KOINEU Logo
Multifractal Recalibration of Neural Networks for Medical Imaging Segmentation

Multifractal Recalibration of Neural Networks for Medical Imaging Segmentation

๋ณธ ๋…ผ๋ฌธ์€ ๋‹ค์ค‘ํ”„๋ž™ํƒˆ ์ด๋ก ์„ ๋”ฅ๋Ÿฌ๋‹ ๊ธฐ๋ฐ˜ ์˜๋ฏธ๋ถ„ํ•  ๋ชจ๋ธ์— ํ†ตํ•ฉํ•˜๋Š” ์ƒˆ๋กœ์šด ํŒจ๋Ÿฌ๋‹ค์ž„์„ ์ œ์‹œํ•œ๋‹ค. ๊ธฐ์กด์˜ ๋‹ค์ค‘ํ”„๋ž™ํƒˆ ์ŠคํŽ™ํŠธ๋Ÿผ(MFS) ๋ถ„์„์€ ์ฃผ๋กœ ์ด๋ฏธ์ง€ ํ…์Šค์ฒ˜์˜ ๋ณต์žก์„ฑ์„ ์ •๋Ÿ‰ํ™”ํ•˜๊ฑฐ๋‚˜, ๋น„์ง€๋„ ํ•™์Šต์—์„œ ํŠน์ง• ์ถ”์ถœ์— ํ™œ์šฉ๋ผ ์™”์œผ๋ฉฐ, ๊ทธ ๊ณผ์ •์—์„œ ๊ณ ์ฐจ ํ†ต๊ณ„๋Ÿ‰์„ ๊ณ„์‚ฐํ•˜๊ธฐ ์œ„ํ•ด ๋Œ€๊ทœ๋ชจ ํ’€๋ง์ด๋‚˜ ์ฐจ์› ์ถ•์†Œ๊ฐ€ ํ•„์ˆ˜์ ์ด์—ˆ๋‹ค. ์ด๋Ÿฌํ•œ ์—ฐ์‚ฐ์€ ๋ฉ”๋ชจ๋ฆฌ์™€ ์‹œ๊ฐ„ ์ธก๋ฉด์—์„œ ๋น„ํšจ์œจ์ ์ด๋ฉฐ, ํŠนํžˆ ํ”ฝ์…€โ€‘๋‹จ์œ„ ์˜ˆ์ธก์ด ์š”๊ตฌ๋˜๋Š” ์˜๋ฏธ๋ถ„ํ•  ์ž‘์—…์—์„œ๋Š” ์‹ค์šฉ์„ฑ์ด ๋–จ์–ด์ง„๋‹ค. ์ €์ž๋“ค์€ ์ด ๋ฌธ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•ด โ€˜๋‹จ์ผํ”„๋ž™ํƒˆ ์žฌ๋ณด์ •(Monofractal Recalibration)โ€™

Network
No Image

Multiscale Hyperbolic-Parabolic Models for Nonlinear Reactive Transport in Heterogeneously Fractured Porous Media

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ํ•„์š”์„ฑ ํŒŒ๋‹จ์˜ ๋ฌผ๋ฆฌ์  ์ค‘์š”์„ฑ : ์ง€ํ•˜์ˆ˜, ์˜ค์—ผ๋ฌผ ์ •ํ™”, ์„์œ ยท๊ฐ€์Šค ๋งค์žฅ์ธต ๋“ฑ์—์„œ ํŒŒ๋‹จ์€ ํ๋ฆ„ยท์ˆ˜์†ก์„ ์ง€๋ฐฐํ•˜๋Š” ๊ณ ์† ๊ฒฝ๋กœ์ด๋ฉฐ, ์‹ค์ œ ํŒŒ๋‹จ์€ ์–‡์€ ํ‹ˆ์ƒˆ์™€ ๋ณต์žกํ•œ ํ‘œ๋ฉด ๊ฑฐ์น ๊ธฐ, ๋‚ด๋ถ€ ์žฅ์• ๋ฌผ ๋“ฑ ๋‹ค์ค‘ ์Šค์ผ€์ผ ๊ตฌ์กฐ๋ฅผ ๊ฐ€์ง„๋‹ค. ์ˆ˜์น˜์ ยท์ด๋ก ์  ๋‚œ์ œ : ๋ฏธ์„ธ ๊ตฌ์กฐ๋ฅผ ์ง์ ‘ ํ•ด์„ํ•˜๋ฉด ๊ณ„์‚ฐ ๋น„์šฉ์ด ํญ๋ฐœ์ ์œผ๋กœ ์ฆ๊ฐ€ํ•˜๊ณ , ๊ธฐ์กด์˜ ๋™์งˆํ™” ๊ธฐ๋ฒ•์€ ์ฃผ๋กœ ์„ ํ˜•ยทํ™•์‚ฐโ€‘์ง€๋ฐฐ ํ๋ฆ„์— ๊ตญํ•œ๋ผ ํŒŒ๋‹จ ๋‚ด๋ถ€์˜ ๊ฐ•๋Œ€๋ฅ˜์™€ ๋น„์„ ํ˜• ๋ฐ˜์‘์„ ์ถฉ๋ถ„ํžˆ ๋ฐ˜์˜ํ•˜์ง€ ๋ชปํ•œ๋‹ค. 2. ๋ชจ๋ธ ์„ค์ • ๋ฐ ์ฃผ์š” ๊ฐ€์ • | ๊ตฌ๋ถ„ | ๋‚ด์šฉ | ์ˆ˜ํ•™์  ํ‘œํ˜„ | | | | | | ๊ธฐํ•˜ํ•™ | ์–‡

Model Mathematics
No Image

Nonparametric Kernel Regression for Coordinated Energy Storage Peak Shaving with Stacked Services

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ํ•„์š”์„ฑ ์ „๋ ฅ ํ”ผํฌ ๋น„์šฉ ์ด ์›”๋ณ„ ๊ณ ์ • ์š”๊ธˆ๋ณด๋‹ค ํ›จ์”ฌ ํฐ ์ƒ์—…ยท์‚ฐ์—… ๋ถ€๋ฌธ์—์„œ BESS ํ™œ์šฉ์ด ๊ธ‰์ฆํ•˜๊ณ  ์žˆ์œผ๋‚˜, ๊ธฐ์กด ๋ฐฉ๋ฒ•์€ ์›”๊ฐ„ ์ˆ˜์ค€์˜ ์ˆ˜์š”ยท๊ฐ€๊ฒฉ ์˜ˆ์ธก ์— ํฌ๊ฒŒ ์˜์กดํ•˜๊ฑฐ๋‚˜, ๋™์  ํ”„๋กœ๊ทธ๋ž˜๋ฐยทํฌํŠธํด๋ฆฌ์˜ค ์ตœ์ ํ™”์™€ ๊ฐ™์€ ๊ณ„์‚ฐ๋Ÿ‰์ด ํฐ ๊ธฐ๋ฒ•์„ ์‚ฌ์šฉํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ์ ‘๊ทผ๋ฒ•์€ ์˜ˆ์ธก ์˜ค์ฐจ ์™€ ์‹ค์‹œ๊ฐ„ ์—ฐ์‚ฐ ๋ถ€๋‹ด ์ด ์ปค์„œ ์ค‘์†Œ๊ธฐ์—…ยท๋น„์˜๋ฆฌ๊ธฐ๊ด€์— ์ ์šฉํ•˜๊ธฐ ์–ด๋ ต๋‹ค. 2. ํ•ต์‹ฌ ์•„์ด๋””์–ด ๋ฐ ๋ฐฉ๋ฒ•๋ก  | ๋‹จ๊ณ„ | ๋ชฉํ‘œ | ํ•ต์‹ฌ ๊ธฐ๋ฒ• | ์ฃผ์š” ๋ณ€์ˆ˜ | | | | | | | Stage 1 โ€“ ํ”ผํฌ ์ ˆ๊ฐ | ์›”๊ฐ„ ํ”ผํฌ ๋ชฉํ‘œ์™€ SOC ๋ณด์œ  ๊ตฌ๊ฐ„์„ ๊ฒฐ์ •

Mathematics
No Image

Novel distance-based masking and adaptive alpha-shape methods for CNN-ready reconstruction of arbitrary 2D CFD flow domains

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ํ•„์š”์„ฑ CNN์€ ๊ทœ์น™์ ์ธ ๊ฒฉ์ž ๋ฐ์ดํ„ฐ๋ฅผ ์ „์ œ๋กœ ํ•˜๋ฏ€๋กœ, ๋น„์ •ํ˜• CFD ๊ฒฐ๊ณผ๋ฅผ ์ง์ ‘ ํ™œ์šฉํ•˜๊ธฐ ์–ด๋ ต๋‹ค. ๊ธฐ์กด์˜ ์ โ€‘๊ธฐ๋ฐ˜ ์‹ ๊ฒฝ๋ง(PointNetยทGCN ๋“ฑ)์€ ๋ฌผ๋ฆฌ์  ํ•ด์„์— ์œ ๋ฆฌํ•˜์ง€๋งŒ ์—ฐ์‚ฐ ๋น„์šฉยท๋ณต์žก๋„๊ฐ€ ๋†’์•„ ๋Œ€๊ทœ๋ชจ 2D/3D ํ๋ฆ„ ๋ฐ์ดํ„ฐ์— ์ ์šฉํ•˜๊ธฐ์—” ๋น„ํšจ์œจ์ ์ด๋‹ค. ๋”ฐ๋ผ์„œ ๋น„์ •ํ˜• ๋ฐ์ดํ„ฐ๋ฅผ ๊ท ์ผ ๊ฒฉ์ž๋กœ ์žฌ๊ตฌ์„ฑํ•˜๋ฉด์„œ ๊ฒฝ๊ณ„ ์™œ๊ณก ์„ ์ตœ์†Œํ™”ํ•˜๋Š” ์ „์ฒ˜๋ฆฌ ๊ธฐ๋ฒ•์ด ํ•„์ˆ˜์ ์ด๋‹ค. 2. ์ฃผ์š” ๊ธฐ๋ฒ• | ๊ธฐ๋ฒ• | ํ•ต์‹ฌ ์•„์ด๋””์–ด | ๊ตฌํ˜„ ๋ฐฉ์‹ | ํŒŒ๋ผ๋ฏธํ„ฐ | | | | | | | ๊ฑฐ๋ฆฌ ๊ธฐ๋ฐ˜ ๋งˆ์Šคํ‚น | ๊ฒฉ์ž์  โ†” ๊ฐ€์žฅ ๊ฐ€๊นŒ์šด ์ƒ˜ํ”Œ ๊ฐ„ ๊ฑฐ๋ฆฌ ๊ณ„

Physics
Numerical simulation of lunar response to gravitational waves and its 3D topographic effect using the spectral-element method

Numerical simulation of lunar response to gravitational waves and its 3D topographic effect using the spectral-element method

๋ณธ ๋…ผ๋ฌธ์€ ๋‹ฌ์ด ์ค‘๋ ฅํŒŒ(GWs)๋ฅผ ์ฆํญ์‹œํ‚ค๋Š” ์ž์—ฐ์ ์ธ ์›จ๋ฒ„ ๋ฐ”๋กœ ๊ธฐ๋Šฅํ•  ์ˆ˜ ์žˆ๋‹ค๋Š” ๊ฐœ๋…์„ ์ œ์‹œํ•˜๋ฉฐ, ์ด๋ฅผ ์ •ํ™•ํ•˜๊ฒŒ ์ดํ•ดํ•˜๊ธฐ ์œ„ํ•œ 3D ์ˆ˜์น˜ ์‹œ๋ฎฌ๋ ˆ์ด์…˜ ๋ฐฉ๋ฒ•์˜ ๊ฐœ๋ฐœ์— ์ดˆ์ ์„ ๋งž์ถ”๊ณ  ์žˆ๋‹ค. ์—ฐ๊ตฌํŒ€์€ ๊ณ ์ฐจ์› 3D ์œ ํ•œ ์š”์†Œ๋ฒ•(์ŠคํŽ™ํŠธ๋Ÿด ์š”์†Œ ๋ฐฉ๋ฒ•)์„ ํ†ตํ•ด ๋‹ฌ์ด ์ค‘๋ ฅํŒŒ๋ฅผ ์–ด๋–ป๊ฒŒ ๋ฐ˜์‘ํ•˜๋Š”์ง€, ํŠนํžˆ 20 mHz ์ดํ•˜ ์ฃผํŒŒ์ˆ˜ ๋ฒ”์œ„์—์„œ์˜ ๋ฐ˜์‘์„ ์‹œ๋ฎฌ๋ ˆ์ด์…˜ํ•˜์˜€๋‹ค. ์ด๋ฅผ ํ†ตํ•ด ๋‹ฌ ํ‘œ๋ฉด ์ง€ํ˜•์— ๋”ฐ๋ฅธ ์ค‘๋ ฅํŒŒ ์‹ ํ˜ธ ์ฆํญ ํšจ๊ณผ๋ฅผ ํ‰๊ฐ€ํ•˜๊ณ ์ž ํ•˜์˜€๋‹ค. ๋…ผ๋ฌธ์€ ์ค€์ •๋Ÿ‰ํ•ด์™€ ๋น„๊ตํ•˜์—ฌ SEM ๋ฐฉ๋ฒ•์˜ ์ •ํ™•์„ฑ์„ ๊ฒ€์ฆํ•˜์˜€๊ณ , ์ฃผํŒŒ์ˆ˜ ํŽธ์ฐจ๋Š” ์ฒซ ๋ฒˆ์งธ ํ”ผํฌ์—์„œ ์•ฝ 1 mHz์—์„œ

No Image

Omni-iEEG: A Large-Scale, Comprehensive iEEG Dataset and Benchmark for Epilepsy Research

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ํ•„์š”์„ฑ ์ž„์ƒ์  ๋ณ‘๋ชฉ : iEEG ํ•ด์„์€ ์ˆ˜์‹œ๊ฐ„~์ˆ˜์ผ์— ๊ฑธ์นœ ์ˆ˜๋™ ๋ฆฌ๋ทฐ๊ฐ€ ํ•„์ˆ˜์ด๋ฉฐ, ์ „๋ฌธ๊ฐ€ ๊ฐ„ ์ผ๊ด€์„ฑ๋„ ๋‚ฎ๋‹ค(Interโ€‘rater reliability). ๋ฐ์ดํ„ฐ ๊ณผํ•™์  ํ•œ๊ณ„ : ํ˜„์žฌ ๊ณต๊ฐœ๋œ iEEG ๋ฐ์ดํ„ฐ์…‹์€ ํฌ๋งทยท์ฑ„๋„ ๋ช…๋ช…ยท๋ฉ”ํƒ€๋ฐ์ดํ„ฐ๊ฐ€ ์„œ๋กœ ๋‹ฌ๋ผ ๋จธ์‹ ๋Ÿฌ๋‹ ํŒŒ์ดํ”„๋ผ์ธ ๊ตฌ์ถ•์ด ์–ด๋ ค์šฐ๋ฉฐ, ํ‘œ์ค€ ๋ฒค์น˜๋งˆํฌ๊ฐ€ ๋ถ€์žฌํ•ด ๊ฒฐ๊ณผ ๋น„๊ต๊ฐ€ ๋ถˆ๊ฐ€๋Šฅํ–ˆ๋‹ค. 2. Omniโ€‘iEEG์˜ ํ•ต์‹ฌ ๊ธฐ์—ฌ | ๊ตฌ๋ถ„ | ๋‚ด์šฉ | ์˜์˜ | | | | | | ๊ทœ๋ชจ | 302๋ช…, 178์‹œ๊ฐ„, 8๊ฐœ ๊ธฐ๊ด€ | ๋‹ค๊ธฐ๊ด€ยท๋‹ค๊ตญ์  ์ผ๋ฐ˜ํ™” ๊ฐ€๋Šฅ์„ฑ ํ™•๋ณด | | ํ‘œ์ค€ํ™” |

Data Computer Science Machine Learning
No Image

On coefficients, potentially abelian quotients, and residual irreducibility of compatible systems

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ํ˜ธํ™˜๊ณ„์™€ ๋Œ€์ˆ˜์  ๋ชจ๋…ธ๋“œ๋กœ๋ฏธ ๊ตฐ : ์ˆ˜์ฒด์˜ $ell$โ€‘adic ํ‘œํ˜„์€ ๋‹ค์–‘ํ•œ ์‚ฐ์ˆ ยท๊ธฐํ•˜ํ•™์  ๊ฐ์ฒด(์˜ˆ: ๋งค๋„๋Ÿฌ์šด ์‚ฌ์˜ ๋‹ค์–‘์ฒด, ์ž๋™ํ˜•์‹)์™€ ์—ฐ๊ฒฐ๋œ๋‹ค. ์ด๋•Œ ๊ฐ $lambda$์— ๋Œ€ํ•œ ์ด๋ฏธ์ง€์˜ Zariski ํ์‡„์ธ $G lambda$๋Š” โ€œ๋Œ€์ˆ˜์  ๋ชจ๋…ธ๋“œ๋กœ๋ฏธ ๊ตฐโ€์ด๋ผ ๋ถˆ๋ฆฌ๋ฉฐ, ๊ทธ ๊ตฌ์กฐ๋Š” ํ˜ธํ™˜๊ณ„ ์ „์ฒด์˜ ์„ฑ์งˆ์„ ์ดํ•ดํ•˜๋Š” ํ•ต์‹ฌ์ด๋‹ค. $lambda$โ€‘๋…๋ฆฝ์„ฑ ๋ฌธ์ œ : Serreโ€‘Waldschmidt ์ด๋ก ์€ ์•„๋ฒจ๋ฆฌ์•ˆ ๊ฒฝ์šฐ์— $G lambda$๊ฐ€ $lambda$โ€‘๋…๋ฆฝ์ž„์„ ๋ณด์˜€์ง€๋งŒ, ์ผ๋ฐ˜์ ์ธ ๋น„์•„๋ฒจ๋ฆฌ์•ˆ ๊ฒฝ์šฐ๋Š” ์•„์ง ๋ฏธํ•ด

System Mathematics
No Image

On Harish-Chandra's integrability theorem in positive characteristic

| ํ•ญ๋ชฉ | ๋‚ด์šฉ ๋ฐ ํ‰๊ฐ€ | | | | | ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ | Harishโ€‘Chandra ์ ๋ถ„์ •๋ฆฌ๋Š” ํŠน์„ฑ 0์—์„œ ๋Œ€ํ‘œ์ ์ธ ๊ฒฐ๊ณผ์ด๋ฉฐ, ์–‘์˜ ํŠน์„ฑ์—์„œ๋Š” ์•„์ง ์™„์ „ํ•œ ์ฆ๋ช…์ด ๋ถ€์žฌํ–ˆ๋‹ค. ๊ธฐ์กด ์—ฐ๊ตฌ(

Mathematics
No Image

On Sharpened Convergence Rate of Generalized Sliced Inverse Regression for Nonlinear Sufficient Dimension Reduction

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ SDR(์ถฉ๋ถ„ ์ฐจ์› ์ถ•์†Œ) ์€ ๊ณ ์ฐจ์› ์˜ˆ์ธก ๋ณ€์ˆ˜ X๋ฅผ ์ €์ฐจ์› ํ‘œํ˜„ Bแต€X(๋˜๋Š” ๋น„์„ ํ˜• ํ•จ์ˆ˜ ์ง‘ํ•ฉ {fโ‚,โ€ฆ,f d}) ๋กœ ์••์ถ•ํ•˜๋ฉด์„œ Y์™€์˜ ๋ชจ๋“  ์ •๋ณด๋ฅผ ๋ณด์กดํ•œ๋‹ค. ์„ ํ˜• SDR ์€ SIR, SAVE ๋“ฑ์œผ๋กœ ์ž˜ ์•Œ๋ ค์ ธ ์žˆ์œผ๋‚˜ ์ฐจ์› p๊ฐ€ ์ปค์งˆ์ˆ˜๋ก โ€œ์ฐจ์›์˜ ์ €์ฃผโ€์— ์ทจ์•ฝํ•˜๋‹ค. ๋น„์„ ํ˜• SDR ์€ RKHS ๊ธฐ๋ฐ˜ GSIR, fโ€‘GSIR ๋“ฑ์œผ๋กœ ํ™•์žฅ๋˜์—ˆ์œผ๋ฉฐ, ํŠนํžˆ GSIR ์€ ์ปค๋„ ๋ณ€ํ™˜์„ ํ†ตํ•ด ์ฐจ์› ์ €์ฃผ๋ฅผ ํšŒํ”ผํ•œ๋‹ค๋Š” ์žฅ์ ์ด ์žˆ๋‹ค(Li & Song, 2017). 2. ๊ธฐ์กด ์ˆ˜๋ ด ์†๋„์™€ ํ•œ๊ณ„ Li & Song(2017)์€ ฮฒ

Mathematics
No Image

Optimal bounds for numerical approximations of finite horizon problems based on dynamic programming approach

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ๋™์ ๊ณ„ํš๋ฒ•๊ณผ HJB ๋ฐฉ์ •์‹ : DP ์›๋ฆฌ์— ์˜ํ•ด ๊ฐ€์น˜ํ•จ์ˆ˜๋Š” ๋น„์„ ํ˜• Hamiltonโ€‘Jacobiโ€‘Bellman(HJB) ๋ฐฉ์ •์‹์˜ ์œ ์ผํ•œ ์ ์„ฑํ•ด(viscosity solution)๋กœ ์ •์˜๋œ๋‹ค. ์ด ๊ฐ€์น˜ํ•จ์ˆ˜๋ฅผ ํ†ตํ•ด ํ”ผ๋“œ๋ฐฑ ์ œ์–ด๋ฒ•์„ ๊ตฌ์„ฑํ•  ์ˆ˜ ์žˆ๋‹ค. ์ˆ˜์น˜์  ์–ด๋ ค์›€ : HJB ๋ฐฉ์ •์‹์€ ๊ณ ์ฐจ์›์—์„œ โ€œ์ฐจ์›์˜ ์ €์ฃผโ€(curse of dimensionality)๋ฅผ ๊ฒช์œผ๋ฉฐ, ์ •ํ™•ํ•œ ์˜ค๋ฅ˜ ๋ถ„์„์ด ๋“œ๋ฌผ๋‹ค. ํŠนํžˆ ์œ ํ•œ์‹œ๊ฐ„ ๋ฌธ์ œ์— ๋Œ€ํ•œ ์ฒด๊ณ„์ ์ธ ์˜ค๋ฅ˜ ์ƒํ•œ์€ ์•„์ง ์ถฉ๋ถ„ํžˆ ์—ฐ๊ตฌ๋˜์ง€ ์•Š์•˜๋‹ค. 2. ์ฃผ์š” ๊ธฐ์—ฌ | ๋ฒˆํ˜ธ | ๋‚ด์šฉ | ๊ธฐ์กด ์—ฐ

Mathematics
No Image

Optimal training-conditional regret for online conformal prediction

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ์ปจํฌ๋ฉ€ ์˜ˆ์ธก ์€ ๊ตํ™˜ ๊ฐ€๋Šฅ(exchangeable) ๋ฐ์ดํ„ฐ ๊ฐ€์ • ํ•˜์— ์œ ํ•œํ‘œ๋ณธ ์ปค๋ฒ„๋ฆฌ์ง€๋ฅผ ๋ณด์žฅํ•œ๋‹ค๋Š” ์žฅ์ ์ด ์žˆ๋‹ค. ํ•˜์ง€๋งŒ ์‹ค์ œ ์ŠคํŠธ๋ฆผ ๋ฐ์ดํ„ฐ๋Š” ์‹œ๊ฐ„์— ๋”ฐ๋ผ ๋ถ„ํฌ๊ฐ€ ๋ณ€๋™(๋“œ๋ฆฌํ”„ํŠธ)ํ•˜๋Š” ๊ฒฝ์šฐ๊ฐ€ ๋งŽ์•„ ๊ตํ™˜ ๊ฐ€๋Šฅ ๊ฐ€์ •์ด ๊นจ์ง„๋‹ค. ๊ธฐ์กด ์˜จ๋ผ์ธ ์ปจํฌ๋ฉ€ ์—ฐ๊ตฌ๋Š” ์‹œ๊ฐ„ ํ‰๊ท  ์ปค๋ฒ„๋ฆฌ์ง€ ํ˜น์€ ์ ๋Œ€์  ๋ ˆ๊ทธ๋ ˆ๋“œ ์— ์ดˆ์ ์„ ๋งž์ถ”์—ˆ์œผ๋ฉฐ, ์ด๋Š” ๊ฐœ๋ณ„ ์‹œ์ ์˜ ์ปค๋ฒ„๋ฆฌ์ง€ ์ •ํ™•์„ฑ์„ ๋ณด์žฅํ•˜์ง€ ๋ชปํ•œ๋‹ค๋Š” ํ•œ๊ณ„๊ฐ€ ์žˆ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์€ ๋…๋ฆฝ ๋ฐ์ดํ„ฐ ๋ผ๋Š” ๋ณด๋‹ค ๊ฐ•ํ•œ ๊ฐ€์ •์„ ๋„์ž…ํ•ด ํ›ˆ๋ จโ€‘์กฐ๊ฑด๋ถ€ ๋ˆ„์  ๋ ˆ๊ทธ๋ ˆ๋“œ ๋ผ๋Š” ํ†ต๊ณ„์  ํƒ€๋‹น์„ฑ์— ์ง์ ‘ ์—ฐ๊ฒฐ๋˜๋Š” ์ง€ํ‘œ๋ฅผ ์ œ์‹œํ•จ์œผ

Mathematics
No Image

Orbital integral bounds the character for cuspidal representations of $GL_n(mathbb{F}_{ell}((t)))$

| ํ•ญ๋ชฉ | ๋‚ด์šฉ ๋ฐ ํ‰๊ฐ€ | | | | | ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ | Harishโ€‘Chandra(1970)์˜ ์ ๋ถ„์ •๋ฆฌ๋Š” $p$โ€‘adic ๊ตฐ์—์„œ ๋ฌธ์ž ๊ฐ€ ๊ตญ์†Œ์  ๊ฐ€์‚ฐํ•จ์ˆ˜ ์ž„์„ ๋ณด์ด๋Š” ํ•ต์‹ฌ ๋„๊ตฌ๋‹ค. 0ํŠน์„ฑ์—์„œ์˜ ์ฆ๋ช…์€ โ€œcuspidal ํ•จ์ˆ˜์˜ ํ‰๊ท ์ด ๊ถค๋„ ์ ๋ถ„์— ์˜ํ•ด ๋กœ๊ทธ ์ธ์ž๋งŒํผ ์ œํ•œ๋œ๋‹คโ€๋Š” ์‚ฌ์‹ค์— ํฌ๊ฒŒ ์˜์กดํ•œ๋‹ค. ์–‘๊ทน์„ฑ(positive characteristic) ๊ฒฝ์šฐ๋Š” ๋™์ผํ•œ ๋…ผ๋ฆฌ๋ฅผ ๊ทธ๋Œ€๋กœ ์˜ฎ๊ธฐ๊ธฐ ์–ด๋ ค์›Œ, ํŠนํžˆ ๋ฌดํ•œํžˆ ๋งŽ์€ ํ† ๋Ÿฌ์Šค(๊ทน๋Œ€ ํ† ๋Ÿฌ์Šค) ๊ตฐ์†Œ ๊ฐ€ ์กด์žฌํ•œ๋‹ค๋Š” ์ ์ด ํฐ ์žฅ์• ๋ฌผ์ด๋‹ค. | | ์ฃผ์š” ๊ณตํ—Œ | 1. ์ •๋ฆฌ A : $GL n(F)$

Mathematics
No Image

Oscillation Criteria in Large-Scale Gene Regulatory Networks with Intrinsic Fluctuations

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ์ƒ๋ฌผํ•™์  ์ค‘์š”์„ฑ : p53โ€‘Mdm2, Hesโ€‘1 ๋“ฑ ํ•ต์‹ฌ ํ”ผ๋“œ๋ฐฑ ํšŒ๋กœ๋Š” ์„ธํฌ ์ฃผ๊ธฐ, ์ŠคํŠธ๋ ˆ์Šค ๋ฐ˜์‘, ๋ถ„ํ™” ๋“ฑ์— ๊ด€์—ฌํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ํšŒ๋กœ๊ฐ€ ์ฃผ๊ธฐ์ (oscillatory) ๋™์ž‘ ์„ ํ•ด์•ผ ์ •์ƒ ๊ธฐ๋Šฅ์„ ์ˆ˜ํ–‰ํ•œ๋‹ค. ๋‚ด์žฌ์  ๋ณ€๋™์˜ ๋ฌธ์ œ : ๋ถ„์ž ์ˆ˜๊ฐ€ ์ˆ˜์‹ญ~์ˆ˜๋ฐฑ ์ˆ˜์ค€์ธ ๊ฒฝ์šฐ, ํ™”ํ•™ ๋ฐ˜์‘์˜ ํ™•๋ฅ ์  ํŠน์„ฑ์œผ๋กœ ์ธํ•ด ํฐ ๋…ธ์ด์ฆˆ ๊ฐ€ ๋ฐœ์ƒํ•œ๋‹ค. ๊ธฐ์กด์˜ ๊ฒฐ์ •๋ก ์  ๋ชจ๋ธ์€ ์ด๋Ÿฌํ•œ ๋ณ€๋™์„ ๋ฌด์‹œํ•˜๊ณ  ์žˆ์–ด ์‹ค์ œ ์„ธํฌ ๋‚ด ๋™์—ญํ•™์„ ๊ณผ๋Œ€ํ‰๊ฐ€ํ•  ์œ„ํ—˜์ด ์žˆ๋‹ค. ๋Œ€๊ทœ๋ชจ ๋„คํŠธ์›Œํฌ ๋ถ„์„์˜ ๋‚œ์ œ : ๋…ธ๋“œ ์ˆ˜๊ฐ€ ๋Š˜์–ด๋‚˜๋ฉด ์ฐจ์›(2n)๋„ ๊ธ‰์ฆํ•˜๊ณ , ์ „ํ†ต์ ์ธ ๋ถ„๊ธฐ

Network Quantitative Biology
No Image

Parameter-free representations outperform single-cell foundation models on downstream benchmarks

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ์งˆ๋ฌธ scRNAโ€‘seq ๋ฐ์ดํ„ฐ์˜ ํŠน์„ฑ : ๊ณ ์ฐจ์›, ํฌ์†Œ์„ฑ, ๋ฐฐ์น˜ ํšจ๊ณผ, ๋“œ๋กญ์•„์›ƒ ๋“ฑ ๊ธฐ์ˆ ์  ๋ณ€์ด๊ฐ€ ํฐ ๋ฐ˜๋ฉด, ์„ธํฌ ์œ ํ˜•์— ๋”ฐ๋ฅธ ์œ ์ „์ž ๋ฐœํ˜„ ํŒจํ„ด์€ ๊ฐ•ํ•œ ํ†ต๊ณ„์  ๊ตฌ์กฐ๋ฅผ ๋ณด์ธ๋‹ค. ํŒŒ์šด๋ฐ์ด์…˜ ๋ชจ๋ธ์˜ ๋“ฑ์žฅ : TranscriptFormer์™€ ๊ฐ™์€ ๋Œ€๊ทœ๋ชจ ์ž๊ธฐ์ง€๋„ ํ•™์Šต ๋ชจ๋ธ์€ ํŠธ๋žœ์Šคํฌ๋จธ๋ฅผ ์ด์šฉํ•ด ์œ ์ „์ž ์ž„๋ฒ ๋”ฉ์„ ํ•™์Šตํ•˜๊ณ , ์ด๋ฅผ ๋‹ค์–‘ํ•œ ๋‹ค์šด์ŠคํŠธ๋ฆผ ์ž‘์—…์— ํ™œ์šฉํ•œ๋‹ค. ํ•ต์‹ฌ ์งˆ๋ฌธ : โ€œ๋ณต์žกํ•œ ๋”ฅ๋Ÿฌ๋‹ ๋ชจ๋ธ ์—†์ด๋„ ๋™์ผํ•œ ์ˆ˜์ค€์˜ ์ƒ๋ฌผํ•™์  ์ •๋ณด๋ฅผ ์ถ”์ถœํ•  ์ˆ˜ ์žˆ๋Š”๊ฐ€?โ€ ์ฆ‰, ํ‘œํ˜„ ๋ณต์žก๋„์™€ ์‹ค์ œ ๋ฐ์ดํ„ฐ์— ๋‚ด์žฌ๋œ ๊ตฌ์กฐ ์‚ฌ์ด์˜ ๊ด€๊ณ„ ๋ฅผ ๊ฒ€์ฆ

Quantitative Biology Model
No Image

Partially observed controlled Markov chains and optimal control of the Wonham filter

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ํ•„์š”์„ฑ ๋ถ€๋ถ„ ๊ด€์ธก ์ตœ์  ์ œ์–ด๋Š” ์ˆจ๊ฒจ์ง„ ๋งˆ์ฝ”ํ”„ ๋ชจ๋ธ(HMM) ๋กœ ๋ถˆ๋ฆฌ๋ฉฐ, ์ œ์–ด์™€ ์ถ”์ •์ด ๋™์‹œ์— ์š”๊ตฌ๋˜๋Š” ๋ณตํ•ฉ์ ์ธ ๋ฌธ์ œ์ด๋‹ค. ๊ธฐ์กด ๋ฌธํ—Œ(

Mathematics
No Image

Physical principles of building protein megacomplexes in a crowded milieu

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋ฌธ์ œ ์ •์˜ ๋‹ค์–‘ํ•œ ํ‘œํ˜„ํ˜• โ†’ ๋‹จ๋ฐฑ์งˆ ํ’๋ถ€๋„ยท์Šคํ…Œ์˜คํ‚ค์˜ค๋ฉ”ํŠธ๋ฆฌ : ์œ ์ „์ฒด๋Š” ๋™์ผํ•˜์ง€๋งŒ, ์„ธํฌ๋Š” ํ™˜๊ฒฝยท์‹œ๊ทธ๋„์— ๋”ฐ๋ผ ๋‹จ๋ฐฑ์งˆ ์–‘๊ณผ ๊ฒฐํ•ฉ ๋น„์œจ์„ ์กฐ์ ˆํ•œ๋‹ค. ๊ธฐ์กด์˜ ๊ณ ์ •โ€‘๋†๋„(์ •์ ) ๋ชจ๋ธ ์€ ์ด๋Ÿฌํ•œ ๋™์  ๋ณ€ํ™”๋ฅผ ํฌ์ฐฉํ•˜์ง€ ๋ชปํ•œ๋‹ค. AI ๊ธฐ๋ฐ˜ ๊ตฌ์กฐ์˜ˆ์ธก์˜ ํ•œ๊ณ„ : AlphaFold ๋“ฑ์œผ๋กœ ๊ฐœ๋ณ„ ๋‹จ๋ฐฑ์งˆ ๊ตฌ์กฐ๋Š” ์˜ˆ์ธก ๊ฐ€๋Šฅํ•˜์ง€๋งŒ, ๋‹ค์ค‘ ๋‹จ๋ฐฑ์งˆ ๋ณตํ•ฉ์ฒด ๊ฐ€ ์–ด๋–ป๊ฒŒ ์กฐ๋ฆฝ๋˜๋Š”์ง€๋Š” ์•„์ง ๋ถˆ๋ช…ํ™•ํ•˜๋‹ค. 2. ๋ฐฉ๋ฒ•๋ก  โ€“ ๊ฑฐ์‹œ์ •์ค€๊ณ„์™€ ๊ตฐ์ค‘ ํšจ๊ณผ ๊ฑฐ์‹œ์ •์ค€๊ณ„ : ์‹œ์Šคํ…œ์ด ์ฃผ๋ณ€ โ€œ์ž…์ž ์ €์žฅ์†Œโ€์™€ ๋ฌผ์งˆยท์—๋„ˆ์ง€ ๊ตํ™˜์„ ํ—ˆ์šฉํ•œ๋‹ค๋Š” ๊ฐ€์ • ํ•˜์—, ๊ฐ ์„œ๋ธŒ์œ ๋‹›์˜ ํ™”

Quantitative Biology
PIANO: Physics-informed Dual Neural Operator for Precipitation Nowcasting

PIANO: Physics-informed Dual Neural Operator for Precipitation Nowcasting

๊ฐ•์ˆ˜ ์˜ˆ๋ณด๋Š” ํ™์ˆ˜ยท์‚ฐ์‚ฌํƒœยท๋†์—… ํ”ผํ•ด ๋“ฑ ์žฌ๋‚œ ๋Œ€์‘์— ์žˆ์–ด ์‹œ๊ฐ„์ ยท๊ณต๊ฐ„์  ์ •ํ™•๋„๊ฐ€ ๋งค์šฐ ์ค‘์š”ํ•œ๋ฐ, ํ˜„์žฌ ๋„๋ฆฌ ์‚ฌ์šฉ๋˜๋Š” ๋ ˆ์ด๋” ๊ธฐ๋ฐ˜ ๋ฐฉ๋ฒ•์€ ๊ณ ๊ฐ€์˜ ์žฅ๋น„์™€ ๋ฐฉ๋Œ€ํ•œ ์—ฐ์‚ฐ ์ž์›์„ ํ•„์š”๋กœ ํ•œ๋‹ค. ํŠนํžˆ ๊ฐœ๋ฐœ๋„์ƒ๊ตญ์ด๋‚˜ ๊ธฐํ›„ ๊ด€์ธก ์ธํ”„๋ผ๊ฐ€ ๋ถ€์กฑํ•œ ์ง€์—ญ์—์„œ๋Š” ์ด๋Ÿฌํ•œ ์ œ์•ฝ์ด ์‹ฌ๊ฐํ•œ ์žฅ๋ฒฝ์ด ๋œ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์€ ์ด๋Ÿฌํ•œ ํ•œ๊ณ„๋ฅผ ๊ทน๋ณตํ•˜๊ธฐ ์œ„ํ•ด ์œ„์„ฑ ์˜์ƒ์„ ์ฃผ์š” ์ž…๋ ฅ ๋ฐ์ดํ„ฐ๋กœ ํ™œ์šฉํ•˜๋ฉด์„œ, ๋ฌผ๋ฆฌ ๋ฒ•์น™์„ ์ง์ ‘ ๋ชจ๋ธ์— ํ†ตํ•ฉํ•˜๋Š” ํ˜์‹ ์ ์ธ ์ ‘๊ทผ์„ ์ œ์‹œํ•œ๋‹ค. ํ•ต์‹ฌ์€ advectionโ€‘diffusion ๋ฐฉ์ •์‹์„ ์†์‹ค ํ•จ์ˆ˜์— ํฌํ•จ์‹œํ‚จ ๋ฌผ๋ฆฌโ€‘์ •๋ณด ์‹ ๊ฒฝ ์—ฐ์‚ฐ์ž(PIANO)์ด๋‹ค.

No Image

Pitts and Intuitionistic Multi-Succedent: Uniform Interpolation for KM

| ํ•ญ๋ชฉ | ๋‚ด์šฉ ๋ฐ ํ‰๊ฐ€ | | | | | ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ | ๊ท ์ผ ๋ณด๊ฐ„์€ โ€œ๋ชจ๋“  ๋ณ€์ˆ˜ p์— ๋Œ€ํ•ด pโ€‘์—†๋Š” ๊ฐ€์žฅ ๊ฐ•ํ•œ(๋˜๋Š” ๊ฐ€์žฅ ์•ฝํ•œ) ๊ณต์‹โ€์„ ์กด์žฌ์‹œํ‚ด์œผ๋กœ์จ ๋…ผ๋ฆฌ ์ฒด๊ณ„์˜ ๋ฉ”ํƒ€โ€‘ํŠน์„ฑ์„ ๊ฐ•ํ•˜๊ฒŒ ๋งŒ๋“ ๋‹ค. ๊ธฐ์กด์—๋Š” ๋ชจ๋ธโ€‘์ด๋ก , ๋ณดํŽธโ€‘๋Œ€์ˆ˜ํ•™์ , ์ฆ๋ช…โ€‘์ด๋ก ์  ๋ฐฉ๋ฒ•์ด ๊ฐ๊ฐ ์ œํ•œ์ ์œผ๋กœ ์ ์šฉ๋ผ ์™”์œผ๋ฉฐ, Pitts(1992) ์˜ ์ฆ๋ช…โ€‘์ด๋ก ์  ์ ‘๊ทผ์€ ์ข…๋ฃŒ(sequent) ๊ณ„์‚ฐ๋ฒ• ์ด ์กด์žฌํ•  ๋•Œ๋งŒ ํ™œ์šฉ ๊ฐ€๋Šฅํ–ˆ๋‹ค. ์ง๊ด€์ฃผ์˜ ๋ชจ๋‹ฌ ๋…ผ๋ฆฌ๋“ค(iSL ๋“ฑ)์—์„œ๋Š” ๋‹จ์ผํ›„์† ๊ณ„์‚ฐ๋ฒ•์ด ์ถฉ๋ถ„ํ–ˆ์ง€๋งŒ, ๋‹ค์ค‘ํ›„์†์ด ํ•„์ˆ˜์ ์ธ ๋…ผ๋ฆฌ(์˜ˆ: LC, KM)์—๋Š” ์ ์šฉ๋˜์ง€ ๋ชปํ–ˆ๋‹ค. | | ์ฃผ

Computer Science Logic
No Image

PL conditions do not guarantee convergence of gradient descent-ascent dynamics

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ PL ์กฐ๊ฑด ์€ ๋น„๋ณผ๋ก ์ตœ์ ํ™”์—์„œ ์„ ํ˜• ์ˆ˜๋ ด ์„ ๋ณด์žฅํ•˜๋Š” ๊ฐ•๋ ฅํ•œ ๋„๊ตฌ๋กœ ๋„๋ฆฌ ํ™œ์šฉ๋œ๋‹ค. ๋ฏธ๋‹ˆ๋งฅ์Šค(minโ€‘max) ๋ฌธ์ œ ์—์„œ๋Š” ๋ณ€์ˆ˜ (x)์™€ (y)๊ฐ€ ๊ฐ๊ฐ ๋ณผ๋กยท์˜ค๋ชฉ ๊ตฌ์กฐ๋ฅผ ๊ฐ€์งˆ ๋•Œ GDA ํ๋ฆ„์ด ์ •์ƒ์ ์— ์ˆ˜๋ ดํ•œ๋‹ค๋Š” ์ „ํ†ต์ ์ธ ๊ฒฐ๊ณผ๊ฐ€ ์žˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๊ฐ•ํ•œ ๋ณผ๋กโ€‘์˜ค๋ชฉ์„ฑ(strong convexโ€‘concavity) ๊ฐ€ ์—†์„ ๊ฒฝ์šฐ, GDA ํ๋ฆ„์€ ์ˆ˜๋ ดํ•˜์ง€ ์•Š์„ ์ˆ˜ ์žˆ๋‹ค(์˜ˆ: (f(x,y) xy)). ์ตœ๊ทผ ์—ฐ๊ตฌ๋“ค์€ ๊ฐ•ํ•œ ์กฐ๊ฑด์„ ์™„ํ™” ํ•˜๊ธฐ ์œ„ํ•ด ์–‘๋ณ€ํ–ฅ PL ์กฐ๊ฑด ์„ ๋„์ž…ํ•˜๊ณ , ๋‘โ€‘์‹œ๊ฐ„ ์Šค์ผ€์ผ ํ˜น์€ ์ˆ˜์ •๋œ GDA

Mathematics
Placenta Accreta Spectrum Detection Using an MRI-based Hybrid CNN-Transformer Model

Placenta Accreta Spectrum Detection Using an MRI-based Hybrid CNN-Transformer Model

๋ณธ ๋…ผ๋ฌธ์€ ํƒœ๋ฐ˜ ๋ถ€์ฐฉ์ฆ(PAS)์ด๋ผ๋Š” ์ž„์‚ฐ๋ถ€์—๊ฒŒ ์น˜๋ช…์ ์ธ ํ•ฉ๋ณ‘์ฆ์„ ์กฐ๊ธฐ์— ์ •ํ™•ํžˆ ์ง„๋‹จํ•˜๊ธฐ ์œ„ํ•œ ์ž๋™ํ™”๋œ ์˜์ƒ ๋ถ„์„ ์‹œ์Šคํ…œ์„ ์ œ์‹œํ•œ๋‹ค. PAS๋Š” ์ดˆ์ŒํŒŒ์™€ MRI๋ฅผ ํ†ตํ•ด ์ง„๋‹จ๋˜์ง€๋งŒ, ํŠนํžˆ MRI๋Š” ๊ณ ํ•ด์ƒ๋„ 3์ฐจ์› ์ •๋ณด๋ฅผ ์ œ๊ณตํ•จ์—๋„ ๋ถˆ๊ตฌํ•˜๊ณ  ํŒ๋…์ž์˜ ์ฃผ๊ด€์  ํŒ๋‹จ์— ํฌ๊ฒŒ ์ขŒ์šฐ๋˜๋Š” ๋ฌธ์ œ์ ์ด ์žˆ๋‹ค. ์ด๋Ÿฌํ•œ ์ง„๋‹จ ๋ณ€๋™์„ฑ์„ ์ตœ์†Œํ™”ํ•˜๊ณ  ๊ฐ๊ด€์ ์ธ ์˜์‚ฌ๊ฒฐ์ •์„ ์ง€์›ํ•˜๊ธฐ ์œ„ํ•ด ์—ฐ๊ตฌํŒ€์€ 3D CNN๊ณผ 3D Vision Transformer(ViT)๋ฅผ ๊ฒฐํ•ฉํ•œ ํ•˜์ด๋ธŒ๋ฆฌ๋“œ ๋ชจ๋ธ์„ ์„ค๊ณ„ํ•˜์˜€๋‹ค. DenseNet121์€ ์ธต ๊ฐ„ ํ”ผ์ฒ˜ ์žฌ์‚ฌ์šฉ์„ ์ด‰์ง„ํ•˜๋Š” dense con

Detection Model
No Image

Positive Charts of Toric Varieties

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ๋น„์Œ์ˆ˜ ๋ถ€๋ถ„ ((X {Sigma}) {ge 0}) ์€ ํ† ๋ฆญ ๋‹ค์–‘์ฒด์˜ ์‹ค์ˆ˜ ๊ตฌ์กฐ๋ฅผ ์ฝ”๋„ˆ๊ฐ€ ์žˆ๋Š” ๋‹ค๋ฉด์ฒด(manifold with corners)๋กœ ๋‚˜ํƒ€๋‚ธ๋‹ค. ๊ธฐ์กด์—๋Š” (mathbb{P}^d)์˜ ๊ฒฝ์šฐ์—๋งŒ ์ „ํ†ต์ ์ธ ์ฐจํŠธ๊ฐ€ ๋น„์Œ์ˆ˜ ๋ถ€๋ถ„์„ ํฌ๊ด„ํ•˜์ง€ ๋ชปํ•œ๋‹ค๋Š” ํ•œ๊ณ„๊ฐ€ ์žˆ์—ˆ๋‹ค. ์–‘์˜ ํŒŒ๋ผ๋ฏธํ„ฐํ™” (positive rational parametrization)๋Š” ๋ชจ๋“  ๊ณ„์ˆ˜๊ฐ€ ๋น„์Œ์ˆ˜์ธ ๋‹คํ•ญ์‹ยท๋ถ„์ˆ˜์‹์œผ๋กœ ์ •์˜๋œ ๋งคํ•‘์œผ๋กœ, ๋ฌผ๋ฆฌํ•™ยท์–‘์˜ ๊ธฐํ•˜ํ•™์—์„œ ์ค‘์š”ํ•œ ์—ญํ• ์„ ํ•œ๋‹ค. ํŠนํžˆ, (u) ๋ฐฉ์ •์‹์€ ์Šค์บํ„ฐ๋ง ์ง„ํญ์˜ ๊ธฐํ•˜ํ•™์ 

Mathematics
No Image

Primal-dual dynamical systems with closed-loop control for convex optimization in continuous and discrete time

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ๋ณผ๋ก ์ตœ์ ํ™”์™€ ์„ ํ˜• ํ‰๋“ฑ ์ œ์•ฝ ์€ ์ด๋ฏธ์ง€ ๋ณต๊ตฌ, ๋จธ์‹ ๋Ÿฌ๋‹, ๋„คํŠธ์›Œํฌ ์ตœ์ ํ™” ๋“ฑ ๋‹ค์–‘ํ•œ ๋ถ„์•ผ์—์„œ ํ•ต์‹ฌ ๋ฌธ์ œ์ด๋ฉฐ, ๋ผ๊ทธ๋ž‘์ง€์•ˆ ์ด์ค‘ ๋ณ€์ˆ˜(ํ”„๋ผ์ž„ + ๋“€์–ผ) ์ ‘๊ทผ์ด ์ผ๋ฐ˜์ ์ด๋‹ค. ๊ธฐ์กด ์—ฐ๊ตฌ๋Š” ํฌ๊ฒŒ ๋‘ ๊ฐˆ๋ž˜๋กœ ๋‚˜๋‰œ๋‹ค. 1. Hessianโ€‘๊ตฌ๋™ ๊ฐ์‡  ๋ฅผ ์ด์šฉํ•œ 2์ฐจ ๋™์  ์‹œ์Šคํ…œ(์˜ˆ: Suโ€‘etโ€‘al., Attouchโ€‘etโ€‘al.) โ€“ ์ง„๋™ ์–ต์ œ์™€ ๊ฐ€์†ํ™”์— ํšจ๊ณผ์ ์ด์ง€๋งŒ ๋Œ€๋ถ€๋ถ„ ๋ฌด์ œ์•ฝ ๋ฌธ์ œ์— ๊ตญํ•œ. 2. ํ๋ฃจํ”„(Closedโ€‘loop) ์ œ์–ด ๋ฅผ ํ†ตํ•œ ๋น„์ž์œจ ์‹œ์Šคํ…œ โ€“ ๊ณ„์ˆ˜๋“ค์ด ํ˜„์žฌ ์ƒํƒœ์— ๋”ฐ๋ผ ์ž๋™ ์กฐ์ •๋˜์–ด ๊ตฌํ˜„์ด ๊ฐ„ํŽธํ•˜์ง€๋งŒ

System Mathematics
No Image

Projective corepresentations and cohomology of compact quantum groups

| ๊ตฌ๋ถ„ | ์ฃผ์š” ๋‚ด์šฉ | ์˜์˜ ๋ฐ ํ‰๊ฐ€ | | | | | | 1. ์‚ฌ์˜ ํ•ต์‹ฌํ‘œํ˜„์˜ ์ •์˜์™€ ๋ถ„๋ฅ˜ | ์ขŒโ€‘์‚ฌ์˜, ์šฐโ€‘์‚ฌ์˜, ์–‘โ€‘์‚ฌ์˜, ๊ฐ•โ€‘์‚ฌ์˜ ๋„ค ์ข…๋ฅ˜๋ฅผ ๋„์ž….<br> ๊ฐ๊ฐ์„ โ€œprojective corepresentationโ€์ด๋ผ ๋ถ€๋ฅด๋ฉฐ, 2โ€‘์ฝ”์‚ฌ์ดํด (Omega)์™€ ์—ฐ๊ฒฐ. | ๊ธฐ์กด ์–‘์ž๊ตฐ ์ด๋ก ์—์„œ๋Š” ์ฃผ๋กœ ์„ ํ˜•(corepresentation)๋งŒ ๋‹ค๋ฃจ์—ˆ์œผ๋‚˜, ์‚ฌ์˜ ํ˜•ํƒœ๋ฅผ ์ฒด๊ณ„ํ™”ํ•จ์œผ๋กœ์จ ๋ฌผ๋ฆฌ์  โ€œrayโ€ ๋Œ€์นญ์„ ์ˆ˜ํ•™์ ์œผ๋กœ ํฌ์ฐฉํ•œ๋‹ค. ํŠนํžˆ ๊ฐ•โ€‘์‚ฌ์˜์€ ๊ณ ์ „ ๊ตฐ์˜ ์‚ฌ์˜ ํ‘œํ˜„๊ณผ ๊ฐ€์žฅ ๊ทผ์ ‘ํ•ด ์ฝ”ํ˜ธ๋ชฐ๋กœ์ง€์™€ ์ง์ ‘ ์—ฐ๊ฒฐ๋˜๋Š” ์ ์ด ํ˜์‹ ์ ์ด๋‹ค. |

Mathematics
No Image

Protect$^*$: Steerable Retrosynthesis through Neuro-Symbolic State Encoding

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ํ•„์š”์„ฑ LLM ๊ธฐ๋ฐ˜ ๋ ˆํŠธ๋กœํ•ฉ์„ฑ : DeepRetro ๋“ฑ ๊ธฐ์กด ์‹œ์Šคํ…œ์€ LLM์˜ ์ฐฝ์˜์  ์ œ์•ˆ๊ณผ MCTS ํƒ์ƒ‰์„ ๊ฒฐํ•ฉํ–ˆ์ง€๋งŒ, ํ™”ํ•™ ์„ ํƒ์„ฑ(chemoselectivity, regioselectivity) ์„ ๋ช…์‹œ์ ์œผ๋กœ ๋‹ค๋ฃจ์ง€ ๋ชปํ•œ๋‹ค. ๋ณดํ˜ธ ๊ทธ๋ฃน ์„ ํƒ์˜ ๋ถ€์žฌ : SMILES ๋ฌธ์ž์—ด๋งŒ์œผ๋กœ ํŠน์ • ์›์ž๋ฅผ โ€œ๋ณดํ˜ธโ€ํ•˜๋„๋ก ์ง€์‹œํ•˜๋Š” ๊ฒƒ์ด ์–ด๋ ค์›Œ, ๋ชจ๋ธ์ด ๋ฏผ๊ฐํ•œ ๊ธฐ๋Šฅ๊ธฐ๋ฅผ ๋ฌด์‹œํ•˜์ง€ ๋ชปํ•˜๊ณ  ๋น„ํ˜„์‹ค์ ์ธ ๊ฒฝ๋กœ๋ฅผ ์ƒ์„ฑํ•œ๋‹ค. 2. ํ•ต์‹ฌ ์•„์ด๋””์–ด โ€“ ์‹ ๊ฒฝโ€‘๊ธฐํ˜ธํ•™์  ํ•˜์ด๋ธŒ๋ฆฌ๋“œ ์•„ํ‚คํ…์ฒ˜ | ๊ตฌ์„ฑ ์š”์†Œ | ์—ญํ•  | ํŠน์ง• | | | | | | SMAR

Quantitative Biology
No Image

Quantum Cellular Automata: The Group, the Space, and the Spectrum

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ์–‘์ž ์…€๋ฃฐ๋Ÿฌ ์ž๋™ํ™”(QCA) ๋Š” ์–‘์ž ์Šคํ•€ ์‹œ์Šคํ…œ์˜ ๊ตญ์†Œ์„ฑ์„ ๋ณด์กดํ•˜๋Š” ์ž๋™๋™ํ˜•์œผ๋กœ, ๋ฌผ๋ฆฌํ•™(์–‘์ž ์ •๋ณด, ์–‘์ž ๋ฌผ์งˆ)์™€ ์ˆ˜ํ•™(๋Œ€์ˆ˜, ์œ„์ƒ) ์‚ฌ์ด์˜ ๋‹ค๋ฆฌ ์—ญํ• ์„ ํ•ด์™”๋‹ค. ๊ธฐ์กด ์—ฐ๊ตฌ๋Š” ์ฃผ๋กœ ๋ณต์†Œ์ˆ˜ ์ฒด (mathbb{C})์™€ (C^{ }) ๋Œ€์ˆ˜ ๊ตฌ์กฐ์— ๊ตญํ•œ๋˜์—ˆ์œผ๋ฉฐ, 1์ฐจ์› ๋ถ„๋ฅ˜๋Š” ์™„์ „ํžˆ ํ•ด๊ฒฐ๋์ง€๋งŒ ๊ณ ์ฐจ์›์—์„œ๋Š” ์•„์ง ์ฒด๊ณ„์ ์ธ ๋ถ„๋ฅ˜ ์ฒด๊ณ„๊ฐ€ ๋ถ€์กฑํ–ˆ๋‹ค. ์ตœ๊ทผ ๋ฌผ๋ฆฌํ•™ ๋ฌธํ—Œ์—์„œ โ€œQCA ์ŠคํŽ™ํŠธ๋Ÿผ ๊ฐ€์„คโ€ (์ฐจ์›์— ๋”ฐ๋ผ (Omega) ์ŠคํŽ™ํŠธ๋Ÿผ์ด ํ˜•์„ฑ๋œ๋‹ค๋Š” ๊ฐ€์„ค)์ด ์ œ์‹œ๋˜์—ˆ์ง€๋งŒ, ์ด๋ฅผ ์ˆ˜ํ•™์ ์œผ๋กœ ์—„๋ฐ€ํžˆ ์ฆ๋ช…ํ•œ ์ž‘์—…์€

Mathematics
No Image

Quasilocalization under coupled mutation-selection dynamics

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋ฌธ์ œ ์ œ๊ธฐ Eigenโ€‘๋ชจ๋ธ ์€ ๋Œ์—ฐ๋ณ€์ด๊ฐ€ ๋นˆ๋ฒˆํ•œ ๋ฌด์„ฑ ์ƒ๋ฌผ(ํŠนํžˆ ๋ฐ”์ด๋Ÿฌ์Šค)์—์„œ ์„ ํƒ๊ณผ ๋Œ์—ฐ๋ณ€์ด์˜ ์ƒํ˜ธ์ž‘์šฉ ์„ ์ •๋Ÿ‰ํ™”ํ•œ๋‹ค. ์ „ํ†ต์ ์ธ โ€œ์ตœ์  ์ ํ•ฉ๋„ ์œ ํ˜•์˜ ์ง€๋ฐฐโ€(survival of the fittest)์™€ โ€œ์˜ค๋ฅ˜ ์žฌ์•™โ€(error catastrophe) ์‚ฌ์ด์— ๊ทน๋‹จ์ ์ธ ๋‘ ์ƒํƒœ ๋งŒ์ด ์ž˜ ์•Œ๋ ค์ ธ ์žˆ๋‹ค. ์‹ค์ œ ๋ฐ”์ด๋Ÿฌ์Šค ์ง‘๋‹จ์€ ์ด ๋‘ ๊ทน๋‹จ ์‚ฌ์ด์˜ ์ค‘๊ฐ„ ์ƒํƒœ, ์ฆ‰ โ€˜์ค€๊ตญ์†Œํ™”โ€™ ์— ๋จธ๋ฌด๋ฅด๋Š” ๊ฒฝ์šฐ๊ฐ€ ๋Œ€๋ถ€๋ถ„์ด๋ฉฐ, ์ด๋ฅผ ์„ค๋ช…ํ•  ๋ณดํŽธ์ ์ธ ์ด๋ก  ์ด ๋ถ€์žฌํ–ˆ๋‹ค. 2. ํ•ต์‹ฌ ์•„์ด๋””์–ด: ์ •๋ณดโ€‘์ด๋ก ์  ์†๋„ ์ œํ•œ๊ณผ Hill ์ˆ˜ ์ตœ๊ทผ surp

Quantitative Biology
No Image

Reactive Coarse Grained Force Field for Metal-Organic Frameworks applied to Modeling ZIF-8 Self-Assembly

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ํ•„์š”์„ฑ MOF ํ•ฉ์„ฑ์˜ ๋ณต์žก์„ฑ : ๊ธˆ์† ์ด์˜จ๊ณผ ์œ ๊ธฐ ๋ฆฌ๊ฐ„๋“œ๊ฐ€ ๋ณตํ•ฉ์ ์œผ๋กœ ๊ฒฐํ•ฉยทํ•ด๋ฆฌ๋˜๋Š” ๊ณผ์ •์€ ์‹คํ—˜์ ์œผ๋กœ ์ตœ์ ํ™”ํ•˜๊ธฐ ์–ด๋ ค์šฐ๋ฉฐ, ์‹œ๋ฎฌ๋ ˆ์ด์…˜์„ ํ†ตํ•œ ๋ฉ”์ปค๋‹ˆ์ฆ˜ ๊ทœ๋ช…์ด ํ•„์ˆ˜์ ์ด๋‹ค. ์›์ž ์ˆ˜์ค€ ์‹œ๋ฎฌ๋ ˆ์ด์…˜์˜ ํ•œ๊ณ„ : ์ „ํ†ต์ ์ธ ์ „์ž๊ตฌ์กฐยท๋ถ„์ž์—ญํ•™(AAโ€‘MD)์€ ์ˆ˜์ฒœ ๊ฐœ ์›์ž ์ˆ˜์ค€์—์„œ๋งŒ ๋‹ค๋ฃฐ ์ˆ˜ ์žˆ์–ด, ์‹ค์ œ ํ•ฉ์„ฑ ์‹œ ์‚ฌ์šฉ๋˜๋Š” mMโ€‘๋†๋„ยท์ˆ˜์‹ญ ๋‚˜๋…ธ๋ฏธํ„ฐ ์Šค์ผ€์ผ์„ ์žฌํ˜„ํ•˜์ง€ ๋ชปํ•œ๋‹ค. 2. ๋ฐฉ๋ฒ•๋ก  โ€“ MSโ€‘CG ๊ธฐ๋ฐ˜ ๋ฐ˜์‘ํ˜• CGโ€‘FF ๊ตฌ์ถ• | ๋‹จ๊ณ„ | ํ•ต์‹ฌ ๋‚ด์šฉ | ์˜์˜ | | | | | | AA ๊ธฐ์ค€ ๋ฐ์ดํ„ฐ ์ƒ์„ฑ | nbโ€‘ZIFโ€‘FF (๋น„

Condensed Matter Framework Model
Rectifying LLM Thought from Lens of Optimization

Rectifying LLM Thought from Lens of Optimization

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ CoT ํ”„๋กฌํ”„ํŠธ ๋Š” ์ธ๊ฐ„์˜ ์‚ฌ๊ณ  ๊ณผ์ •์„ ๋ชจ๋ฐฉํ•ด ๋‹จ๊ณ„๋ณ„ ์ถ”๋ก ์„ ๊ฐ€๋Šฅํ•˜๊ฒŒ ํ–ˆ์ง€๋งŒ, โ€˜overthinkingโ€™ ํ˜„์ƒ์ด ๋นˆ๋ฒˆํžˆ ๋ฐœ์ƒํ•œ๋‹ค(์ˆ˜์ฒœ ํ† ํฐ๊นŒ์ง€ ํ™•์žฅ). ๊ธฐ์กด RLVR ๊ธฐ๋ฐ˜ ์ตœ์ ํ™”๋Š” ์ตœ์ข… ๋ณด์ƒ ์—๋งŒ ์ง‘์ค‘ํ•ด ์ค‘๊ฐ„ ์ถ”๋ก  ๊ณผ์ •์˜ ์งˆ์„ ์ง์ ‘์ ์œผ๋กœ ์ œ์–ดํ•˜์ง€ ๋ชปํ•œ๋‹ค๋Š” ํ•œ๊ณ„๊ฐ€ ์žˆ๋‹ค. 2. ํ•ต์‹ฌ ์•„์ด๋””์–ด CoT โ†” Gradient Descent ๋งคํ•‘: ๊ฐ ์ถ”๋ก  ๋‹จ๊ณ„๋ฅผ ํŒŒ๋ผ๋ฏธํ„ฐ ์—…๋ฐ์ดํŠธ๋กœ ํ•ด์„ํ•จ์œผ๋กœ์จ โ€œ์ถ”๋ก ์ด ์–ผ๋งˆ๋‚˜ ์ž˜ ์ตœ์ ํ™”๋˜๊ณ  ์žˆ๋Š”๊ฐ€โ€๋ฅผ ์ •๋Ÿ‰ํ™”ํ•œ๋‹ค. ๋Œ€๋ฆฌ ๋ชฉํ‘œ ํ•จ์ˆ˜ ๐’ฅ : ์ •๋‹ต ํ† ํฐ ์‹œํ€€์Šค์— ๋Œ€ํ•œ ๋กœ๊ทธ ํ™•๋ฅ (ํผํ”Œ๋ ‰์‹œํ‹ฐ ์—ญ

No Image

Regularity and Pathwise bounds for probabilistic solutions of PDEs

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ํ™•๋ฅ ์  ์ „์—ญ ์กด์žฌ์„ฑ ๋ฌธ์ œ์—์„œ๋Š” ๋ณดํ†ต ์•™์ƒ๋ธ” ๊ฒฝ๊ณ„ (์˜ˆ: ๊ธฐ๋Œ€๊ฐ’, ํ™•๋ฅ ์  ์ƒํ•œ)๋งŒ์„ ํ™•๋ณดํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ๊ฒฝ๊ณ„๋Š” ์ „์—ญ ์กด์žฌ์™€ ์œ ์ผ์„ฑ์„ ๋ณด์ด๋Š” ๋ฐ๋Š” ์ถฉ๋ถ„ํ•˜์ง€๋งŒ, ๊ฐœ๋ณ„ ์‹คํ˜„(trajectory) ์ˆ˜์ค€ ์—์„œ์˜ ์„ฑ์žฅ๋ฅ ์ด๋‚˜ ์žฅ๊ธฐ ๊ฑฐ๋™์„ ํŒŒ์•…ํ•˜๊ธฐ์—” ๋ถ€์กฑํ•˜๋‹ค. ํŠนํžˆ weak turbulence ๊ฐ€์„ค, Sobolevโ€‘norm ์„ฑ์žฅ ๋ถ„์„ ๋“ฑ์—์„œ๋Š” ๊ฒฝ๋กœ๋ณ„ ์ƒํ•œ ์ด ํ•„์ˆ˜์ ์ด๋‹ค. 2. ๊ธฐ์กด ์ ‘๊ทผ๋ฒ•๊ณผ ํ•œ๊ณ„ Bourgain(1996) ์€ ์ง€์—ญ์  ์ž˜์ •์˜์„ฑ ๋ฐ โ€œ์‹œ๊ฐ„โ€‘ํฌ๊ธฐ ๋‘ ๋ฐฐํ™”โ€ ์ถ”์ •์„ ์ด์šฉํ•ด Gaussian ์•™์ƒ๋ธ” ๊ฒฝ๊ณ„๋ฅผ ๋กœ๊ทธํ˜• ๊ฐœ๋ณ„

Mathematics
ReinforceGen: Hybrid Skill Policies with Automated Data Generation and Reinforcement Learning

ReinforceGen: Hybrid Skill Policies with Automated Data Generation and Reinforcement Learning

ReinforceGen์€ ๋กœ๋ด‡ ๊ณตํ•™์—์„œ ์žฅ๊ธฐ ์กฐ์ž‘์ด๋ผ๋Š” ๋‚œ์ œ๋ฅผ ํ•ด๊ฒฐํ•˜๊ธฐ ์œ„ํ•ด ์ œ์•ˆ๋œ ํ˜์‹ ์ ์ธ ์‹œ์Šคํ…œ์ž…๋‹ˆ๋‹ค. ์ด ์‹œ์Šคํ…œ์€ ์ž‘์—…์„ ์—ฌ๋Ÿฌ ์ž‘์€ ๋ถ€๋ถ„์œผ๋กœ ๋ถ„ํ•ดํ•˜๊ณ , ๊ฐ ๋ถ€๋ถ„์— ๋Œ€ํ•ด ๋ชจ๋ฐฉ ํ•™์Šต๊ณผ ๊ฐ•ํ™” ํ•™์Šต์„ ํ†ตํ•ด ์ตœ์ ์˜ ๊ฒฝ๋กœ์™€ ๋™์ž‘์„ ์ฐพ์•„๋‚ด๋Š” ๋ฐฉ์‹์œผ๋กœ ๊ตฌ์„ฑ๋˜์–ด ์žˆ์Šต๋‹ˆ๋‹ค. ํŠนํžˆ, 10๋ช…์˜ ์ธ๊ฐ„ ๋ฐ๋ชจ๋ฅผ ๊ธฐ๋ฐ˜์œผ๋กœ ์ƒ์„ฑ๋œ ๋ฐ์ดํ„ฐ์…‹์—์„œ ์‹œ์ž‘ํ•˜์—ฌ, ์‹ค์ œ ํ™˜๊ฒฝ์—์„œ์˜ ์˜จ๋ผ์ธ ์ ์‘ ๋ฐ ์„ธ๋ถ€ ์กฐ์ •์„ ํ†ตํ•ด ์„ฑ๋Šฅ์„ ๋”์šฑ ํ–ฅ์ƒ์‹œํ‚ต๋‹ˆ๋‹ค. Robosuite ๋ฐ์ดํ„ฐ์…‹์—์„œ์˜ ํ‰๊ฐ€ ๊ฒฐ๊ณผ๋Š” ReinforceGen์˜ ํšจ๊ณผ์„ฑ์„ ์ž…์ฆํ•ฉ๋‹ˆ๋‹ค. 80%์˜ ๋†’์€ ์„ฑ๊ณต๋ฅ ๊ณผ ์•™๋ธ”๋ ˆ์ด์…˜ ์—ฐ๊ตฌ

Data Learning
No Image

Relating biomarkers and phenotypes using dynamical trap spaces

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ํ•„์š”์„ฑ ํ‘œํ˜„ํ˜• ์ •์˜์˜ ์ด๋ถ„๋ฒ•์  ํ•œ๊ณ„ ์ „ํ†ต์ ์œผ๋กœ๋Š” ์†Œ์ˆ˜์˜ ๋ฐ”์ด์˜ค๋งˆ์ปค(์˜ˆ: CD4, IFNโ€‘ฮณ)๋งŒ์„ ์‚ฌ์šฉํ•˜๊ฑฐ๋‚˜, ์ „์‚ฌยท๋‹จ๋ฐฑ์งˆยท๋Œ€์‚ฌ ์ „์‚ฐ ๋ฐ์ดํ„ฐ๋ฅผ ์ „๋ถ€ ํ™œ์šฉํ•˜๋Š” ๋‘ ๊ทน๋‹จ์ด ์กด์žฌํ•œ๋‹ค. ์ „์ž๋Š” ์ •๋ณด ์†์‹ค ์œ„ํ—˜์ด, ํ›„์ž๋Š” ์‹ค์ œ ํ‘œํ˜„ํ˜•๊ณผ์˜ ์—ฐ๊ด€์„ฑ์„ ํŒ๋‹จํ•˜๊ธฐ ์–ด๋ ค์šด ๊ณผ์ž‰ ์ •๋ณด๋ฅผ ์ดˆ๋ž˜ํ•œ๋‹ค. ๋™์  ๋„คํŠธ์›Œํฌ ๊ด€์ ์˜ ๋ถ€์žฌ KEGGยทReactome ๋“ฑ ๊ฒฝ๋กœ ๋ฐ์ดํ„ฐ๋ฒ ์ด์Šค๋Š” ์ •์  ์—ฐ๊ฒฐ๊ด€๊ณ„๋งŒ ์ œ๊ณตํ•œ๋‹ค. ์‹ค์ œ ์„ธํฌ๋Š” ์™ธ๋ถ€ ์ž๊ทน์— ๋”ฐ๋ผ ๋™์ ์œผ๋กœ ์ „์ด๋˜๋ฏ€๋กœ, ๋™์  ํ•จ์ •๊ณต๊ฐ„ ์„ ์ด์šฉํ•œ ์ ‘๊ทผ์ด ํ•„์š”ํ•˜๋‹ค. 2. ํ•ต์‹ฌ ๊ฐœ๋… ๋ฐ ์ •์˜ | ์šฉ์–ด | ์ •์˜ (

Quantitative Biology
No Image

Relative uniform convergence and Archimedean property in pre-ordered vector spaces

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ์•„ํ‚ค๋ฉ”๋ฐ์Šค ์„ฑ์งˆ์€ Kadison์˜ ๋Œ€ํ‘œ์ •๋ฆฌ, Choiโ€‘Effros์˜ C โ€‘๋Œ€์ˆ˜ ํ‘œํ˜„ ๋“ฑ ๋‹ค์–‘ํ•œ ๋ถ„์•ผ์—์„œ ํ•ต์‹ฌ์ ์ธ ๊ฐ€์ •์ด๋‹ค. ์ตœ๊ทผ Paulsenโ€‘Tomforde์˜ ordered โ€‘vector spaces ์™€ ๊ฐ™์€ ์—ฐ๊ตฌ์—์„œ โ€œ์•„ํ‚ค๋ฉ”๋ฐ์Šคํ™”โ€๊ฐ€ ๊ตฌ์กฐ์  ๋ถ„์„์— ํ•„์ˆ˜์ ์ธ ๋„๊ตฌ๋กœ ๋ถ€๊ฐ๋˜๊ณ  ์žˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๊ธฐ์กด ๊ฒฐ๊ณผ๋“ค์€ ์ฃผ๋กœ ์ˆœ์„œ ๋‹จ์œ„ ๊ฐ€ ์กด์žฌํ•˜๊ฑฐ๋‚˜ ์™„์ „ํ•œ ๊ฒฉ์ž (vector lattice) ๊ตฌ์กฐ๋ฅผ ์ „์ œ๋กœ ํ•œ๋‹ค. ๋ณธ ๋…ผ๋ฌธ์€ ์ด๋Ÿฌํ•œ ์ œํ•œ์„ ์—†์• ๊ณ , ์ „์ˆœ์„œ ๋ฒกํ„ฐ๊ณต๊ฐ„ ์ „๋ฐ˜์— ์ ์šฉ ๊ฐ€๋Šฅํ•œ ์ผ๋ฐ˜์ ์ธ ์•„ํ‚ค๋ฉ”๋ฐ์Šคํ™” ์ ˆ์ฐจ๋ฅผ ์ œ์‹œํ•œ๋‹ค๋Š” ์ 

Mathematics
No Image

Remarks on the inverse Littlewood conjecture

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ Littlewood ์ถ”์ธก ์€ 1980๋…„๋Œ€ Konyagin, McGeheeโ€‘Pignoโ€‘Smith ์— ์˜ํ•ด ์ฆ๋ช…๋˜์—ˆ์œผ๋ฉฐ, (|widehat{mathbf 1 A}| 1) ์˜ ํ•˜ํ•œ์ด (log N) ์ž„์„ ๋ณด์—ฌ์ค€๋‹ค. ์ผ๋ฐ˜์ ์ธ ์ง‘ํ•ฉ์€ (|widehat{mathbf 1 A}| 1) ๊ฐ€ (N^{1/2}) ์— ๊ฐ€๊น๊ฒŒ ์ปค์ง€๋Š” ๊ฒƒ์ด ๋ณดํ†ต์ด๋ฉฐ, ๋กœ๊ทธ ์ˆ˜์ค€ ์ดํ•˜๋กœ ์ž‘์•„์ง€๋Š” ๊ฒฝ์šฐ๋Š” ๋งค์šฐ ๋“œ๋ฌผ๋‹ค. ๋”ฐ๋ผ์„œ โ€œ์ž‘์€ (|widehat{mathbf 1 A}| 1)โ€ ๊ฐ€ ์–ด๋–ค ๋ง์…ˆ์  ๊ตฌ์กฐ ๋ฅผ ๊ฐ•์ œํ•˜๋Š”์ง€

Mathematics
No Image

Riemannian foliations on CROSSes

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ CROSS ๋Š” ๊ณ ์ „์ ์ธ ๋Œ€์นญ ๊ณต๊ฐ„์œผ๋กœ, ๊ตฌ๋ฉด (S^{n}) ์™ธ์—๋„ ๋ณต์†Œยท์‚ฌ์›ยท์˜ฅํƒ„ ํ”„๋กœ์ ํŠธ ๊ณต๊ฐ„์„ ํฌํ•จํ•œ๋‹ค. ๊ตฌ๋ฉด ์œ„์˜ ๋ฆฌ๋งŒ ํฌ๋ฆฌ์ผ€์ด์…˜ ๋ถ„๋ฅ˜๋Š” ์ˆ˜์‹ญ ๋…„์— ๊ฑธ์ณ ์—ฌ๋Ÿฌ ๋‹จ๊ณ„๋กœ ์™„์„ฑ๋˜์—ˆ์œผ๋ฉฐ, ํŠนํžˆ

Mathematics
Robustness of Probabilistic Models to Low-Quality Data: A Multi-Perspective Analysis

Robustness of Probabilistic Models to Low-Quality Data: A Multi-Perspective Analysis

๋ณธ ๋…ผ๋ฌธ์€ ์ €ํ’ˆ์งˆ ๋ฐ์ดํ„ฐ๊ฐ€ ๋‹ค์–‘ํ•œ ๋ชจ๋ธ์˜ ๊ฒฌ๊ณ ์„ฑ์— ๋ฏธ์น˜๋Š” ์ฐจ๋ณ„์ ์ธ ์˜ํ–ฅ์„ ์ฒด๊ณ„์ ์œผ๋กœ ์กฐ์‚ฌํ•˜๊ณ  ๋ถ„์„ํ•œ ์—ฐ๊ตฌ์ด๋‹ค. ํŠนํžˆ, ์ž๋™ํšŒ๊ท€ ์–ธ์–ด ๋ชจ๋ธ๊ณผ ํด๋ž˜์Šค ์กฐ๊ฑด ํ™•์‚ฐ ๋ชจ๋ธ, ๊ทธ๋ฆฌ๊ณ  ๋ถ„๋ฅ˜๊ธฐ ๊ฐ„์˜ ์„ฑ๋Šฅ ์ฐจ์ด๋ฅผ ๊ฐ•์กฐํ•œ๋‹ค. GPT 2์™€ ๊ฐ™์€ ์ž๋™ํšŒ๊ท€ ์–ธ์–ด ๋ชจ๋ธ์€ ํ† ํฐ ์˜ค์—ผ๋ฅ ์ด 50%์— ๋‹ฌํ•˜๋”๋ผ๋„ ๊ฒฌ๊ณ ์„ฑ์„ ์œ ์ง€ํ•˜๋ฉฐ, ์ด๋Š” ํ•ด๋‹น ๋ชจ๋ธ๋“ค์ด ์ €ํ’ˆ์งˆ ๋ฐ์ดํ„ฐ์—์„œ๋„ ๋›ฐ์–ด๋‚œ ์„ฑ๋Šฅ์„ ๋ฐœํœ˜ํ•  ์ˆ˜ ์žˆ๋Š” ๊ฐ•๊ฑด์„ฑ์˜ ํ•œ ์˜ˆ์‹œ๋ฅผ ๋ณด์—ฌ์ค€๋‹ค. ๋ฐ˜๋ฉด, ํด๋ž˜์Šค ์กฐ๊ฑด ํ™•์‚ฐ ๋ชจ๋ธ์€ ๊ฐ™์€ ์ •๋„์˜ ์˜ค์—ผ์—๋„ ๋ถˆ๊ตฌํ•˜๊ณ  ์žฌ์•™์ ์ธ ์„ฑ๋Šฅ ์ €ํ•˜๋ฅผ ๊ฒฝํ—˜ํ•œ๋‹ค. ์ด๋Š” ์ด๋ฏธ์ง€ ๋ ˆ์ด๋ธ” ์ผ๊ด€์„ฑ์ด ๊ธฐ์ค€์น˜ ๋Œ€๋น„

Data Analysis Model
Robustness Test for AI Forecasting of Hurricane Florence Using FourCastNetv2 and Random Perturbations of the Initial Condition

Robustness Test for AI Forecasting of Hurricane Florence Using FourCastNetv2 and Random Perturbations of the Initial Condition

: ํ—ˆ๋ฆฌ์ผ€์ธ๊ณผ ๊ฐ™์€ ๊ทนํ•œ ๊ธฐ์ƒ ํ˜„์ƒ์„ ์ •ํ™•ํ•˜๊ฒŒ ์˜ˆ์ธกํ•˜๊ธฐ ์œ„ํ•ด์„œ๋Š” ๊ธฐ์ƒ ์˜ˆ์ธก ๋ชจ๋ธ์˜ ๊ฒฌ๊ณ ์„ฑ๊ณผ ์ž…๋ ฅ ์žก์Œ์ด๋‚˜ ๋ถˆํ™•์‹ค์„ฑ์— ๋Œ€ํ•œ ๋ฏผ๊ฐ๋„๋ฅผ ์ดํ•ดํ•˜๋Š” ๊ฒƒ์ด ์ค‘์š”ํ•˜๋‹ค. ์ด ๋…ผ๋ฌธ์—์„œ๋Š” FCNv2 ๋ชจ๋ธ์ด ์ดˆ๊ธฐ ์กฐ๊ฑด์— ๊ฐ€ํ•ด์ง„ ์žก์Œ์— ์–ด๋–ป๊ฒŒ ๋ฐ˜์‘ํ•˜๋Š”์ง€, ๊ทธ๋ฆฌ๊ณ  ๋ฌด์ž‘์œ„์ ์ธ ์ดˆ๊ธฐ ์กฐ๊ฑด ํ•˜์—์„œ ์–ด๋–ป๊ฒŒ ์˜ˆ์ธก์„ ์ƒ์„ฑํ•˜๋Š”์ง€๋ฅผ ๋ถ„์„ํ–ˆ๋‹ค. ๊ทธ ๊ฒฐ๊ณผ, ๋ชจ๋ธ์€ ์ €์—์„œ ์ค‘๋“ฑ๋„์˜ ์žก์Œ ์ˆ˜์ค€์—์„œ๋„ ํ—ˆ๋ฆฌ์ผ€์ธ์˜ ํŠน์ง•์„ ์ž˜ ๋ณด์กดํ–ˆ์œผ๋ฉฐ, ๋†’์€ ์ˆ˜์ค€์˜ ์žก์Œ์ด ์ฃผ์ž…๋˜์–ด๋„ ์ „๋ฐ˜์ ์ธ ํญํ’ ๊ฒฝ๋กœ์™€ ๊ตฌ์กฐ๋ฅผ ์œ ์ง€ํ•จ์„ ๋ณด์˜€๋‹ค. ๋˜ํ•œ, FCNv2๋Š” ๋ชจ๋“  ์ˆ˜์ค€์˜ ์žก์Œ ํ•˜์—์„œ ์ผ๊ด€๋˜๊ฒŒ ํญํ’ ๊ฐ•๋„์™€ ์ง€

No Image

Separating Oblivious and Adaptive Models of Variable Selection

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ โ„“2 vs โ„“โˆž : ์ „ํ†ต์ ์ธ ํฌ์†Œ ๋ณต๊ตฌ๋Š” โ„“2 ์˜ค์ฐจ์— ์ดˆ์ ์„ ๋งž์ถ”์–ด (n O(klog d)) ์ƒ˜ํ”Œ์ด๋ฉด ํšจ์œจ์ ์ธ ๋ณต๊ตฌ๊ฐ€ ๊ฐ€๋Šฅํ•จ์ด ์ž˜ ์•Œ๋ ค์ ธ ์žˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์‹ค์ œ ์‘์šฉ(์˜ˆ: ๋ณ€์ˆ˜ ์„ ํƒ, ์œ ์ „์ž ๋งˆ์ปค ํƒ์ƒ‰)์—์„œ๋Š” ๊ฐœ๋ณ„ ๊ณ„์ˆ˜์˜ ์ •ํ™•๋„๊ฐ€ ๋” ์ค‘์š”ํ•ด โ„“โˆž ์˜ค์ฐจ๊ฐ€ ํ•ต์‹ฌ ์ง€ํ‘œ๊ฐ€ ๋œ๋‹ค. ๋ชจ๋ธ ์ฐจ์ด์˜ ์ค‘์š”์„ฑ : ๊ธฐ์กด ๋ฌธํ—Œ์€ ๋Œ€๋ถ€๋ถ„ โ€œfor eachโ€(๋ง๊ฐํ˜•) ๊ฐ€์ • ํ•˜์— ์ƒํ•œ์„ ์ œ์‹œํ–ˆ์œผ๋ฉฐ, โ€œfor allโ€(์ ์‘ํ˜•) ์ƒํ™ฉ์—์„œ๋Š” ๊ฐ•๋ ฅํ•œ ํ•˜ํ•œ์ด ๊ฑฐ์˜ ์•Œ๋ ค์ง€์ง€ ์•Š์•˜๋‹ค. ์ด ๋…ผ๋ฌธ์€ ๋‘ ๋ชจ๋ธ ์‚ฌ์ด์— ํ†ต๊ณ„์ ยท๊ณ„์‚ฐ์  ๊ฒฉ์ฐจ๊ฐ€ ์กด์žฌํ•จ์„ ์ตœ

Model Mathematics
No Image

Sequential Membership Inference Attacks

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ํšŒ์›์ถ”๋ก  ๊ณต๊ฒฉ ์€ ๋ชจ๋ธ์ด ํ•™์Šต์— ์‚ฌ์šฉ๋œ ๊ฐœ๋ณ„ ๋ ˆ์ฝ”๋“œ๋ฅผ ์‹๋ณ„ํ•จ์œผ๋กœ์จ ๊ฐœ์ธ ํ”„๋ผ์ด๋ฒ„์‹œ๋ฅผ ์œ„ํ˜‘ํ•œ๋‹ค. ๊ธฐ์กด ์—ฐ๊ตฌ๋Š” ์ฃผ๋กœ ์ •์  ๋ชจ๋ธ (๋‹จ์ผ ์Šค๋ƒ…์ƒท)๋งŒ์„ ๋Œ€์ƒ์œผ๋กœ ํ–ˆ๋‹ค. ์‹ค์ œ ์„œ๋น„์Šค์—์„œ๋Š” ์—ฐ์† ํ•™์Šต/ํŒŒ์ธํŠœ๋‹/์—ฐํ•ฉํ•™์Šต ๋“ฑ์œผ๋กœ ๋ชจ๋ธ์ด ์ง€์†์ ์œผ๋กœ ์—…๋ฐ์ดํŠธ๋œ๋‹ค. ๊ฐ ์—…๋ฐ์ดํŠธ๋งˆ๋‹ค ์ƒˆ๋กœ์šด ๋ชจ๋ธ ๋ฒ„์ „์ด ๊ณต๊ฐœยทAPI๋ฅผ ํ†ตํ•ด ์ ‘๊ทผ ๊ฐ€๋Šฅํ•˜๋ฏ€๋กœ, ๊ณต๊ฒฉ์ž๋Š” ์‹œํ€€์Šค ์ •๋ณด๋ฅผ ํ™œ์šฉํ•  ์—ฌ์ง€๊ฐ€ ์žˆ๋‹ค. Jagielski et al. (2023) ๋“ฑ์€ ๊ฒฝํ—˜์ ์œผ๋กœ โ€œ์—ฌ๋Ÿฌ ์Šค๋ƒ…์ƒท์˜ MI ์ ์ˆ˜๋ฅผ ํ•ฉ์‚ฐํ•˜๋ฉด ์ •ํ™•๋„๊ฐ€ ์ƒ์Šนํ•œ๋‹คโ€๋Š” ๊ฒƒ์„ ๋ณด์˜€์ง€๋งŒ, ์ตœ์  ๊ณต๊ฒฉ ์—

Computer Science Machine Learning
No Image

Some rational subvarieties of moduli spaces of stable vector bundles

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ยตโ€‘์•ˆ์ •์„ฑ ์€ ๊ณก์„  ์œ„์—์„œ๋Š” Mumfordโ€‘Takemoto ์ด๋ก ์œผ๋กœ ์™„์ „ํžˆ ์ •๋ฆฝ๋ผ ์žˆ์œผ๋‚˜, ์ฐจ์›์ด 2 ์ด์ƒ์ธ ๊ฒฝ์šฐ๋Š” ์•„์ง ๊ตฌ์กฐ๊ฐ€ ๋ถˆ์™„์ „ํ•˜๋‹ค. ํŠนํžˆ ๋ชจ๋“ˆ๋ฆฌ ๊ณต๊ฐ„์˜ ๋น„๊ณตํ—ˆ์„ฑ(nonโ€‘emptiness) ๋ฅผ ๋ณด์žฅํ•˜๋Š” ์ผ๋ฐ˜์ ์ธ ์ •๋ฆฌ๋Š” ์กด์žฌํ•˜์ง€ ์•Š๋Š”๋‹ค. ๋”ฐ๋ผ์„œ ๊ตฌ์ฒด์ ์ธ ๋ฒกํ„ฐ๋‹ค๋ฐœ ํŒจ๋ฐ€๋ฆฌ ๋ฅผ ์ง์ ‘ ๋งŒ๋“ค์–ด์„œ ๋ชจ๋“ˆ๋ฆฌ ๊ณต๊ฐ„ ์•ˆ์— โ€œ๋ˆˆ์— ๋ณด์ด๋Š”โ€ ๋ถ€๋ถ„์„ ์ฐพ์•„๋‚ด๋Š” ๊ฒƒ์ด ํ˜„์žฌ ์—ฐ๊ตฌ์˜ ํ•ต์‹ฌ ๊ณผ์ œ์ด๋‹ค. 2. ์ฃผ์š” ์•„์ด๋””์–ด์™€ ๊ตฌ์„ฑ | ๋‹จ๊ณ„ | ํ•ต์‹ฌ ๋‚ด์šฉ | ์ˆ˜ํ•™์  ๋„๊ตฌ | | | | | | (i) ์„ ํƒ | $Wsubset H^0(X,L

Mathematics
No Image

SSI-GAN: Semi-Supervised Swin-Inspired Generative Adversarial Networks for Neuronal Spike Classification

์ด ๋…ผ๋ฌธ์€ ์‹ ๊ฒฝ์ƒ๋ฌผํ•™์  ๋ฐ์ดํ„ฐ์™€ ๋ฐ”์ด๋Ÿฌ์Šค ๊ฐ์—ผ ์—ฐ๊ตฌ ์‚ฌ์ด์˜ ๊ฒฉ์ฐจ๋ฅผ ๋ฉ”์šฐ๊ธฐ ์œ„ํ•ด ์ตœ์‹  ๋”ฅ๋Ÿฌ๋‹ ๊ตฌ์กฐ๋ฅผ ์ฐฝ์˜์ ์œผ๋กœ ์ ์šฉํ•œ ์ ์ด ๊ฐ€์žฅ ํฐ ๊ฐ•์ ์ด๋‹ค. ๋จผ์ €, ์Šค์œˆ(Swin) ํŠธ๋žœ์Šคํฌ๋จธ์˜ ํ•ต์‹ฌ ์•„์ด๋””์–ด์ธ โ€˜์ด๋™ ์œˆ๋„์šฐโ€™ ๋ฉ”์ปค๋‹ˆ์ฆ˜์„ ๋””์Šคํฌ๋ฆฌ๋ฏธ๋„ค์ดํ„ฐ์— ๋„์ž…ํ•จ์œผ๋กœ์จ ๊ณ ์ฃผํŒŒ ์ŠคํŒŒ์ดํฌ์˜ ๊ตญ์†Œ์  ํŒจํ„ด์„ ํšจ์œจ์ ์œผ๋กœ ํฌ์ฐฉํ•œ๋‹ค๋Š” ์ ์€ ๊ธฐ์กด 1โ€‘D CNN ๊ธฐ๋ฐ˜ ๋ชจ๋ธ์ด ๋†“์น˜๊ธฐ ์‰ฌ์šด ๋ฏธ์„ธํ•œ ์‹œ๊ฐ„โ€‘์ฃผํŒŒ์ˆ˜ ์ •๋ณด๋ฅผ ๋ณด์™„ํ•œ๋‹ค. ํŠธ๋žœ์Šคํฌ๋จธ ๊ธฐ๋ฐ˜ ์ œ๋„ˆ๋ ˆ์ดํ„ฐ๋Š” ์‹œํ€€์Šค ์ „์ฒด์˜ ์žฅ๊ธฐ ์˜์กด์„ฑ์„ ํ•™์Šตํ•˜๋ฉด์„œ๋„, ๋ผ๋ฒจ์ด ๋ถ€์กฑํ•œ ์ƒํ™ฉ์—์„œ ๊ฐ€์งœ ์ƒ˜ํ”Œ์„ ์ƒ์„ฑํ•ด ๋””์Šคํฌ๋ฆฌ๋ฏธ๋„ค์ดํ„ฐ๋ฅผ ์ง€์†์ ์œผ๋กœ ๋„

Network
Story2MIDI: Emotionally Aligned Music Generation from Text

Story2MIDI: Emotionally Aligned Music Generation from Text

Story2MIDI๋Š” ํ…์ŠคํŠธโ€‘์Œ์•… ๊ฐ์ • ๋งคํ•‘์ด๋ผ๋Š” ๋น„๊ต์  ์ƒˆ๋กœ์šด ์—ฐ๊ตฌ ์˜์—ญ์— ๋„์ „ํ•˜๋Š” ์‹œ๋„์ด๋‹ค. ๊ธฐ์กด ์—ฐ๊ตฌ๋Š” ์ฃผ๋กœ ํ…์ŠคํŠธโ€‘์Œ์•… ๊ฐ„์˜ ๋‹จ์ˆœ ์—ฐ๊ด€์„ฑ(์˜ˆ: ํ‚ค์›Œ๋“œ ๊ธฐ๋ฐ˜ ๋งค์นญ)์ด๋‚˜ ์Œ์•… ์ƒ์„ฑ์— ๊ฐ์ • ๋ผ๋ฒจ์„ ๋ถ€์—ฌํ•˜๋Š” ๋ฐฉ์‹์— ๋จธ๋ฌผ๋ €๋‹ค. ๋ณธ ๋…ผ๋ฌธ์€ ๋‘ ๊ฐ€์ง€ ์ฃผ์š” ํ˜์‹ ์„ ์ œ์‹œํ•œ๋‹ค. ์ฒซ์งธ, ํ…์ŠคํŠธ ๊ฐ์„ฑ ๋ถ„์„ ์ฝ”ํผ์Šค์™€ ์Œ์•… ๊ฐ์ • ๋ถ„๋ฅ˜ ์ฝ”ํผ์Šค๋ฅผ ์œตํ•ฉํ•ด โ€˜ํ…์ŠคํŠธโ€‘์Œ์•… ๊ฐ์ • ์ผ์น˜โ€™ ์Œ์„ ๋งŒ๋“  Story2MIDI ๋ฐ์ดํ„ฐ์…‹์„ ๊ตฌ์ถ•ํ•˜์˜€๋‹ค. ๋ฐ์ดํ„ฐ ์ •์ œ ๊ณผ์ •์—์„œ ๊ฐ์ • ๋ผ๋ฒจ์„ 5๊ฐ€์ง€ ๊ธฐ๋ณธ ๊ฐ์ •(ํ–‰๋ณต, ์Šฌํ””, ๋ถ„๋…ธ, ๋†€๋ผ์›€, ํ‰์˜จ)์œผ๋กœ ํ†ต์ผํ•˜๊ณ , ํ…์ŠคํŠธ์™€ ์Œ์•… ์–‘์ชฝ

No Image

Symmetry properties for positive solutions of mixed boundary value problems in a sub-spherical sector

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ์ด๋™ ํ‰๋ฉด๋ฒ• ์€ Gidasโ€‘Niโ€‘Nirenberg(1979) ์ดํ›„ ๋ฐ˜์„ ํ˜• ํƒ€์›ํ˜• ๋ฐฉ์ •์‹์˜ ๋Œ€์นญยท๋‹จ์กฐ์„ฑ์„ ์ž…์ฆํ•˜๋Š” ํ•ต์‹ฌ ๋„๊ตฌ์ด๋‹ค. ๊ธฐ์กด ๊ฒฐ๊ณผ๋Š” ์ „ํ˜•์ ์ธ ๋””๋ฆฌํด๋ ˆ ํ˜น์€ ์ „๋ถ€ ๋…ธ์ด๋งŒ ๊ฒฝ๊ณ„์— ํ•œ์ •๋ผ ์žˆ์—ˆ์œผ๋ฉฐ, ํ˜ผํ•ฉ ๊ฒฝ๊ณ„์—์„œ๋Š” ๋Œ€์นญ์„ฑ์ด ์‰ฝ๊ฒŒ ๊นจ์ง„๋‹ค(์˜ˆ:

Mathematics
No Image

The Complexity Landscape of Two-Stage Robust Selection Problems with Budgeted Uncertainty

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋ฌธ์ œ ์ •์˜ ๊ฐ•๊ฑด ์กฐํ•ฉ ์ตœ์ ํ™”์—์„œ ๊ฐ€์žฅ ๋„๋ฆฌ ์“ฐ์ด๋Š” ๋ถˆํ™•์‹ค์„ฑ ๋ชจ๋ธ์ธ ์˜ˆ์‚ฐ ์ œํ•œ ๋ถˆํ™•์‹ค์„ฑ ์€ ๊ฐ ์›์†Œ์˜ ๋น„์šฉ์ด ๊ตฌ๊ฐ„ (

Mathematics
No Image

The Influence of Width Ratios on Structural Beauty in Male Faces

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ์ด๋ก ์  ํ† ๋Œ€ ์ง„ํ™”ยท์ƒ๋ฌผํ•™์  ๊ด€์  : ํ‰๊ท  ์–ผ๊ตด์€ ๊ฑด๊ฐ•ยท๋ฐœ๋‹ฌ ์•ˆ์ •์„ฑ์„ ์‹œ์‚ฌํ•œ๋‹ค๋Š” ๊ฐ€์„ค์— ๊ธฐ๋ฐ˜ํ•ด ๋งค๋ ฅ์œผ๋กœ ์ž‘์šฉํ•œ๋‹ค(Pallett et al., 2010; Rhodes, 2006). ์ธ์ง€ยท์ฒ˜๋ฆฌ ์œ ์ฐฝ์„ฑ ๊ด€์  : ์ธ๊ฐ„์€ ๋‚ด๋ถ€์— โ€˜ํ”„๋กœํ† ํƒ€์ž… ์–ผ๊ตดโ€™์„ ๋ณด์œ ํ•˜๊ณ , ์ด์™€ ์œ ์‚ฌํ•œ ์–ผ๊ตด์„ ๋” ์‰ฝ๊ฒŒ ์ฒ˜๋ฆฌํ•จ์œผ๋กœ์จ ๊ธ์ •์  ์ •์„œ๋ฅผ ์œ ๋ฐœํ•œ๋‹ค(Langlois & Roggman, 1990; Alter & Oppenheimer, 2009). ์‚ฌํšŒยท๋ฌธํ™”์  ๋งฅ๋ฝ : ์•„๋ฆ„๋‹ค์›€์€ ๋ฌธํ™”ยท์—ญ์‚ฌยท๋ฏธ๋””์–ด์— ์˜ํ•ด ํ˜•์„ฑ๋˜๋ฉฐ, โ€˜halo effectโ€™๋กœ ์ธํ•ด ์™ธ๋ชจ๊ฐ€

Quantitative Biology
No Image

The lingering phenomenon and pattern formation in a nonlocal population model with cognitive map

1. ๋ชจ๋ธ ๊ตฌ์„ฑ ๋ฐ ์ˆ˜ํ•™์  ํ”„๋ ˆ์ž„์›Œํฌ ๋ณ€์ˆ˜ ์ •์˜ u(x,t) : ๊ฐœ์ฒด ๋ฐ€๋„ (๋ฌด์ฐจ์›) m(x,t) : ์ธ์ง€์ง€๋„ (ํ™˜๊ฒฝ ํ’ˆ์งˆ s(x) ์— ๋Œ€ํ•œ ๊ธฐ์–ต) s(x) : ์„œ์‹์ง€ ํ’ˆ์งˆ(๋˜๋Š” ๊ณต๊ฐ„์  ์ž์› ์šฉ๋Ÿ‰) ๋™์—ญํ•™์‹

Model Mathematics
No Image

The OU number and Reidemeister moves of type III for link diagrams

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ๋ ˆ์ „๋“œ๋ฆฌ์ŠคํŠธ ์ด๋™๊ณผ ๋ณต์žก๋„ : ๋‘ ๋‹ค์ด์–ด๊ทธ๋žจ์ด ๊ฐ™์€ ๋งํฌ๋ฅผ ๋‚˜ํƒ€๋‚ด๋Š”์ง€ ์—ฌ๋ถ€๋Š” ๋ ˆ์ „๋“œ๋ฆฌ์ŠคํŠธ ์ด๋™(RI, RII, RIII)์œผ๋กœ ์™„์ „ํžˆ ํŒ์ •๋œ๋‹ค. ํ•˜์ง€๋งŒ ์‹ค์ œ ๋ฌผ๋ฆฌยทํ™”ํ•™ ์‹œ์Šคํ…œ(์˜ˆ: ๊ณ ๋ถ„์ž ๊ณ ๋ฆฌ ์‚ฌ์Šฌ)์—์„œ๋Š” ํŠน์ • ์œ ํ˜•์˜ ์ด๋™ ์ด ์–ผ๋งˆ๋‚˜ ๋งŽ์ด ํ•„์š”ํ•œ์ง€๊ฐ€ ๋ฌผ์งˆ์˜ ๋™์—ญํ•™์— ์ง์ ‘์ ์ธ ์˜ํ–ฅ์„ ๋ฏธ์นœ๋‹ค. RIIIฮฑ ์ด๋™์˜ ๋ถ€์กฑํ•œ ์—ฐ๊ตฌ : ๊ธฐ์กด ์—ฐ๊ตฌ๋Š” ์ฃผ๋กœ RIยทRII ํ˜น์€ ์ „์ฒด RIII ์ด๋™ ์ˆ˜์— ์ดˆ์ ์„ ๋งž์ท„์œผ๋ฉฐ, ๋‹ค์ค‘ ์ปดํฌ๋„ŒํŠธ ๋งํฌ ์—์„œ ์ค‘๊ฐ„ ๊ตฌ๊ฐ„์ด ๋‹ค๋ฅธ ์ปดํฌ๋„ŒํŠธ์— ์†ํ•˜๋Š” RIIIฮฑ์— ๋Œ€ํ•œ ์ •๋Ÿ‰์  ํ•˜ํ•œ์€ ๊ฑฐ์˜ ์—†์—ˆ๋‹ค. 2

Mathematics
No Image

The Representational Alignment Hypothesis: Evidence for and Consequences of Invariant Semantic Structure Across Embedding Modalities

1. ์—ฐ๊ตฌ ์งˆ๋ฌธ ๋ฐ ๊ฐ€์„ค์˜ ์˜์˜ ํ•ต์‹ฌ ์งˆ๋ฌธ : ์„œ๋กœ ๋…๋ฆฝ์ ์œผ๋กœ ํ•™์Šต๋œ ํ…์ŠคํŠธยท์‹œ๊ฐยท์ฒญ๊ฐยท์‹ ๊ฒฝ ์ž„๋ฒ ๋”ฉ์ด ๊ณตํ†ต๋œ ์˜๋ฏธ ๊ธฐํ•˜ํ•™ ์„ ๋‚ดํฌํ•˜๋Š”๊ฐ€? ๊ฐ€์„ค : ์ด๋Ÿฌํ•œ ๊ณตํ†ต ๊ตฌ์กฐ๋Š” ์˜๋ฏธ ์ž์ฒด์˜ ๋ณธ์งˆ์  ์†์„ฑ์ด ์•„๋‹ˆ๋ผ, ์ธ๊ฐ„ยท์ง€๊ตฌ ํ™˜๊ฒฝ์— ์˜ํ•ด ์ œํ•œ๋œ ๋ฐ์ดํ„ฐ์™€ ์•Œ๊ณ ๋ฆฌ์ฆ˜์ด ๋งŒ๋“ค์–ด๋‚ธ โ€˜์กฐ๊ฑด๋ถ€ ๋ถˆ๋ณ€์„ฑโ€™ ์ผ ๊ฐ€๋Šฅ์„ฑ์ด ์žˆ๋‹ค. > ์˜์˜ : ๋งŒ์•ฝ RAH๊ฐ€ ์ž…์ฆ๋œ๋‹ค๋ฉด, โ€œ์˜๋ฏธ๋Š” ๋ชจ๋‹ฌ๋ฆฌํ‹ฐ์— ๋…๋ฆฝ์ ์ธ ๊ด€๊ณ„๋ง์œผ๋กœ ์กด์žฌํ•œ๋‹คโ€๋Š” ๋ฉ”ํƒ€์„ธ๋งŒํ‹ฑ์Šค์˜ ํ•ต์‹ฌ ์ „์ œ์— ์‹ค์ฆ์  ๊ทผ๊ฑฐ๋ฅผ ์ œ๊ณตํ•œ๋‹ค. ๋™์‹œ์—, ์ธ๊ฐ„ ์ค‘์‹ฌ ๋ฐ์ดํ„ฐ๊ฐ€ ๋งŒ๋“  โ€˜์ธ์œ„์ โ€™ ๊ตฌ์กฐ์™€ ๊ตฌ๋ถ„ํ•ด์•ผ ํ•˜๋Š” ์ƒˆ๋กœ์šด ์ฒ ํ•™์ ยท๋ฐฉ๋ฒ•๋ก ์  ๊ณผ์ œ๋ฅผ

Quantitative Biology
No Image

Theory of temporal three-photon interference

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ์—ญ์‚ฌ์  ํ๋ฆ„ : ๋‹จ์ผ๊ด‘์ž ๊ฐ„์„ญ(Young) โ†’ ๋‘๊ด‘์ž ๊ฐ„์„ญ(Hanburyโ€‘Brownโ€‘Twiss, HOM) โ†’ ์‚ผ๊ด‘์ž ๊ฐ„์„ญ์œผ๋กœ์˜ ํ™•์žฅ ํ•„์š”์„ฑ. ๋””๋ž™ ๋ช…์ œ์˜ ํ™•์žฅ : ๊ธฐ์กด์—๋Š” โ€œ๊ด‘์ž๋Š” ์ž๊ธฐ ์ž์‹ ๊ณผ๋งŒ ๊ฐ„์„ญํ•œ๋‹คโ€๊ฐ€ 1ยท๊ด‘์ž, 2ยท๊ด‘์ž ๊ฒฝ์šฐ์—๋งŒ ๋ช…์‹œ์ ์œผ๋กœ ์ ์šฉ๋˜์—ˆ์œผ๋ฉฐ, ์‚ผ๊ด‘์ž ์ด์ƒ์—์„œ๋Š” ์•„์ง ์ฒด๊ณ„์ ์ธ ์„œ์ˆ ์ด ๋ถ€์กฑํ–ˆ๋‹ค. ์‹คํ—˜์  ์ด‰์ง„ : CPDC์™€ TOPDC๋ฅผ ํ†ตํ•œ ์‚ผ๊ด‘์ž ์–ฝํž˜ ์ƒ์„ฑ์ด ์‹คํ˜„๋˜๋ฉด์„œ, ์ด๋ก ์  ํ‹€ ์—†์ด ์‹คํ—˜์„ ํ•ด์„ํ•˜๊ธฐ ์–ด๋ ค์šด ์ƒํ™ฉ์ด ๋ฐœ์ƒํ–ˆ๋‹ค. 2. ์ฃผ์š” ์•„์ด๋””์–ด ๋ฐ ๋ฐฉ๋ฒ•๋ก  | ๋‹จ๊ณ„ | ํ•ต์‹ฌ ๋‚ด์šฉ | ์˜์˜ |

Quantum Physics
Topological Order in Deep State

Topological Order in Deep State

์œ„์ƒ ์งˆ์„œ(topological order)๋Š” ์ „ํ†ต์ ์ธ ๋Œ€์นญ ํŒŒ๊ดด ๊ฐœ๋…์œผ๋กœ๋Š” ์„ค๋ช…๋˜์ง€ ์•Š๋Š” ๋ฌผ์งˆ์˜ ์ƒˆ๋กœ์šด ์ข…๋ฅ˜๋ฅผ ์ •์˜ํ•œ๋‹ค. ํŠนํžˆ ๋ถ„์ˆ˜ ์ฐจ์› ์ ˆ์—ฐ์ฒด(Fractional Chern Insulator, FCI)๋Š” ์–‘์ž ํ™€ ํšจ๊ณผ๋ฅผ ๊ฒฉ์ž ์‹œ์Šคํ…œ์— ๊ตฌํ˜„ํ•œ ํ˜•ํƒœ๋กœ, ์ „์ž๋“ค์ด ๊ฐ•ํ•˜๊ฒŒ ์ƒํ˜ธ์ž‘์šฉํ•˜๋ฉด์„œ ๋ถ„์ˆ˜ ์ „ํ•˜์™€ ๋น„๊ฐ€ํ™˜(anyon) ํ†ต๊ณ„๋ฅผ ๊ฐ–๋Š” ์ค€์ž…์ž๋ฅผ ํ˜•์„ฑํ•œ๋‹ค. ์ด๋Ÿฌํ•œ ํ˜„์ƒ์€ ํŒŒ๋™ํ•จ์ˆ˜์˜ ๋น„๊ตญ์†Œ์  ์–ฝํž˜ ๊ตฌ์กฐ์™€ ๋‹ค์ค‘ ์ถ•ํ‡ด๋œ ๋ฐ”๋‹ฅ ์ƒํƒœ์— ์˜ํ•ด ํŠน์ง•์ง€์–ด์ง€๋ฉฐ, ์ด๋ฅผ ์ •ํ™•ํžˆ ๊ธฐ์ˆ ํ•˜๋ ค๋ฉด ๊ณ ์ฐจ์› ๋ณต์žกํ•œ ์ƒ๊ด€๊ด€๊ณ„๋ฅผ ํฌ์ฐฉํ•  ์ˆ˜ ์žˆ๋Š” ๋ฐฉ๋ฒ•์ด ํ•„์š”ํ•˜๋‹ค. ์ „ํ†ต์ ์ธ ๋ณ€๋ถ„

No Image

Two-mode dominance and deterministic parameter bias bounds for equatorial Kerr-de Sitter ringdown

1. ์—ฐ๊ตฌ ๋ฐฐ๊ฒฝ ๋ฐ ๋™๊ธฐ ๋ธ”๋ž™ํ™€ ๋ง๋‹ค์šด ์€ ์‹ค์ œ ์ค‘๋ ฅํŒŒ ๊ด€์ธก์—์„œ ํ•ต์‹ฌ์ ์ธ ๋ถ„์„ ๋Œ€์ƒ์ด๋ฉฐ, ์ผ๋ฐ˜์ ์œผ๋กœ ์ง€์ˆ˜ ๊ฐ์‡  ์ง„๋™ (QNMs)์˜ ํ•ฉ์œผ๋กœ ๋ชจ๋ธ๋ง๋œ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ๋น„์ •๊ทœ์„ฑ(nonโ€‘normality) , ์ž”์ฐจ(tail) , ๋‹ค๋ฅธ ํด์˜ ๋ˆ„์ˆ˜(leakage) ๋“ฑ์œผ๋กœ ์ธํ•ด ์ œํ•œ๋œ ์‹œ๊ฐ„ ๊ตฌ๊ฐ„์—์„œ ๋ช‡ ๊ฐœ์˜ ๋ชจ๋“œ๋งŒ ์‚ฌ์šฉํ•ด ํŒŒ๋ผ๋ฏธํ„ฐ๋ฅผ ์ถ”์ •ํ•˜๋Š” ๊ฒƒ์ด ์ˆ˜ํ•™์ ์œผ๋กœ ๋ถˆ์•ˆ์ •ํ•  ์ˆ˜ ์žˆ๋‹ค. ๊ธฐ์กด ์—ฐ๊ตฌ๋“ค์€ ์ŠคํŽ™ํŠธ๋Ÿผ ํ˜น์€ ์ „์ด(transient) ํšจ๊ณผ๋ฅผ ๊ฐœ๋ณ„์ ์œผ๋กœ ๋‹ค๋ฃจ์—ˆ์ง€๋งŒ, ์‹œ๊ฐ„โ€‘๋„๋ฉ”์ธ PDE ํ•ด์„ ๊ณผ ๋ฐ์ดํ„ฐ ์ถ”์ • ์„ ๋™์‹œ์— ์—ฐ๊ฒฐํ•œ ์ •๋Ÿ‰์  ํ”„๋ ˆ์ž„์›Œํฌ๋Š” ๋ถ€์กฑํ–ˆ๋‹ค. 2

MATH-PH

< Category Statistics (Total: 2829) >

Electrical Engineering and Systems Science
100
General
731
General Relativity
22
HEP-EX
17
HEP-LAT
3
HEP-PH
39
HEP-TH
19
MATH-PH
36
NUCL-EX
2
NUCL-TH
5
Quantum Physics
41

Start searching

Enter keywords to search articles

โ†‘โ†“
โ†ต
ESC
โŒ˜K Shortcut