Korea Institute for Advanced Study

Yang Y., Yang W., Son Y., Liu S.

Choi S., Lee Y., Kim S., Park C., Hwang H., Park F.C.

Kwon K., Lee Y.J., Jung Y., Soltis I., Na Y., Romero L., Kim M.C., Rodeheaver N., Kim H., Lee C., Ko S., Lee J., Yeo W.

The widespread emergence of airborne diseases has transformed our lifestyle, and respirators have become an essential part of daily life. Nevertheless, finding respirators that fit well can be challenging due to the variety of human facial sizes and shapes, potentially compromising protection. In addition, the current respirators do not inform the user of the air quality in case of continuous long-term use. Here, we introduce a smart filtering facepiece respirator incorporating a humidity sensor and pressure sensory feedback for self-fit adjusting and maintaining an adequate fit. The humidity detection sensor uses laser-induced graphene, and the pressure sensor array based on the dielectric elastomeric sponge monitors the respirator contact on the user's face, providing real-time closed-loop feedback and the wearer's fitting status. Those membrane sensors show outstanding performance, such as a low humidity hysteresis of 0.131 % and a precise pressure detection limit of 0.23 ± 0.02 kPa. As a result of the self-fit adjusting mode, the overall fit factor is increased by 10 % on average compared to the commercial respirator. This significant improvement in fit factor, coupled with the innovative design, has the potential to develop next-generation facepiece respirators as essential personal protective equipment.

Park H., Park I.W., Kim D., Nah H., YANG J., Yeo J., Choi J., Choi J., Park H., Choi H.

Gonzales J.E., Kim I., Bastiray A., Hwang W., Cho J.

Viral proteins frequently mutate to evade host innate immune responses, yet the impact of these mutations on the molecular energy landscape remains unclear. Epistasis, the intramolecular communications between mutations, often renders the combined mutational effects unpredictable. Nonstructural protein 1 (NS1) is a major virulence factor of the influenza A virus (IAV) that activates host PI3K by binding to its p85β subunit. Here, we present a deep analysis of the impact of evolutionary mutations in NS1 that emerged between the 1918 pandemic IAV strain and its descendant PR8 strain. Our analysis reveals how the mutations rewired interresidue communications, which underlie long-range allosteric and epistatic networks in NS1. Our findings show that PR8 NS1 binds to p85β with approximately 10-fold greater affinity than 1918 NS1 due to allosteric mutational effects, which are further tuned by epistasis. NMR chemical shift perturbation and methyl-axis order parameter analyses revealed that the mutations induced long-range structural and dynamic changes in PR8 NS1, relative to 1918 NS1, enhancing its affinity to p85β. Complementary molecular dynamics simulations and graph theory-based network analysis for conformational dynamics on the submicrosecond timescales uncover how these mutations rewire the dynamic network, which underlies the allosteric epistasis. Significantly, we find that conformational dynamics of residues with high betweenness centrality play a crucial role in communications between network communities and are highly conserved across influenza A virus evolution. These findings advance our mechanistic understanding of the allosteric and epistatic communications between distant residues and provide insight into their role in the molecular evolution of NS1.

Choi K., Seo D., Su W., Zhao K.

In this paper, we prove that an ancient smooth curve-shortening flow with finite entropy embedded in $\mathbb{R}^{2}$ has a unique tangent flow at infinity. To this end, we show that its rescaled flows backwardly converge to a line with multiplicity m≥3 exponentially fast in any compact region, unless the flow is a shrinking circle, a static line, a paper clip, or a translating grim reaper. In addition, we figure out the exact numbers of tips, vertices, and inflection points of the curves at negative enough time. Moreover, the exponential growth rate of graphical radius and the convergence of vertex regions to grim reaper curves will be shown.

Choi T., Han Y.D.

In the realm of relativistic quantum mechanics, we address a fundamental question: Which one, between the Dirac or the Foldy-Wouthuysen density, accurately provide a probability density for finding a massive particle with spin 1/2 at a certain position and time. Recently, concerns about the Dirac density’s validity have arisen due to the Zitterbewegung phenomenon, characterized by a peculiar fast-oscillating solution of the coordinate operator that disrupts the classical relation among velocity, momentum, and energy. To explore this, we applied Newton and Wigner’s method to define proper position operators and their eigenstates in both representations, identifying ’localized states’ orthogonal to their spatially displaced counterparts. Our analysis shows that both densities could represent the probability of locating a particle within a few Compton wavelengths. However, a critical analysis of Lorentz transformation properties reveals that only the Dirac density meets all essential physical criteria for a relativistic probability density. These criteria include covariance of the position eigenstate, adherence to a continuity equation, and Lorentz invariance of the probability of finding a particle. Our results provide a clear and consistent interpretation of the probability density for a massive spin-1/2 particle in relativistic quantum mechanics.

Choe J.

Abstract McCullough and Peeva found sequences of counterexamples to the Eisenbud–Goto conjecture on the Castelnuovo–Mumford regularity by using Rees-like algebras, where entries of each sequence have increasing dimensions and codimensions. In this paper we suggest another method to construct counterexamples to the conjecture with any fixed dimension $n\geq 3$ and any fixed codimension $e\geq 2$. Our strategy is an unprojection process and utilizes the possible complexity of homogeneous ideals with three generators. Furthermore, our counterexamples exhibit how singularities affect the Castelnuovo–Mumford regularity.

Duan Z., Jia Q., Lee S.

Abstract We study ℤ N one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, the associated TFT in the five-dimensional bulk is the BF model. We revisit its canonical quantization and construct topological boundary states on several important classes of four manifolds that are spin, non-spin and torsional. We highlight a web of four-dimensional dualities, which can be naturally interpreted within the SymTFT framework. We also point out an intriguing class of four-dimensional gauge theories that exhibit mixed ’t Hooft anomaly between one-form symmetries. In the second part of this work, we extend the SymTFT to account for various quantities protected by supersymmetry (SUSY) in SUSY gauge theories. We proposed that their behaviour under various symmetry operations are entirely captured by the topological boundary of the SymTFT, resulting in strong constraints. Concrete examples are considered, including the Witten index, the lens space index and the Donaldson-Witten and Vafa-Witten partition functions.

Hubisz J., Lee S.J., Li H., Sambasivam B.

Yu J.W., Yoo C., Cho S., Seo M., Kim Y.

Macromolecular self-assembly is essential in life and interfacial science. A macromolecule consisting of chemically distinct components tends to self-assemble in a selective solvent to minimize the exposure of the solvophobic segments to the medium while the solvophilic segments adopt extended conformations. While micelles composed of linear block copolymers represent classic examples of such solution assembly, recent interest focuses on the self-assembly of complex macromolecules with nonlinear architectures, such as star, graft, and bottlebrush. Such macromolecules include several to hundreds of polymer chains covalently tied to a core and a backbone. The pre-programmed, non-exchangeable chain arrangement makes a huge difference in their self-assembly. The field has witnessed tremendous advances in synthetic methodologies to construct the desired architectures, leading to discoveries of exotic self-assembly behavior. Thanks to the rapid evolution of computing power, computer simulation has also been an emerging and complementary approach for understanding the association mechanism and further predicting the self-assembling morphologies. However, simulating the self-assembly of architected macromolecules has posed a challenge as a huge number of objects should be included in the simulations. Comparing experimental results with simulations is not always straightforward, as synthetic routes to well-defined model systems with systematically controlled structural parameters are not often available. In this manuscript, we propose to bridge a gap between experiments and simulations in self-assembly of architected macromolecules. We focus on the key articles in this area reporting experimental evidence and simulation details and also cover recent examples in the literature. We start with discussing simulation methodologies applicable to investigate solution self-assembly across multiple levels of chemical resolution from all-atom to particle dynamics. Then, we delve into topological design, synthesis, and simulation of nonlinear macromolecules, including dendritic/star, network, and graft/bottlebrush polymers, to understand the architectural effect on the self-assembly behavior. We expand our discourse to embrace recent advances toward realizing more complex systems. For example, self-assembly in the presence of strong Coulombic interactions, such as in the case of polyelectrolytes, geometric constraints, and other components in solutions, exemplified by inorganic fillers, are introduced. Finally, the challenges and perspectives are discussed in the final section of the manuscript.

Abbas G., Adhikari R., Chun E.J., Singh N.

We review the problem of flavour tracing back to the days when the standard model was just coming together. We focus on the recently discussed new solutions of this problem, namely the Froggatt and Nielsen mechanism based on a novel discrete $$\mathcal {Z}_{\textrm{N}} \times \mathcal {Z}_{\textrm{M}}$$ flavour symmetry, and the standard hierarchical VEVs model. The standard HVM, and the Froggatt and Nielsen mechanism based on the $$\mathcal {Z}_{\textrm{N}} \times \mathcal {Z}_{\textrm{M}}$$ flavour symmetry, can be recovered from a new dark-technicolour paradigm, where the hierarchical VEVs or the flavon VEV may appear as the chiral multi-fermion condensates. In particular, there appears a novel feature that the solution of the flavour problem based on the discrete flavour symmetry can provide the so-called flavonic dark matter. This predicts a specific relation between the mass and the symmetry-breaking scale, which can be contrasted with the standard QCD axion. Moreover, a possible direction towards the Grand Unified framework is also discussed.

Osorio Quero C., Rondon Ojeda I., Martinez-Carranza J.

We introduce a hybrid approach that combines deep image prior (DIP) with generative adversarial networks (GANs) to improve the resolution of single-pixel imaging (SPI). SPI excels in challenging conditions such as low light or limited spectral camera availability, particularly in the near-infrared (NIR) range from 850 to 1550 nm. By employing an unsupervised image super-resolution technique based on DIP, we reduce the need for extensive direct SPI image datasets. This innovation simplifies enhancing image quality in specific NIR bands. We provide numerical and experimental evidence to support our method and detail the enhancements in UNet and GAN architectures across four neural network configurations.

Kawai H., Kawana K., Oda K., Yagyu K.

Abstract In models with non-minimal Higgs sectors, enforcing (near) Higgs alignment, necessary to prevent significant deviations in the Higgs boson coupling from the standard model prediction, causes a serious fine-tuning problem. We demonstrate that the Higgs alignment is naturally deduced from the multicritical point principle (MPP) in the general two Higgs doublet model while keeping non-zero CP-violating phases. Furthermore, we discuss the possibility of realizing the Yukawa alignment from the MPP, which is necessary to prevent flavor-changing neutral currents mediated by Higgs bosons at tree level, and find that it seems difficult to realize it by the MPP due to the non-diagonal structure of the CKM matrix.

Abhinand M., Curto R.E., Hwang I.S., Lee W.Y., Prasad T.

In this paper we consider the subnormality of block Toeplitz operators TΦ, where Φ is an n × n matrix-valued function on the unit circle $$\mathbb{T}$$ of the form $$\Phi=Q\Phi^{\ast}\;\;\;\;(Q\;\text{is}\; \text{a}\; \text{finite}\; \text{Blaschke-Potapov}\; \text{product})$$ This is related to a matrix-valued version of Halmos’ Problem 5 and the Nakazi–Takahashi Theorem. We ask whether TΦ is either normal or analytic if TΦ is subnormal, where Φ is of the above form. We give answers to this problem for different cases of the symbol. Moreover, we provide a sufficient condition for the answer to be affirmative when Φ* is not of bounded type.