arXiv subjects
Publications and source records attributed to Seungwon Kim.
We study various constructions of spanning solids for knotted surfaces in the 4-sphere. In particular, we consider a 4-dimensional analogue of Murasugi sum, which we use to define a notion of arborescent knotted surfaces. We give a variety of examples and applications to broken surface diagrams, such as deciding which resolutions of the crossings in these diagrams yield spanning solids.
We construct an irreducible embedded projective plane in $S^4$. This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list. Moreover, we answer both Questions (i) and (ii) of Problem 4.37: (i) the connected sum $R\# R$ is a Klein bottle in $S^4$ with extremal normal Euler number that does not admit an unknotted projective plane summand, and (ii) we show that our projective plane $R$ is irreducible by showing that the peripheral map $\pi_1 (\partial (S^4\setminus\mathring{N}(R)))\to \pi_1 (S^4 \setminus \mathring{N}(R))$ has kernel of order $2$.
In this paper, we construct infinitely many non-isotopic 3-knots in the 5-sphere, each of which has four critical points with respect to the standard height function of the 5-sphere. This contrasts with a theorem of Scharlemann which says that any 2-knot in the 4-sphere with four critical points is unknotted, and also provides infinitely many knotted solid tori in the 4-sphere and 5-ball, which resolves the last remaining case of the conjecture by Budney and Gabai on the existence of knotted handlebodies. We also construct various knotted and linked handlebodies, discs, and spheres in the 4-sphere, 5-ball, and 5-sphere, extending recent works of Hughes, Miller, and the first author, and a recent work of the authors. All of our examples are explicit and are constructed using barbell diffeomorphisms.
For each integer $n\ge 2$, we construct infinitely many $n$-component Brunnian links of 3-balls in $S^4$. Our main tool is the third author's result on the existence of splitting spheres for the trivial two-component link of $2$-spheres in $S^{4}$; we also give a new proof of this.
For window applications in hot climates, it is desirable to have windows with high visible transparency, while maintaining strong reflectance in both the ultraviolet and near infrared, to minimize unwanted heat gain. Given that more than 70% of incident solar energy is at wavelengths shorter than 1000 nm, achieving spectrally abrupt transitions from transparent to reflecting at the boundaries of the visible is essential. Such abrupt transitions at multiple wavelengths typically would require tens of dielectric layers, which is impractical for most window applications. Here, we propose and realize a structure comprising only eight planar layers that achieves sharp reflectance changes at ~390 and ~680 nm, resulting in high visible transmittance (>70%), and high near-infrared (>80%) and UV (>60%) reflectance, as well as high mid-infrared emissivity (>90%) for additional radiative cooling. We demonstrate that our engineered window reduces air temperature by up to 3.8 {\deg}C inside an enclosed box simulating a vehicle, compared to a box with a reference window.
Recent advances in LLMs have made automated scientific research the next frontline in the path to artificial superintelligence. However, these systems are bound either to tasks of narrow scope or the limited creative capabilities of LLMs. We propose Spacer, a scientific discovery system that develops creative and factually grounded concepts without external intervention. Spacer attempts to achieve this via 'deliberate decontextualization,' an approach that disassembles information into atomic units - keywords - and draws creativity from unexplored connections between them. Spacer consists of (i) Nuri, an inspiration engine that builds keyword sets, and (ii) the Manifesting Pipeline that refines these sets into elaborate scientific statements. Nuri extracts novel, high-potential keyword sets from a keyword graph built with 180,000 academic publications in biological fields. The Manifesting Pipeline finds links between keywords, analyzes their logical structure, validates their plausibility, and ultimately drafts original scientific concepts. According to our experiments, the evaluation metric of Nuri accurately classifies high-impact publications with an AUROC score of 0.737. Our Manifesting Pipeline also successfully reconstructs core concepts from the latest top-journal articles solely from their keyword sets. An LLM-based scoring system estimates that this reconstruction was sound for over 85% of the cases. Finally, our embedding space analysis shows that outputs from Spacer are significantly more similar to leading publications compared with those from SOTA LLMs.
Audio-driven talking head generation requires precise synchronization between facial animations and audio signals. This paper introduces ATL-Diff, a novel approach addressing synchronization limitations while reducing noise and computational costs. Our framework features three key components: a Landmark Generation Module converting audio to facial landmarks, a Landmarks-Guide Noise approach that decouples audio by distributing noise according to landmarks, and a 3D Identity Diffusion network preserving identity characteristics. Experiments on MEAD and CREMA-D datasets demonstrate that ATL-Diff outperforms state-of-the-art methods across all metrics. Our approach achieves near real-time processing with high-quality animations, computational efficiency, and exceptional preservation of facial nuances. This advancement offers promising applications for virtual assistants, education, medical communication, and digital platforms. The source code is available at: \href{https://github.com/sonvth/ATL-Diff}{https://github.com/sonvth/ATL-Diff}
We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split, alternating link into the 4-ball are smoothly isotopic fixing boundary. In other words, any same-genus Seifert surfaces for a non-split, alternating link become smoothly isotopic fixing boundary once their interiors are pushed into the 4-ball. We conclude that a smooth surface in $S^4$ obtained by gluing two Seifert surfaces for a non-split alternating link is always smoothly unknotted.
Understanding the pivotal role of oxygen-containing organic compounds in serving as an energy source for living organisms and contributing to protein formation is crucial in the field of biochemistry. This study addresses the challenge of comprehending protein-protein interactions (PPI) and developing predicitive models for proteins and organic compounds, with a specific focus on quantifying their binding affinity. Here, we introduce the active Bayesian Committee Machine (BCM) potential, specifically designed to predict oxygen-containing organic compounds within eight groups of CHO. The BCM potential adopts a committee-based approach to tackle scalability issues associated with kernel regressors, particularly when dealing with large datasets. Its adaptable structure allows for efficient and cost-effective expansion, maintaing both transferability and scalability. Through systematic benchmarking, we position the sparse BCM potential as a promising contender in the pursuit of a universal machine learning potential.
We prove that the double branched cover of a twist-roll spun knot in $S^4$ is smoothly preserved when four twists are added, and that the double branched cover of a twist-roll spun knot connected sum with a trivial projective plane is preserved after two twists are added. As a consequence, we conclude that the members of a family of homotopy $\mathbb{CP}^2$s recently constructed by Miyazawa are each diffeomorphic to $\mathbb{CP}^2$. We also apply our techniques to show that the double branched covers of odd-twisted turned tori are all diffeomorphic to $S^2 \times S^2$, and show that a family of homotopy 4-spheres constructed by Juh\'asz and Powell are all diffeomorphic to $S^4$.
The human brain remains continuously active, whether an individual is working or at rest. Mental activity is a daily process, and if the brain becomes excessively active, known as overload, it can adversely affect human health. Recently, advancements in early prediction of mental health conditions have emerged, aiming to prevent serious consequences and enhance the overall quality of life. Consequently, the estimation of mental status has garnered significant attention from diverse researchers due to its potential benefits. While various signals are employed to assess mental state, the electroencephalogram, containing extensive information about the brain, is widely utilized by researchers. In this paper, we categorize mental workload into three states (low, middle, and high) and estimate a continuum of mental workload levels. Our method leverages information from multiple spatial dimensions to achieve optimal results in mental estimation. For the time domain approach, we employ Temporal Convolutional Networks. In the frequency domain, we introduce a novel architecture based on combining residual blocks, termed the Multi-Dimensional Residual Block. The integration of these two domains yields significant results compared to individual estimates in each domain. Our approach achieved a 74.98% accuracy in the three-class classification, surpassing the provided data results at 69.00%. Specially, our method demonstrates efficacy in estimating continuous levels, evidenced by a corresponding Concordance Correlation Coefficient (CCC) result of 0.629. The combination of time and frequency domain analysis in our approach highlights the exciting potential to improve healthcare applications in the future.
We show that there exist split, orientable, 2-component surface-links in $S^4$ with non-isotopic splitting spheres in their complements. In particular, for non-negative integers $m,n$ with $m\ge 4$, the unlink $L_{m,n}$ consisting of one component of genus $m$ and one component of genus $n$ contains in its complement two smooth splitting spheres that are not topologically isotopic in $S^4\setminus L_{m,n}$. This contrasts with link theory in the classical dimension, as any two splitting spheres in the complement of a 2-component split link $L\subset S^3$ are isotopic in $S^3\setminus L$.
For every integer $g\ge 2$ we construct 3-dimensional genus-$g$ 1-handlebodies smoothly embedded in $S^4$ with the same boundary, and which are defined by the same cut systems of their boundary, yet which are not isotopic rel. boundary via any locally flat isotopy even when their interiors are pushed into $B^5$. This proves a conjecture of Budney-Gabai for genus at least 2.
We answer a question of Livingston from 1982 by producing Seifert surfaces of the same genus for a knot in $S^3$ that do not become isotopic when their interiors are pushed into $B^4$. In particular, we identify examples where the surfaces are not even topologically isotopic in $B^4$, examples that are topologically but not smoothly isotopic, and examples of infinite families of surfaces that are distinct only up to isotopy rel. boundary. Our main proofs distinguish surfaces using the cobordism maps on Khovanov homology, and our calculations demonstrate the stability and computability of these maps under certain satellite operations.
The untwisting number of a knot K is the minimum number of null-homologous twists required to convert K to the unknot. Such a twist can be viewed as a generalization of a crossing change, since a classical crossing change can be effected by a null-homologous twist on 2 strands. While the unknotting number gives an upper bound on the smooth 4-genus, the untwisting number gives an upper bound on the topological 4-genus. The surgery description number, which allows multiple null-homologous twists in a single twisting region to count as one operation, lies between the topological 4-genus and the untwisting number. We show that the untwisting and surgery description numbers are different for infinitely many knots, though we also find that the untwisting number is at most twice the surgery description number plus 1.
A 2-component oriented link in $S^3$ is called weakly doubly slice if it is a cross-section of an unknotted sphere in $S^4$, and strongly doubly slice if it is a cross-section of a 2-component trivial spherical link in $S^4$. We give the first example of 2-component boundary links which are weakly doubly slice but not strongly doubly slice. We also introduce a new invariant $g_{st}$ of homotopically trivial links that measures the failure of a link from being strongly doubly slice and that bounds the doubly slice genus $g_{ds}$ from below. Our examples have arbitrarily large doubly slice genus but satisfy $g_{st}=1$. We also prove that the Conway-Orson signature lower bound on $g_{ds}$ is actually a lower bound on $g_{st}$.
We study immersed surfaces in smooth 4-manifolds via singular banded unlink diagrams. Such a diagram consists of a singular link with bands inside a Kirby diagram of the ambient 4-manifold, representing a level set of the surface with respect to an associated Morse function. We show that every self-transverse immersed surface in a smooth, orientable, closed 4-manifold can be represented by a singular banded unlink diagram, and that such representations are uniquely determined by the ambient isotopy or equivalence class of the surface up to a set of singular band moves which we define explicitly. By introducing additional finger, Whitney, and cusp diagrammatic moves, we can use these singular band moves to describe homotopies or regular homotopies as well. Using these techniques, we introduce bridge trisections of immersed surfaces in arbitrary trisected 4-manifolds and prove that such bridge trisections exist and are unique up to simple perturbation moves. We additionally give some examples of how singular banded unlink diagrams may be used to perform computations or produce explicit homotopies of surfaces.
We show that the differences between various concordance invariants of knots, including Rasmussen's $s$-invariant and its generalizations $s_n$-invariants, give lower bounds to the Turaev genus of knots. Using the fact that our bounds are nontrivial for some quasi-alternating knots, we show the additivity of Turaev genus for a certain class of knots. This leads us to the first example of an infinite family of quasi-alternating knots with Turaev genus exactly $g$ for any fixed positive integer $g$, solving a question of Champanerkar-Kofman.