-
Ring isomorphisms in norm between Banach algebras of continuous functions
Authors:
Natsumi Shibata,
Izuho Matsuzaki,
Takeshi Miura
Abstract:
Let $X$ and $Y$ be locally compact Hausdorff spaces and let $\mathbb{K}\in \{\mathbb{R},\mathbb{C}\}$. We say that a bijection $T\colon C_0(X,\mathbb{K})\to C_0(Y,\mathbb{K})$ is a ring isomorphism in norm if \[ \|T(f+g)\|=\|T(f)+T(g)\|,\qquad \|T(fg)\|=\|T(f)T(g)\| \] for every $f,g\in C_0(X,\mathbb{K})$. We determine the form of such maps. When $\mathbb{K}=\mathbb{C}$, under the additional assum…
▽ More
Let $X$ and $Y$ be locally compact Hausdorff spaces and let $\mathbb{K}\in \{\mathbb{R},\mathbb{C}\}$. We say that a bijection $T\colon C_0(X,\mathbb{K})\to C_0(Y,\mathbb{K})$ is a ring isomorphism in norm if \[ \|T(f+g)\|=\|T(f)+T(g)\|,\qquad \|T(fg)\|=\|T(f)T(g)\| \] for every $f,g\in C_0(X,\mathbb{K})$. We determine the form of such maps. When $\mathbb{K}=\mathbb{C}$, under the additional assumption that $\|T(\overline f)\|=\|T(f)\|$ for every $f\in C_0(X,\mathbb{C})$, there exist a continuous function $w\colon Y\to\{λ\in\mathbb{C}:|λ|=1\}$, a homeomorphism $\varphi\colon Y\to X$, and a closed and open subset $Y_0\subset Y$ such that \[ T(f)(y)= \begin{cases} w(y)f(\varphi(y)),& y\in Y_0,\\ w(y)\overline{f(\varphi(y))},& y\in Y\setminus Y_0, \end{cases} \] for every $f\in C_0(X,\mathbb{C})$ and $y\in Y$. When $\mathbb{K}=\mathbb{R}$, there exist a continuous function $w\colon Y\to\{\pm1\}$ and a homeomorphism $\varphi\colon Y\to X$ such that \[ T(f)(y)=w(y)f(\varphi(y)) \] for every $f\in C_0(X,\mathbb{R})$ and $y\in Y$. In particular, the real case extends the norm version of the Gelfand--Kolmogoroff theorem to the locally compact setting.
△ Less
Submitted 4 August, 2026;
originally announced August 2026.
-
Order Isomorphisms between Positive Cones of $C_0(X)$
Authors:
Natsumi Shibata,
Izuho Matsuzaki,
Takeshi Miura
Abstract:
Let $X$ and $Y$ be locally compact Hausdorff spaces. We study order isomorphisms \[ T:C_0^+(X)\to C_0^+(Y), \] where $C_0(X)$ denotes the Banach space of all real-valued continuous functions on $X$ vanishing at infinity, and \[ C_0^+(X)=\{f\in C_0(X):f\ge0\} \] is its positive cone.
We assume that $T$ is positive homogeneous. That is, \[ T(rf)=rT(f) \qquad (r>0,\,f\in C_0^+(X)). \] Under this as…
▽ More
Let $X$ and $Y$ be locally compact Hausdorff spaces. We study order isomorphisms \[ T:C_0^+(X)\to C_0^+(Y), \] where $C_0(X)$ denotes the Banach space of all real-valued continuous functions on $X$ vanishing at infinity, and \[ C_0^+(X)=\{f\in C_0(X):f\ge0\} \] is its positive cone.
We assume that $T$ is positive homogeneous. That is, \[ T(rf)=rT(f) \qquad (r>0,\,f\in C_0^+(X)). \] Under this assumption, we prove that $T$ is represented as a weighted composition operator induced by a homeomorphism from $Y$ onto $X$ and a bounded continuous weight function. Moreover, we show that $T$ extends uniquely to a linear order isomorphism between $C_0(X)$ and $C_0(Y)$.
△ Less
Submitted 30 June, 2026;
originally announced June 2026.
-
Globalization of local sign structures for phase-isometries on uniform algebras
Authors:
Yuta Enami,
Daisuke Hirota,
Izuho Matsuzaki,
Takeshi Miura
Abstract:
We study surjective phase-isometries between the unit spheres of uniform algebras. Although such maps preserve maximal convex sets up to signs, the resulting local sign ambiguity prevents a direct application of the usual Banach--Stone type arguments for isometries. The main point of the paper is to prove that these local sign structures can be globalized on the Choquet boundary. To this end, we r…
▽ More
We study surjective phase-isometries between the unit spheres of uniform algebras. Although such maps preserve maximal convex sets up to signs, the resulting local sign ambiguity prevents a direct application of the usual Banach--Stone type arguments for isometries. The main point of the paper is to prove that these local sign structures can be globalized on the Choquet boundary. To this end, we refine an additive Bishop-type construction and use it to propagate the sign information among the maximal convex sets associated with boundary points.
As a consequence, every surjective phase-isometry admits a boundary representation by means of a global sign function, a unimodular weight, a homeomorphism between the Choquet boundaries, and a clopen decomposition into complex-linear and conjugate-linear parts. We then extend this representation to the maximal ideal spaces and obtain the corresponding real-algebraic Banach--Stone type representation.
△ Less
Submitted 20 June, 2026;
originally announced June 2026.
-
Calibration energy and mean curvature flow
Authors:
Tatsuya Miura,
Fabian Rupp
Abstract:
We introduce the calibration energy for oriented immersions into Euclidean space, quantifying the deviation from calibrated geometry. A key property is that this energy may remain finite for infinite-volume immersions, while a null-Lagrangian structure ensures that it has the same first variation as the volume functional. We establish an exact dissipation identity for the calibration energy along…
▽ More
We introduce the calibration energy for oriented immersions into Euclidean space, quantifying the deviation from calibrated geometry. A key property is that this energy may remain finite for infinite-volume immersions, while a null-Lagrangian structure ensures that it has the same first variation as the volume functional. We establish an exact dissipation identity for the calibration energy along oriented, proper mean curvature flows in arbitrary dimensions and codimensions, under a mild local-volume bound. This provides a new, finite variational framework for mean curvature flow beyond the finite-volume setting. Our result yields several applications, including rigidity for solitons and convergence for two-dimensional immortal solutions. In particular, every proper self-expander with finite constant-coefficient calibration energy must be a plane in all dimensions and codimensions.
△ Less
Submitted 10 June, 2026; v1 submitted 3 June, 2026;
originally announced June 2026.
-
Norm additive mappings between the positive cones of continuous function algebras
Authors:
Natsumi Shibata,
Takeshi Miura
Abstract:
We study bijections between the positive cones of spaces of continuous functions vanishing at infinity that satisfy a norm additive condition. Such maps arise naturally in the study of nonlinear functional equations and norm-preserving structures on function spaces.
While in the compact (unital) case these maps can often be analyzed via linear extension techniques, the non-unital setting…
▽ More
We study bijections between the positive cones of spaces of continuous functions vanishing at infinity that satisfy a norm additive condition. Such maps arise naturally in the study of nonlinear functional equations and norm-preserving structures on function spaces.
While in the compact (unital) case these maps can often be analyzed via linear extension techniques, the non-unital setting $C_0(X)$ requires a different approach due to the absence of a distinguished unit element.
In this paper, we show that every bijection $T:C_0^+(X)\to C_0^+(Y)$ between the positive cones of $C_0(X)$ and $C_0(Y)$ satisfying \[ \|T(f+g)\|=\|Tf+Tg\| \] for all $f,g\in C_0^+(X)$ admits a representation of the form \[ Tf(y)=h(y)f(τ(y)), \] where $τ:Y\to X$ is a homeomorphism and $h$ is a bounded continuous function from $Y$ to $(0,\infty)$.
This yields a complete characterization of norm additive bijections on positive cones of $C_0^+(X)$.
△ Less
Submitted 29 April, 2026;
originally announced April 2026.
-
Scale-critical curve diffusion flows
Authors:
Tatsuya Miura,
Glen Wheeler
Abstract:
We introduce and study a one-parameter family of curve diffusion flows with a scale-critical cubic curvature term for closed immersed planar curves. We first classify all closed stationary solutions, showing that they are precisely circles or a unique family of ``super-lemniscates''. We then analyse the dynamical stability of homothetic circles. Under a sharp spectral condition, we establish, by p…
▽ More
We introduce and study a one-parameter family of curve diffusion flows with a scale-critical cubic curvature term for closed immersed planar curves. We first classify all closed stationary solutions, showing that they are precisely circles or a unique family of ``super-lemniscates''. We then analyse the dynamical stability of homothetic circles. Under a sharp spectral condition, we establish, by purely variational methods, that any small perturbation of an $ω$-fold circle monotonically approaches the unit $ω$-circle after rescaling, translation, and reparametrisation. As a corollary, we determine the sharp ranges of the parameter for the stability of an embedded circle, and of all $ω$-circles. We also uncover a striking arithmetic structure in the stability landscape, where the stability of $ω$-circles depends non-monotonically on $ω$.
△ Less
Submitted 2 April, 2026;
originally announced April 2026.
-
Mathematical Modeling of Lesion Pattern Formation in Dendritic Keratitis
Authors:
Mari Masunaga,
Reo Shimatani,
Kazumi Shinozaki,
Tomohiro Iida,
Yoshinao Oda,
Takashi Miura
Abstract:
Dendritic keratitis is a form of eye infection caused by herpes simplex virus (HSV). The virus spreads via direct cell-to-cell infection among corneal epithelial cells. This leads to the formation of dendritic lesions characterized by terminal bulbs at their tips. Under immunosuppression, the condition may progress to geographic keratitis, which is a map-shaped lesion with dendritic tails. The mec…
▽ More
Dendritic keratitis is a form of eye infection caused by herpes simplex virus (HSV). The virus spreads via direct cell-to-cell infection among corneal epithelial cells. This leads to the formation of dendritic lesions characterized by terminal bulbs at their tips. Under immunosuppression, the condition may progress to geographic keratitis, which is a map-shaped lesion with dendritic tails. The mechanism of this pattern formation remains to be elucidated. In this study, we propose a mathematical model to elucidate the mechanisms of lesion pattern formation in dendritic keratitis. Our model shows that increased production of infection-suppressive cytokines induces dendritic patterns with terminal bulbs, whereas reduced cytokine levels lead to geographic patterns. Furthermore, altering the spatial distribution of cytokine production can reproduce dendritic tails. By including external cytokine secretion, we could reproduce tapered lesions observed in non-HSV keratitis. By clarifying the mechanisms behind terminal bulb formation and reproducing atypical lesion morphologies, our findings enhance the understanding of herpetic keratitis and highlight the utility of mathematical modeling in ophthalmology.
△ Less
Submitted 4 February, 2026; v1 submitted 2 February, 2026;
originally announced February 2026.
-
Additive and multiplicative maps in norm on the positive cone of continuous function algebras
Authors:
Takeshi Miura,
Natsumi Shibata
Abstract:
Let $X$ and $Y$ be locally compact Hausdorff spaces. We denote by $C_0^+(X)$ the positive cone of all real-valued continuous functions on $X$ vanishing at infinity. In this paper, we consider a bijection $T\colon C_0^+(X) \to C_0^+(Y)$ satisfying the following two norm conditions for all $f, g \in C_0^+(X)$: \[
\|T(f+g)\| = \|T(f)+T(g)\|,\qquad
\|T(f \cdot g)\| = \|T(f) \cdot T(g)\|. \] The ma…
▽ More
Let $X$ and $Y$ be locally compact Hausdorff spaces. We denote by $C_0^+(X)$ the positive cone of all real-valued continuous functions on $X$ vanishing at infinity. In this paper, we consider a bijection $T\colon C_0^+(X) \to C_0^+(Y)$ satisfying the following two norm conditions for all $f, g \in C_0^+(X)$: \[
\|T(f+g)\| = \|T(f)+T(g)\|,\qquad
\|T(f \cdot g)\| = \|T(f) \cdot T(g)\|. \] The main result of this paper is that such a map $T$ is a composition operator of the form $T(f) = f \circ τ$, induced by a homeomorphism $τ\colon Y \to X$.
△ Less
Submitted 27 January, 2026;
originally announced January 2026.
-
A variant of Tingley's problem for positive unit spheres of continuous functions that vanish at infinity
Authors:
Kazuki Ezumi,
Min-Ruei Lin,
Takeshi Miura
Abstract:
Let $S(C_0(X))^+$ and $S(C_0(Y))^+$ denote the positive parts of the unit spheres of $C_0(X)$ and $C_0(Y)$, where $X$ and $Y$ are locally compact Hausdorff spaces. We prove that every surjective isometry from $S(C_0(X))^+$ onto $S(C_0(Y))^+$ is a composition operator induced by a homeomorphism between $X$ and $Y$ . As a consequence, such a map extends to a surjective reallinear isometry from…
▽ More
Let $S(C_0(X))^+$ and $S(C_0(Y))^+$ denote the positive parts of the unit spheres of $C_0(X)$ and $C_0(Y)$, where $X$ and $Y$ are locally compact Hausdorff spaces. We prove that every surjective isometry from $S(C_0(X))^+$ onto $S(C_0(Y))^+$ is a composition operator induced by a homeomorphism between $X$ and $Y$ . As a consequence, such a map extends to a surjective reallinear isometry from $C_0(X)$ onto $C_0(Y)$. We also characterize surjective phase-isometries on the positive unit sphere.
△ Less
Submitted 25 January, 2026;
originally announced January 2026.
-
Ring isomorphisms in norm between Banach algebras of continuous complex-valued functions
Authors:
T. Miura,
T. Takahashi
Abstract:
Let $X$ and $Y$ be compact Hausdorff spaces, and let $C(X)$ and $C(Y)$ denote the commutative Banach algebras of all continuous complex-valued functions on $X$ and $Y$, respectively. We study bijective maps $T$ from $C(X)$ onto $C(Y)$ which preserve the ring structure in the norm in the following sense: \[ \|T(f+g)\|=\|T(f)+T(g)\|,\quad \|T(fg)\|=\|T(f)T(g)\| \qquad(f,g\in C(X)). \] Our main objec…
▽ More
Let $X$ and $Y$ be compact Hausdorff spaces, and let $C(X)$ and $C(Y)$ denote the commutative Banach algebras of all continuous complex-valued functions on $X$ and $Y$, respectively. We study bijective maps $T$ from $C(X)$ onto $C(Y)$ which preserve the ring structure in the norm in the following sense: \[ \|T(f+g)\|=\|T(f)+T(g)\|,\quad \|T(fg)\|=\|T(f)T(g)\| \qquad(f,g\in C(X)). \] Our main objective is to clarify whether such maps must necessarily be induced by homeomorphisms between the underlying spaces. Under the additional assumption that $T(\overline{f})=\overline{T(f)}$ for $f\in C(X)$, we prove that $T$ is a real-linear isometry. As a consequence, we obtain a concrete representation of such maps as weighted composition operators.
△ Less
Submitted 16 January, 2026;
originally announced January 2026.
-
Thin-film limit of the parabolic $p$-Laplace equation in a moving thin domain
Authors:
Tatsu-Hiko Miura
Abstract:
We consider the parabolic $p$-Laplace equation with $p>2$ in a moving thin domain under a Neumann type boundary condition corresponding to the total mass conservation. When the moving thin domain shrinks to a given closed moving hypersurface as its thickness tends to zero, we rigorously derive a limit problem by showing the weak convergence of the weighted average of a weak solution to the thin-do…
▽ More
We consider the parabolic $p$-Laplace equation with $p>2$ in a moving thin domain under a Neumann type boundary condition corresponding to the total mass conservation. When the moving thin domain shrinks to a given closed moving hypersurface as its thickness tends to zero, we rigorously derive a limit problem by showing the weak convergence of the weighted average of a weak solution to the thin-domain problem and characterizing the limit function as a unique weak solution to the limit problem. The limit problem obtained in this paper is a system of a nonlinear partial differential equation and an algebraic equation on the moving hypersurface. This seems to be somewhat strange, but we also find that the limit problem can be seen as a new kind of local mass conservation law on the moving hypersurface with a normal flux.
△ Less
Submitted 14 January, 2026;
originally announced January 2026.
-
Phase transition thresholds and chiral magnetic fields of general degree
Authors:
Slim Ibrahim,
Tatsuya Miura,
Carlos Román,
Ikkei Shimizu
Abstract:
We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first determine the minimal energy for arbitrary topological degree, thereby revealing two types of phase transitions consistent with physical observations. In addition, we prove the uniqueness of the energy minimizer in degree…
▽ More
We study a variational problem for the Landau--Lifshitz energy with Dzyaloshinskii--Moriya interactions arising in 2D micromagnetics, focusing on the Bogomol'nyi regime. We first determine the minimal energy for arbitrary topological degree, thereby revealing two types of phase transitions consistent with physical observations. In addition, we prove the uniqueness of the energy minimizer in degrees $0$ and $-1$, and nonexistence of minimizers for all other degrees. Finally, we show that the homogeneous state remains stable even beyond the threshold at which the skyrmion loses stability, and we uncover a new stability transition driven by the Zeeman energy.
△ Less
Submitted 30 December, 2025;
originally announced December 2025.
-
Robust Backdoor Removal by Reconstructing Trigger-Activated Changes in Latent Representation
Authors:
Kazuki Iwahana,
Yusuke Yamasaki,
Akira Ito,
Takayuki Miura,
Toshiki Shibahara
Abstract:
Backdoor attacks pose a critical threat to machine learning models, causing them to behave normally on clean data but misclassify poisoned data into a poisoned class. Existing defenses often attempt to identify and remove backdoor neurons based on Trigger-Activated Changes (TAC) which is the activation differences between clean and poisoned data. These methods suffer from low precision in identify…
▽ More
Backdoor attacks pose a critical threat to machine learning models, causing them to behave normally on clean data but misclassify poisoned data into a poisoned class. Existing defenses often attempt to identify and remove backdoor neurons based on Trigger-Activated Changes (TAC) which is the activation differences between clean and poisoned data. These methods suffer from low precision in identifying true backdoor neurons due to inaccurate estimation of TAC values. In this work, we propose a novel backdoor removal method by accurately reconstructing TAC values in the latent representation. Specifically, we formulate the minimal perturbation that forces clean data to be classified into a specific class as a convex quadratic optimization problem, whose optimal solution serves as a surrogate for TAC. We then identify the poisoned class by detecting statistically small $L^2$ norms of perturbations and leverage the perturbation of the poisoned class in fine-tuning to remove backdoors. Experiments on CIFAR-10, GTSRB, and TinyImageNet demonstrated that our approach consistently achieves superior backdoor suppression with high clean accuracy across different attack types, datasets, and architectures, outperforming existing defense methods.
△ Less
Submitted 11 November, 2025;
originally announced November 2025.
-
Is the Hard-Label Cryptanalytic Model Extraction Really Polynomial?
Authors:
Akira Ito,
Takayuki Miura,
Yosuke Todo
Abstract:
Deep Neural Networks (DNNs) have attracted significant attention, and their internal models are now considered valuable intellectual assets. Extracting such a model via oracle access to a DNN is conceptually similar to extracting a secret key from a block cipher. Consequently, cryptanalytic techniques, particularly differential-like attacks, have been actively explored. ReLU-based DNNs are the mos…
▽ More
Deep Neural Networks (DNNs) have attracted significant attention, and their internal models are now considered valuable intellectual assets. Extracting such a model via oracle access to a DNN is conceptually similar to extracting a secret key from a block cipher. Consequently, cryptanalytic techniques, particularly differential-like attacks, have been actively explored. ReLU-based DNNs are the most common and widely deployed architectures. While early works (e.g., Crypto 2020, Eurocrypt 2024) assume access to exact output logits, which are typically not exposed, more recent works (e.g., Asiacrypt 2024, Eurocrypt 2025) focus on the hard-label setting, where only the final classification result (e.g., "dog" or "car") is available. Notably, Carlini et al. (Eurocrypt 2025) showed that model extraction is feasible in polynomial time even under this restricted setting.
In this paper, we show that a key assumption underlying their attack becomes increasingly unrealistic as the target depth grows. While prior works noted neurons whose activation states rarely change, we analyze their concrete impact on hard-label extraction: even a single neuron that is (almost) always active can prevent the attack from proceeding unless its parameters are recovered, and ignoring it incurs a non-negligible error. A straightforward solution is to extract these parameters by observing a state switch of such a neuron, but observing such a switch becomes exponentially harder as depth increases, implying that hard-label extraction is not always polynomial time. To address this limitation, we propose a novel attack called cross-layer extraction. Rather than extracting secret parameters (e.g., weights and biases) directly, we exploit cross-layer interactions to recover them from deeper layers, reducing query complexity and addressing limitations of existing approaches.
△ Less
Submitted 26 March, 2026; v1 submitted 8 October, 2025;
originally announced October 2025.
-
Sparse-Autoencoder-Guided Internal Representation Unlearning for Large Language Models
Authors:
Tomoya Yamashita,
Akira Ito,
Yuuki Yamanaka,
Masanori Yamada,
Takayuki Miura,
Toshiki Shibahara
Abstract:
As large language models (LLMs) are increasingly deployed across various applications, privacy and copyright concerns have heightened the need for more effective LLM unlearning techniques. Many existing unlearning methods aim to suppress undesirable outputs through additional training (e.g., gradient ascent), which reduces the probability of generating such outputs. While such suppression-based ap…
▽ More
As large language models (LLMs) are increasingly deployed across various applications, privacy and copyright concerns have heightened the need for more effective LLM unlearning techniques. Many existing unlearning methods aim to suppress undesirable outputs through additional training (e.g., gradient ascent), which reduces the probability of generating such outputs. While such suppression-based approaches can control model outputs, they may not eliminate the underlying knowledge embedded in the model's internal activations; muting a response is not the same as forgetting it. Moreover, such suppression-based methods often suffer from model collapse. To address these issues, we propose a novel unlearning method that directly intervenes in the model's internal activations. In our formulation, forgetting is defined as a state in which the activation of a forgotten target is indistinguishable from that of ``unknown'' entities. Our method introduces an unlearning objective that modifies the activation of the target entity away from those of known entities and toward those of unknown entities in a sparse autoencoder latent space. By aligning the target's internal activation with those of unknown entities, we shift the model's recognition of the target entity from ``known'' to ``unknown'', achieving genuine forgetting while avoiding over-suppression and model collapse. Empirically, we show that our method effectively aligns the internal activations of the forgotten target, a result that the suppression-based approaches do not reliably achieve. Additionally, our method effectively reduces the model's recall of target knowledge in question-answering tasks without significant damage to the non-target knowledge.
△ Less
Submitted 19 September, 2025;
originally announced September 2025.
-
Concept Unlearning in Large Language Models via Self-Constructed Knowledge Triplets
Authors:
Tomoya Yamashita,
Yuuki Yamanaka,
Masanori Yamada,
Takayuki Miura,
Toshiki Shibahara,
Tomoharu Iwata
Abstract:
Machine Unlearning (MU) has recently attracted considerable attention as a solution to privacy and copyright issues in large language models (LLMs). Existing MU methods aim to remove specific target sentences from an LLM while minimizing damage to unrelated knowledge. However, these approaches require explicit target sentences and do not support removing broader concepts, such as persons or events…
▽ More
Machine Unlearning (MU) has recently attracted considerable attention as a solution to privacy and copyright issues in large language models (LLMs). Existing MU methods aim to remove specific target sentences from an LLM while minimizing damage to unrelated knowledge. However, these approaches require explicit target sentences and do not support removing broader concepts, such as persons or events. To address this limitation, we introduce Concept Unlearning (CU) as a new requirement for LLM unlearning. We leverage knowledge graphs to represent the LLM's internal knowledge and define CU as removing the forgetting target nodes and associated edges. This graph-based formulation enables a more intuitive unlearning and facilitates the design of more effective methods. We propose a novel method that prompts the LLM to generate knowledge triplets and explanatory sentences about the forgetting target and applies the unlearning process to these representations. Our approach enables more precise and comprehensive concept removal by aligning the unlearning process with the LLM's internal knowledge representations. Experiments on real-world and synthetic datasets demonstrate that our method effectively achieves concept-level unlearning while preserving unrelated knowledge.
△ Less
Submitted 19 September, 2025;
originally announced September 2025.
-
Embeddedness and graphicality of the elastic flow for complete curves
Authors:
Tatsuya Miura,
Fabian Rupp
Abstract:
We study positivity-preserving properties for the elastic flow of non-compact, complete curves in Euclidean space. Despite the fact that the canonical elastic energy is infinite in this context, we extend our recent work based on the adapted elastic energy to derive nontrivial optimal thresholds for maintaining planar embeddedness and graphicality, respectively. We also obtain a new Li--Yau type i…
▽ More
We study positivity-preserving properties for the elastic flow of non-compact, complete curves in Euclidean space. Despite the fact that the canonical elastic energy is infinite in this context, we extend our recent work based on the adapted elastic energy to derive nontrivial optimal thresholds for maintaining planar embeddedness and graphicality, respectively. We also obtain a new Li--Yau type inequality for complete planar curves.
△ Less
Submitted 26 August, 2025;
originally announced August 2025.
-
Stability of flat-core pinned p-elasticae
Authors:
Tatsuya Miura,
Kensuke Yoshizawa
Abstract:
We classify the stability of flat-core $p$-elasticae in $\mathbf{R}^d$ subject to the pinned boundary condition. Together with previous work, this completes the classification of stable pinned $p$-elasticae in $\mathbf{R}^d$ for all $p\in(1,\infty)$ and $d\geq2$.
We classify the stability of flat-core $p$-elasticae in $\mathbf{R}^d$ subject to the pinned boundary condition. Together with previous work, this completes the classification of stable pinned $p$-elasticae in $\mathbf{R}^d$ for all $p\in(1,\infty)$ and $d\geq2$.
△ Less
Submitted 13 August, 2025;
originally announced August 2025.
-
Difference estimate for weak solutions to the Navier-Stokes equations in a thin spherical shell and on the unit sphere
Authors:
Tatsu-Hiko Miura
Abstract:
We consider the Navier-Stokes equations in a three-dimensional thin spherical shell and on the two-dimensional unit sphere, and estimate the difference of weak solutions on the thin spherical shell and the unit sphere. Assuming that the weak solution on the thin spherical shell is a Leray-Hopf weak solution satisfying the energy inequality, we derive difference estimates for the two weak solutions…
▽ More
We consider the Navier-Stokes equations in a three-dimensional thin spherical shell and on the two-dimensional unit sphere, and estimate the difference of weak solutions on the thin spherical shell and the unit sphere. Assuming that the weak solution on the thin spherical shell is a Leray-Hopf weak solution satisfying the energy inequality, we derive difference estimates for the two weak solutions by the weak-strong uniqueness argument. The main idea is to extend the weak solution on the unit sphere properly to an approximate solution on the thin spherical shell, and to use the extension as a strong solution in the weak-strong uniqueness argument.
△ Less
Submitted 9 July, 2025;
originally announced July 2025.
-
Weak solutions to the parabolic $p$-Laplace equation in a moving domain under a Neumann type boundary condition
Authors:
Tatsu-Hiko Miura
Abstract:
This paper studies the parabolic $p$-Laplace equation with $p>2$ in a moving domain under a Neumann type boundary condition corresponding to the total mass conservation. We establish the existence and uniqueness of a weak solution by the Galerkin method in evolving Bochner spaces and a monotonicity argument. The main difficulty is in characterizing the weak limit of the nonlinear gradient term, wh…
▽ More
This paper studies the parabolic $p$-Laplace equation with $p>2$ in a moving domain under a Neumann type boundary condition corresponding to the total mass conservation. We establish the existence and uniqueness of a weak solution by the Galerkin method in evolving Bochner spaces and a monotonicity argument. The main difficulty is in characterizing the weak limit of the nonlinear gradient term, where we need to deal with a term which comes from the boundary condition and cannot be absorbed into a monotone operator. To overcome this difficulty, we prove a uniform-in-time Friedrichs type inequality on a moving domain with time-dependent basis functions and make use of it to get the strong convergence of approximate solutions. We also show that the time derivative exists in the $L^2$ sense when given data have a better regularity, and discuss extension of the existence and uniqueness results to a Leray-Lions type operator.
△ Less
Submitted 29 January, 2026; v1 submitted 18 May, 2025;
originally announced May 2025.
-
Status of the International Linear Collider
Authors:
Y. Abe,
S. Arai,
S. Araki,
H. Araki,
Y. Arimoto,
A. Aryshev,
S. Asai,
R. Bajpai,
T. Behnke,
S. Belomestnykh,
I. Bozovic,
J. E. Brau,
K. Buesser,
P. N. Burrows,
N. Catalan-Lasheras,
E. Cenni,
S. Chen,
J. Clark,
D. Delikaris,
M. Demarteau,
D. Denisov,
S. Doebert,
T. Dohmae,
R. Dowd,
G. Dugan
, et al. (127 additional authors not shown)
Abstract:
This paper is not a proposal for a CERN future project but provides information on the International Linear Collider (ILC) considered for Japan in order to facilitate the European Strategy discussion in a global context. It describes progress to date, ongoing engineering studies, updated cost estimate for the machine at $\sqrt{s}=250~\rm GeV$ and the situation in Japan. The physics of the ILC is n…
▽ More
This paper is not a proposal for a CERN future project but provides information on the International Linear Collider (ILC) considered for Japan in order to facilitate the European Strategy discussion in a global context. It describes progress to date, ongoing engineering studies, updated cost estimate for the machine at $\sqrt{s}=250~\rm GeV$ and the situation in Japan. The physics of the ILC is not presented here, but jointly for all Linear Collider projects in a separate document ``A Linear Collider Vision for the Future of Particle Physics'' submitted for the forthcoming European Strategy deliberations.
△ Less
Submitted 5 June, 2025; v1 submitted 16 May, 2025;
originally announced May 2025.
-
Quantitative Analysis of Cell Membrane Tension in Time-Series Imaging and A Minimal Lattice Model of Single Cell Motion
Authors:
Hiroki Nishitani,
Takashi Miura
Abstract:
Cell membrane tension directly influences various cellular functions. In this study, we developed a method to estimate surface tension from time-series data. We obtained the curvature-velocity relationship from time-series of binarized cell shape images, and the effective surface tension term was calculated from linear regression.
During the process, we observed an S-shaped pattern in the curvat…
▽ More
Cell membrane tension directly influences various cellular functions. In this study, we developed a method to estimate surface tension from time-series data. We obtained the curvature-velocity relationship from time-series of binarized cell shape images, and the effective surface tension term was calculated from linear regression.
During the process, we observed an S-shaped pattern in the curvature-velocity relationship. To understand the dynamics, we constructed a minimal lattice model describing single-cell motion. The model consists of surface tension and protrusion formation, and the characteristic parameters are obtained from experimental observations. We found that similar patterns emerged in the curvature-velocity relationship.
△ Less
Submitted 21 April, 2025;
originally announced April 2025.
-
A new energy method for shortening and straightening complete curves
Authors:
Tatsuya Miura,
Fabian Rupp
Abstract:
We introduce a novel energy method that reinterprets ``curve shortening'' as ``tangent aligning''. This conceptual shift enables the variational study of infinite-length curves evolving by the curve shortening flow, as well as higher order flows such as the elastic flow, which involves not only the curve shortening but also the curve straightening effect. For the curve shortening flow, we prove co…
▽ More
We introduce a novel energy method that reinterprets ``curve shortening'' as ``tangent aligning''. This conceptual shift enables the variational study of infinite-length curves evolving by the curve shortening flow, as well as higher order flows such as the elastic flow, which involves not only the curve shortening but also the curve straightening effect. For the curve shortening flow, we prove convergence to a straight line under mild assumptions on the ends of the initial curve. For the elastic flow, we establish a global well-posedness theory, and investigate the precise long-time behavior of solutions. In fact, our method applies to a more general class of geometric evolution equations including the surface diffusion flow, Chen's flow, and the free elastic flow.
△ Less
Submitted 8 October, 2025; v1 submitted 4 April, 2025;
originally announced April 2025.
-
Surjective isometries on function spaces with derivatives
Authors:
M. G. Cabrera-Padilla,
A. Jiménez-Vargas,
Takeshi Miura,
Moisés Villegas-Vallecillos
Abstract:
Let $A$ be a complex Banach space with a norm $\|f\|=\|f\|_X+\|d(f)\|_Y$ for $f\in A$, where $d$ is a complex linear map from $A$ onto a Banach space $B$, and $\|\cdot\|_K$ represents the supremum norm on a compact Hausdorff space $K$. In this paper, we characterize surjective isometries on $(A,\|\cdot\|)$, which may be nonlinear. This unifies former results on surjective isometries between specif…
▽ More
Let $A$ be a complex Banach space with a norm $\|f\|=\|f\|_X+\|d(f)\|_Y$ for $f\in A$, where $d$ is a complex linear map from $A$ onto a Banach space $B$, and $\|\cdot\|_K$ represents the supremum norm on a compact Hausdorff space $K$. In this paper, we characterize surjective isometries on $(A,\|\cdot\|)$, which may be nonlinear. This unifies former results on surjective isometries between specific function spaces.
△ Less
Submitted 6 March, 2025;
originally announced March 2025.
-
Thin-film limit of the Cahn-Hilliard equation in a curved thin domain
Authors:
Tatsu-Hiko Miura
Abstract:
We consider the Cahn-Hilliard equation with Neumann boundary conditions in a three-dimensional curved thin domain around a given closed surface. When the thickness of the curved thin domain tends to zero, we show that the weighted average in the thin direction of a weak solution to the thin-domain problem converges on the limit surface in an appropriate sense. Moreover, we rigorously derive a limi…
▽ More
We consider the Cahn-Hilliard equation with Neumann boundary conditions in a three-dimensional curved thin domain around a given closed surface. When the thickness of the curved thin domain tends to zero, we show that the weighted average in the thin direction of a weak solution to the thin-domain problem converges on the limit surface in an appropriate sense. Moreover, we rigorously derive a limit problem, which is the surface Cahn-Hilliard equation with weighted Laplacian, by characterizing the limit function as a unique weak solution to the limit problem. The proof is based on a detailed analysis of the weighted average and the use of Sobolev inequalities and elliptic regularity estimates on the curved thin domain with constants explicitly depending on the thickness. This is the first result on a rigorous thin-film limit of nonlinear fourth order equations in general curved thin domains.
△ Less
Submitted 13 December, 2025; v1 submitted 1 February, 2025;
originally announced February 2025.
-
Regularity and structure of non-planar $p$-elasticae
Authors:
Florian Gruen,
Tatsuya Miura
Abstract:
We prove regularity and structure results for $p$-elasticae in $\mathbb{R}^n$, with arbitrary $p\in (1,\infty)$ and $n\geq2$. Planar $p$-elasticae are already classified and known to lose regularity. In this paper, we show that every non-planar $p$-elastica is analytic and three-dimensional, with the only exception of flat-core solutions of arbitrary dimensions. Subsequently, we classify pinned…
▽ More
We prove regularity and structure results for $p$-elasticae in $\mathbb{R}^n$, with arbitrary $p\in (1,\infty)$ and $n\geq2$. Planar $p$-elasticae are already classified and known to lose regularity. In this paper, we show that every non-planar $p$-elastica is analytic and three-dimensional, with the only exception of flat-core solutions of arbitrary dimensions. Subsequently, we classify pinned $p$-elasticae in $\mathbb{R}^n$ and, as an application, establish a Li-Yau type inequality for the $p$-bending energy of closed curves in $\mathbb{R}^n$. This extends previous works for $p=2$ and $n\geq2$ as well as for $p\in (1,\infty)$ and $n=2$.
△ Less
Submitted 24 October, 2025; v1 submitted 14 January, 2025;
originally announced January 2025.
-
Migrating elastic flows II
Authors:
Tatsuya Miura
Abstract:
We solve a variant of Huisken's problem for open curves: we construct migrating elastic flows under the natural boundary conditions, extending previous work from the nonlocal flow to the purely local flow.
We solve a variant of Huisken's problem for open curves: we construct migrating elastic flows under the natural boundary conditions, extending previous work from the nonlocal flow to the purely local flow.
△ Less
Submitted 2 June, 2025; v1 submitted 6 November, 2024;
originally announced November 2024.
-
Asymptotic circularity of immortal area-preserving curvature flows
Authors:
Tatsuya Miura
Abstract:
For a class of area-preserving curvature flows of closed planar curves, we prove that every immortal solution becomes asymptotically circular without any additional assumptions on initial data. As a particular corollary, every solution of zero enclosed area blows up in finite time. This settles an open problem posed by Escher--Ito in 2005 for Gage's area-preserving curve shortening flow, and moreo…
▽ More
For a class of area-preserving curvature flows of closed planar curves, we prove that every immortal solution becomes asymptotically circular without any additional assumptions on initial data. As a particular corollary, every solution of zero enclosed area blows up in finite time. This settles an open problem posed by Escher--Ito in 2005 for Gage's area-preserving curve shortening flow, and moreover extends it to the surface diffusion flow of arbitrary order. We also establish a general existence theorem for nontrivial immortal solutions under almost circularity and rotational symmetry.
△ Less
Submitted 17 November, 2024; v1 submitted 8 October, 2024;
originally announced October 2024.
-
Smooth compactness of elasticae
Authors:
Tatsuya Miura
Abstract:
We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.
We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.
△ Less
Submitted 17 November, 2025; v1 submitted 1 September, 2024;
originally announced September 2024.
-
Stable beam operation of approximately 1 mA beam under highly efficient energy recovery conditions at compact energy-recovery linac
Authors:
Hiroshi Sakai,
Dai Arakawa,
Takaaki Furuya,
Kaiichi Haga,
Masayuki Hagiwara,
Kentaro Harada,
Yosuke Honda,
Teruya Honma,
Eiji Kako,
Ryukou Kato,
Yuuji Kojima,
Taro Konomi,
Hiroshi Matsumura,
Taichi Miura,
Takako Miura,
Shinya Nagahashi,
Hirotaka Nakai,
Norio Nakamura,
Kota Nakanishi,
Kazuyuki Nigorikawa,
Takashi Nogami,
Takashi Obina,
Feng Qiu,
Hidenori Sagehashi,
Shogo Sakanaka
, et al. (15 additional authors not shown)
Abstract:
A compact energy-recovery linac (cERL) has been un-der construction at KEK since 2009 to develop key technologies for the energy-recovery linac. The cERL began operating in 2013 to create a high-current beam with a low-emittance beam with stable continuous wave (CW) superconducting cavities. Owing to the development of critical components, such as the DC gun, superconducting cavities, and the desi…
▽ More
A compact energy-recovery linac (cERL) has been un-der construction at KEK since 2009 to develop key technologies for the energy-recovery linac. The cERL began operating in 2013 to create a high-current beam with a low-emittance beam with stable continuous wave (CW) superconducting cavities. Owing to the development of critical components, such as the DC gun, superconducting cavities, and the design of ideal beam transport optics, we have successfully established approximately 1 mA stable CW operation with a small beam emittance and extremely small beam loss. This study presents the details of our key technologies and experimental results for achieving 100% energy recovery operation with extremely small beam loss during a stable, approximately 1 mA CW beam operation.
△ Less
Submitted 24 August, 2024;
originally announced August 2024.
-
WhisperMask: A Noise Suppressive Mask-Type Microphone for Whisper Speech
Authors:
Hirotaka Hiraki,
Shusuke Kanazawa,
Takahiro Miura,
Manabu Yoshida,
Masaaki Mochimaru,
Jun Rekimoto
Abstract:
Whispering is a common privacy-preserving technique in voice-based interactions, but its effectiveness is limited in noisy environments. In conventional hardware- and software-based noise reduction approaches, isolating whispered speech from ambient noise and other speech sounds remains a challenge. We thus propose WhisperMask, a mask-type microphone featuring a large diaphragm with low sensitivit…
▽ More
Whispering is a common privacy-preserving technique in voice-based interactions, but its effectiveness is limited in noisy environments. In conventional hardware- and software-based noise reduction approaches, isolating whispered speech from ambient noise and other speech sounds remains a challenge. We thus propose WhisperMask, a mask-type microphone featuring a large diaphragm with low sensitivity, making the wearer's voice significantly louder than the background noise. We evaluated WhisperMask using three key metrics: signal-to-noise ratio, quality of recorded voices, and speech recognition rate. Across all metrics, WhisperMask consistently outperformed traditional noise-suppressing microphones and software-based solutions. Notably, WhisperMask showed a 30% higher recognition accuracy for whispered speech recorded in an environment with 80 dB background noise compared with the pin microphone and earbuds. Furthermore, while a denoiser decreased the whispered speech recognition rate of these two microphones by approximately 20% at 30-60 dB noise, WhisperMask maintained a high performance even without denoising, surpassing the other microphones' performances by a significant margin.WhisperMask's design renders the wearer's voice as the dominant input and effectively suppresses background noise without relying on signal processing. This device allows for reliable voice interactions, such as phone calls and voice commands, in a wide range of noisy real-world scenarios while preserving user privacy.
△ Less
Submitted 22 August, 2024;
originally announced August 2024.
-
Elastic curves and self-intersections
Authors:
Tatsuya Miura
Abstract:
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some open problems in related topics.
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some open problems in related topics.
△ Less
Submitted 17 November, 2025; v1 submitted 6 August, 2024;
originally announced August 2024.
-
Thin-film limit of the Ginzburg-Landau heat flow in a curved thin domain
Authors:
Tatsu-Hiko Miura
Abstract:
We consider the Ginzburg-Landau heat flow without magnetic effect in a curved thin domain under the Naumann boundary condition. When the curved thin domain shrinks to a given closed hypersurface as the thickness of the thin domain tends to zero, we show that the weighted average of a weak solution to the thin-domain problem converges weakly on the limit surface under the assumption that the initia…
▽ More
We consider the Ginzburg-Landau heat flow without magnetic effect in a curved thin domain under the Naumann boundary condition. When the curved thin domain shrinks to a given closed hypersurface as the thickness of the thin domain tends to zero, we show that the weighted average of a weak solution to the thin-domain problem converges weakly on the limit surface under the assumption that the initial data is of class $L^\infty$ and satisfies some conditions. Moreover, under the same assumption, we derive a limit equation by characterizing the limit function as a weak solution, and prove a difference estimate on the limit surface of an averaged weak solution to the thin-domain problem and a weak solution to the limit problem explicitly in terms of the thickness of the thin domain. We also derive a difference estimate in the curved thin domain of weak solutions to the thin-domain problem and to the limit problem, but without requiring that the initial data of the thin-domain problem is of class $L^\infty$.
△ Less
Submitted 22 April, 2024;
originally announced April 2024.
-
The free elastic flow for closed planar curves
Authors:
Tatsuya Miura,
Glen Wheeler
Abstract:
The free elastic flow is the $L^2$-gradient flow for Euler's elastic energy, or equivalently the Willmore flow with translation invariant initial data. In contrast to elastic flows under length penalisation or preservation, it is more challenging to study the free elastic flow's asymptotic behavior, and convergence for closed curves is lost. In this paper, we nevertheless determine the asymptotic…
▽ More
The free elastic flow is the $L^2$-gradient flow for Euler's elastic energy, or equivalently the Willmore flow with translation invariant initial data. In contrast to elastic flows under length penalisation or preservation, it is more challenging to study the free elastic flow's asymptotic behavior, and convergence for closed curves is lost. In this paper, we nevertheless determine the asymptotic shape of the flow for initial curves that are geometrically close to circles, possibly multiply-covered, proving that an appropriate rescaling smoothly converges to a unique round circle.
△ Less
Submitted 23 June, 2025; v1 submitted 19 April, 2024;
originally announced April 2024.
-
Spline-Interpolated Model Predictive Path Integral Control with Stein Variational Inference for Reactive Navigation
Authors:
Takato Miura,
Naoki Akai,
Kohei Honda,
Susumu Hara
Abstract:
This paper presents a reactive navigation method that leverages a Model Predictive Path Integral (MPPI) control enhanced with spline interpolation for the control input sequence and Stein Variational Gradient Descent (SVGD). The MPPI framework addresses a nonlinear optimization problem by determining an optimal sequence of control inputs through a sampling-based approach. The efficacy of MPPI is s…
▽ More
This paper presents a reactive navigation method that leverages a Model Predictive Path Integral (MPPI) control enhanced with spline interpolation for the control input sequence and Stein Variational Gradient Descent (SVGD). The MPPI framework addresses a nonlinear optimization problem by determining an optimal sequence of control inputs through a sampling-based approach. The efficacy of MPPI is significantly influenced by the sampling noise. To rapidly identify routes that circumvent large and/or newly detected obstacles, it is essential to employ high levels of sampling noise. However, such high noise levels result in jerky control input sequences, leading to non-smooth trajectories. To mitigate this issue, we propose the integration of spline interpolation within the MPPI process, enabling the generation of smooth control input sequences despite the utilization of substantial sampling noises. Nonetheless, the standard MPPI algorithm struggles in scenarios featuring multiple optimal or near-optimal solutions, such as environments with several viable obstacle avoidance paths, due to its assumption that the distribution over an optimal control input sequence can be closely approximated by a Gaussian distribution. To address this limitation, we extend our method by incorporating SVGD into the MPPI framework with spline interpolation. SVGD, rooted in the optimal transportation algorithm, possesses the unique ability to cluster samples around an optimal solution. Consequently, our approach facilitates robust reactive navigation by swiftly identifying obstacle avoidance paths while maintaining the smoothness of the control input sequences. The efficacy of our proposed method is validated on simulations with a quadrotor, demonstrating superior performance over existing baseline techniques.
△ Less
Submitted 16 April, 2024;
originally announced April 2024.
-
Phase-isometries between the positive cones of the Banach space of continuous real-valued functions
Authors:
Daisuke Hirota,
Izuho Matsuzaki,
Takeshi Miura
Abstract:
For a locally compact Hausdorff space $L$, we denote by $C_0(L,\mathbb{R})$ the Banach space of all continuous real-valued functions on $L$ vanishing at infinity equipped with the supremum norm. We prove that every surjective phase-isometry $T\colon C_0^+(X,\mathbb{R}) \to C_0^+(Y,\mathbb{R})$ between the positive cones of $C_0(X,\mathbb{R})$ and $C_0(Y,\mathbb{R})$ is a composition operator induc…
▽ More
For a locally compact Hausdorff space $L$, we denote by $C_0(L,\mathbb{R})$ the Banach space of all continuous real-valued functions on $L$ vanishing at infinity equipped with the supremum norm. We prove that every surjective phase-isometry $T\colon C_0^+(X,\mathbb{R}) \to C_0^+(Y,\mathbb{R})$ between the positive cones of $C_0(X,\mathbb{R})$ and $C_0(Y,\mathbb{R})$ is a composition operator induced by a homeomorphism between $X$ and $Y$. Furthermore, we show that any surjective phase-isometry $T\colon C_0^+(X,\mathbb{R}) \to C_0^+(Y,\mathbb{R})$ extends to a surjective linear isometry from $C_0(X,\mathbb{R})$ onto $C_0(Y,\mathbb{R})$.
△ Less
Submitted 9 April, 2024;
originally announced April 2024.
-
Mid-career pitfall of consecutive success in science
Authors:
Noriyuki Higashide,
Takahiro Miura,
Yuta Tomokiyo,
Kimitaka Asatani,
Ichiro Sakata
Abstract:
The creativity of scientists often manifests as localized hot streaks of significant success. Understanding the underlying mechanisms of these influential phases can enhance the effectiveness of support systems and funding allocation, fostering groundbreaking discoveries worthy of accolades. Historically, analyses have suggested that hot streaks occur randomly over time. However, our research, thr…
▽ More
The creativity of scientists often manifests as localized hot streaks of significant success. Understanding the underlying mechanisms of these influential phases can enhance the effectiveness of support systems and funding allocation, fostering groundbreaking discoveries worthy of accolades. Historically, analyses have suggested that hot streaks occur randomly over time. However, our research, through meticulous examination, reveals that these phases are not flatly distributed but are more frequent at the early and late stages of scientists' careers. Notably, both early and late hot streaks are marked by dense tie collaborations, with the former typically involving close partnerships with particular authors and the latter being characterized by involvement in large-scale projects compared with single-top or ordinary papers. This pattern indicates that mid-career researchers lack both intimate relations and resources to keep big projects, leading to``mid-career pitfal'' of consecutive success. This insight holds profound implications for the development of policies and initiatives aimed at bolstering innovative research and discovery.
△ Less
Submitted 9 March, 2024;
originally announced March 2024.
-
Uniqueness and minimality of Euler's elastica with monotone curvature
Authors:
Tatsuya Miura,
Glen Wheeler
Abstract:
For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped boundary condition. We also partly extend this unique minimality to the length-penalised case; this result is new even in view of local minimality. As an application we prove uniqueness of global minimisers in the strai…
▽ More
For an old problem of Euler's elastica we prove the novel global property that every planar elastica with non-constant monotone curvature is uniquely minimal subject to the clamped boundary condition. We also partly extend this unique minimality to the length-penalised case; this result is new even in view of local minimality. As an application we prove uniqueness of global minimisers in the straightening problem for generic boundary angles.
△ Less
Submitted 28 March, 2025; v1 submitted 20 February, 2024;
originally announced February 2024.
-
Time-resolved force microscopy using delay-time modulation method
Authors:
Hiroyuki Mogi,
Rin Wakabayashi,
Shoji Yoshida,
Yusuke Arashida,
Atsushi Taninaka,
Katsuya Iwaya,
Takeshi Miura,
Osamu Takeuchi,
Hidemi Shigekawa
Abstract:
We developed a time-resolved force microscopy technique by integrating atomic force microscopy using a tuning-fork-type cantilever with the delay time modulation method for optical pump-probe light. We successfully measured the dynamics of surface recombination and diffusion of photoexcited carriers in bulk WSe2, which is challenging owing to the effect of tunneling current in time-resolved scanni…
▽ More
We developed a time-resolved force microscopy technique by integrating atomic force microscopy using a tuning-fork-type cantilever with the delay time modulation method for optical pump-probe light. We successfully measured the dynamics of surface recombination and diffusion of photoexcited carriers in bulk WSe2, which is challenging owing to the effect of tunneling current in time-resolved scanning tunneling microscopy. The obtained results were comprehensively explained with the model based on the dipole-dipole interaction induced by photo illumination.
△ Less
Submitted 11 January, 2024;
originally announced January 2024.
-
Variational stabilization of degenerate p-elasticae
Authors:
Tatsuya Miura,
Kensuke Yoshizawa
Abstract:
A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar $p$-elasticae. It was known that in the non-degenerate regime $p\in(1,2]$, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime $p\in(2,\infty)$ there emerge uncou…
▽ More
A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar $p$-elasticae. It was known that in the non-degenerate regime $p\in(1,2]$, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime $p\in(2,\infty)$ there emerge uncountably many local minimizers with diverging energy.
△ Less
Submitted 26 March, 2025; v1 submitted 11 October, 2023;
originally announced October 2023.
-
Remarks on overestimating the effects of inhomogeneities on the Hubble constant
Authors:
Taishi Miura,
Takahiro Tanaka
Abstract:
The Hubble constant is one of the most important parameters in cosmology. Discrepancies in values of the Hubble constant estimated from various measurements, the so-called Hubble tension, are a serious problem. In this paper, we study the effects of small-scale inhomogeneities of structure formation on the measurement of the Hubble constant using the luminosity distance-redshift relation. By adopt…
▽ More
The Hubble constant is one of the most important parameters in cosmology. Discrepancies in values of the Hubble constant estimated from various measurements, the so-called Hubble tension, are a serious problem. In this paper, we study the effects of small-scale inhomogeneities of structure formation on the measurement of the Hubble constant using the luminosity distance-redshift relation. By adopting the adhesion model in Newtonian cosmology as the model of structure formation, we investigate whether or not the effects of inhomogeneities can be sufficiently large to affect the current observations of the Hubble constant. We show that inappropriate treatment of the effects of inhomogeneities can cause a large deviation of the measured value of the Hubble constant from the background value, whose magnitude is comparable with the Hubble tension. Our main message is the importance of adopting an appropriate model of structure formation to investigate the effects of inhomogeneities. We also add discussion on the spatial averaging approach used to estimate the measured Hubble constant in the inhomogeneous universe.
△ Less
Submitted 31 January, 2025; v1 submitted 5 September, 2023;
originally announced September 2023.
-
Approximation of a solution to the stationary Navier-Stokes equations in a curved thin domain by a solution to thin-film limit equations
Authors:
Tatsu-Hiko Miura
Abstract:
We consider the stationary Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under the slip boundary conditions. Our aim is to show that a solution to the bulk equations is approximated by a solution to limit equations on the surface appearing in the thin-film limit of the bulk equations. To this end, we take the average of the bulk solution in the thi…
▽ More
We consider the stationary Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under the slip boundary conditions. Our aim is to show that a solution to the bulk equations is approximated by a solution to limit equations on the surface appearing in the thin-film limit of the bulk equations. To this end, we take the average of the bulk solution in the thin direction and estimate the difference of the averaged bulk solution and the surface solution. Then we combine an obtained difference estimate on the surface with an estimate for the difference of the bulk solution and its average to get a difference estimate for the bulk and surface solutions in the thin domain, which shows that the bulk solution is approximated by the surface one when the thickness of the thin domain is sufficiently small.
△ Less
Submitted 23 August, 2023; v1 submitted 9 August, 2023;
originally announced August 2023.
-
On Rényi Differential Privacy in Statistics-Based Synthetic Data Generation
Authors:
Takayuki Miura,
Toshiki Shibahara,
Masanobu Kii,
Atsunori Ichikawa,
Juko Yamamoto,
Koji Chida
Abstract:
Privacy protection with synthetic data generation often uses differentially private statistics and model parameters to quantitatively express theoretical security. However, these methods do not take into account privacy protection due to the randomness of data generation. In this paper, we theoretically evaluate Rényi differential privacy of the randomness in data generation of a synthetic data ge…
▽ More
Privacy protection with synthetic data generation often uses differentially private statistics and model parameters to quantitatively express theoretical security. However, these methods do not take into account privacy protection due to the randomness of data generation. In this paper, we theoretically evaluate Rényi differential privacy of the randomness in data generation of a synthetic data generation method that uses the mean vector and the covariance matrix of an original dataset. Specifically, for a fixed $α> 1$, we show the condition of $\varepsilon$ such that the synthetic data generation satisfies $(α, \varepsilon)$-Rényi differential privacy under a bounded neighboring condition and an unbounded neighboring condition, respectively. In particular, under the unbounded condition, when the size of the original dataset and synthetic datase is 10 million, the mechanism satisfies $(4, 0.576)$-Rényi differential privacy. We also show that when we translate it into the traditional $(\varepsilon, δ)$-differential privacy, the mechanism satisfies $(4.00, 10^{-10})$-differential privacy.
△ Less
Submitted 31 March, 2023;
originally announced March 2023.
-
Migrating elastic flows
Authors:
Tomoya Kemmochi,
Tatsuya Miura
Abstract:
Huisken's problem asks whether there is an elastic flow of closed planar curves that is initially contained in the upper half-plane but `migrates' to the lower half-plane at a positive time. Here we consider variants of Huisken's problem for open curves under the natural boundary condition, and construct various migrating elastic flows both analytically and numerically.
Huisken's problem asks whether there is an elastic flow of closed planar curves that is initially contained in the upper half-plane but `migrates' to the lower half-plane at a positive time. Here we consider variants of Huisken's problem for open curves under the natural boundary condition, and construct various migrating elastic flows both analytically and numerically.
△ Less
Submitted 17 April, 2024; v1 submitted 22 March, 2023;
originally announced March 2023.
-
Transient photocurrent and optical absorption of disordered thin-film semiconductors: in-depth injection and nonlinear response
Authors:
Kazuhiko Seki,
Naoya Muramatsu,
Tomoaki Miura,
Tadaaki Ikoma
Abstract:
The time-of-flight method is a fundamental approach for characterizing the transport properties of semiconductors. Recently, the transient photocurrent and optical absorption kinetics have been simultaneously measured for thin films; pulsed-light excitation of thin films should give rise to non-negligible in-depth carrier injection. Yet, the effects of in-depth carrier injection on the transient c…
▽ More
The time-of-flight method is a fundamental approach for characterizing the transport properties of semiconductors. Recently, the transient photocurrent and optical absorption kinetics have been simultaneously measured for thin films; pulsed-light excitation of thin films should give rise to non-negligible in-depth carrier injection. Yet, the effects of in-depth carrier injection on the transient currents and optical absorption have not yet been elucidated theoretically. Here, by considering the in-depth carrier injection in simulations, we found a 1/t^{1-alpha/2} initial time (t) dependence rather than the conventional $1/t^{1-alpha}$ dependence under a weak external electric field, where alpha<1 is the index of dispersive diffusion.The asymptotic transient currents are not influenced by the initial in-depth carrier injection and follow the conventional 1/t^{1+alpha} time dependence. We also present the relation between the field-dependent mobility coefficient and the diffusion coefficient when the transport is dispersive. The field dependence of the transport coefficients influences the transit time in the photocurrent kinetics dividing two power-law decay regimes. The classical Scher--Montroll theory predicts a_1+a_2=2 when the initial photocurrent decay is given by 1/t^{a_1} and the asymptotic photocurrent decay is given by 1/t^{a_2}. The results shed light on the interpretation of the power-law exponent of 1/t^{a_1} when a_1+a_2neq 2.
△ Less
Submitted 20 February, 2023; v1 submitted 19 February, 2023;
originally announced February 2023.
-
Membership Inference Attacks against Diffusion Models
Authors:
Tomoya Matsumoto,
Takayuki Miura,
Naoto Yanai
Abstract:
Diffusion models have attracted attention in recent years as innovative generative models. In this paper, we investigate whether a diffusion model is resistant to a membership inference attack, which evaluates the privacy leakage of a machine learning model. We primarily discuss the diffusion model from the standpoints of comparison with a generative adversarial network (GAN) as conventional model…
▽ More
Diffusion models have attracted attention in recent years as innovative generative models. In this paper, we investigate whether a diffusion model is resistant to a membership inference attack, which evaluates the privacy leakage of a machine learning model. We primarily discuss the diffusion model from the standpoints of comparison with a generative adversarial network (GAN) as conventional models and hyperparameters unique to the diffusion model, i.e., time steps, sampling steps, and sampling variances. We conduct extensive experiments with DDIM as a diffusion model and DCGAN as a GAN on the CelebA and CIFAR-10 datasets in both white-box and black-box settings and then confirm if the diffusion model is comparably resistant to a membership inference attack as GAN. Next, we demonstrate that the impact of time steps is significant and intermediate steps in a noise schedule are the most vulnerable to the attack. We also found two key insights through further analysis. First, we identify that DDIM is vulnerable to the attack for small sample sizes instead of achieving a lower FID. Second, sampling steps in hyperparameters are important for resistance to the attack, whereas the impact of sampling variances is quite limited.
△ Less
Submitted 22 March, 2023; v1 submitted 7 February, 2023;
originally announced February 2023.
-
General rigidity principles for stable and minimal elastic curves
Authors:
Tatsuya Miura,
Kensuke Yoshizawa
Abstract:
For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers. Our results extend Maddocks' and Sachkov's rigidity principles for Euler's elastica by a new, unified and geometric approach. This in particular leads to complete classification of stable closed $p$-elasticae for all…
▽ More
For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers. Our results extend Maddocks' and Sachkov's rigidity principles for Euler's elastica by a new, unified and geometric approach. This in particular leads to complete classification of stable closed $p$-elasticae for all $p\in(1,\infty)$ and of stable pinned $p$-elasticae for $p\in(1,2]$. Our proof is based on a simple but robust `cut-and-paste' trick without computing the energy nor its second variation, which works well for planar periodic curves but also extends to some non-periodic or non-planar cases. An analytically remarkable point is that our method is directly valid for the highly singular regime $p\in(1,\frac{3}{2}]$ in which the second variation may not exist even for smooth variations.
△ Less
Submitted 30 March, 2024; v1 submitted 19 January, 2023;
originally announced January 2023.
-
Tingley's problem for complex Banach spaces which do not satisfy the Hausdorff distance condition
Authors:
David Cabezas,
María Cueto-Avellaneda,
Yuta Enami,
Takeshi Miura,
Antonio M. Peralta
Abstract:
In 2022, Hatori gave a sufficient condition for complex Banach spaces to have the complex Mazur--Ulam property. In this paper, we introduce a class of complex Banach spaces $B$ that do not satisfy the condition but enjoy the property that every surjective isometry on the unit sphere of such $B$ admits an extension to a surjective real linear isometry on the whole space $B$. Typical examples of Ban…
▽ More
In 2022, Hatori gave a sufficient condition for complex Banach spaces to have the complex Mazur--Ulam property. In this paper, we introduce a class of complex Banach spaces $B$ that do not satisfy the condition but enjoy the property that every surjective isometry on the unit sphere of such $B$ admits an extension to a surjective real linear isometry on the whole space $B$. Typical examples of Banach spaces studied in this note are the spaces ${\rm Lip}([0,1])$ of all Lipschitz complex-valued functions on $[0,1]$ and $C^1([0,1])$ of all continuously differentiable complex-valued functions on $[0,1]$ equipped with the norm $|f(0)|+\|f'\|_\infty$.
△ Less
Submitted 2 June, 2023; v1 submitted 31 October, 2022;
originally announced October 2022.
-
Pinned planar p-elasticae
Authors:
Tatsuya Miura,
Kensuke Yoshizawa
Abstract:
Building on our previous work, we classify all planar $p$-elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. As an application we establish a Li--Yau type inequality for the $p$-bending energy, and in particular discover a unique exponent $p \simeq 1.5728$ for full optimality. We also prove existence of minimal $p$-elastic netwo…
▽ More
Building on our previous work, we classify all planar $p$-elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. As an application we establish a Li--Yau type inequality for the $p$-bending energy, and in particular discover a unique exponent $p \simeq 1.5728$ for full optimality. We also prove existence of minimal $p$-elastic networks, extending a recent result of Dall'Acqua--Novaga--Pluda.
△ Less
Submitted 26 June, 2023; v1 submitted 13 September, 2022;
originally announced September 2022.
-
Error estimate for classical solutions to the heat equation in a moving thin domain and its limit equation
Authors:
Tatsu-Hiko Miura
Abstract:
We consider the Neumann type problem of the heat equation in a moving thin domain around a given closed moving hypersurface. The main result of this paper is an error estimate in the sup-norm for classical solutions to the thin domain problem and a limit equation on the moving hypersurface which appears in the thin-film limit of the heat equation. To prove the error estimate, we show a uniform a p…
▽ More
We consider the Neumann type problem of the heat equation in a moving thin domain around a given closed moving hypersurface. The main result of this paper is an error estimate in the sup-norm for classical solutions to the thin domain problem and a limit equation on the moving hypersurface which appears in the thin-film limit of the heat equation. To prove the error estimate, we show a uniform a priori estimate for a classical solution to the thin domain problem based on the maximum principle. Moreover, we construct a suitable approximate solution to the thin domain problem from a classical solution to the limit equation based on an asymptotic expansion of the thin domain problem and apply the uniform a priori estimate to the difference of the approximate solution and a classical solution to the thin domain problem.
△ Less
Submitted 2 August, 2022;
originally announced August 2022.