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Akira Yasuhara

Publications and source records attributed to Akira Yasuhara.

At least 19 recordsLinked to original sources
arXiv2026

Multi-Angle Beam Scanning Transmission Electron Microscopy for Diffraction-Contrast-Free Magnetic Imaging

Recent development of the differential phase contrast (DPC) scanning transmission electron microscopy (STEM) technique has significantly advanced materials science supported by high-sensitivity detectors and powerful data processing. Especially the 4D-STEM technique, employing a pixelated camera as a STEM detector, enables extensive information acquisition through post-processing of large datasets. However, magnetic or electric field imaging using DPC is often disturbed by diffraction contrasts intrinsic to the crystalline material. In this paper, we demonstrate elimination of the diffraction contrasts for magnetic field imaging by using angularly distributed multiple electron beams generated by a multi-hole aperture within the 4D-STEM framework. This multi-angle beam configuration suppresses irrelevant crystalline contrast and yields direct magnetic information with high sensitivity from the specimen. Furthermore, we performed various image analysis to extract and interpret magnetic domain structures and domain walls.

physics.ins-det↗
arXiv2026

Milnor-type invariants for surface-links and cut-diagrams

We generalize Milnor link invariants to surface-links in 4-space, possibly with boundary. To this end, we introduce the notion of cut-diagram, which is a 2-dimensional analogue of Gauss diagrams. To each cut-diagram, we associate a group extending the fundamental group of the exterior of a surface-link, and we extract Milnor-type invariants from its successive nilpotent quotients. We show that this yields concordance invariants for surface-links, and that some even are link-homotopy invariants. We give several concrete applications, including realization and classification results. The theory of cut-diagrams is further investigated, heading towards a combinatorial approach to surfaces in 4-space.

math.GT↗
arXiv2026

Combinatorial link concordance using cut-diagrams

Cut-diagrams are diagrammatic objects, defined in dimensions 1 and 2, that generalize links in 3-space and surface-links in 4-space; in dimension 1, this coincides with the theory of welded links. Using cut-diagrams, we introduce an equivalence relation called cut-concordance, which encompasses the topological notion of concordance for classical links. Our main result is that the nilpotent peripheral system of 1-dimensional cut-diagrams is an invariant of cut-concordance, giving along the way a combinatorial version of a theorem of Stallings. We also investigate the relationship with several other equivalence relations in diagrammatic knot theory, in particular in connection with link-homotopy.

math.GT↗
arXiv2026

Structure and unique factorization in concordance groups of links

Donald and Owens introduced two link concordance groups with a marked component and showed that they contain the knot concordance group as a direct summand with infinitely generated complements. While not explicitly posed by Donald and Owens, the problem of determining the structure of these complements arises naturally from their work. In this paper, we completely resolve this problem by proving that both complements are isomorphic to $\mathbb{Z}^{\infty} \oplus (\mathbb{Z}/2\mathbb{Z})^{\infty}$. Moreover, we introduce a notion of prime element and establish a unique prime decomposition theorem. This yields a canonical normal form, providing a complete description of the group structure.

math.GT↗
arXiv2026

Electron Recoil via Sample Momentum Transfer under Optical-Mode Excitation

The interaction between free electrons and optical modes underlies a variety of quantum and nanoscale light-matter phenomena, yet the associated momentum exchange with the sample largely remained overlooked. Here, we experimentally demonstrate the momentum transfer from free electrons to planar samples during optical mode excitation using momentum-resolved electron energy-loss spectroscopy. The momentum transfer to the sample modifies the apparent dispersion relation which is significant when the planner sample is tilted. Under specific conditions, the sample receives momentum opposite to the electron beam direction.

physics.optics↗
arXiv2026

Compressive multi-beam scanning transmission electron microscopy

We demonstrate a multi-beam scanning transmission electron microscopy (STEM) imaging that integrates down-sampling with super-resolution image reconstruction via a compressive sensing framework. A custom condenser aperture with six randomly positioned circular holes is employed to produce a multi-beam STEM probe, with the beam shape and distribution tuned through defocus. While the raw multi-beam images exhibit overlapping patterns, reconstruction using Adam optimization and total variation normalization yields high-fidelity images that closely reproduce the original sample structures, even from substantially down-sampled data. The proposed approach offers a pathway toward significant acceleration of such techniques through multibeam sparse sampling and computational reconstruction potentially useful for the analytical scanning methods in general.

physics.ins-det↗
arXiv2025

Welded graphs, Wirtinger groups and knotted punctured spheres

We develop a general diagrammatic theory of welded graphs, and provide an extension of Satoh's Tube map from welded graphs to ribbon surface-links. As a topological application, we obtain a complete link-homotopy classification of so-called knotted punctured spheres in $4$-space, by means of the $4$-dimensional Milnor invariants introduced previously by the authors. On the algebraic side, we show that the theory of welded graphs can be reinterpreted as a theory of Wirtinger group presentations, up to a natural set of transformations; these groups arise as the fundamental group of the exterior of the surface-link obtained from the given welded graph by the extended Tube map. Finally, we address the injectivity question for the Tube map, identifying a new family of local moves on welded links, called $Υ$ moves, under which the (non extended) Tube map is invariant.

math.GT↗
arXiv2025

The classification of links up to clasp-pass moves

We give a complete classification of links up to clasp-pass moves, which coincides with Habiro's $C_3$-equivalence. We also classify links up to band-pass and band-# moves, which are versions of the usual pass- and #-move, respectively, where each pair of parallel strands belong to the same component. This recovers and generalizes widely a number of partial results in the study of these local moves. The proofs make use of clasper theory.

math.GT↗
arXiv2024

Semicircular-aperture illumination scanning transmission electron microscopy

Scanning transmission electron microscopy (STEM) provides high-resolution visualization of atomic structures as well as various functional imaging modes utilizing phase contrast. In this study we introduce a semicircular aperture in STEM bright field imaging, which gives a phase contrast transfer function that becomes complex and includes both lower and higher spatial frequency contrast transfer. This approach offers significant advantages over conventional phase plate methods, having no charge accumulation, degradation, or unwanted background noise, which are all problematic in the phase plate material. Also compared to the differential phase contrast or ptychography equipment, this semicircular aperture is far less costly. We apply this approach to visualization of polymer, biological and magnetic samples.

physics.optics↗
arXiv2023

Higher order Kirk invariants of link maps

We define numerical link-homotopy invariants of link maps of any number of components, which naturally generalize the Kirk invariant. The Kirk invariant is a link-homotopy invariant of 2-component link maps given by linking numbers of loops based at self-singularities of each component with the other spherical component; our invariants use instead ingredients from Milnor's higher order link invariants, and are extracted from the reduced fundamental groups of the exterior. We provide practical algorithms to compute these invariants from an appropriate cross-section, as well as families of examples that are therewith detected. The main proofs use the combinatorial theory of cut-diagrams previously developed by the authors.

math.GT↗
arXiv2022

k-reduced groups and Milnor invariants

We characterize, in an algebraic and in a diagrammatic way, Milnor string link invariants indexed by sequences where any index appears at most $k$ times, for any fixed $k\ge 1$. The algebraic characterization is given in terms of an Artin-like action on the so-called $k$-reduced free groups; the diagrammatic characterization uses the langage of welded knot theory. The link case is also addressed.

math.GT↗
arXiv2021

Link concordances as surfaces in 4-space and the 4-dimensional Milnor invariants

Fixing two concordant links in $3$--space, we study the set of all embedded concordances between them, as knotted annuli in $4$--space. When regarded up to surface-concordance or link-homotopy, the set $\mathcal{C}(L)$ of concordances from a link $L$ to itself forms a group. In order to investigate these groups, we define Milnor-type invariants of $\mathcal{C}(L)$, which are integers defined modulo a certain indeterminacy given by Milnor invariants of $L$. We show in particular that, for a slice link $L$, these invariants classify $\mathcal{C}(L)$ up to link-homotopy.

math.GT↗
arXiv2020

Combinatorial approach to Milnor invariants of welded links

For a classical link, Milnor defined a family of isotopy invariants, called Milnor $\overlineμ$-invariants. Recently, Chrisman extended Milnor $\overlineμ$-invariants to welded links by a topological approach. The aim of this paper is to show that Milnor $\overlineμ$-invariants can be extended to welded links by a combinatorial approach. The proof contains an alternative proof for the invariance of the original $\overlineμ$-invariants of classical links.

math.GT↗
arXiv2020

The Dabkowski-Sahi invariant and $4$-moves for links

Dabkowski and Sahi defined an invariant of a link in the $3$-sphere, which is preserved under $4$-moves. This invariant is a quotient of the fundamental group of the complement of the link. It is generally difficult to distinguish the Dabkowski-Sahi invariants of given links. In this paper, we give a necessary condition for the existence of an isomorphism between the Dabkowski-Sahi invariant of a link and that of the corresponding trivial link. Using this condition, we provide a practical obstruction to a link to be trivial up to $4$-moves.

math.GT↗
arXiv2019

Generalized virtualization on welded links

Let $n$ be a positive integer. The aim of this paper is to study two local moves $V(n)$ and $V^{n}$ on welded links, which are generalizations of the crossing virtualization. We show that the $V(n)$-move is an unknotting operation on welded knots for any $n$, and give a classification of welded links up to $V(n)$-moves. On the other hand, we give a necessary condition for which two welded links are equivalent up to $V^{n}$-moves. This leads to show that the $V^{n}$-move is not an unknotting operation on welded knots except for $n=1$. We also discuss relations among $V^{n}$-moves, associated core groups and the multiplexing of crossings.

math.GT↗
arXiv2019

Milnor invariants, $2n$-moves and $V^{n}$-moves for welded string links

In a previous paper, the authors proved that Milnor link-homotopy invariants modulo $n$ classify classical string links up to $2n$-move and link-homotopy. As analogues to the welded case, in terms of Milnor invariants, we give here two classifications of welded string links up to $2n$-move and self-crossing virtualization, and up to $V^{n}$-move and self-crossing virtualization, respectively.

math.GT↗
arXiv2019

Classification of string links up to $2n$-moves and link-homotopy

Two string links are equivalent up to $2n$-moves and link-homotopy if and only if their all Milnor link-homotopy invariants are congruent modulo $n$. Moreover, the set of the equivalence classes forms a finite group generated by elements of order $n$. The classification induces that if two string links are equivalent up to $2n$-moves for every $n>0$, then they are link-homotopic.

math.GT↗