathbb{C} P^3$ (P3) $\mathbb{C} P^3$ as the homogeneous space $\mathrm{Sp}(2)/(\mathrm{U}(1) \times \mathrm{Sp}(1))$ with non-standard almost complex structure (Q1) complex quadric $Q_3$ with standard complex structure (Q2) blow up of $S^6$ along isotropy $2$-sphere, diffeomorphic to $Q_3$ (S) $S^2 \times S^4$, obtained as equivariant gluing along orbits of two $S^6$'s

math.GT↗

arXiv2025

Notes on the cohomology of partial Hessenberg varieties

Hessenberg varieties are a family of subvarieties of full flag varieties. This family contains well-known varieties such as Springer fibers, Peterson varieties, and permutohedral varieties. It was introduced by De Mari-Procesi-Shayman in 1992 and has been actively studied in this decade. In particular, unexpected relations to hyperplane arrangements and the Stanley-Stembridge conjecture in graph theory have been discovered. Hessenberg varieties can be defined in partial flag varieties. In this paper, we study their cohomology by relating them to the cohomology of Hessenberg varieties in the full flag varieties.

math.AG↗

arXiv2025

Regular semisimple Hessenberg varieties with cohomology rings generated in degree two

A regular semisimple Hessenberg variety $\mathrm{Hess}(S,h)$ is a smooth subvariety of the flag variety determined by a square matrix $S$ with distinct eigenvalues and a Hessenberg function $h$. The cohomology ring $H^*(\mathrm{Hess}(S,h))$ is independent of the choice of $S$ and is not explicitly described except for a few cases. In this paper, we characterize the Hessenberg function $h$ such that $H^*(\mathrm{Hess}(S,h))$ is generated in degree two as a ring. It turns out that such $h$ is what is called a (double) lollipop.

math.AG↗

arXiv2025

Extending Games beyond the Finite Horizon

This paper argues that the finite horizon paradox, where game theory contradicts intuition, stems from the limitations of standard number systems in modelling the cognitive perception of infinity. To address this issue, we propose a new framework based on Alternative Set Theory (AST). This framework represents different cognitive perspectives on a long history of events using distinct topologies. These topologies define an indiscernibility equivalence that formally treats huge, indistinguishable quantities as equivalent. This offers criterion-dependent resolutions to long-standing paradoxes, such as Selten's chain store paradox and Rosenthal's centipede game. Our framework reveals new intuitive subgame perfect equilibria, the characteristics of which depend on the chosen temporal perspective and payoff evaluation. Ultimately, by grounding its mathematical foundation in different modes of human cognition, our work expands the explanatory power of game theory for long-horizon scenarios.

cs.GT↗

arXiv2025

SOME: Symmetric One-Hot Matching Elector -- A Lightweight Microsecond Decoder for Quantum Error Correction

Conventional quantum error correction (QEC) decoders such as Minimum-Weight Perfect Matching (MWPM) and Union-Find (UF) offer high thresholds and fast decoding, respectively, but both suffer from high topological complexity. In contrast, Ising model-based decoders reduce topological complexity but demand considerable decoding time. We propose the Symmetric One-Hot Matching Elector (SOME), a novel decoder that reformulates the QEC decoding task as a Quadratic Unconstrained Binary Optimization (QUBO) problem -- termed the One-Hot QUBO (OHQ). Each variable in the QUBO represents whether a given pair of flipped syndromes is matched, while the error probabilities between the pair are encoded as interaction coefficients (weight). Constraints ensure that each flipped syndrome is matched exactly once. Valid solutions of OHQ correspond to self-inverse permutation matrices, characterized by symmetric one-hot encoding. To solve the OHQ efficiently, SOME reformulates the decoding task as the construction of permutation matrices that minimize the total weight. It initializes each candidate matrix from one of the minimum-weight syndrome pairs, then iteratively appends additional pairs in ascending order of weight, and finally selects the permutation matrix with the lowest total energy. SOME achieves up to a 99.9x reduction in variable count and reduces decoding times from milliseconds to microseconds on a single-threaded commodity CPU. OHQ also maintains performance up to a 10.5% physical error rate, surpassing the highest known threshold of MWPM@.

cs.ET↗

arXiv2025

Full-body WPT: wireless powering with meandered e-textiles

We present Full-body WPT, wireless power networking around the human body using a meandered textile coil. Unlike traditional inductive systems that emit strong fields into the deep tissue inside the body, the meander coil enables localized generation of strong magnetic field constrained to the skin surface, even when scaled to the size of the human body. Such localized inductive system enhances both safety and efficiency of wireless power around the body. Furthermore, the use of low-loss conductive yarn achieve energy-efficient and lightweight design. We analyze the performance of our design through simulations and experimental prototypes, demonstrating high power transfer efficiency and adaptability to user movement and posture. Our system provides a safe and efficient distributed power network using meandered textile coils integrated into wearable materials, highlighting the potential of body-centric wireless power networking as a foundational layer for ubiquitous health monitoring, augmented reality, and human-machine interaction systems.

cs.HC↗

arXiv2025

Lookup Table-based Multiplication-free All-digital DNN Accelerator Featuring Self-Synchronous Pipeline Accumulation

Deep neural networks (DNNs) have been widely applied in our society, yet reducing power consumption due to large-scale matrix computations remains a critical challenge. MADDNESS is a known approach to improving energy efficiency by substituting matrix multiplication with table lookup operations. Previous research has employed large analog computing circuits to convert inputs into LUT addresses, which presents challenges to area efficiency and computational accuracy. This paper proposes a novel MADDNESS-based all-digital accelerator featuring a self-synchronous pipeline accumulator, resulting in a compact, energy-efficient, and PVT-invariant computation. Post-layout simulation using a commercial 22nm process showed that 2.5 times higher energy efficiency (174 TOPS/W) and 5 times higher area efficiency (2.01 TOPS/mm2) can be achieved compared to the conventional accelerator.

cs.AR↗

arXiv2025

Gamma vectors of partitioned permutohedra

We determine that $γ$-vectors of partitioned permutohedra, thereby generalizing a result of Foata and Schützenberger. Our result is closely related to a result of Athanasiadis on the representation of the symmetric group on the cohomology of the permutohedral variety. We explain how to derive Athanasiadis' result from ours and vice versa.

math.CO↗

arXiv2025

Hardware-Friendly Delayed-Feedback Reservoir for Multivariate Time-Series Classification

Reservoir computing (RC) is attracting attention as a machine-learning technique for edge computing. In time-series classification tasks, the number of features obtained using a reservoir depends on the length of the input series. Therefore, the features must be converted to a constant-length intermediate representation (IR), such that they can be processed by an output layer. Existing conversion methods involve computationally expensive matrix inversion that significantly increases the circuit size and requires processing power when implemented in hardware. In this article, we propose a simple but effective IR, namely, dot-product-based reservoir representation (DPRR), for RC based on the dot product of data features. Additionally, we propose a hardware-friendly delayed-feedback reservoir (DFR) consisting of a nonlinear element and delayed feedback loop with DPRR. The proposed DFR successfully classified multivariate time series data that has been considered particularly difficult to implement efficiently in hardware. In contrast to conventional DFR models that require analog circuits, the proposed model can be implemented in a fully digital manner suitable for high-level syntheses. A comparison with existing machine-learning methods via field-programmable gate array implementation using 12 multivariate time-series classification tasks confirmed the superior accuracy and small circuit size of the proposed method.

cs.LG↗

arXiv2025

Online Training and Inference System on Edge FPGA Using Delayed Feedback Reservoir

A delayed feedback reservoir (DFR) is a hardwarefriendly reservoir computing system. Implementing DFRs in embedded hardware requires efficient online training. However, two main challenges prevent this: hyperparameter selection, which is typically done by offline grid search, and training of the output linear layer, which is memory-intensive. This paper introduces a fast and accurate parameter optimization method for the reservoir layer utilizing backpropagation and gradient descent by adopting a modular DFR model. A truncated backpropagation strategy is proposed to reduce memory consumption associated with the expansion of the recursive structure while maintaining accuracy. The computation time is significantly reduced compared to grid search. Additionally, an in-place Ridge regression for the output layer via 1-D Cholesky decomposition is presented, reducing memory usage to be 1/4. These methods enable the realization of an online edge training and inference system of DFR on an FPGA, reducing computation time by about 1/13 and power consumption by about 1/27 compared to software implementation on the same board.

cs.AR↗

arXiv2025

Fast Parameter Optimization of Delayed Feedback Reservoir with Backpropagation and Gradient Descent

A delayed feedback reservoir (DFR) is a reservoir computing system well-suited for hardware implementations. However, achieving high accuracy in DFRs depends heavily on selecting appropriate hyperparameters. Conventionally, due to the presence of a non-linear circuit block in the DFR, the grid search has only been the preferred method, which is computationally intensive and time-consuming and thus performed offline. This paper presents a fast and accurate parameter optimization method for DFRs. To this end, we leverage the well-known backpropagation and gradient descent framework with the state-of-the-art DFR model for the first time to facilitate parameter optimization. We further propose a truncated backpropagation strategy applicable to the recursive dot-product reservoir representation to achieve the highest accuracy with reduced memory usage. With the proposed lightweight implementation, the computation time has been significantly reduced by up to 1/700 of the grid search.

cs.AR↗

arXiv2024

Friction jointing of distributed rigid capacitors to stretchable liquid metal coil for full-body wireless charging clothing

For full-body wireless power transfer (WPT), a liquid metal (LM)-based meandered textile coil has been proposed. Multiple rigid capacitors must be inserted in a long coil for efficiency; however, the conventional adhesive jointing suffers from the fragile connection between a rubber tube filled with LM and the capacitor due to the poor adhesion of the rubbers. This paper presents a friction-based jointing, which covers the capacitor with a rigid capsule to enhance the frictional force between the tube and capsule. By experimentally optimizing the capsule design, the LM coil with capacitors showed 3.1 times higher stretch tolerance (31.8 N) and 3.5 times higher bending tolerance (25.9 N) than the adhesive jointing. Moreover, the WPT garment prototype shows excellent mechanical durability against repeated stretching and washing over 100 times. Our full-body meandered textile coil can enable wireless charging to wearable devices around the body for long-term continuous healthcare monitoring, activity recognition, and AR/VR.

cs.HC↗

arXiv2024

Automorphisms of GKM graphs and regular semisimple Hessenberg varieties

A regular semisimple Hessenberg variety $\mathrm{Hess}(S,h)$ is a smooth subvariety of the full flag variety $\mathrm{Fl}(\mathbb{C}^n)$ associated with a regular semisimple matrix $S$ of order $n$ and a function $h$ from $\{1,2,\dots,n\}$ to itself satisfying a certain condition. We show that when $\mathrm{Hess}(S,h)$ is connected and not the entire space $\mathrm{Fl}(\mathbb{C}^n)$, the reductive part of the identity component $\mathrm{Aut}^0(\mathrm{Hess}(S,h))$ of the automorphism group $\mathrm{Aut}(\mathrm{Hess}(S,h))$ of $\mathrm{Hess}(S,h)$ is an algebraic torus of dimension $n-1$ and $\mathrm{Aut}(\mathrm{Hess}(S,h))/\mathrm{Aut}^0(\mathrm{Hess}(S,h))$ is isomorphic to a subgroup of $\mathfrak{S}_n$ or $\mathfrak{S}_n\rtimes \{\pm 1\}$, where $\mathfrak{S}_n$ is the symmetric group of degree $n$. As a byproduct of our argument, we show that $\mathrm{Aut}(X)/\mathrm{Aut}^0(X)$ is a finite group for any projective GKM manifold $X$.

math.AG↗

arXiv2024

SPulseGen: Succinct pulse generator architecture maximizing gate fidelity for superconducting quantum computers

This paper proposes a cost-effective architecture for an RF pulse generator for superconducting qubits. Most existing works use arbitrary waveform generators (AWGs) that require both a large amount of high-bandwidth memories and high-performance analog circuits to achieve the highest gate fidelity with an optimized RF pulse waveform. The proposed pulse generator architecture significantly simplifies both the generator circuit and the waveform of the RF pulse to a cost-aware square pulses. This architecture eliminates the requirement for power- and cost-intensive AWG, a major obstacle in realizing scalable quantum computers. Additionally, this paper proposes a process to optimize pulse waveforms to maximize fidelity of gate operations for single and multiple qubits. Quantum dynamics simulation of transmon qubits, wherein the state of system evolves with time, demonstrates that our pulse generator can achieve practically the same gate fidelity as ideal RF pulses, while substantially reducing the performance requirements of memory and analog circuits.

quant-ph↗

arXiv2023

Backward stochastic difference equations on lattices with application to market equilibrium analysis

We study backward stochastic difference equations (BSΔE) driven by a d-dimensional stochastic process on a lattice whose increments have only d + 1 possible values that generates the lattice. Regarding the driving process as a d dimensional asset price process, we give applications to an optimal investment problem and a market equilibrium analysis, where utility functionals are defined through BSΔE.

math.PR↗

arXiv2023

Modular law through GKM theory

The solution of Shareshian-Wachs conjecture by Brosnan-Chow and Guay-Paquet tied the graded chromatic symmetric functions on indifference graphs (or unit interval graphs) and the cohomology of regular semisimple Hessenberg varieties with the dot action. A similar result holds between unicellular LLT polynomials and twins of regular semisimple Hessenberg varieties. A recent result by Abreu-Nigro enabled us to prove these results by showing the modular law for the geometrical objects, and this is indeed done by Precup-Sommers and Kiem-Lee. In this paper, we give elementary and simpler proofs to the modular law through GKM theory.

math.AT↗