355 research outputs found

    Halmazelmélet; Partíció kalkulus, Végtelen gráfok elmélete = Set Theory; Partition Calculus , Theory of Infinite Graphs

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    Előzetes tervünknek megfelelően a halmazelmélet alábbi területein végeztünk kutatást és értünk el számos eredményt: I. Kombinatorika II. A valósak számsosságinvariánsai és ideálelmélet III. Halmazelméleti topológia Ezek mellett Sági Gábor kiterjedt kutatást végzett a modellelmélet területén , amely eredmények kapcsolódnak a kombinatorikához is. Eredményeinket 38 közleményben publikáltuk, amelyek majdnem mind az adott terület vezető nemzetközi lapjaiban jelentel meg (5 cikket csak benyújtottunk). Számos nemzetközi konferencián is résztvettünk, és hárman közűlünk (Juhász, Sádi, Soukup) plenáris/meghívott előadók voltak számos alkalommal. | Following our research plan, we have mainly done research -- and established a number of significant results -- in several areas of set theory: I. Combinatorics II. Cardinal invariants of the continuum and ideal theory III. Set-theoretic topology In addition to these, G. Sági has done extended research in model theory that had ramifications to combinatorics. We presented our results in 38 publications, almost all of which appeared or will appear in the leading international journals of these fields (5 of these papers have been submitted but not accepted as yet). We also participated at a number of international conferences, three of us (Juhász, Sági, Soukup) as plenary and/or invited speakers at many of these

    심층학습을 이용한 액체계의 성질 예측

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    학위논문(박사)--서울대학교 대학원 :자연과학대학 화학부,2020. 2. 정연준.최근 기계학습 기술의 급격한 발전과 이의 화학 분야에 대한 적용은 다양한 화학적 성질에 대한 구조-성질 정량 관계를 기반으로 한 예측 모형의 개발을 가속하고 있다. 용매화 자유 에너지는 그러한 기계학습의 적용 예중 하나이며 다양한 용매 내의 화학반응에서 중요한 역할을 하는 근본적 성질 중 하나이다. 본 연구에서 우리는 목표로 하는 용매화 자유 에너지를 원자간의 상호작용으로부터 구할 수 있는 새로운 심층학습 기반 용매화 모형을 소개한다. 제안된 심층학습 모형의 계산 과정은 용매와 용질 분자에 대한 부호화 함수가 각 원자와 분자들의 구조적 성질에 대한 벡터 표현을 추출하며, 이를 토대로 원자간 상호작용을 복잡한 퍼셉트론 신경망 대신 벡터간의 간단한 내적으로 구할 수 있다. 952가지의 유기용질과 147가지의 유기용매를 포함하는 6,493가지의 실험치를 토대로 기계학습 모형의 교차 검증 시험을 실시한 결과, 평균 절대 오차 기준 0.2 kcal/mol 수준으로 매우 높은 정확도를 가진다. 스캐폴드-기반 교차 검증의 결과 역시 0.6 kcal/mol 수준으로, 외삽으로 분류할 수 있는 비교적 새로운 분자 구조에 대한 예측에 대해서도 우수한 정확도를 보인다. 또한, 제안된 특정 기계학습 모형은 그 구조 상 특정 용매에 특화되지 않았기 때문에 높은 양도성을 가지며 학습에 이용할 데이터의 수를 늘이는 데 용이하다. 원자간 상호작용에 대한 분석을 통해 제안된 심층학습 모형 용매화 자유 에너지에 대한 그룹-기여도를 잘 재현할 수 있음을 알 수 있으며, 기계학습을 통해 단순히 목표로 하는 성질만을 예측하는 것을 넘어 더욱 상세한 물리화학적 이해를 하는 것이 가능할 것이라 기대할 수 있다.Recent advances in machine learning technologies and their chemical applications lead to the developments of diverse structure-property relationship based prediction models for various chemical properties; the free energy of solvation is one of them and plays a dominant role as a fundamental measure of solvation chemistry. Here, we introduce a novel machine learning-based solvation model, which calculates the target solvation free energy from pairwise atomistic interactions. The novelty of our proposed solvation model involves rather simple architecture: two encoding function extracts vector representations of the atomic and the molecular features from the given chemical structure, while the inner product between two atomistic features calculates their interactions, instead of black-boxed perceptron networks. The cross-validation result on 6,493 experimental measurements for 952 organic solutes and 147 organic solvents achieves an outstanding performance, which is 0.2 kcal/mol in MUE. The scaffold-based split method exhibits 0.6 kcal/mol, which shows that the proposed model guarantees reasonable accuracy even for extrapolated cases. Moreover, the proposed model shows an excellent transferability for enlarging training data due to its solvent-non-specific nature. Analysis of the atomistic interaction map shows there is a great potential that our proposed model reproduces group contributions on the solvation energy, which makes us believe that the proposed model not only provides the predicted target property, but also gives us more detailed physicochemical insights.1. Introduction 1 2. Delfos: Deep Learning Model for Prediction of Solvation Free Energies in Generic Organic Solvents 7 2.1. Methods 7 2.1.1. Embedding of Chemical Contexts 7 2.1.2. Encoder-Predictor Network 9 2.2. Results and Discussions 13 2.2.1. Computational Setup and Results 13 2.2.2. Transferability of the Model for New Compounds 17 2.2.3. Visualization of Attention Mechanism 26 3. Group Contribution Method for the Solvation Energy Estimation with Vector Representations of Atom 29 3.1. Model Description 29 3.1.1. Word Embedding 29 3.1.2. Network Architecture 33 3.2. Results and Discussions 39 3.2.1. Computational Details 39 3.2.2. Prediction Accuracy 42 3.2.3. Model Transferability 44 3.2.4. Group Contributions of Solvation Energy 49 4. Empirical Structure-Property Relationship Model for Liquid Transport Properties 55 5. Concluding Remarks 61 A. Analyzing Kinetic Trapping as a First-Order Dynamical Phase Transition in the Ensemble of Stochastic Trajectories 65 A1. Introduction 65 A2. Theory 68 A3. Lattice Gas Model 70 A4. Mathematical Model 73 A5. Dynamical Phase Transitions 75 A6. Conclusion 82 B. Reaction-Path Thermodynamics of the Michaelis-Menten Kinetics 85 B1. Introduction 85 B2. Reaction Path Thermodynamics 88 B3. Fixed Observation Time 94 B4. Conclusions 101Docto

    The Decomposition Theorem and the topology of algebraic maps

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    We give a motivated introduction to the theory of perverse sheaves, culminating in the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical constructions used in the study of topological properties of algebraic varieties. While most proofs are omitted, we discuss several approaches to the Decomposition Theorem, indicate some important applications and examples.Comment: 117 pages. New title. Major structure changes. Final version of a survey to appear in the Bulletin of the AM

    Local model Hamiltonian calculation of RIXS amplitudes of Sr3NiIrO6

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    The spin-orbit-coupled insulator Sr 3 NiIrO 6 is a strongly correlated transition metal compound, where an interplay of geometric frustration and spin anisotropy gives rise to novel magnetic phases. Resonant inelastic x-ray scattering (RIXS) is a powerful probe of the low-lying quasi-particle excitations that underpin these emergent properties. In this work, we partition the active space into approximately non-interacting parts in order to introduce a tight-binding single-particle model Hamiltonian describing the distorted IrO6 octahedra in Sr3NiIrO6. We then use this model to calculate its RIXS spectrum at the Ir L3-edge in the sub-electronvolt range. The results of this calculation are compared with experiments performed at the European Synchrotron Radiation Facility, and with a multiplet crystal field model calculation. We find that this one electron model largely agrees with the full-multiplet model and describes the d-d excitations observed in experiment. The addition of an exchange field term explains the low-lying temperature-dependent magnetic feature, disambiguating the sign of the crystal-field term, and suggesting that the feature is well localized at low temperatures, and is best described as an orbitally- entangled local spin-flip excitation. However, the correspondence at room temperature diminishes, suggesting that dispersive description is necessary to model this regime. The drastic reduction in active space entailed by this model facilitates the creation of extended non-collinear Heisenberg-like models, which can be calculated at a lower computational cost than full multiplet extended models
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